Diferential Person Functioning (DPF) e Multidimensional Item Response Theory (MIRT)

  library(tidyverse)
  library(sjmisc)
 
  library(TAM)
  library(mirt)
  library(psych)
  library(readxl)
  library(knitr)
  library(RColorBrewer)

  #library(xlsx)

 source("http://www.labape.com.br/rprimi/R/utils_construct_maps.R")

2. Lê/importa banco

# Abre direto da internet (con é um endereço do arquivo) 
 con<-url("http://www.labape.com.br/rprimi/TRI/2019_slides_exerc/senna_v1_54_ex3.RDS") 
 sennav1 <-  readRDS(con) 

 con<-url("http://www.labape.com.br/rprimi/TRI/2019_slides_exerc/senna_v1_54_ex3_dic.RDS") 
 dic <-  readRDS(con)

3. Organiza base e separa info sobre escala E

  sennav1$senna_it_rspnd <- apply(
    sennav1[ , 1:54], 
    MARGIN = 1, 
    function(x){sum(!is.na(x))}
    )
  
  frq(sennav1$senna_it_rspnd)

## 
## # x <integer> 
## # total N=11249  valid N=11249  mean=51.32  sd=8.99
##  
##   val  frq raw.prc valid.prc cum.prc
##     0   33    0.29      0.29    0.29
##     1   60    0.53      0.53    0.83
##     2  104    0.92      0.92    1.75
##     3   60    0.53      0.53    2.28
##     4   26    0.23      0.23    2.52
##     5   10    0.09      0.09    2.60
##     6   17    0.15      0.15    2.76
##     7   10    0.09      0.09    2.84
##     8    3    0.03      0.03    2.87
##     9    4    0.04      0.04    2.91
##    10    9    0.08      0.08    2.99
##    11    3    0.03      0.03    3.01
##    12    2    0.02      0.02    3.03
##    13    1    0.01      0.01    3.04
##    14    1    0.01      0.01    3.05
##    15    2    0.02      0.02    3.07
##    17    3    0.03      0.03    3.09
##    18    2    0.02      0.02    3.11
##    19    2    0.02      0.02    3.13
##    20    1    0.01      0.01    3.14
##    21    1    0.01      0.01    3.15
##    22    4    0.04      0.04    3.18
##    23    3    0.03      0.03    3.21
##    24    2    0.02      0.02    3.23
##    25    2    0.02      0.02    3.24
##    26    4    0.04      0.04    3.28
##    27    5    0.04      0.04    3.32
##    28    5    0.04      0.04    3.37
##    29    4    0.04      0.04    3.40
##    30    2    0.02      0.02    3.42
##    31    2    0.02      0.02    3.44
##    32    6    0.05      0.05    3.49
##    33    7    0.06      0.06    3.56
##    34    5    0.04      0.04    3.60
##    35    5    0.04      0.04    3.64
##    36    4    0.04      0.04    3.68
##    37    4    0.04      0.04    3.72
##    38    7    0.06      0.06    3.78
##    39    6    0.05      0.05    3.83
##    40    6    0.05      0.05    3.88
##    41    8    0.07      0.07    3.96
##    42   12    0.11      0.11    4.06
##    43   16    0.14      0.14    4.20
##    44   14    0.12      0.12    4.33
##    45   26    0.23      0.23    4.56
##    46   29    0.26      0.26    4.82
##    47   66    0.59      0.59    5.40
##    48   72    0.64      0.64    6.04
##    49  150    1.33      1.33    7.38
##    50  248    2.20      2.20    9.58
##    51  548    4.87      4.87   14.45
##    52 1199   10.66     10.66   25.11
##    53 2678   23.81     23.81   48.92
##    54 5746   51.08     51.08  100.00
##  <NA>    0    0.00        NA      NA

  sennav1 <-  sennav1 %>% filter( senna_it_rspnd >=30 )
 

  dic_e <- dic %>% filter(factor == "E")
  vars_e <- dic_e$coditem
  labels_e <- dic_e$text 
  poles_e <- dic_e$pole

4. Inverte itens negativos e transforma de 1-5 para 0-4

  dt <- sennav1[ , vars_e]
  dt <- mutate_if(dt, poles_e == 0, ~(6 -.))
  dt <- map_df(dt, ~.-1)
  
  map(dt, frq)

## $i67.E.Soc.00
## 
## # x <numeric> 
## # total N=10866  valid N=10626  mean=2.20  sd=1.30
##  
##   val  frq raw.prc valid.prc cum.prc
##     0 1443   13.28     13.58   13.58
##     1 1747   16.08     16.44   30.02
##     2 2707   24.91     25.48   55.50
##     3 2713   24.97     25.53   81.03
##     4 2016   18.55     18.97  100.00
##  <NA>  240    2.21        NA      NA
## 
## 
## $i73.E.Soc.00
## 
## # x <numeric> 
## # total N=10866  valid N=10637  mean=2.62  sd=1.23
##  
##   val  frq raw.prc valid.prc cum.prc
##     0  814    7.49      7.65    7.65
##     1 1138   10.47     10.70   18.35
##     2 2601   23.94     24.45   42.80
##     3 2839   26.13     26.69   69.49
##     4 3245   29.86     30.51  100.00
##  <NA>  229    2.11        NA      NA
## 
## 
## $i55.E.Act.10
## 
## # x <numeric> 
## # total N=10866  valid N=10555  mean=2.96  sd=1.09
##  
##   val  frq raw.prc valid.prc cum.prc
##     0  304    2.80      2.88    2.88
##     1  884    8.14      8.38   11.26
##     2 1989   18.30     18.84   30.10
##     3 3134   28.84     29.69   59.79
##     4 4244   39.06     40.21  100.00
##  <NA>  311    2.86        NA      NA
## 
## 
## $i63.E.Act.10
## 
## # x <numeric> 
## # total N=10866  valid N=10677  mean=2.72  sd=1.13
##  
##   val  frq raw.prc valid.prc cum.prc
##     0  419    3.86      3.92    3.92
##     1 1227   11.29     11.49   15.42
##     2 2538   23.36     23.77   39.19
##     3 3224   29.67     30.20   69.38
##     4 3269   30.08     30.62  100.00
##  <NA>  189    1.74        NA      NA
## 
## 
## $i76.E.Act.10
## 
## # x <numeric> 
## # total N=10866  valid N=10667  mean=2.07  sd=1.26
##  
##   val  frq raw.prc valid.prc cum.prc
##     0 1470   13.53     13.78   13.78
##     1 2099   19.32     19.68   33.46
##     2 2964   27.28     27.79   61.24
##     3 2470   22.73     23.16   84.40
##     4 1664   15.31     15.60  100.00
##  <NA>  199    1.83        NA      NA
## 
## 
## $i71.E.Soc.10
## 
## # x <numeric> 
## # total N=10866  valid N=10648  mean=2.83  sd=1.11
##  
##   val  frq raw.prc valid.prc cum.prc
##     0  350    3.22      3.29    3.29
##     1 1177   10.83     11.05   14.34
##     2 2043   18.80     19.19   33.53
##     3 3478   32.01     32.66   66.19
##     4 3600   33.13     33.81  100.00
##  <NA>  218    2.01        NA      NA
## 
## 
## $i75.E.Soc.10
## 
## # x <numeric> 
## # total N=10866  valid N=10619  mean=2.71  sd=1.15
##  
##   val  frq raw.prc valid.prc cum.prc
##     0  528    4.86      4.97    4.97
##     1 1228   11.30     11.56   16.54
##     2 2129   19.59     20.05   36.59
##     3 3632   33.43     34.20   70.79
##     4 3102   28.55     29.21  100.00
##  <NA>  247    2.27        NA      NA
## 
## 
## $i84.E.Soc.11
## 
## # x <numeric> 
## # total N=10866  valid N=10690  mean=2.77  sd=1.03
##  
##   val  frq raw.prc valid.prc cum.prc
##     0  311    2.86      2.91    2.91
##     1 1021    9.40      9.55   12.46
##     2 2229   20.51     20.85   33.31
##     3 4370   40.22     40.88   74.19
##     4 2759   25.39     25.81  100.00
##  <NA>  176    1.62        NA      NA
## 
## 
## $i87.E.Soc.11
## 
## # x <numeric> 
## # total N=10866  valid N=10715  mean=1.58  sd=1.18
##  
##   val  frq raw.prc valid.prc cum.prc
##     0 2275   20.94     21.23   21.23
##     1 3065   28.21     28.60   49.84
##     2 2981   27.43     27.82   77.66
##     3 1664   15.31     15.53   93.19
##     4  730    6.72      6.81  100.00
##  <NA>  151    1.39        NA      NA

  design1 <- TAM::designMatrices(resp=dt, modeltype=c("PCM"), ndim = 1 )
  design2 <- TAM::designMatrices(resp=dt, modeltype=c("PCM"), ndim = 2 )
 
  design1$B

## , , Dim01
## 
##              Cat0 Cat1 Cat2 Cat3 Cat4
## i67.E.Soc.00    0    1    2    3    4
## i73.E.Soc.00    0    1    2    3    4
## i55.E.Act.10    0    1    2    3    4
## i63.E.Act.10    0    1    2    3    4
## i76.E.Act.10    0    1    2    3    4
## i71.E.Soc.10    0    1    2    3    4
## i75.E.Soc.10    0    1    2    3    4
## i84.E.Soc.11    0    1    2    3    4
## i87.E.Soc.11    0    1    2    3    4

  design2$B

## , , Dim01
## 
##              Cat0 Cat1 Cat2 Cat3 Cat4
## i67.E.Soc.00    0    0    0    0    0
## i73.E.Soc.00    0    0    0    0    0
## i55.E.Act.10    0    0    0    0    0
## i63.E.Act.10    0    0    0    0    0
## i76.E.Act.10    0    0    0    0    0
## i71.E.Soc.10    0    0    0    0    0
## i75.E.Soc.10    0    0    0    0    0
## i84.E.Soc.11    0    0    0    0    0
## i87.E.Soc.11    0    0    0    0    0
## 
## , , Dim02
## 
##              Cat0 Cat1 Cat2 Cat3 Cat4
## i67.E.Soc.00    0    1    2    3    4
## i73.E.Soc.00    0    0    0    0    0
## i55.E.Act.10    0    1    2    3    4
## i63.E.Act.10    0    0    0    0    0
## i76.E.Act.10    0    0    0    0    0
## i71.E.Soc.10    0    1    2    3    4
## i75.E.Soc.10    0    0    0    0    0
## i84.E.Soc.11    0    0    0    0    0
## i87.E.Soc.11    0    0    0    0    0

  dim(design2$B)

## [1] 9 5 2

  design2$B[ ,, 1] <-  design1$B
  design2$B[ ,, 2] <-  design1$B
  
  
  design2$B[1 ,, 2] <- c(4,3,2,1,0)
  design2$B[2 ,, 2] <- c(4,3,2,1,0)
  
  dimnames( design2$B)[[3]] <- c("trait", "acq")
  
  B <-design2$B

7. Calibra MIRT controla por aquiescecia usando TAM

  fit2 <-  tam.mml(
    dt,  
    irtmodel = "PCM",
    B = B, 
    control=list( maxiter=100, 
      increment.factor=1.03, 
      fac.oldxsi=.4,
      Msteps=10)
    )

## ....................................................
## Processing Data      2019-11-24 19:54:26 
##     * Response Data: 10866 Persons and  9 Items 
##     * Numerical integration with 441 nodes
##     * Created Design Matrices   ( 2019-11-24 19:54:26 )
##     * Calculated Sufficient Statistics   ( 2019-11-24 19:54:26 )
## ....................................................
## Iteration 1     2019-11-24 19:54:26
## E Step
## M Step Intercepts   |----------
##   Deviance = 280988.807
##   Maximum item intercept parameter change: 0.202114
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.351722
## ....................................................
## Iteration 2     2019-11-24 19:54:27
## E Step
## M Step Intercepts   |----------
##   Deviance = 278848.5355 | Absolute change: 2140.271 | Relative change: 0.00767539
##   Maximum item intercept parameter change: 0.10396
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.095716
## ....................................................
## Iteration 3     2019-11-24 19:54:28
## E Step
## M Step Intercepts   |----------
##   Deviance = 278358.3106 | Absolute change: 490.2249 | Relative change: 0.00176113
##   Maximum item intercept parameter change: 0.205906
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.043352
## ....................................................
## Iteration 4     2019-11-24 19:54:28
## E Step
## M Step Intercepts   |----------
##   Deviance = 277921.2584 | Absolute change: 437.0522 | Relative change: 0.00157258
##   Maximum item intercept parameter change: 0.111823
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.024928
## ....................................................
## Iteration 5     2019-11-24 19:54:29
## E Step
## M Step Intercepts   |----------
##   Deviance = 277697.0989 | Absolute change: 224.1595 | Relative change: 0.00080721
##   Maximum item intercept parameter change: 0.022797
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.015701
## ....................................................
## Iteration 6     2019-11-24 19:54:29
## E Step
## M Step Intercepts   |----------
##   Deviance = 277540.2308 | Absolute change: 156.8682 | Relative change: 0.00056521
##   Maximum item intercept parameter change: 0.021498
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.010461
## ....................................................
## Iteration 7     2019-11-24 19:54:30
## E Step
## M Step Intercepts   |----------
##   Deviance = 277393.7693 | Absolute change: 146.4615 | Relative change: 0.00052799
##   Maximum item intercept parameter change: 0.020246
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.007506
## ....................................................
## Iteration 8     2019-11-24 19:54:30
## E Step
## M Step Intercepts   |----------
##   Deviance = 277253.7921 | Absolute change: 139.9772 | Relative change: 0.00050487
##   Maximum item intercept parameter change: 0.019042
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.006566
## ....................................................
## Iteration 9     2019-11-24 19:54:31
## E Step
## M Step Intercepts   |----------
##   Deviance = 277120.8445 | Absolute change: 132.9475 | Relative change: 0.00047975
##   Maximum item intercept parameter change: 0.14285
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.006107
## ....................................................
## Iteration 10     2019-11-24 19:54:31
## E Step
## M Step Intercepts   |----------
##   Deviance = 276909.5306 | Absolute change: 211.314 | Relative change: 0.00076312
##   Maximum item intercept parameter change: 0.065292
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.007765
## ....................................................
## Iteration 11     2019-11-24 19:54:32
## E Step
## M Step Intercepts   |----------
##   Deviance = 276776.0185 | Absolute change: 133.5121 | Relative change: 0.00048238
##   Maximum item intercept parameter change: 0.032385
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.006669
## ....................................................
## Iteration 12     2019-11-24 19:54:32
## E Step
## M Step Intercepts   |----------
##   Deviance = 276654.9591 | Absolute change: 121.0593 | Relative change: 0.00043758
##   Maximum item intercept parameter change: 0.014604
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.00592
## ....................................................
## Iteration 13     2019-11-24 19:54:33
## E Step
## M Step Intercepts   |----------
##   Deviance = 276540.7647 | Absolute change: 114.1944 | Relative change: 0.00041294
##   Maximum item intercept parameter change: 0.010435
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.005165
## ....................................................
## Iteration 14     2019-11-24 19:54:33
## E Step
## M Step Intercepts   |----------
##   Deviance = 276432.3792 | Absolute change: 108.3856 | Relative change: 0.00039209
##   Maximum item intercept parameter change: 0.009899
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.004754
## ....................................................
## Iteration 15     2019-11-24 19:54:34
## E Step
## M Step Intercepts   |----------
##   Deviance = 276326.3174 | Absolute change: 106.0618 | Relative change: 0.00038383
##   Maximum item intercept parameter change: 0.074281
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.004552
## ....................................................
## Iteration 16     2019-11-24 19:54:34
## E Step
## M Step Intercepts   |----------
##   Deviance = 276207.8067 | Absolute change: 118.5107 | Relative change: 0.00042906
##   Maximum item intercept parameter change: 0.03298
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.005248
## ....................................................
## Iteration 17     2019-11-24 19:54:35
## E Step
## M Step Intercepts   |----------
##   Deviance = 276107.3774 | Absolute change: 100.4293 | Relative change: 0.00036373
##   Maximum item intercept parameter change: 0.015466
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.004916
## ....................................................
## Iteration 18     2019-11-24 19:54:35
## E Step
## M Step Intercepts   |----------
##   Deviance = 276012.7618 | Absolute change: 94.6156 | Relative change: 0.00034279
##   Maximum item intercept parameter change: 0.009251
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.004512
## ....................................................
## Iteration 19     2019-11-24 19:54:35
## E Step
## M Step Intercepts   |----------
##   Deviance = 275920.8112 | Absolute change: 91.9506 | Relative change: 0.00033325
##   Maximum item intercept parameter change: 0.009143
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.004136
## ....................................................
## Iteration 20     2019-11-24 19:54:36
## E Step
## M Step Intercepts   |----------
##   Deviance = 275830.5512 | Absolute change: 90.26 | Relative change: 0.00032723
##   Maximum item intercept parameter change: 0.026528
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.00397
## ....................................................
## Iteration 21     2019-11-24 19:54:36
## E Step
## M Step Intercepts   |----------
##   Deviance = 275738.8516 | Absolute change: 91.6997 | Relative change: 0.00033256
##   Maximum item intercept parameter change: 0.008907
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.004189
## ....................................................
## Iteration 22     2019-11-24 19:54:37
## E Step
## M Step Intercepts   |----------
##   Deviance = 275652.092 | Absolute change: 86.7596 | Relative change: 0.00031474
##   Maximum item intercept parameter change: 0.040693
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003926
## ....................................................
## Iteration 23     2019-11-24 19:54:37
## E Step
## M Step Intercepts   |----------
##   Deviance = 275566.3952 | Absolute change: 85.6967 | Relative change: 0.00031098
##   Maximum item intercept parameter change: 0.055037
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003985
## ....................................................
## Iteration 24     2019-11-24 19:54:38
## E Step
## M Step Intercepts   |----------
##   Deviance = 275472.7291 | Absolute change: 93.6662 | Relative change: 0.00034002
##   Maximum item intercept parameter change: 0.00781
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.00408
## ....................................................
## Iteration 25     2019-11-24 19:54:38
## E Step
## M Step Intercepts   |----------
##   Deviance = 275399.8647 | Absolute change: 72.8644 | Relative change: 0.00026458
##   Maximum item intercept parameter change: 0.014679
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003676
## ....................................................
## Iteration 26     2019-11-24 19:54:39
## E Step
## M Step Intercepts   |----------
##   Deviance = 275327.7283 | Absolute change: 72.1364 | Relative change: 0.000262
##   Maximum item intercept parameter change: 0.007181
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003684
## ....................................................
## Iteration 27     2019-11-24 19:54:39
## E Step
## M Step Intercepts   |----------
##   Deviance = 275259.528 | Absolute change: 68.2003 | Relative change: 0.00024777
##   Maximum item intercept parameter change: 0.007097
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003374
## ....................................................
## Iteration 28     2019-11-24 19:54:39
## E Step
## M Step Intercepts   |----------
##   Deviance = 275192.4567 | Absolute change: 67.0712 | Relative change: 0.00024372
##   Maximum item intercept parameter change: 0.007012
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003213
## ....................................................
## Iteration 29     2019-11-24 19:54:40
## E Step
## M Step Intercepts   |----------
##   Deviance = 275126.7604 | Absolute change: 65.6963 | Relative change: 0.00023879
##   Maximum item intercept parameter change: 0.029034
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003115
## ....................................................
## Iteration 30     2019-11-24 19:54:40
## E Step
## M Step Intercepts   |----------
##   Deviance = 275062.7117 | Absolute change: 64.0487 | Relative change: 0.00023285
##   Maximum item intercept parameter change: 0.006532
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.00325
## ....................................................
## Iteration 31     2019-11-24 19:54:41
## E Step
## M Step Intercepts   |----------
##   Deviance = 275003.2707 | Absolute change: 59.4409 | Relative change: 0.00021615
##   Maximum item intercept parameter change: 0.006411
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003001
## ....................................................
## Iteration 32     2019-11-24 19:54:41
## E Step
## M Step Intercepts   |----------
##   Deviance = 274945.1788 | Absolute change: 58.0919 | Relative change: 0.00021129
##   Maximum item intercept parameter change: 0.006289
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002883
## ....................................................
## Iteration 33     2019-11-24 19:54:42
## E Step
## M Step Intercepts   |----------
##   Deviance = 274887.9793 | Absolute change: 57.1996 | Relative change: 0.00020808
##   Maximum item intercept parameter change: 0.006168
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002821
## ....................................................
## Iteration 34     2019-11-24 19:54:42
## E Step
## M Step Intercepts   |----------
##   Deviance = 274831.9415 | Absolute change: 56.0377 | Relative change: 0.0002039
##   Maximum item intercept parameter change: 0.012134
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002778
## ....................................................
## Iteration 35     2019-11-24 19:54:43
## E Step
## M Step Intercepts   |----------
##   Deviance = 274779.3063 | Absolute change: 52.6353 | Relative change: 0.00019155
##   Maximum item intercept parameter change: 0.022014
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002835
## ....................................................
## Iteration 36     2019-11-24 19:54:43
## E Step
## M Step Intercepts   |----------
##   Deviance = 274724.8299 | Absolute change: 54.4764 | Relative change: 0.00019829
##   Maximum item intercept parameter change: 0.030423
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003137
## ....................................................
## Iteration 37     2019-11-24 19:54:44
## E Step
## M Step Intercepts   |----------
##   Deviance = 274669.8108 | Absolute change: 55.019 | Relative change: 0.00020031
##   Maximum item intercept parameter change: 0.005603
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003024
## ....................................................
## Iteration 38     2019-11-24 19:54:44
## E Step
## M Step Intercepts   |----------
##   Deviance = 274619.9548 | Absolute change: 49.856 | Relative change: 0.00018155
##   Maximum item intercept parameter change: 0.013151
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002775
## ....................................................
## Iteration 39     2019-11-24 19:54:45
## E Step
## M Step Intercepts   |----------
##   Deviance = 274573.1099 | Absolute change: 46.8449 | Relative change: 0.00017061
##   Maximum item intercept parameter change: 0.005374
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002717
## ....................................................
## Iteration 40     2019-11-24 19:54:45
## E Step
## M Step Intercepts   |----------
##   Deviance = 274527.5443 | Absolute change: 45.5656 | Relative change: 0.00016598
##   Maximum item intercept parameter change: 0.005265
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002578
## ....................................................
## Iteration 41     2019-11-24 19:54:45
## E Step
## M Step Intercepts   |----------
##   Deviance = 274482.6545 | Absolute change: 44.8898 | Relative change: 0.00016354
##   Maximum item intercept parameter change: 0.007297
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002479
## ....................................................
## Iteration 42     2019-11-24 19:54:46
## E Step
## M Step Intercepts   |----------
##   Deviance = 274438.6708 | Absolute change: 43.9837 | Relative change: 0.00016027
##   Maximum item intercept parameter change: 0.005089
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002501
## ....................................................
## Iteration 43     2019-11-24 19:54:46
## E Step
## M Step Intercepts   |----------
##   Deviance = 274395.5659 | Absolute change: 43.105 | Relative change: 0.00015709
##   Maximum item intercept parameter change: 0.157599
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002456
## ....................................................
## Iteration 44     2019-11-24 19:54:47
## E Step
## M Step Intercepts   |----------
##   Deviance = 274304.6566 | Absolute change: 90.9092 | Relative change: 0.00033142
##   Maximum item intercept parameter change: 0.110858
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.007149
## ....................................................
## Iteration 45     2019-11-24 19:54:47
## E Step
## M Step Intercepts   |----------
##   Deviance = 274206.5682 | Absolute change: 98.0884 | Relative change: 0.00035772
##   Maximum item intercept parameter change: 0.054907
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.010924
## ....................................................
## Iteration 46     2019-11-24 19:54:48
## E Step
## M Step Intercepts   |----------
##   Deviance = 274152.6305 | Absolute change: 53.9377 | Relative change: 0.00019674
##   Maximum item intercept parameter change: 0.092672
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.009181
## ....................................................
## Iteration 47     2019-11-24 19:54:48
## E Step
## M Step Intercepts   |----------
##   Deviance = 274085.6469 | Absolute change: 66.9836 | Relative change: 0.00024439
##   Maximum item intercept parameter change: 0.041817
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.008679
## ....................................................
## Iteration 48     2019-11-24 19:54:48
## E Step
## M Step Intercepts   |----------
##   Deviance = 274044.0158 | Absolute change: 41.6312 | Relative change: 0.00015191
##   Maximum item intercept parameter change: 0.020553
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.006875
## ....................................................
## Iteration 49     2019-11-24 19:54:49
## E Step
## M Step Intercepts   |----------
##   Deviance = 274011.2522 | Absolute change: 32.7636 | Relative change: 0.00011957
##   Maximum item intercept parameter change: 0.04515
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.004985
## ....................................................
## Iteration 50     2019-11-24 19:54:49
## E Step
## M Step Intercepts   |----------
##   Deviance = 273977.6394 | Absolute change: 33.6129 | Relative change: 0.00012268
##   Maximum item intercept parameter change: 0.025479
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.004869
## ....................................................
## Iteration 51     2019-11-24 19:54:50
## E Step
## M Step Intercepts   |----------
##   Deviance = 273946.3398 | Absolute change: 31.2996 | Relative change: 0.00011425
##   Maximum item intercept parameter change: 0.003248
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003793
## ....................................................
## Iteration 52     2019-11-24 19:54:50
## E Step
## M Step Intercepts   |----------
##   Deviance = 273918.5308 | Absolute change: 27.809 | Relative change: 0.00010152
##   Maximum item intercept parameter change: 0.029968
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.0029
## ....................................................
## Iteration 53     2019-11-24 19:54:51
## E Step
## M Step Intercepts   |----------
##   Deviance = 273889.5263 | Absolute change: 29.0045 | Relative change: 0.0001059
##   Maximum item intercept parameter change: 0.003132
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.003192
## ....................................................
## Iteration 54     2019-11-24 19:54:51
## E Step
## M Step Intercepts   |----------
##   Deviance = 273862.9266 | Absolute change: 26.5997 | Relative change: 9.713e-05
##   Maximum item intercept parameter change: 0.002892
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002536
## ....................................................
## Iteration 55     2019-11-24 19:54:51
## E Step
## M Step Intercepts   |----------
##   Deviance = 273837.3731 | Absolute change: 25.5535 | Relative change: 9.332e-05
##   Maximum item intercept parameter change: 0.002883
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002113
## ....................................................
## Iteration 56     2019-11-24 19:54:52
## E Step
## M Step Intercepts   |----------
##   Deviance = 273812.394 | Absolute change: 24.9791 | Relative change: 9.123e-05
##   Maximum item intercept parameter change: 0.015012
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001825
## ....................................................
## Iteration 57     2019-11-24 19:54:52
## E Step
## M Step Intercepts   |----------
##   Deviance = 273787.1656 | Absolute change: 25.2284 | Relative change: 9.215e-05
##   Maximum item intercept parameter change: 0.019153
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001774
## ....................................................
## Iteration 58     2019-11-24 19:54:53
## E Step
## M Step Intercepts   |----------
##   Deviance = 273761.5669 | Absolute change: 25.5988 | Relative change: 9.351e-05
##   Maximum item intercept parameter change: 0.002604
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002029
## ....................................................
## Iteration 59     2019-11-24 19:54:53
## E Step
## M Step Intercepts   |----------
##   Deviance = 273737.8112 | Absolute change: 23.7557 | Relative change: 8.678e-05
##   Maximum item intercept parameter change: 0.002597
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.0017
## ....................................................
## Iteration 60     2019-11-24 19:54:53
## E Step
## M Step Intercepts   |----------
##   Deviance = 273714.5897 | Absolute change: 23.2215 | Relative change: 8.484e-05
##   Maximum item intercept parameter change: 0.003064
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001495
## ....................................................
## Iteration 61     2019-11-24 19:54:54
## E Step
## M Step Intercepts   |----------
##   Deviance = 273691.1336 | Absolute change: 23.4561 | Relative change: 8.57e-05
##   Maximum item intercept parameter change: 0.00336
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001376
## ....................................................
## Iteration 62     2019-11-24 19:54:54
## E Step
## M Step Intercepts   |----------
##   Deviance = 273668.8759 | Absolute change: 22.2577 | Relative change: 8.133e-05
##   Maximum item intercept parameter change: 0.00298
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001314
## ....................................................
## Iteration 63     2019-11-24 19:54:55
## E Step
## M Step Intercepts   |----------
##   Deviance = 273647.0175 | Absolute change: 21.8584 | Relative change: 7.988e-05
##   Maximum item intercept parameter change: 0.017886
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001247
## ....................................................
## Iteration 64     2019-11-24 19:54:55
## E Step
## M Step Intercepts   |----------
##   Deviance = 273625.0431 | Absolute change: 21.9744 | Relative change: 8.031e-05
##   Maximum item intercept parameter change: 0.002303
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001283
## ....................................................
## Iteration 65     2019-11-24 19:54:56
## E Step
## M Step Intercepts   |----------
##   Deviance = 273604.523 | Absolute change: 20.5201 | Relative change: 7.5e-05
##   Maximum item intercept parameter change: 0.002238
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001186
## ....................................................
## Iteration 66     2019-11-24 19:54:56
## E Step
## M Step Intercepts   |----------
##   Deviance = 273584.4123 | Absolute change: 20.1107 | Relative change: 7.351e-05
##   Maximum item intercept parameter change: 0.002315
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001134
## ....................................................
## Iteration 67     2019-11-24 19:54:56
## E Step
## M Step Intercepts   |----------
##   Deviance = 273564.6645 | Absolute change: 19.7479 | Relative change: 7.219e-05
##   Maximum item intercept parameter change: 0.002256
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.00111
## ....................................................
## Iteration 68     2019-11-24 19:54:57
## E Step
## M Step Intercepts   |----------
##   Deviance = 273546.0827 | Absolute change: 18.5817 | Relative change: 6.793e-05
##   Maximum item intercept parameter change: 0.0022
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001078
## ....................................................
## Iteration 69     2019-11-24 19:54:57
## E Step
## M Step Intercepts   |----------
##   Deviance = 273527.9682 | Absolute change: 18.1145 | Relative change: 6.623e-05
##   Maximum item intercept parameter change: 0.012756
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001056
## ....................................................
## Iteration 70     2019-11-24 19:54:58
## E Step
## M Step Intercepts   |----------
##   Deviance = 273509.6287 | Absolute change: 18.3395 | Relative change: 6.705e-05
##   Maximum item intercept parameter change: 0.019525
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001164
## ....................................................
## Iteration 71     2019-11-24 19:54:58
## E Step
## M Step Intercepts   |----------
##   Deviance = 273490.778 | Absolute change: 18.8507 | Relative change: 6.893e-05
##   Maximum item intercept parameter change: 0.002083
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001213
## ....................................................
## Iteration 72     2019-11-24 19:54:59
## E Step
## M Step Intercepts   |----------
##   Deviance = 273473.3093 | Absolute change: 17.4687 | Relative change: 6.388e-05
##   Maximum item intercept parameter change: 0.002605
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001086
## ....................................................
## Iteration 73     2019-11-24 19:54:59
## E Step
## M Step Intercepts   |----------
##   Deviance = 273456.1325 | Absolute change: 17.1768 | Relative change: 6.281e-05
##   Maximum item intercept parameter change: 0.026258
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001037
## ....................................................
## Iteration 74     2019-11-24 19:55:00
## E Step
## M Step Intercepts   |----------
##   Deviance = 273437.2571 | Absolute change: 18.8754 | Relative change: 6.903e-05
##   Maximum item intercept parameter change: 0.002477
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.002073
## ....................................................
## Iteration 75     2019-11-24 19:55:00
## E Step
## M Step Intercepts   |----------
##   Deviance = 273421.3824 | Absolute change: 15.8747 | Relative change: 5.806e-05
##   Maximum item intercept parameter change: 0.018861
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001628
## ....................................................
## Iteration 76     2019-11-24 19:55:00
## E Step
## M Step Intercepts   |----------
##   Deviance = 273404.4328 | Absolute change: 16.9496 | Relative change: 6.199e-05
##   Maximum item intercept parameter change: 0.0043
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001448
## ....................................................
## Iteration 77     2019-11-24 19:55:01
## E Step
## M Step Intercepts   |----------
##   Deviance = 273389.4974 | Absolute change: 14.9354 | Relative change: 5.463e-05
##   Maximum item intercept parameter change: 0.002327
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001256
## ....................................................
## Iteration 78     2019-11-24 19:55:01
## E Step
## M Step Intercepts   |----------
##   Deviance = 273375.2913 | Absolute change: 14.2061 | Relative change: 5.197e-05
##   Maximum item intercept parameter change: 0.002268
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001081
## ....................................................
## Iteration 79     2019-11-24 19:55:02
## E Step
## M Step Intercepts   |----------
##   Deviance = 273361.2762 | Absolute change: 14.0151 | Relative change: 5.127e-05
##   Maximum item intercept parameter change: 0.007772
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000977
## ....................................................
## Iteration 80     2019-11-24 19:55:02
## E Step
## M Step Intercepts   |----------
##   Deviance = 273347.5003 | Absolute change: 13.7759 | Relative change: 5.04e-05
##   Maximum item intercept parameter change: 0.009703
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000976
## ....................................................
## Iteration 81     2019-11-24 19:55:03
## E Step
## M Step Intercepts   |----------
##   Deviance = 273333.9734 | Absolute change: 13.527 | Relative change: 4.949e-05
##   Maximum item intercept parameter change: 0.002161
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000987
## ....................................................
## Iteration 82     2019-11-24 19:55:03
## E Step
## M Step Intercepts   |----------
##   Deviance = 273321.3129 | Absolute change: 12.6605 | Relative change: 4.632e-05
##   Maximum item intercept parameter change: 0.002108
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000864
## ....................................................
## Iteration 83     2019-11-24 19:55:03
## E Step
## M Step Intercepts   |----------
##   Deviance = 273308.763 | Absolute change: 12.5499 | Relative change: 4.592e-05
##   Maximum item intercept parameter change: 0.012246
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000801
## ....................................................
## Iteration 84     2019-11-24 19:55:04
## E Step
## M Step Intercepts   |----------
##   Deviance = 273295.9994 | Absolute change: 12.7636 | Relative change: 4.67e-05
##   Maximum item intercept parameter change: 0.002539
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.00106
## ....................................................
## Iteration 85     2019-11-24 19:55:04
## E Step
## M Step Intercepts   |----------
##   Deviance = 273283.9819 | Absolute change: 12.0175 | Relative change: 4.397e-05
##   Maximum item intercept parameter change: 0.009557
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000935
## ....................................................
## Iteration 86     2019-11-24 19:55:04
## E Step
## M Step Intercepts   |----------
##   Deviance = 273272.1339 | Absolute change: 11.848 | Relative change: 4.336e-05
##   Maximum item intercept parameter change: 0.001898
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000931
## ....................................................
## Iteration 87     2019-11-24 19:55:05
## E Step
## M Step Intercepts   |----------
##   Deviance = 273260.7578 | Absolute change: 11.3761 | Relative change: 4.163e-05
##   Maximum item intercept parameter change: 0.013632
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.00082
## ....................................................
## Iteration 88     2019-11-24 19:55:05
## E Step
## M Step Intercepts   |----------
##   Deviance = 273249.0331 | Absolute change: 11.7247 | Relative change: 4.291e-05
##   Maximum item intercept parameter change: 0.001669
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000815
## ....................................................
## Iteration 89     2019-11-24 19:55:06
## E Step
## M Step Intercepts   |----------
##   Deviance = 273238.3729 | Absolute change: 10.6602 | Relative change: 3.901e-05
##   Maximum item intercept parameter change: 0.004572
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000727
## ....................................................
## Iteration 90     2019-11-24 19:55:06
## E Step
## M Step Intercepts   |----------
##   Deviance = 273228.29 | Absolute change: 10.0829 | Relative change: 3.69e-05
##   Maximum item intercept parameter change: 0.00158
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000713
## ....................................................
## Iteration 91     2019-11-24 19:55:06
## E Step
## M Step Intercepts   |----------
##   Deviance = 273218.3995 | Absolute change: 9.8905 | Relative change: 3.62e-05
##   Maximum item intercept parameter change: 0.00154
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000658
## ....................................................
## Iteration 92     2019-11-24 19:55:07
## E Step
## M Step Intercepts   |----------
##   Deviance = 273208.648 | Absolute change: 9.7515 | Relative change: 3.569e-05
##   Maximum item intercept parameter change: 0.001501
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.00063
## ....................................................
## Iteration 93     2019-11-24 19:55:07
## E Step
## M Step Intercepts   |----------
##   Deviance = 273199.1509 | Absolute change: 9.4971 | Relative change: 3.476e-05
##   Maximum item intercept parameter change: 0.018367
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000612
## ....................................................
## Iteration 94     2019-11-24 19:55:08
## E Step
## M Step Intercepts   |----------
##   Deviance = 273188.8333 | Absolute change: 10.3176 | Relative change: 3.777e-05
##   Maximum item intercept parameter change: 0.009672
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001133
## ....................................................
## Iteration 95     2019-11-24 19:55:08
## E Step
## M Step Intercepts   |----------
##   Deviance = 273179.4086 | Absolute change: 9.4247 | Relative change: 3.45e-05
##   Maximum item intercept parameter change: 0.002664
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.001211
## ....................................................
## Iteration 96     2019-11-24 19:55:09
## E Step
## M Step Intercepts   |----------
##   Deviance = 273170.51 | Absolute change: 8.8986 | Relative change: 3.258e-05
##   Maximum item intercept parameter change: 0.001586
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000939
## ....................................................
## Iteration 97     2019-11-24 19:55:09
## E Step
## M Step Intercepts   |----------
##   Deviance = 273162.0729 | Absolute change: 8.4371 | Relative change: 3.089e-05
##   Maximum item intercept parameter change: 0.012923
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000772
## ....................................................
## Iteration 98     2019-11-24 19:55:09
## E Step
## M Step Intercepts   |----------
##   Deviance = 273153.2644 | Absolute change: 8.8085 | Relative change: 3.225e-05
##   Maximum item intercept parameter change: 0.010216
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000727
## ....................................................
## Iteration 99     2019-11-24 19:55:10
## E Step
## M Step Intercepts   |----------
##   Deviance = 273144.9995 | Absolute change: 8.265 | Relative change: 3.026e-05
##   Maximum item intercept parameter change: 0.00242
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000857
## ....................................................
## Iteration 100     2019-11-24 19:55:10
## E Step
## M Step Intercepts   |----------
##   Deviance = 273137.2239 | Absolute change: 7.7755 | Relative change: 2.847e-05
##   Maximum item intercept parameter change: 0.006985
##   Maximum item slope parameter change: 0
##   Maximum regression parameter change: 0
##   Maximum variance parameter change: 0.000712
## ....................................................
## Item Parameters
##    xsi.index         xsi.label     est
## 1          1 i67.E.Soc.00_Cat1 -1.1953
## 2          2 i67.E.Soc.00_Cat2 -0.8648
## 3          3 i67.E.Soc.00_Cat3  0.1079
## 4          4 i67.E.Soc.00_Cat4  1.2316
## 5          5 i73.E.Soc.00_Cat1 -2.1330
## 6          6 i73.E.Soc.00_Cat2 -1.4287
## 7          7 i73.E.Soc.00_Cat3 -0.2564
## 8          8 i73.E.Soc.00_Cat4  0.3619
## 9          9 i55.E.Act.10_Cat1 -3.1093
## 10        10 i55.E.Act.10_Cat2 -1.7121
## 11        11 i55.E.Act.10_Cat3 -0.6977
## 12        12 i55.E.Act.10_Cat4 -0.1291
## 13        13 i63.E.Act.10_Cat1 -2.8393
## 14        14 i63.E.Act.10_Cat2 -1.1739
## 15        15 i63.E.Act.10_Cat3 -0.4833
## 16        16 i63.E.Act.10_Cat4  0.4741
## 17        17 i76.E.Act.10_Cat1 -1.4576
## 18        18 i76.E.Act.10_Cat2 -0.5374
## 19        19 i76.E.Act.10_Cat3  0.2006
## 20        20 i76.E.Act.10_Cat4  1.3333
## 21        21 i71.E.Soc.10_Cat1 -3.0011
## 22        22 i71.E.Soc.10_Cat2 -1.4333
## 23        23 i71.E.Soc.10_Cat3 -0.6600
## 24        24 i71.E.Soc.10_Cat4  0.1831
## 25        25 i75.E.Soc.10_Cat1 -2.5804
## 26        26 i75.E.Soc.10_Cat2 -1.2869
## 27        27 i75.E.Soc.10_Cat3 -0.6116
## 28        28 i75.E.Soc.10_Cat4  0.4060
## 29        29 i84.E.Soc.11_Cat1 -3.1189
## 30        30 i84.E.Soc.11_Cat2 -1.6175
## 31        31 i84.E.Soc.11_Cat3 -0.7829
## 32        32 i84.E.Soc.11_Cat4  0.7072
## 33        33 i87.E.Soc.11_Cat1 -0.8253
## 34        34 i87.E.Soc.11_Cat2 -0.0824
## 35        35 i87.E.Soc.11_Cat3  0.9435
## 36        36 i87.E.Soc.11_Cat4  2.2619
## ...................................
## Regression Coefficients
##      V1 V2
## [1,]  0  0
## 
## Variance:
##         [,1]    [,2]
## [1,]  0.6084 -0.1231
## [2,] -0.1231  0.2943
## 
## Correlation Matrix:
##        [,1]   [,2]
## [1,]  1.000 -0.291
## [2,] -0.291  1.000
## 
## 
## EAP Reliability:
##  Dim1  Dim2 
## 0.743 0.571 
## 
## -----------------------------
## Start:  2019-11-24 19:54:26
## End:  2019-11-24 19:55:11 
## Time difference of 45.24235 secs

   summary(fit2) 

## ------------------------------------------------------------
## TAM 3.1-45 (2019-03-18 16:53:26) 
## R version 3.5.1 (2018-07-02) x86_64, darwin15.6.0 | nodename=MacBookPro2018.local | login=rprimi 
## 
## Date of Analysis: 2019-11-24 19:55:11 
## Time difference of 45.24235 secs
## Computation time: 45.24235 
## 
## Multidimensional Item Response Model in TAM 
## 
## IRT Model: PCM
## Call:
## tam.mml(resp = dt, irtmodel = "PCM", B = B, control = list(maxiter = 100, 
##     increment.factor = 1.03, fac.oldxsi = 0.4, Msteps = 10))
## 
## ------------------------------------------------------------
## Number of iterations = 100 
## Numeric integration with 441 integration points
## 
## Deviance = 273137.2 
## Log likelihood = -136568.6 
## Number of persons = 10866 
## Number of persons used = 10866 
## Number of items = 9 
## Number of estimated parameters = 39 
##     Item threshold parameters = 36 
##     Item slope parameters = 0 
##     Regression parameters = 0 
##     Variance/covariance parameters = 3 
## 
## AIC = 273215  | penalty = 78    | AIC=-2*LL + 2*p 
## AIC3 = 273254  | penalty = 117    | AIC3=-2*LL + 3*p 
## BIC = 273500  | penalty = 362.44    | BIC=-2*LL + log(n)*p 
## aBIC = 273376  | penalty = 238.49    | aBIC=-2*LL + log((n-2)/24)*p  (adjusted BIC) 
## CAIC = 273539  | penalty = 401.44    | CAIC=-2*LL + [log(n)+1]*p  (consistent AIC) 
## AICc = 273216  | penalty = 78.29    | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC) 
## 
## ------------------------------------------------------------
## EAP Reliability
##  Dim1  Dim2 
## 0.743 0.571 
## ------------------------------------------------------------
## Covariances and Variances
##        V1     V2
## V1  0.608 -0.123
## V2 -0.123  0.294
## ------------------------------------------------------------
## Correlations and Standard Deviations (in the diagonal)
##        V1     V2
## V1  0.780 -0.291
## V2 -0.291  0.543
## ------------------------------------------------------------
## Regression Coefficients
##      V1 V2
## [1,]  0  0
## ------------------------------------------------------------
## Item Parameters -A*Xsi
##                      item     N     M xsi.item AXsi_.Cat0 AXsi_.Cat1
## i67.E.Soc.00 i67.E.Soc.00 10626 2.199   -0.180          0     -1.195
## i73.E.Soc.00 i73.E.Soc.00 10637 2.617   -0.864          0     -2.134
## i55.E.Act.10 i55.E.Act.10 10555 2.960   -1.413          0     -3.110
## i63.E.Act.10 i63.E.Act.10 10677 2.721   -1.006          0     -2.840
## i76.E.Act.10 i76.E.Act.10 10667 2.071   -0.115          0     -1.458
## i71.E.Soc.10 i71.E.Soc.10 10648 2.827   -1.227          0     -3.002
## i75.E.Soc.10 i75.E.Soc.10 10619 2.711   -1.018          0     -2.581
## i84.E.Soc.11 i84.E.Soc.11 10690 2.771   -1.203          0     -3.120
## i87.E.Soc.11 i87.E.Soc.11 10715 1.581    0.575          0     -0.826
##              AXsi_.Cat2 AXsi_.Cat3 AXsi_.Cat4 B.Cat0.Dim1 B.Cat0.Dim2
## i67.E.Soc.00     -2.060     -1.952     -0.719           0           4
## i73.E.Soc.00     -3.563     -3.820     -3.458           0           4
## i55.E.Act.10     -4.823     -5.521     -5.650           0           0
## i63.E.Act.10     -4.014     -4.497     -4.022           0           0
## i76.E.Act.10     -1.996     -1.793     -0.459           0           0
## i71.E.Soc.10     -4.436     -5.096     -4.906           0           0
## i75.E.Soc.10     -3.869     -4.480     -4.071           0           0
## i84.E.Soc.11     -4.738     -5.521     -4.813           0           0
## i87.E.Soc.11     -0.907      0.037      2.300           0           0
##              B.Cat1.Dim1 B.Cat1.Dim2 B.Cat2.Dim1 B.Cat2.Dim2 B.Cat3.Dim1
## i67.E.Soc.00           1           3           2           2           3
## i73.E.Soc.00           1           3           2           2           3
## i55.E.Act.10           1           1           2           2           3
## i63.E.Act.10           1           1           2           2           3
## i76.E.Act.10           1           1           2           2           3
## i71.E.Soc.10           1           1           2           2           3
## i75.E.Soc.10           1           1           2           2           3
## i84.E.Soc.11           1           1           2           2           3
## i87.E.Soc.11           1           1           2           2           3
##              B.Cat3.Dim2 B.Cat4.Dim1 B.Cat4.Dim2
## i67.E.Soc.00           1           4           0
## i73.E.Soc.00           1           4           0
## i55.E.Act.10           3           4           4
## i63.E.Act.10           3           4           4
## i76.E.Act.10           3           4           4
## i71.E.Soc.10           3           4           4
## i75.E.Soc.10           3           4           4
## i84.E.Soc.11           3           4           4
## i87.E.Soc.11           3           4           4
## 
## Item Parameters Xsi
##                      xsi se.xsi
## i67.E.Soc.00_Cat1 -1.195  0.034
## i67.E.Soc.00_Cat2 -0.865  0.026
## i67.E.Soc.00_Cat3  0.108  0.024
## i67.E.Soc.00_Cat4  1.232  0.030
## i73.E.Soc.00_Cat1 -2.133  0.049
## i73.E.Soc.00_Cat2 -1.429  0.031
## i73.E.Soc.00_Cat3 -0.256  0.024
## i73.E.Soc.00_Cat4  0.362  0.025
## i55.E.Act.10_Cat1 -3.109  0.098
## i55.E.Act.10_Cat2 -1.712  0.038
## i55.E.Act.10_Cat3 -0.698  0.024
## i55.E.Act.10_Cat4 -0.129  0.022
## i63.E.Act.10_Cat1 -2.839  0.071
## i63.E.Act.10_Cat2 -1.174  0.030
## i63.E.Act.10_Cat3 -0.483  0.023
## i63.E.Act.10_Cat4  0.474  0.024
## i76.E.Act.10_Cat1 -1.458  0.035
## i76.E.Act.10_Cat2 -0.537  0.024
## i76.E.Act.10_Cat3  0.201  0.023
## i76.E.Act.10_Cat4  1.333  0.033
## i71.E.Soc.10_Cat1 -3.001  0.085
## i71.E.Soc.10_Cat2 -1.433  0.034
## i71.E.Soc.10_Cat3 -0.660  0.024
## i71.E.Soc.10_Cat4  0.183  0.023
## i75.E.Soc.10_Cat1 -2.580  0.067
## i75.E.Soc.10_Cat2 -1.287  0.032
## i75.E.Soc.10_Cat3 -0.612  0.023
## i75.E.Soc.10_Cat4  0.406  0.024
## i84.E.Soc.11_Cat1 -3.119  0.093
## i84.E.Soc.11_Cat2 -1.617  0.035
## i84.E.Soc.11_Cat3 -0.783  0.023
## i84.E.Soc.11_Cat4  0.707  0.024
## i87.E.Soc.11_Cat1 -0.825  0.026
## i87.E.Soc.11_Cat2 -0.082  0.022
## i87.E.Soc.11_Cat3  0.944  0.027
## i87.E.Soc.11_Cat4  2.262  0.054

   tam.threshold(fit2)

##                   Cat1        Cat2       Cat3      Cat4
## i67.E.Soc.00 -1.633392 -0.75759888  0.1758728 1.4784851
## i73.E.Soc.00 -2.466339 -1.37173462 -0.3326111 0.7160339
## i55.E.Act.10 -3.306976 -1.80368042 -0.7671204 0.2414246
## i63.E.Act.10 -3.000092 -1.36166382 -0.4153748 0.7601624
## i76.E.Act.10 -1.751129 -0.59921265  0.3040466 1.5823059
## i71.E.Soc.10 -3.174957 -1.59292603 -0.6290588 0.4928284
## i75.E.Soc.10 -2.800140 -1.42684937 -0.5224915 0.6797791
## i84.E.Soc.11 -3.301849 -1.74105835 -0.6611023 0.8918152
## i87.E.Soc.11 -1.152191 -0.04696655  1.0168762 2.4723816

  tam.threshold(fit1)

##                    Cat1         Cat2       Cat3      Cat4
## i67.E.Soc.00 -1.0970764 -0.477996826  0.1181946 0.9559021
## i73.E.Soc.00 -1.3902283 -0.824249268 -0.1868591 0.5393372
## i55.E.Act.10 -1.9666443 -1.146881104 -0.5241394 0.2577209
## i63.E.Act.10 -1.8910217 -0.993072510 -0.2850037 0.5642395
## i76.E.Act.10 -1.1446838 -0.402374268  0.2666931 1.0998230
## i71.E.Soc.10 -1.9851379 -1.013397217 -0.4281921 0.4706726
## i75.E.Soc.10 -1.6989441 -0.910308838 -0.3509216 0.6321716
## i84.E.Soc.11 -2.0232239 -1.136077881 -0.4677429 0.8275452
## i87.E.Soc.11 -0.9024353  0.003570557  0.7480774 1.6216736

8. Examina validade dos parâmetros dos sujeitos

  library(scales)

  scores <- tibble(
   trait_e_orig = fit1$person$EAP,
   trait_e_rec =fit2$person$EAP.Dim1,
   acq_e =  fit2$person$EAP.Dim2
  )

  sennav1 <- bind_cols(sennav1, scores)

  names(sennav1)

##  [1] "i03.NV.NV.10"         "i04.A.Cmp.10"         "i05.O.Img.10"        
##  [4] "i06.C.Ord.10"         "i07.N.Vol.00"         "i09.A.Cmp.10"        
##  [7] "i10.O.Img.10"         "i11.C.Ord.10"         "i12.N.Vol.00"        
## [10] "i13.NV.NV.10"         "i14.A.Tru.10"         "i17.N.Anx.00"        
## [13] "i24.O.Aes.10"         "i25.A.Cmp.10"         "i27.N.Dep.00"        
## [16] "i29.A.Cmp.10"         "i30.O.Int.10"         "i32.N.Vol.00"        
## [19] "i33.NV.NV.10"         "i34.A.Tru.10"         "i36.C.Conc.00"       
## [22] "i37.N.Anx.10"         "i39.A.Cmp.10"         "i40.O.Aes.10"        
## [25] "i42.N.Anx.00"         "i44.A.Pol.00"         "i46.C.Conc.00"       
## [28] "i48.NV.NV.10"         "i49.A.Cmp.10"         "i51.C.Ord.00"        
## [31] "i52.NV.NV.10"         "i53.A.Pol.00"         "i54.O.Int.10"        
## [34] "i55.E.Act.10"         "i56.NV.NV.10"         "i60.NV.NV.00"        
## [37] "i63.E.Act.10"         "i66.O.Int.10"         "i67.E.Soc.00"        
## [40] "i70.O.Img.11"         "i71.E.Soc.10"         "i73.E.Soc.00"        
## [43] "i74.NV.NV.10"         "i75.E.Soc.10"         "i76.E.Act.10"        
## [46] "i77.C.SD.11"          "i79.N.Vol.11"         "i82.N.Vol.11"        
## [49] "i83.C.Conc.11"        "i84.E.Soc.11"         "i87.E.Soc.11"        
## [52] "i88.N.Dep.11"         "i89.C.Achv.11"        "i91.C.SD.11"         
## [55] "missR"                "admiss_missR"         "acq_avr"             
## [58] "acq_sd"               "num_items"            "Caderno"             
## [61] "age2"                 "grade"                "atrasado"            
## [64] "atrasado2"            "VL_PROFICIENCIA_LP"   "VL_PROFICIENCIA_MT"  
## [67] "vign_consist"         "vign_consist_count"   "F1.Cons"             
## [70] "F2.Extr"              "F3.EmSt"              "F4.Agre"             
## [73] "F5.Opns"              "F6.NVLoc"             "gender"              
## [76] "rwn_id"               "NM_REGIONAL_ESCOLA"   "grade2"              
## [79] "grade_5"              "grade_9"              "grade_10"            
## [82] "freq"                 "cd_esc_grade"         "rwn_id2"             
## [85] "VL_PROFICIENCIA_LP_r" "VL_PROFICIENCIA_MT_r" "senna_it_rspnd"      
## [88] "trait_e_orig"         "trait_e_rec"          "acq_e"

 sennav1 %>%  ggplot(aes(x=trait_e_orig )) + 
   geom_histogram(color="white", fill="orange", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

 sennav1 %>%  ggplot(aes(x= trait_e_rec )) + 
   geom_histogram(color="white", fill="orange", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

 sennav1 %>%  ggplot(aes(x= acq_e )) + 
   geom_histogram(color="white", fill="orange", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

sennav1 %>%  ggplot(aes(x= trait_e_orig, y =  trait_e_rec)) + 
   geom_point(color="blue", fill="white", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   scale_y_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

sennav1 %>%  ggplot(aes(x= trait_e_orig, y =  trait_e_rec)) + 
   geom_point(color="blue", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   scale_y_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

sennav1 %>%  ggplot(aes(x= acq_e, y =  trait_e_rec)) + 
   geom_point(color="blue", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   scale_y_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

 names(sennav1)

##  [1] "i03.NV.NV.10"         "i04.A.Cmp.10"         "i05.O.Img.10"        
##  [4] "i06.C.Ord.10"         "i07.N.Vol.00"         "i09.A.Cmp.10"        
##  [7] "i10.O.Img.10"         "i11.C.Ord.10"         "i12.N.Vol.00"        
## [10] "i13.NV.NV.10"         "i14.A.Tru.10"         "i17.N.Anx.00"        
## [13] "i24.O.Aes.10"         "i25.A.Cmp.10"         "i27.N.Dep.00"        
## [16] "i29.A.Cmp.10"         "i30.O.Int.10"         "i32.N.Vol.00"        
## [19] "i33.NV.NV.10"         "i34.A.Tru.10"         "i36.C.Conc.00"       
## [22] "i37.N.Anx.10"         "i39.A.Cmp.10"         "i40.O.Aes.10"        
## [25] "i42.N.Anx.00"         "i44.A.Pol.00"         "i46.C.Conc.00"       
## [28] "i48.NV.NV.10"         "i49.A.Cmp.10"         "i51.C.Ord.00"        
## [31] "i52.NV.NV.10"         "i53.A.Pol.00"         "i54.O.Int.10"        
## [34] "i55.E.Act.10"         "i56.NV.NV.10"         "i60.NV.NV.00"        
## [37] "i63.E.Act.10"         "i66.O.Int.10"         "i67.E.Soc.00"        
## [40] "i70.O.Img.11"         "i71.E.Soc.10"         "i73.E.Soc.00"        
## [43] "i74.NV.NV.10"         "i75.E.Soc.10"         "i76.E.Act.10"        
## [46] "i77.C.SD.11"          "i79.N.Vol.11"         "i82.N.Vol.11"        
## [49] "i83.C.Conc.11"        "i84.E.Soc.11"         "i87.E.Soc.11"        
## [52] "i88.N.Dep.11"         "i89.C.Achv.11"        "i91.C.SD.11"         
## [55] "missR"                "admiss_missR"         "acq_avr"             
## [58] "acq_sd"               "num_items"            "Caderno"             
## [61] "age2"                 "grade"                "atrasado"            
## [64] "atrasado2"            "VL_PROFICIENCIA_LP"   "VL_PROFICIENCIA_MT"  
## [67] "vign_consist"         "vign_consist_count"   "F1.Cons"             
## [70] "F2.Extr"              "F3.EmSt"              "F4.Agre"             
## [73] "F5.Opns"              "F6.NVLoc"             "gender"              
## [76] "rwn_id"               "NM_REGIONAL_ESCOLA"   "grade2"              
## [79] "grade_5"              "grade_9"              "grade_10"            
## [82] "freq"                 "cd_esc_grade"         "rwn_id2"             
## [85] "VL_PROFICIENCIA_LP_r" "VL_PROFICIENCIA_MT_r" "senna_it_rspnd"      
## [88] "trait_e_orig"         "trait_e_rec"          "acq_e"

  corr.test(sennav1[, c(65, 66, 88:90, 57, 67, 69:74)])

## Call:corr.test(x = sennav1[, c(65, 66, 88:90, 57, 67, 69:74)])
## Correlation matrix 
##                    VL_PROFICIENCIA_LP VL_PROFICIENCIA_MT trait_e_orig
## VL_PROFICIENCIA_LP               1.00               0.66         0.13
## VL_PROFICIENCIA_MT               0.66               1.00         0.09
## trait_e_orig                     0.13               0.09         1.00
## trait_e_rec                      0.09               0.06         0.95
## acq_e                            0.11               0.08         0.10
## acq_avr                          0.05               0.05         0.25
## vign_consist                     0.39               0.32         0.16
## F1.Cons                          0.15               0.19         0.10
## F2.Extr                          0.13               0.09         1.00
## F3.EmSt                          0.10               0.13         0.19
## F4.Agre                          0.18               0.13         0.38
## F5.Opns                          0.18               0.15         0.41
## F6.NVLoc                        -0.23              -0.20        -0.11
##                    trait_e_rec acq_e acq_avr vign_consist F1.Cons F2.Extr
## VL_PROFICIENCIA_LP        0.09  0.11    0.05         0.39    0.15    0.13
## VL_PROFICIENCIA_MT        0.06  0.08    0.05         0.32    0.19    0.09
## trait_e_orig              0.95  0.10    0.25         0.16    0.10    1.00
## trait_e_rec               1.00 -0.21    0.10         0.12    0.07    0.95
## acq_e                    -0.21  1.00    0.50         0.10    0.08    0.10
## acq_avr                   0.10  0.50    1.00         0.08    0.08    0.26
## vign_consist              0.12  0.10    0.08         1.00    0.09    0.16
## F1.Cons                   0.07  0.08    0.08         0.09    1.00    0.10
## F2.Extr                   0.95  0.10    0.26         0.16    0.10    1.00
## F3.EmSt                   0.19 -0.03   -0.13         0.08    0.38    0.19
## F4.Agre                   0.28  0.30    0.32         0.20    0.37    0.38
## F5.Opns                   0.30  0.33    0.48         0.13    0.34    0.41
## F6.NVLoc                 -0.15  0.12    0.29        -0.17   -0.31   -0.11
##                    F3.EmSt F4.Agre F5.Opns F6.NVLoc
## VL_PROFICIENCIA_LP    0.10    0.18    0.18    -0.23
## VL_PROFICIENCIA_MT    0.13    0.13    0.15    -0.20
## trait_e_orig          0.19    0.38    0.41    -0.11
## trait_e_rec           0.19    0.28    0.30    -0.15
## acq_e                -0.03    0.30    0.33     0.12
## acq_avr              -0.13    0.32    0.48     0.29
## vign_consist          0.08    0.20    0.13    -0.17
## F1.Cons               0.38    0.37    0.34    -0.31
## F2.Extr               0.19    0.38    0.41    -0.11
## F3.EmSt               1.00    0.30    0.15    -0.37
## F4.Agre               0.30    1.00    0.41    -0.14
## F5.Opns               0.15    0.41    1.00    -0.04
## F6.NVLoc             -0.37   -0.14   -0.04     1.00
## Sample Size 
##                    VL_PROFICIENCIA_LP VL_PROFICIENCIA_MT trait_e_orig
## VL_PROFICIENCIA_LP              10123              10123        10123
## VL_PROFICIENCIA_MT              10123              10123        10123
## trait_e_orig                    10123              10123        10866
## trait_e_rec                     10123              10123        10866
## acq_e                           10123              10123        10866
## acq_avr                         10123              10123        10866
## vign_consist                    10090              10090        10830
## F1.Cons                         10123              10123        10866
## F2.Extr                         10123              10123        10866
## F3.EmSt                         10123              10123        10866
## F4.Agre                         10123              10123        10866
## F5.Opns                         10123              10123        10866
## F6.NVLoc                        10123              10123        10866
##                    trait_e_rec acq_e acq_avr vign_consist F1.Cons F2.Extr
## VL_PROFICIENCIA_LP       10123 10123   10123        10090   10123   10123
## VL_PROFICIENCIA_MT       10123 10123   10123        10090   10123   10123
## trait_e_orig             10866 10866   10866        10830   10866   10866
## trait_e_rec              10866 10866   10866        10830   10866   10866
## acq_e                    10866 10866   10866        10830   10866   10866
## acq_avr                  10866 10866   10866        10830   10866   10866
## vign_consist             10830 10830   10830        10830   10830   10830
## F1.Cons                  10866 10866   10866        10830   10866   10866
## F2.Extr                  10866 10866   10866        10830   10866   10866
## F3.EmSt                  10866 10866   10866        10830   10866   10866
## F4.Agre                  10866 10866   10866        10830   10866   10866
## F5.Opns                  10866 10866   10866        10830   10866   10866
## F6.NVLoc                 10866 10866   10866        10830   10866   10866
##                    F3.EmSt F4.Agre F5.Opns F6.NVLoc
## VL_PROFICIENCIA_LP   10123   10123   10123    10123
## VL_PROFICIENCIA_MT   10123   10123   10123    10123
## trait_e_orig         10866   10866   10866    10866
## trait_e_rec          10866   10866   10866    10866
## acq_e                10866   10866   10866    10866
## acq_avr              10866   10866   10866    10866
## vign_consist         10830   10830   10830    10830
## F1.Cons              10866   10866   10866    10866
## F2.Extr              10866   10866   10866    10866
## F3.EmSt              10866   10866   10866    10866
## F4.Agre              10866   10866   10866    10866
## F5.Opns              10866   10866   10866    10866
## F6.NVLoc             10866   10866   10866    10866
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##                    VL_PROFICIENCIA_LP VL_PROFICIENCIA_MT trait_e_orig
## VL_PROFICIENCIA_LP                  0                  0            0
## VL_PROFICIENCIA_MT                  0                  0            0
## trait_e_orig                        0                  0            0
## trait_e_rec                         0                  0            0
## acq_e                               0                  0            0
## acq_avr                             0                  0            0
## vign_consist                        0                  0            0
## F1.Cons                             0                  0            0
## F2.Extr                             0                  0            0
## F3.EmSt                             0                  0            0
## F4.Agre                             0                  0            0
## F5.Opns                             0                  0            0
## F6.NVLoc                            0                  0            0
##                    trait_e_rec acq_e acq_avr vign_consist F1.Cons F2.Extr
## VL_PROFICIENCIA_LP           0     0       0            0       0       0
## VL_PROFICIENCIA_MT           0     0       0            0       0       0
## trait_e_orig                 0     0       0            0       0       0
## trait_e_rec                  0     0       0            0       0       0
## acq_e                        0     0       0            0       0       0
## acq_avr                      0     0       0            0       0       0
## vign_consist                 0     0       0            0       0       0
## F1.Cons                      0     0       0            0       0       0
## F2.Extr                      0     0       0            0       0       0
## F3.EmSt                      0     0       0            0       0       0
## F4.Agre                      0     0       0            0       0       0
## F5.Opns                      0     0       0            0       0       0
## F6.NVLoc                     0     0       0            0       0       0
##                    F3.EmSt F4.Agre F5.Opns F6.NVLoc
## VL_PROFICIENCIA_LP       0       0       0        0
## VL_PROFICIENCIA_MT       0       0       0        0
## trait_e_orig             0       0       0        0
## trait_e_rec              0       0       0        0
## acq_e                    0       0       0        0
## acq_avr                  0       0       0        0
## vign_consist             0       0       0        0
## F1.Cons                  0       0       0        0
## F2.Extr                  0       0       0        0
## F3.EmSt                  0       0       0        0
## F4.Agre                  0       0       0        0
## F5.Opns                  0       0       0        0
## F6.NVLoc                 0       0       0        0
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option

9. Calibra MIRT controlando por aquiescecia usando pacore MIRT

 parms <- dt %>% 
    mirt(2, itemtype = 'graded', pars = 'values',TOL = .001)
 

# fix loadins 1 and -1 of random intercept factors F2, 
# fix est=F 
# estimates variance of F2
 
  parms[parms$name=="a2", ]$value <- c(-1,-1, 1,1,1,1,1,1,1)
  parms[parms$name=="a2", ]$est <- FALSE
  
  parms[parms$name=="a1", ]$value <- abs(parms[parms$name=="a1", ]$value)
  
  parms[parms$name=="COV_22", ]$est <- TRUE  
  
  

  
  # calibrate item parameters
   
  fit3  <- dt %>% 
      mirt(2, pars = parms,itemtype = 'graded', TOL = .001)

## 
Iteration: 1, Log-Lik: -136690.972, Max-Change: 0.38926
Iteration: 2, Log-Lik: -134543.526, Max-Change: 0.21731
Iteration: 3, Log-Lik: -134090.013, Max-Change: 0.12575
Iteration: 4, Log-Lik: -133952.299, Max-Change: 0.08109
Iteration: 5, Log-Lik: -133901.585, Max-Change: 0.05446
Iteration: 6, Log-Lik: -133878.588, Max-Change: 0.03913
Iteration: 7, Log-Lik: -133865.991, Max-Change: 0.02952
Iteration: 8, Log-Lik: -133858.081, Max-Change: 0.02316
Iteration: 9, Log-Lik: -133852.686, Max-Change: 0.01886
Iteration: 10, Log-Lik: -133848.821, Max-Change: 0.01577
Iteration: 11, Log-Lik: -133845.983, Max-Change: 0.01332
Iteration: 12, Log-Lik: -133843.855, Max-Change: 0.01141
Iteration: 13, Log-Lik: -133840.753, Max-Change: 0.01130
Iteration: 14, Log-Lik: -133839.119, Max-Change: 0.00624
Iteration: 15, Log-Lik: -133838.452, Max-Change: 0.00486
Iteration: 16, Log-Lik: -133837.999, Max-Change: 0.00425
Iteration: 17, Log-Lik: -133837.701, Max-Change: 0.00328
Iteration: 18, Log-Lik: -133837.500, Max-Change: 0.00273
Iteration: 19, Log-Lik: -133837.365, Max-Change: 0.00501
Iteration: 20, Log-Lik: -133837.148, Max-Change: 0.00224
Iteration: 21, Log-Lik: -133837.077, Max-Change: 0.00179
Iteration: 22, Log-Lik: -133837.025, Max-Change: 0.00161
Iteration: 23, Log-Lik: -133836.994, Max-Change: 0.00128
Iteration: 24, Log-Lik: -133836.973, Max-Change: 0.00109
Iteration: 25, Log-Lik: -133836.958, Max-Change: 0.00198
Iteration: 26, Log-Lik: -133836.935, Max-Change: 0.00094

  # examines results
  summary(fit3)

##                 F1     F2    h2
## i67.E.Soc.00 0.531 -0.293 0.368
## i73.E.Soc.00 0.504 -0.299 0.344
## i55.E.Act.10 0.664  0.259 0.508
## i63.E.Act.10 0.451  0.309 0.299
## i76.E.Act.10 0.409  0.316 0.267
## i71.E.Soc.10 0.580  0.282 0.416
## i75.E.Soc.10 0.438  0.311 0.288
## i84.E.Soc.11 0.365  0.322 0.237
## i87.E.Soc.11 0.221  0.338 0.163
## 
## SS loadings:  2.059 0.831 
## Proportion Var:  0.229 0.092 
## 
## Factor correlations: 
## 
##    F1 F2
## F1  1  0
## F2  0  1

  coef(fit3 , simplify=TRUE, irt.parms = TRUE)

## $items
##                 a1 a2    d1    d2     d3     d4
## i67.E.Soc.00 1.237 -1 2.459 1.167 -0.279 -1.933
## i73.E.Soc.00 1.153 -1 3.166 1.960  0.397 -1.089
## i55.E.Act.10 1.755  1 4.980 3.097  1.307 -0.623
## i63.E.Act.10 0.998  1 3.804 2.113  0.567 -1.028
## i76.E.Act.10 0.885  1 2.241 0.895 -0.530 -2.045
## i71.E.Soc.10 1.407  1 4.401 2.468  0.978 -0.952
## i75.E.Soc.10 0.961  1 3.539 2.023  0.705 -1.117
## i84.E.Soc.11 0.773  1 4.002 2.303  0.836 -1.279
## i87.E.Soc.11 0.448  1 1.483 0.041 -1.364 -2.857
## 
## $means
## F1 F2 
##  0  0 
## 
## $cov
##    F1    F2
## F1  1    NA
## F2  0 0.467

  scores2 <-  fscores(fit3)

10. Examina validade dos parâmetros dos sujeitos

 sennav1 <- bind_cols(sennav1, as.data.frame(scores2))


 corr.test(sennav1[, c(65, 66, 88:90, 57, 67, 69:74, 91:92)])

## Call:corr.test(x = sennav1[, c(65, 66, 88:90, 57, 67, 69:74, 91:92)])
## Correlation matrix 
##                    VL_PROFICIENCIA_LP VL_PROFICIENCIA_MT trait_e_orig
## VL_PROFICIENCIA_LP               1.00               0.66         0.13
## VL_PROFICIENCIA_MT               0.66               1.00         0.09
## trait_e_orig                     0.13               0.09         1.00
## trait_e_rec                      0.09               0.06         0.95
## acq_e                            0.11               0.08         0.10
## acq_avr                          0.05               0.05         0.25
## vign_consist                     0.39               0.32         0.16
## F1.Cons                          0.15               0.19         0.10
## F2.Extr                          0.13               0.09         1.00
## F3.EmSt                          0.10               0.13         0.19
## F4.Agre                          0.18               0.13         0.38
## F5.Opns                          0.18               0.15         0.41
## F6.NVLoc                        -0.23              -0.20        -0.11
## F1                               0.05               0.02         0.95
## F2                               0.14               0.10         0.39
##                    trait_e_rec acq_e acq_avr vign_consist F1.Cons F2.Extr
## VL_PROFICIENCIA_LP        0.09  0.11    0.05         0.39    0.15    0.13
## VL_PROFICIENCIA_MT        0.06  0.08    0.05         0.32    0.19    0.09
## trait_e_orig              0.95  0.10    0.25         0.16    0.10    1.00
## trait_e_rec               1.00 -0.21    0.10         0.12    0.07    0.95
## acq_e                    -0.21  1.00    0.50         0.10    0.08    0.10
## acq_avr                   0.10  0.50    1.00         0.08    0.08    0.26
## vign_consist              0.12  0.10    0.08         1.00    0.09    0.16
## F1.Cons                   0.07  0.08    0.08         0.09    1.00    0.10
## F2.Extr                   0.95  0.10    0.26         0.16    0.10    1.00
## F3.EmSt                   0.19 -0.03   -0.13         0.08    0.38    0.19
## F4.Agre                   0.28  0.30    0.32         0.20    0.37    0.38
## F5.Opns                   0.30  0.33    0.48         0.13    0.34    0.41
## F6.NVLoc                 -0.15  0.12    0.29        -0.17   -0.31   -0.11
## F1                        0.96 -0.09    0.15         0.10    0.09    0.94
## F2                        0.09  0.95    0.54         0.14    0.11    0.39
##                    F3.EmSt F4.Agre F5.Opns F6.NVLoc    F1   F2
## VL_PROFICIENCIA_LP    0.10    0.18    0.18    -0.23  0.05 0.14
## VL_PROFICIENCIA_MT    0.13    0.13    0.15    -0.20  0.02 0.10
## trait_e_orig          0.19    0.38    0.41    -0.11  0.95 0.39
## trait_e_rec           0.19    0.28    0.30    -0.15  0.96 0.09
## acq_e                -0.03    0.30    0.33     0.12 -0.09 0.95
## acq_avr              -0.13    0.32    0.48     0.29  0.15 0.54
## vign_consist          0.08    0.20    0.13    -0.17  0.10 0.14
## F1.Cons               0.38    0.37    0.34    -0.31  0.09 0.11
## F2.Extr               0.19    0.38    0.41    -0.11  0.94 0.39
## F3.EmSt               1.00    0.30    0.15    -0.37  0.18 0.03
## F4.Agre               0.30    1.00    0.41    -0.14  0.32 0.39
## F5.Opns               0.15    0.41    1.00    -0.04  0.33 0.43
## F6.NVLoc             -0.37   -0.14   -0.04     1.00 -0.11 0.08
## F1                    0.18    0.32    0.33    -0.11  1.00 0.18
## F2                    0.03    0.39    0.43     0.08  0.18 1.00
## Sample Size 
##                    VL_PROFICIENCIA_LP VL_PROFICIENCIA_MT trait_e_orig
## VL_PROFICIENCIA_LP              10123              10123        10123
## VL_PROFICIENCIA_MT              10123              10123        10123
## trait_e_orig                    10123              10123        10866
## trait_e_rec                     10123              10123        10866
## acq_e                           10123              10123        10866
## acq_avr                         10123              10123        10866
## vign_consist                    10090              10090        10830
## F1.Cons                         10123              10123        10866
## F2.Extr                         10123              10123        10866
## F3.EmSt                         10123              10123        10866
## F4.Agre                         10123              10123        10866
## F5.Opns                         10123              10123        10866
## F6.NVLoc                        10123              10123        10866
## F1                              10123              10123        10866
## F2                              10123              10123        10866
##                    trait_e_rec acq_e acq_avr vign_consist F1.Cons F2.Extr
## VL_PROFICIENCIA_LP       10123 10123   10123        10090   10123   10123
## VL_PROFICIENCIA_MT       10123 10123   10123        10090   10123   10123
## trait_e_orig             10866 10866   10866        10830   10866   10866
## trait_e_rec              10866 10866   10866        10830   10866   10866
## acq_e                    10866 10866   10866        10830   10866   10866
## acq_avr                  10866 10866   10866        10830   10866   10866
## vign_consist             10830 10830   10830        10830   10830   10830
## F1.Cons                  10866 10866   10866        10830   10866   10866
## F2.Extr                  10866 10866   10866        10830   10866   10866
## F3.EmSt                  10866 10866   10866        10830   10866   10866
## F4.Agre                  10866 10866   10866        10830   10866   10866
## F5.Opns                  10866 10866   10866        10830   10866   10866
## F6.NVLoc                 10866 10866   10866        10830   10866   10866
## F1                       10866 10866   10866        10830   10866   10866
## F2                       10866 10866   10866        10830   10866   10866
##                    F3.EmSt F4.Agre F5.Opns F6.NVLoc    F1    F2
## VL_PROFICIENCIA_LP   10123   10123   10123    10123 10123 10123
## VL_PROFICIENCIA_MT   10123   10123   10123    10123 10123 10123
## trait_e_orig         10866   10866   10866    10866 10866 10866
## trait_e_rec          10866   10866   10866    10866 10866 10866
## acq_e                10866   10866   10866    10866 10866 10866
## acq_avr              10866   10866   10866    10866 10866 10866
## vign_consist         10830   10830   10830    10830 10830 10830
## F1.Cons              10866   10866   10866    10866 10866 10866
## F2.Extr              10866   10866   10866    10866 10866 10866
## F3.EmSt              10866   10866   10866    10866 10866 10866
## F4.Agre              10866   10866   10866    10866 10866 10866
## F5.Opns              10866   10866   10866    10866 10866 10866
## F6.NVLoc             10866   10866   10866    10866 10866 10866
## F1                   10866   10866   10866    10866 10866 10866
## F2                   10866   10866   10866    10866 10866 10866
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##                    VL_PROFICIENCIA_LP VL_PROFICIENCIA_MT trait_e_orig
## VL_PROFICIENCIA_LP                  0               0.00            0
## VL_PROFICIENCIA_MT                  0               0.00            0
## trait_e_orig                        0               0.00            0
## trait_e_rec                         0               0.00            0
## acq_e                               0               0.00            0
## acq_avr                             0               0.00            0
## vign_consist                        0               0.00            0
## F1.Cons                             0               0.00            0
## F2.Extr                             0               0.00            0
## F3.EmSt                             0               0.00            0
## F4.Agre                             0               0.00            0
## F5.Opns                             0               0.00            0
## F6.NVLoc                            0               0.00            0
## F1                                  0               0.02            0
## F2                                  0               0.00            0
##                    trait_e_rec acq_e acq_avr vign_consist F1.Cons F2.Extr
## VL_PROFICIENCIA_LP           0     0       0            0       0       0
## VL_PROFICIENCIA_MT           0     0       0            0       0       0
## trait_e_orig                 0     0       0            0       0       0
## trait_e_rec                  0     0       0            0       0       0
## acq_e                        0     0       0            0       0       0
## acq_avr                      0     0       0            0       0       0
## vign_consist                 0     0       0            0       0       0
## F1.Cons                      0     0       0            0       0       0
## F2.Extr                      0     0       0            0       0       0
## F3.EmSt                      0     0       0            0       0       0
## F4.Agre                      0     0       0            0       0       0
## F5.Opns                      0     0       0            0       0       0
## F6.NVLoc                     0     0       0            0       0       0
## F1                           0     0       0            0       0       0
## F2                           0     0       0            0       0       0
##                    F3.EmSt F4.Agre F5.Opns F6.NVLoc   F1   F2
## VL_PROFICIENCIA_LP    0.00       0       0        0 0.00 0.00
## VL_PROFICIENCIA_MT    0.00       0       0        0 0.02 0.00
## trait_e_orig          0.00       0       0        0 0.00 0.00
## trait_e_rec           0.00       0       0        0 0.00 0.00
## acq_e                 0.00       0       0        0 0.00 0.00
## acq_avr               0.00       0       0        0 0.00 0.00
## vign_consist          0.00       0       0        0 0.00 0.00
## F1.Cons               0.00       0       0        0 0.00 0.00
## F2.Extr               0.00       0       0        0 0.00 0.00
## F3.EmSt               0.00       0       0        0 0.00 0.01
## F4.Agre               0.00       0       0        0 0.00 0.00
## F5.Opns               0.00       0       0        0 0.00 0.00
## F6.NVLoc              0.00       0       0        0 0.00 0.00
## F1                    0.00       0       0        0 0.00 0.00
## F2                    0.01       0       0        0 0.00 0.00
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option

 names(sennav1)

##  [1] "i03.NV.NV.10"         "i04.A.Cmp.10"         "i05.O.Img.10"        
##  [4] "i06.C.Ord.10"         "i07.N.Vol.00"         "i09.A.Cmp.10"        
##  [7] "i10.O.Img.10"         "i11.C.Ord.10"         "i12.N.Vol.00"        
## [10] "i13.NV.NV.10"         "i14.A.Tru.10"         "i17.N.Anx.00"        
## [13] "i24.O.Aes.10"         "i25.A.Cmp.10"         "i27.N.Dep.00"        
## [16] "i29.A.Cmp.10"         "i30.O.Int.10"         "i32.N.Vol.00"        
## [19] "i33.NV.NV.10"         "i34.A.Tru.10"         "i36.C.Conc.00"       
## [22] "i37.N.Anx.10"         "i39.A.Cmp.10"         "i40.O.Aes.10"        
## [25] "i42.N.Anx.00"         "i44.A.Pol.00"         "i46.C.Conc.00"       
## [28] "i48.NV.NV.10"         "i49.A.Cmp.10"         "i51.C.Ord.00"        
## [31] "i52.NV.NV.10"         "i53.A.Pol.00"         "i54.O.Int.10"        
## [34] "i55.E.Act.10"         "i56.NV.NV.10"         "i60.NV.NV.00"        
## [37] "i63.E.Act.10"         "i66.O.Int.10"         "i67.E.Soc.00"        
## [40] "i70.O.Img.11"         "i71.E.Soc.10"         "i73.E.Soc.00"        
## [43] "i74.NV.NV.10"         "i75.E.Soc.10"         "i76.E.Act.10"        
## [46] "i77.C.SD.11"          "i79.N.Vol.11"         "i82.N.Vol.11"        
## [49] "i83.C.Conc.11"        "i84.E.Soc.11"         "i87.E.Soc.11"        
## [52] "i88.N.Dep.11"         "i89.C.Achv.11"        "i91.C.SD.11"         
## [55] "missR"                "admiss_missR"         "acq_avr"             
## [58] "acq_sd"               "num_items"            "Caderno"             
## [61] "age2"                 "grade"                "atrasado"            
## [64] "atrasado2"            "VL_PROFICIENCIA_LP"   "VL_PROFICIENCIA_MT"  
## [67] "vign_consist"         "vign_consist_count"   "F1.Cons"             
## [70] "F2.Extr"              "F3.EmSt"              "F4.Agre"             
## [73] "F5.Opns"              "F6.NVLoc"             "gender"              
## [76] "rwn_id"               "NM_REGIONAL_ESCOLA"   "grade2"              
## [79] "grade_5"              "grade_9"              "grade_10"            
## [82] "freq"                 "cd_esc_grade"         "rwn_id2"             
## [85] "VL_PROFICIENCIA_LP_r" "VL_PROFICIENCIA_MT_r" "senna_it_rspnd"      
## [88] "trait_e_orig"         "trait_e_rec"          "acq_e"               
## [91] "F1"                   "F2"

 sennav1 %>%  ggplot(aes(x=F1 )) + 
   geom_histogram(color="white", fill="orange", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

 sennav1 %>%  ggplot(aes(x= F2 )) + 
   geom_histogram(color="white", fill="orange", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

sennav1 %>%  ggplot(aes(x= F1, y =  trait_e_rec)) + 
   geom_point(color="blue", fill="white", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   scale_y_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

sennav1 %>%  ggplot(aes(x= F2, y =  acq_e)) + 
   geom_point(color="blue", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   scale_y_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

sennav1 %>%  ggplot(aes(x= F2, y =  F1)) + 
   geom_point(color="red", alpha = .5) +
   scale_x_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   scale_y_continuous(breaks = breaks_width(.5), limits = c(-3, 3)) +
   theme_minimal()

Exercício: rode a mesma análise com a escala C