Exercícios 5: Calibração, estimação, ajuste e invariância dos parâmetros no MIRT
Ricardo Primi
30 de outubro de 2017
Ative as bibliotecas e abra o arquivo de dados do enem
setwd("~/Dropbox (Personal)/TRI/2017_exercicios")
load("enem2015b.RData")
# save.image("~/Dropbox (Personal)/TRI/2017_exercicios/enem2015b.RData")
library(psych)
library(mirt)
library(dplyr)
library(ggplot2)
library(stringr)Análise TRI 3 parâmetros usando o MIRT com a especificação de prioris
Especifica o modelo e extrai o dataframe com os parâmetros
- Examine o dataframe com os valores iniciais e fixos dos parâmetros
- Note que a média da distribuição é M = 0 e DP = 1
# Especifica o modelo
m3pl <- mirt.model( "th_ch = 1-45
PRIOR = (1-45, a1, lnorm, 1, 0.3),
(1-45, d, norm, 0, 1),
(1-45, g, norm, -1.386294, .2)"
)
# Extrai data frame com valores iniciais
df <- mirt(score_ch,
model = m3pl,
itemtype="3PL",
pars = 'values')Calibração dos parâmetros dos itens no modo default
- Veja a métrica dos parâmetros
# Calibra itens
ch_m3pl1 <- mirt(score_ch,
model = m3pl, TOL = .001,
itemtype="3PL")# parâmetros dos itens
ch_m3pl_pars1 <- coef(ch_m3pl1 , simplify=TRUE, IRTpars=TRUE)
View(ch_m3pl_pars1$items)## Warning: execução do comando ''/usr/bin/otool' -L '/Library/Frameworks/
## R.framework/Resources/modules/R_de.so'' teve status 69 describe(ch_m3pl_pars1$items)## vars n mean sd median trimmed mad min max range skew kurtosis
## a 1 45 1.28 0.56 1.28 1.27 0.59 0.34 2.36 2.02 0.14 -0.96
## b 2 45 1.09 1.38 1.18 1.07 0.88 -2.11 6.28 8.39 0.69 3.18
## g 3 45 0.18 0.09 0.16 0.16 0.09 0.06 0.44 0.38 1.07 0.73
## u 4 45 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00 NaN NaN
## se
## a 0.08
## b 0.21
## g 0.01
## u 0.00- Mas note qual a média da distribuição das notas a partir da qual estamos calibrando
- Note que o ENEM está na escala M=500 e DP=100. Esses valores correspondem a média dos alunos das escolas públicas em 2009
- Precisamos fazer o calculo para \(z =\frac{ENEM-500}{100}\) na escala 0 e 1
- Essa amostra em 2015 está praticamente meio desvio padrão acima da média
M <- (mean(enem_2015$NU_NOTA_CH, na.rm = TRUE) - 500) / 100
DP <- sd(enem_2015$NU_NOTA_CH, na.rm = TRUE) / 100
M## [1] 0.593585 DP## [1] 0.7050225Calibração dos parâmetros dos itens fixando a métrica na distribuição observada
- Vamos então fixar a M e DP nesses alores e ver o que acontece.
# Fixando os parâmetros M e DP
df[df$name == "MEAN_1", ]$value <- M
df[df$name == "COV_11", ]$value <- DP*DP
# Calibrando novamente
ch_m3pl2 <- mirt(score_ch,
model = m3pl, TOL = .001,
itemtype="3PL",
pars = df
)
# Parâmetros dos itens
ch_m3pl_pars2 <- coef(ch_m3pl2 , simplify=TRUE, IRTpars=TRUE)
# Calibrando novamente com empiricalhist = TRUE
ch_m3pl3 <- mirt(score_ch,
model = m3pl, TOL = .001,
itemtype="3PL",
empiricalhist = TRUE
)
ch_m3pl_pars3 <- coef(ch_m3pl3 , simplify=TRUE, IRTpars=TRUE)
# Calibrando novamente eliminando itens 11 17, 26, 33, 36, 40
m3plb <- mirt.model( "th_ch = 1-10, 12-16, 18-25, 27-32, 34-35, 37-39, 41-45
PRIOR = (1-10, 12-16, 18-25, 27-32, 34-35, 37-39, 41-45 , a1, lnorm, 1, 0.3),
(1-10, 12-16, 18-25, 27-32, 34-35, 37-39, 41-45 , d, norm, 0, 1),
(1-10, 12-16, 18-25, 27-32, 34-35, 37-39, 41-45 , g, norm, -1.386294, .2)"
)
dfb <- mirt(score_ch,
model = m3plb,
itemtype="3PL",
pars = 'values')
dfb[dfb$name == "MEAN_1", ]$value <- M
dfb[dfb$name == "COV_11", ]$value <- DP*DP
ch_m3pl4 <- mirt(score_ch,
model = m3plb, TOL = .001,
itemtype="3PL",
pars = dfb
)
ch_m3pl_pars4 <- coef(ch_m3pl4 , simplify=TRUE, IRTpars=TRUE)
View(ch_m3pl_pars4$items) describe(ch_m3pl_pars2$items)## vars n mean sd median trimmed mad min max range skew kurtosis
## a 1 45 1.79 0.78 1.72 1.78 0.83 0.43 3.31 2.87 0.13 -0.96
## b 2 45 1.37 0.99 1.40 1.34 0.66 -0.90 5.23 6.13 0.85 3.66
## g 3 45 0.17 0.09 0.15 0.16 0.09 0.06 0.44 0.38 1.02 0.63
## u 4 45 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00 NaN NaN
## se
## a 0.12
## b 0.15
## g 0.01
## u 0.00 describe(ch_m3pl_pars3$items)## vars n mean sd median trimmed mad min max range skew kurtosis
## a 1 45 3.43 1.61 3.5 3.42 1.45 0.65 6.44 5.78 0.01 -0.97
## b 2 45 0.05 0.64 0.1 0.06 0.35 -1.80 2.65 4.45 0.62 5.74
## g 3 45 0.22 0.09 0.2 0.21 0.09 0.07 0.47 0.40 0.75 0.17
## u 4 45 1.00 0.00 1.0 1.00 0.00 1.00 1.00 0.00 NaN NaN
## se
## a 0.24
## b 0.10
## g 0.01
## u 0.00 describe(ch_m3pl_pars4$items, na.rm = TRUE)## vars n mean sd median trimmed mad min max range skew kurtosis
## a 1 45 1.60 0.90 1.70 1.61 0.80 0.00 3.29 3.29 -0.23 -0.67
## b 2 45 NaN NaN 1.42 1.41 0.83 -Inf Inf Inf NaN NaN
## g 3 45 0.16 0.07 0.15 0.15 0.07 0.06 0.35 0.29 0.74 0.08
## u 4 45 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00 NaN NaN
## se
## a 0.13
## b NaN
## g 0.01
## u 0.00Comparando a métrica das estimativas de theta
- Estima os thetas segundo os 3 modelos
# Estima habilidades usando os tres modelos
theta_ch1 = fscores(ch_m3pl1 , method = "EAP", full.scores.SE = TRUE)
theta_ch2 = fscores(ch_m3pl2 , method = "EAP", full.scores.SE = TRUE)
theta_ch3 = fscores(ch_m3pl3 , method = "EAP", full.scores.SE = TRUE)
theta_ch4 = fscores(ch_m3pl4 , method = "EAP", full.scores.SE = TRUE)
# Adiciona na base
df_scores <- as.data.frame(cbind(theta_ch1 = theta_ch1[ , 1],
theta_ch2 = theta_ch2[ , 1],
theta_ch3 = theta_ch3[ , 1],
theta_ch4 = theta_ch4[ , 1]))
# Transformando a nota na base de 500/100 para 0/1
describe(enem_2015$NU_NOTA_CHz)
names(enem_2015)
enem_2015 <- enem_2015[ , c(1:167)]
enem_2015$NU_NOTA_CHz <- (enem_2015$NU_NOTA_CH - 500)/100
enem_2015 <- cbind(enem_2015, df_scores) describe(enem_2015[ , c(167:172)])## vars n mean sd median trimmed mad min max range
## totCH 1 119827 19.06 6.67 18.00 18.63 5.93 0.00 43.00 43.00
## NU_NOTA_CHz 2 119827 0.59 0.71 0.65 0.62 0.69 -5.00 3.23 8.23
## theta_ch1 3 119827 0.00 0.89 -0.06 -0.03 0.94 -2.30 3.24 5.55
## theta_ch2 4 119827 0.59 0.63 0.55 0.57 0.66 -1.04 2.88 3.92
## theta_ch3 5 119827 -0.56 0.55 -0.51 -0.54 0.60 -2.07 1.41 3.48
## theta_ch4 6 119827 0.59 0.63 0.55 0.57 0.66 -0.93 2.88 3.81
## skew kurtosis se
## totCH 0.57 -0.03 0.02
## NU_NOTA_CHz -0.33 0.29 0.00
## theta_ch1 0.26 -0.36 0.00
## theta_ch2 0.26 -0.36 0.00
## theta_ch3 -0.27 -0.56 0.00
## theta_ch4 0.29 -0.37 0.00- Vamos ver a distribuição e a relação entre esses escores estimados
# Distribuição dos escores
ggplot(data=enem_2015, aes(x=NU_NOTA_CHz)) +
geom_histogram(alpha =.4, fill ="red", color="gray", binwidth=.25)+
scale_x_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3))## Warning: Removed 15 rows containing non-finite values (stat_bin).
ggplot(data=enem_2015, aes(x=theta_ch1)) +
geom_histogram(alpha =.4, fill ="blue", color="gray", binwidth=.25)+
scale_x_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3))## Warning: Removed 11 rows containing non-finite values (stat_bin).
ggplot(data=enem_2015, aes(x=theta_ch2)) +
geom_histogram(alpha =.4, fill ="orange", color="gray", binwidth=.25)+
scale_x_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3))
ggplot(data=enem_2015, aes(x=theta_ch3)) +
geom_histogram(alpha =.4, fill ="green",color="gray", binwidth=.25)+
scale_x_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3))
ggplot(data=enem_2015, aes(x=theta_ch4)) +
geom_histogram(alpha =.4, fill ="yellow", color="gray", binwidth=.25)+
scale_x_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3))
# Correlação entre estimações
ggplot(data=enem_2015, aes(y=NU_NOTA_CHz, x=theta_ch1, colour = theta_ch1)) +
geom_point(alpha = 1/8) +
geom_smooth(method = "lm") +
scale_x_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3)) +
scale_y_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3)) ## Warning: Removed 24 rows containing non-finite values (stat_smooth).## Warning: Removed 24 rows containing missing values (geom_point).
ggplot(data=enem_2015, aes(y=NU_NOTA_CHz, x=theta_ch2, colour = theta_ch2)) +
geom_point(alpha = 1/8) +
geom_smooth(method = "lm") +
scale_x_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3)) +
scale_y_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3)) ## Warning: Removed 15 rows containing non-finite values (stat_smooth).## Warning: Removed 15 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_smooth).
ggplot(data=enem_2015, aes(y=NU_NOTA_CHz, x=theta_ch3, colour = theta_ch3)) +
geom_point(alpha = 1/8) +
geom_smooth(method = "lm") +
scale_x_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3)) +
scale_y_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3))## Warning: Removed 15 rows containing non-finite values (stat_smooth).## Warning: Removed 15 rows containing missing values (geom_point).
ggplot(data=enem_2015, aes(y=NU_NOTA_CHz, x=theta_ch4, colour = theta_ch4)) +
geom_point(alpha = 1/8) +
geom_smooth(method = "lm") +
scale_x_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3)) +
scale_y_continuous(breaks=seq(-3, 3, .5), limits = c(-3, 3))## Warning: Removed 15 rows containing non-finite values (stat_smooth).
## Warning: Removed 15 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_smooth).
##### Testes de ajuste do modelo
ch_fit <- M2(ch_m3pl2)
ch_itemfit <- itemfit(ch_m3pl2, fit_stats = c("S_X2", "X2", "infit" )) ch_fit ## M2 df p RMSEA RMSEA_5 RMSEA_95 SRMSR TLI
## stats 12777.97 900 0 0.0104948 0.01033381 0.01065653 0.01143787 0.9867429
## CFI
## stats 0.9879481 ch_itemfit ## item X2 df.X2 p.X2 S_X2 df.S_X2 p.S_X2
## 1 ch1 497.502 7 0 136.780 36 0.000
## 2 ch2 2039.428 7 0 43.784 35 0.147
## 3 ch3 398.793 7 0 62.070 36 0.004
## 4 ch4 717.628 7 0 44.340 36 0.160
## 5 ch5 337.234 7 0 103.707 35 0.000
## 6 ch6 579.398 7 0 49.357 37 0.084
## 7 ch7 176.420 7 0 50.869 37 0.064
## 8 ch8 426.919 7 0 140.848 36 0.000
## 9 ch9 2555.050 7 0 337.003 36 0.000
## 10 ch10 291.800 7 0 228.887 36 0.000
## 11 ch11 1234.331 7 0 324.433 38 0.000
## 12 ch12 1323.351 7 0 63.963 36 0.003
## 13 ch13 739.277 7 0 77.131 35 0.000
## 14 ch14 902.405 7 0 74.770 36 0.000
## 15 ch15 331.005 7 0 61.412 36 0.005
## 16 ch16 98.731 7 0 70.525 37 0.001
## 17 ch17 186.851 7 0 69.003 36 0.001
## 18 ch18 487.626 7 0 74.788 37 0.000
## 19 ch19 775.253 7 0 57.454 35 0.010
## 20 ch20 46.872 7 0 107.870 37 0.000
## 21 ch21 2024.368 7 0 321.871 36 0.000
## 22 ch22 346.049 7 0 53.114 37 0.042
## 23 ch23 97.532 7 0 69.512 37 0.001
## 24 ch24 454.470 7 0 280.494 35 0.000
## 25 ch25 1317.571 7 0 163.716 37 0.000
## 26 ch26 233.542 7 0 145.595 37 0.000
## 27 ch27 1036.216 7 0 41.467 35 0.209
## 28 ch28 211.648 7 0 38.062 36 0.376
## 29 ch29 1843.715 7 0 329.915 36 0.000
## 30 ch30 279.211 7 0 46.001 36 0.123
## 31 ch31 182.756 7 0 51.012 37 0.062
## 32 ch32 319.716 7 0 77.767 37 0.000
## 33 ch33 750.164 7 0 287.569 37 0.000
## 34 ch34 170.399 7 0 51.578 37 0.056
## 35 ch35 367.942 7 0 292.504 36 0.000
## 36 ch36 161.450 7 0 106.194 37 0.000
## 37 ch37 81.557 7 0 49.213 37 0.086
## 38 ch38 216.401 7 0 44.286 36 0.162
## 39 ch39 857.427 7 0 209.210 35 0.000
## 40 ch40 103.553 7 0 46.156 38 0.171
## 41 ch41 182.993 7 0 29.494 37 0.805
## 42 ch42 2331.394 7 0 84.147 36 0.000
## 43 ch43 232.512 7 0 38.655 36 0.351
## 44 ch44 1007.336 7 0 107.761 37 0.000
## 45 ch45 285.512 7 0 102.744 37 0.000 itemfit(ch_m3pl2, group.bins=40, empirical.plot = 9)
itemfit(ch_m3pl2, group.bins=40, empirical.plot = 11)
itemfit(ch_m3pl2, group.bins=40, empirical.plot = 21)
itemfit(ch_m3pl2, group.bins=40, empirical.plot = 29)
itemfit(ch_m3pl2, group.bins=40, empirical.plot = 41)
itemfit(ch_m3pl2, group.bins=40, empirical.plot = 40)
##### Testando DIF em relação ao gênero
- Primeiro vamos testar se há diferenças nas notas entre homens e mulheres
library(mosaic)## Loading required package: ggformula##
## New to ggformula? Try the tutorials:
## learnr::run_tutorial("introduction", package = "ggformula")
## learnr::run_tutorial("refining", package = "ggformula")## Loading required package: mosaicData## Loading required package: Matrix##
## The 'mosaic' package masks several functions from core packages in order to add
## additional features. The original behavior of these functions should not be affected by this.
##
## Note: If you use the Matrix package, be sure to load it BEFORE loading mosaic.##
## Attaching package: 'mosaic'## The following object is masked from 'package:Matrix':
##
## mean## The following objects are masked from 'package:dplyr':
##
## count, do, tally## The following objects are masked from 'package:psych':
##
## logit, read.file, rescale## The following objects are masked from 'package:stats':
##
## binom.test, cor, cor.test, cov, fivenum, IQR, median,
## prop.test, quantile, sd, t.test, var## The following objects are masked from 'package:base':
##
## max, mean, min, prod, range, sample, sum gf_dens(~theta_ch2 , data = enem_2015, color = ~ as.factor(TP_SEXO))
t.test(~theta_ch2 | TP_SEXO, data = enem_2015)## theta_ch2 ~ TP_SEXO##
## Welch Two Sample t-test
##
## data: theta_ch2 by TP_SEXO
## t = -50.217, df = 102920, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1919142 -0.1774959
## sample estimates:
## mean in group F mean in group M
## 0.5147622 0.6994673 cor(enem_2015$theta_ch2, as.numeric(as.factor(enem_2015$TP_SEXO)), use = "pair")## [1] 0.1449739- Testando DIF usando os difR. Ver: https://ppw.kuleuven.be/okp/_pdf/Magis2010AGFAA.pdf
library(difR)
table(enem_2015$TP_SEXO)
dif_ch <- difLogistic(Data = score_ch,
group = enem_2015$TP_SEXO,
focal.name = "M")
dif_ch2 <- dichoDif(Data=score_ch,
group=enem_2015$TP_SEXO,
focal.name="M",
method=c("MH", "Std", "Lord", "Raju"),
model="1PL", purify=TRUE, nrIter=20) dif_ch## $Logistik
## [1] 687.8937463 4.6066715 70.8187302 184.7517926 64.4682556
## [6] 99.9173844 28.0607986 36.1242083 401.3211756 159.6420028
## [11] 70.1062967 204.6175310 452.1480447 172.5950083 147.5415597
## [16] 58.9531628 111.7497923 80.2270536 106.8054199 39.7047487
## [21] 108.5023373 16.0293155 109.5018026 194.4217612 91.6197820
## [26] 485.8829354 417.7531264 0.4424562 274.0619486 340.6120533
## [31] 659.5030667 31.1126802 744.9171892 22.3067908 85.5347065
## [36] 60.2069826 214.6615507 109.6043512 32.2938317 53.0033386
## [41] 100.0387546 733.3292438 57.7843914 176.1384491 584.2717749
##
## $logitPar
## (Intercept) SCORE GROUP SCORE:GROUP
## [1,] -2.6177738 0.12302258 0.122987647 0.0108286031
## [2,] -2.5386497 0.18193856 0.000000000 0.0000000000
## [3,] -3.2032076 0.14655526 0.166584407 -0.0125841011
## [4,] -1.7712136 0.12728756 0.496846083 -0.0203300890
## [5,] -5.0565113 0.17004176 0.243164569 -0.0148745388
## [6,] -2.8516014 0.12605362 -0.029938453 -0.0048752998
## [7,] -3.0864427 0.08997327 -0.169792873 0.0045341115
## [8,] -2.4504448 0.12155318 0.096502071 -0.0010702296
## [9,] -1.3157188 0.14176181 0.115566804 -0.0223466925
## [10,] -3.3958936 0.08983932 0.044424001 0.0068331288
## [11,] -0.4822236 0.07973361 0.308859251 -0.0124427619
## [12,] -3.4748237 0.17746999 0.382931938 -0.0107230035
## [13,] -4.2068523 0.19527382 -0.137556739 -0.0079623906
## [14,] -2.9230871 0.15186633 -0.035974560 -0.0068822726
## [15,] -3.4423971 0.13336186 -0.033777602 0.0092536700
## [16,] -2.6678056 0.07375614 0.242485478 -0.0069966152
## [17,] -1.4734929 0.08594657 -0.400670509 0.0170853708
## [18,] -1.8174740 0.08667087 0.128029056 -0.0009249320
## [19,] -2.8486060 0.15896201 0.209167667 -0.0041012282
## [20,] -2.8220663 0.05649091 0.193297455 -0.0121781829
## [21,] -1.1965372 0.11617757 0.442581410 -0.0209722397
## [22,] -2.8116361 0.11904167 0.007338503 0.0021594295
## [23,] -2.0417852 0.04300257 -0.467376358 0.0209978511
## [24,] -4.4074782 0.14328987 -0.131420805 0.0148990588
## [25,] -2.4877554 0.13229279 0.278555991 -0.0178991181
## [26,] -0.7066440 0.05363425 -0.104160555 0.0187858698
## [27,] -3.2929825 0.17118484 0.054318769 0.0114960863
## [28,] -3.1991584 0.11736152 0.000000000 0.0000000000
## [29,] -3.1558900 0.17841562 0.198381374 -0.0209388146
## [30,] -2.9784034 0.09471286 0.166683239 0.0041418730
## [31,] -2.0702845 0.07394783 0.022047026 0.0144886732
## [32,] -2.1204968 0.08174531 0.082206021 -0.0005998082
## [33,] -1.5307903 0.08042058 0.046119492 -0.0184965291
## [34,] -2.5833934 0.10152615 -0.014026198 -0.0022650245
## [35,] -3.9423402 0.11929278 0.034074728 0.0048935074
## [36,] -1.7080292 0.06589876 -0.222108907 0.0133358304
## [37,] -1.5089342 0.06906010 -0.118519587 -0.0030725984
## [38,] -2.5398098 0.10563321 -0.410078273 0.0216580408
## [39,] -3.9789227 0.16478661 0.197088320 -0.0115385939
## [40,] -1.5510960 0.03537444 -0.265116739 0.0098172119
## [41,] -2.4782209 0.09328286 -0.315175019 0.0098160640
## [42,] -1.9140741 0.16790595 -0.219097945 -0.0096712077
## [43,] -2.5014173 0.11082439 -0.161888986 0.0033649986
## [44,] -1.2790010 0.11468368 -0.072516214 -0.0057325099
## [45,] -1.6354360 0.07389130 -0.149074281 -0.0074331404
##
## $logitSe
## (Intercept) SCORE GROUP SCORE:GROUP
## [1,] 0.02760459 0.001424478 0.04357762 0.002186193
## [2,] 0.02412591 0.001382200 0.00000000 0.000000000
## [3,] 0.02967710 0.001514261 0.04579529 0.002220094
## [4,] 0.02753360 0.001551461 0.04286061 0.002297794
## [5,] 0.04101658 0.001809333 0.06247460 0.002638787
## [6,] 0.02830312 0.001435989 0.04434114 0.002127118
## [7,] 0.03115145 0.001470964 0.04928863 0.002194475
## [8,] 0.02722053 0.001423375 0.04259532 0.002129444
## [9,] 0.03062007 0.001845265 0.04646853 0.002625449
## [10,] 0.03404685 0.001575303 0.05167451 0.002280864
## [11,] 0.02690683 0.001512042 0.04260256 0.002256805
## [12,] 0.03129603 0.001657948 0.04817567 0.002471196
## [13,] 0.03414766 0.001736364 0.05376365 0.002576536
## [14,] 0.02914222 0.001548300 0.04557831 0.002289884
## [15,] 0.03076940 0.001492800 0.04799368 0.002240279
## [16,] 0.02951049 0.001418651 0.04505474 0.002064358
## [17,] 0.02501917 0.001330824 0.04015766 0.002025555
## [18,] 0.02528793 0.001311117 0.03954118 0.001953459
## [19,] 0.02938644 0.001597605 0.04603678 0.002411652
## [20,] 0.03340883 0.001596071 0.05223077 0.002373964
## [21,] 0.02800798 0.001615779 0.04382485 0.002387892
## [22,] 0.02814483 0.001414605 0.04401742 0.002111714
## [23,] 0.02811716 0.001389634 0.04497444 0.002072160
## [24,] 0.03735401 0.001679164 0.05760481 0.002494697
## [25,] 0.02767854 0.001474175 0.04251672 0.002146568
## [26,] 0.02394821 0.001269694 0.03873798 0.001969577
## [27,] 0.03064398 0.001632828 0.04885974 0.002542156
## [28,] 0.02277263 0.001057497 0.00000000 0.000000000
## [29,] 0.03080126 0.001691660 0.04722480 0.002452984
## [30,] 0.02990237 0.001428916 0.04546651 0.002086316
## [31,] 0.02604469 0.001301825 0.04055970 0.001945478
## [32,] 0.02604171 0.001309073 0.04052427 0.001936535
## [33,] 0.02481350 0.001301672 0.03857129 0.001891288
## [34,] 0.02744027 0.001366716 0.04297163 0.002026284
## [35,] 0.03555965 0.001614837 0.05431901 0.002362774
## [36,] 0.02497739 0.001267971 0.03958494 0.001902914
## [37,] 0.02453684 0.001267049 0.03866200 0.001875702
## [38,] 0.02723187 0.001370752 0.04391550 0.002102384
## [39,] 0.03299397 0.001610657 0.05062255 0.002361552
## [40,] 0.02570986 0.001294132 0.04085948 0.001928711
## [41,] 0.02718304 0.001349367 0.04350350 0.002032873
## [42,] 0.03133393 0.001898283 0.04821493 0.002743421
## [43,] 0.02712193 0.001382613 0.04292030 0.002069070
## [44,] 0.02755616 0.001574964 0.04285407 0.002310778
## [45,] 0.02479602 0.001277880 0.03920196 0.001889478
##
## $parM0
## (Intercept) SCORE GROUP SCORE:GROUP
## [1,] -2.6177738 0.12302258 0.122987647 0.0108286031
## [2,] -2.5811301 0.18436007 0.106487091 -0.0058154885
## [3,] -3.2032076 0.14655526 0.166584407 -0.0125841011
## [4,] -1.7712136 0.12728756 0.496846083 -0.0203300890
## [5,] -5.0565113 0.17004176 0.243164569 -0.0148745388
## [6,] -2.8516014 0.12605362 -0.029938453 -0.0048752998
## [7,] -3.0864427 0.08997327 -0.169792873 0.0045341115
## [8,] -2.4504448 0.12155318 0.096502071 -0.0010702296
## [9,] -1.3157188 0.14176181 0.115566804 -0.0223466925
## [10,] -3.3958936 0.08983932 0.044424001 0.0068331288
## [11,] -0.4822236 0.07973361 0.308859251 -0.0124427619
## [12,] -3.4748237 0.17746999 0.382931938 -0.0107230035
## [13,] -4.2068523 0.19527382 -0.137556739 -0.0079623906
## [14,] -2.9230871 0.15186633 -0.035974560 -0.0068822726
## [15,] -3.4423971 0.13336186 -0.033777602 0.0092536700
## [16,] -2.6678056 0.07375614 0.242485478 -0.0069966152
## [17,] -1.4734929 0.08594657 -0.400670509 0.0170853708
## [18,] -1.8174740 0.08667087 0.128029056 -0.0009249320
## [19,] -2.8486060 0.15896201 0.209167667 -0.0041012282
## [20,] -2.8220663 0.05649091 0.193297455 -0.0121781829
## [21,] -1.1965372 0.11617757 0.442581410 -0.0209722397
## [22,] -2.8116361 0.11904167 0.007338503 0.0021594295
## [23,] -2.0417852 0.04300257 -0.467376358 0.0209978511
## [24,] -4.4074782 0.14328987 -0.131420805 0.0148990588
## [25,] -2.4877554 0.13229279 0.278555991 -0.0178991181
## [26,] -0.7066440 0.05363425 -0.104160555 0.0187858698
## [27,] -3.2929825 0.17118484 0.054318769 0.0114960863
## [28,] -3.2104945 0.11800593 0.024367170 -0.0013313708
## [29,] -3.1558900 0.17841562 0.198381374 -0.0209388146
## [30,] -2.9784034 0.09471286 0.166683239 0.0041418730
## [31,] -2.0702845 0.07394783 0.022047026 0.0144886732
## [32,] -2.1204968 0.08174531 0.082206021 -0.0005998082
## [33,] -1.5307903 0.08042058 0.046119492 -0.0184965291
## [34,] -2.5833934 0.10152615 -0.014026198 -0.0022650245
## [35,] -3.9423402 0.11929278 0.034074728 0.0048935074
## [36,] -1.7080292 0.06589876 -0.222108907 0.0133358304
## [37,] -1.5089342 0.06906010 -0.118519587 -0.0030725984
## [38,] -2.5398098 0.10563321 -0.410078273 0.0216580408
## [39,] -3.9789227 0.16478661 0.197088320 -0.0115385939
## [40,] -1.5510960 0.03537444 -0.265116739 0.0098172119
## [41,] -2.4782209 0.09328286 -0.315175019 0.0098160640
## [42,] -1.9140741 0.16790595 -0.219097945 -0.0096712077
## [43,] -2.5014173 0.11082439 -0.161888986 0.0033649986
## [44,] -1.2790010 0.11468368 -0.072516214 -0.0057325099
## [45,] -1.6354360 0.07389130 -0.149074281 -0.0074331404
##
## $seM0
## (Intercept) SCORE GROUP SCORE:GROUP
## [1,] 0.02760459 0.001424478 0.04357762 0.002186193
## [2,] 0.03138575 0.001850609 0.04958891 0.002804420
## [3,] 0.02967710 0.001514261 0.04579529 0.002220094
## [4,] 0.02753360 0.001551461 0.04286061 0.002297794
## [5,] 0.04101658 0.001809333 0.06247460 0.002638787
## [6,] 0.02830312 0.001435989 0.04434114 0.002127118
## [7,] 0.03115145 0.001470964 0.04928863 0.002194475
## [8,] 0.02722053 0.001423375 0.04259532 0.002129444
## [9,] 0.03062007 0.001845265 0.04646853 0.002625449
## [10,] 0.03404685 0.001575303 0.05167451 0.002280864
## [11,] 0.02690683 0.001512042 0.04260256 0.002256805
## [12,] 0.03129603 0.001657948 0.04817567 0.002471196
## [13,] 0.03414766 0.001736364 0.05376365 0.002576536
## [14,] 0.02914222 0.001548300 0.04557831 0.002289884
## [15,] 0.03076940 0.001492800 0.04799368 0.002240279
## [16,] 0.02951049 0.001418651 0.04505474 0.002064358
## [17,] 0.02501917 0.001330824 0.04015766 0.002025555
## [18,] 0.02528793 0.001311117 0.03954118 0.001953459
## [19,] 0.02938644 0.001597605 0.04603678 0.002411652
## [20,] 0.03340883 0.001596071 0.05223077 0.002373964
## [21,] 0.02800798 0.001615779 0.04382485 0.002387892
## [22,] 0.02814483 0.001414605 0.04401742 0.002111714
## [23,] 0.02811716 0.001389634 0.04497444 0.002072160
## [24,] 0.03735401 0.001679164 0.05760481 0.002494697
## [25,] 0.02767854 0.001474175 0.04251672 0.002146568
## [26,] 0.02394821 0.001269694 0.03873798 0.001969577
## [27,] 0.03064398 0.001632828 0.04885974 0.002542156
## [28,] 0.03000991 0.001450027 0.04668540 0.002146554
## [29,] 0.03080126 0.001691660 0.04722480 0.002452984
## [30,] 0.02990237 0.001428916 0.04546651 0.002086316
## [31,] 0.02604469 0.001301825 0.04055970 0.001945478
## [32,] 0.02604171 0.001309073 0.04052427 0.001936535
## [33,] 0.02481350 0.001301672 0.03857129 0.001891288
## [34,] 0.02744027 0.001366716 0.04297163 0.002026284
## [35,] 0.03555965 0.001614837 0.05431901 0.002362774
## [36,] 0.02497739 0.001267971 0.03958494 0.001902914
## [37,] 0.02453684 0.001267049 0.03866200 0.001875702
## [38,] 0.02723187 0.001370752 0.04391550 0.002102384
## [39,] 0.03299397 0.001610657 0.05062255 0.002361552
## [40,] 0.02570986 0.001294132 0.04085948 0.001928711
## [41,] 0.02718304 0.001349367 0.04350350 0.002032873
## [42,] 0.03133393 0.001898283 0.04821493 0.002743421
## [43,] 0.02712193 0.001382613 0.04292030 0.002069070
## [44,] 0.02755616 0.001574964 0.04285407 0.002310778
## [45,] 0.02479602 0.001277880 0.03920196 0.001889478
##
## $cov.M0
## NULL
##
## $cov.M1
## NULL
##
## $deltaR2
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [36] 0 0 0 0 0 0 0 0 0 0
##
## $alpha
## [1] 0.05
##
## $thr
## [1] 5.991465
##
## $DIFitems
## [1] 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
## [24] 25 26 27 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
##
## $member.type
## [1] "group"
##
## $match
## [1] "score"
##
## $type
## [1] "both"
##
## $p.adjust.method
## NULL
##
## $adjusted.p
## NULL
##
## $purification
## [1] FALSE
##
## $names
## [1] "ch1" "ch2" "ch3" "ch4" "ch5" "ch6" "ch7" "ch8" "ch9" "ch10"
## [11] "ch11" "ch12" "ch13" "ch14" "ch15" "ch16" "ch17" "ch18" "ch19" "ch20"
## [21] "ch21" "ch22" "ch23" "ch24" "ch25" "ch26" "ch27" "ch28" "ch29" "ch30"
## [31] "ch31" "ch32" "ch33" "ch34" "ch35" "ch36" "ch37" "ch38" "ch39" "ch40"
## [41] "ch41" "ch42" "ch43" "ch44" "ch45"
##
## $anchor.names
## NULL
##
## $criterion
## [1] "LRT"
##
## $save.output
## [1] FALSE
##
## $output
## [1] "out" "default"
##
## attr(,"class")
## [1] "Logistic" dif_ch2## $DIF
## M-H Stand. Lord Raju
## ch1 "DIF" "NoDIF" "DIF" "DIF"
## ch2 "NoDIF" "NoDIF" "DIF" "DIF"
## ch3 "DIF" "NoDIF" "DIF" "DIF"
## ch4 "DIF" "NoDIF" "DIF" "DIF"
## ch5 "DIF" "NoDIF" "NoDIF" "NoDIF"
## ch6 "DIF" "NoDIF" "DIF" "DIF"
## ch7 "DIF" "NoDIF" "DIF" "DIF"
## ch8 "DIF" "NoDIF" "DIF" "DIF"
## ch9 "DIF" "NoDIF" "DIF" "DIF"
## ch10 "DIF" "NoDIF" "DIF" "DIF"
## ch11 "NoDIF" "NoDIF" "NoDIF" "NoDIF"
## ch12 "DIF" "NoDIF" "DIF" "DIF"
## ch13 "DIF" "NoDIF" "DIF" "DIF"
## ch14 "DIF" "NoDIF" "DIF" "DIF"
## ch15 "DIF" "NoDIF" "DIF" "DIF"
## ch16 "NoDIF" "NoDIF" "NoDIF" "NoDIF"
## ch17 "DIF" "NoDIF" "DIF" "DIF"
## ch18 "DIF" "NoDIF" "DIF" "DIF"
## ch19 "DIF" "NoDIF" "DIF" "DIF"
## ch20 "DIF" "NoDIF" "DIF" "DIF"
## ch21 "NoDIF" "NoDIF" "DIF" "DIF"
## ch22 "NoDIF" "NoDIF" "DIF" "DIF"
## ch23 "DIF" "NoDIF" "DIF" "DIF"
## ch24 "DIF" "NoDIF" "DIF" "DIF"
## ch25 "DIF" "NoDIF" "DIF" "DIF"
## ch26 "DIF" "NoDIF" "DIF" "DIF"
## ch27 "DIF" "NoDIF" "DIF" "DIF"
## ch28 "DIF" "NoDIF" "NoDIF" "NoDIF"
## ch29 "DIF" "NoDIF" "DIF" "DIF"
## ch30 "DIF" "NoDIF" "DIF" "DIF"
## ch31 "DIF" "NoDIF" "DIF" "DIF"
## ch32 "NoDIF" "NoDIF" "NoDIF" "NoDIF"
## ch33 "DIF" "NoDIF" "DIF" "DIF"
## ch34 "DIF" "NoDIF" "DIF" "DIF"
## ch35 "DIF" "NoDIF" "DIF" "DIF"
## ch36 "DIF" "NoDIF" "DIF" "DIF"
## ch37 "DIF" "NoDIF" "DIF" "DIF"
## ch38 "NoDIF" "NoDIF" "NoDIF" "NoDIF"
## ch39 "DIF" "NoDIF" "NoDIF" "NoDIF"
## ch40 "DIF" "NoDIF" "DIF" "DIF"
## ch41 "DIF" "NoDIF" "DIF" "DIF"
## ch42 "DIF" "NoDIF" "DIF" "DIF"
## ch43 "DIF" "NoDIF" "DIF" "DIF"
## ch44 "DIF" "NoDIF" "DIF" "DIF"
## ch45 "DIF" "NoDIF" "DIF" "DIF"
##
## $props
## NULL
##
## $thrTID
## [1] 1.5
##
## $correct
## [1] TRUE
##
## $exact
## [1] FALSE
##
## $alpha
## [1] 0.05
##
## $MHstat
## [1] "MHChisq"
##
## $stdWeight
## [1] "focal"
##
## $thrSTD
## [1] 0.1
##
## $BDstat
## [1] "BD"
##
## $member.type
## [1] "group"
##
## $match
## [1] "score"
##
## $type
## [1] "both"
##
## $criterion
## [1] "LRT"
##
## $model
## [1] "1PL"
##
## $c
## NULL
##
## $engine
## [1] "ltm"
##
## $discr
## [1] 1
##
## $irtParam
## NULL
##
## $same.scale
## [1] TRUE
##
## $signed
## [1] FALSE
##
## $purification
## [1] TRUE
##
## $nrPur
## [1] 4 0 3 3
##
## $convergence
## [1] TRUE TRUE TRUE TRUE
##
## $anchor.names
## NULL
##
## $p.adjust.method
## NULL
##
## $save.output
## [1] FALSE
##
## $output
## [1] "out" "default"
##
## attr(,"class")
## [1] "dichoDif" # plot(dif_ch)Resolvendo DIF
# 11, 16, 32 , 38
ch_m3pl_dif <- multipleGroup(
data = score_ch, model = m3pl,
group = enem_2015$TP_SEXO,
invariance = c( ch_itens[c(2, 5, 11, 16, 21, 22, 28, 32, 38, 39)],
'free_means', 'free_var'),
itemtype="3PL",
TOL = .001
)
ch_m3pl_pars_dif <- coef(ch_m3pl_dif, simplify=TRUE, IRTpars=TRUE) ch_m3pl_pars_dif## $F
## $items
## a b g u
## ch1 1.431 1.116 0.234 1
## ch2 1.400 -0.209 0.184 1
## ch3 2.106 1.030 0.218 1
## ch4 0.971 0.111 0.263 1
## ch5 2.102 1.621 0.066 1
## ch6 1.108 1.066 0.139 1
## ch7 2.034 2.026 0.154 1
## ch8 1.540 1.094 0.278 1
## ch9 0.836 -1.281 0.106 1
## ch10 1.546 2.317 0.106 1
## ch11 0.419 -1.751 0.156 1
## ch12 1.490 0.506 0.119 1
## ch13 2.431 0.801 0.150 1
## ch14 1.212 0.552 0.142 1
## ch15 1.952 1.377 0.166 1
## ch16 0.949 2.727 0.149 1
## ch17 2.261 1.465 0.453 1
## ch18 0.571 1.192 0.149 1
## ch19 1.519 0.539 0.224 1
## ch20 1.166 3.371 0.119 1
## ch21 0.644 -1.109 0.117 1
## ch22 1.378 1.262 0.191 1
## ch23 1.464 3.151 0.206 1
## ch24 1.982 1.681 0.082 1
## ch25 0.895 0.409 0.099 1
## ch26 1.106 2.345 0.515 1
## ch27 1.634 0.602 0.180 1
## ch28 2.168 1.546 0.189 1
## ch29 1.350 0.230 0.121 1
## ch30 0.880 2.217 0.101 1
## ch31 1.313 2.140 0.262 1
## ch32 0.644 1.784 0.141 1
## ch33 0.463 0.739 0.112 1
## ch34 1.656 1.595 0.234 1
## ch35 1.603 1.944 0.085 1
## ch36 2.127 1.940 0.336 1
## ch37 1.149 1.988 0.353 1
## ch38 2.434 1.373 0.272 1
## ch39 1.488 1.079 0.083 1
## ch40 0.465 6.686 0.255 1
## ch41 1.196 1.790 0.206 1
## ch42 1.020 -0.896 0.112 1
## ch43 1.527 1.348 0.254 1
## ch44 0.645 -0.781 0.155 1
## ch45 0.489 1.590 0.160 1
##
## $means
## th_ch
## 0
##
## $cov
## th_ch
## th_ch 1
##
##
## $M
## $items
## a b g u
## ch1 1.312 0.646 0.198 1
## ch2 1.400 -0.209 0.184 1
## ch3 2.086 1.181 0.235 1
## ch4 0.809 -0.228 0.211 1
## ch5 2.102 1.621 0.066 1
## ch6 1.088 1.100 0.102 1
## ch7 2.235 2.018 0.156 1
## ch8 1.859 1.114 0.326 1
## ch9 0.831 -0.857 0.113 1
## ch10 1.334 2.202 0.111 1
## ch11 0.419 -1.751 0.156 1
## ch12 1.463 0.391 0.112 1
## ch13 2.564 0.998 0.144 1
## ch14 1.355 0.721 0.140 1
## ch15 1.708 1.194 0.148 1
## ch16 0.949 2.727 0.149 1
## ch17 2.199 1.296 0.417 1
## ch18 0.692 1.002 0.184 1
## ch19 1.634 0.523 0.255 1
## ch20 1.450 3.403 0.133 1
## ch21 0.644 -1.109 0.117 1
## ch22 1.378 1.262 0.191 1
## ch23 1.108 2.821 0.166 1
## ch24 2.087 1.486 0.088 1
## ch25 0.869 0.504 0.092 1
## ch26 0.494 -0.171 0.200 1
## ch27 1.694 0.348 0.150 1
## ch28 2.168 1.546 0.189 1
## ch29 1.261 0.347 0.075 1
## ch30 0.950 1.751 0.110 1
## ch31 0.907 1.480 0.210 1
## ch32 0.644 1.784 0.141 1
## ch33 0.425 1.734 0.129 1
## ch34 1.582 1.659 0.231 1
## ch35 1.642 1.804 0.095 1
## ch36 1.732 1.784 0.325 1
## ch37 1.274 2.092 0.336 1
## ch38 2.434 1.373 0.272 1
## ch39 1.488 1.079 0.083 1
## ch40 0.506 4.401 0.194 1
## ch41 1.326 1.655 0.177 1
## ch42 1.171 -0.334 0.121 1
## ch43 1.583 1.341 0.235 1
## ch44 0.768 -0.322 0.168 1
## ch45 0.856 2.295 0.259 1
##
## $means
## th_ch
## 0.354
##
## $cov
## th_ch
## th_ch 0.829 describe(ch_m3pl_pars_dif$F$items)## vars n mean sd median trimmed mad min max range skew kurtosis
## a 1 45 1.35 0.56 1.38 1.34 0.60 0.42 2.43 2.02 0.14 -0.92
## b 2 45 1.25 1.39 1.35 1.23 0.95 -1.75 6.69 8.44 0.86 3.68
## g 3 45 0.19 0.09 0.16 0.17 0.07 0.07 0.52 0.45 1.47 2.37
## u 4 45 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00 NaN NaN
## se
## a 0.08
## b 0.21
## g 0.01
## u 0.00 describe(ch_m3pl_pars_dif$M$items)## vars n mean sd median trimmed mad min max range skew kurtosis
## a 1 45 1.34 0.57 1.33 1.33 0.59 0.42 2.56 2.14 0.24 -0.85
## b 2 45 1.15 1.16 1.26 1.15 0.80 -1.75 4.40 6.15 0.00 0.63
## g 3 45 0.18 0.08 0.16 0.17 0.06 0.07 0.42 0.35 1.03 0.85
## u 4 45 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00 NaN NaN
## se
## a 0.08
## b 0.17
## g 0.01
## u 0.00 gf_point(ch_m3pl_pars_dif$F$items[ , 2] ~ ch_m3pl_pars_dif$M$items[ , 2])
theta_ch5 = fscores(ch_m3pl_dif , method = "EAP", full.scores.SE = TRUE,
mean = c(M, M), cov = c(DP**2, DP**2))
theta_ch5 = fscores(ch_m3pl_dif , method = "WLE")
enem_2015 <- cbind(enem_2015[, 1:172], theta_ch5 = theta_ch5[ , 1])
names(enem_2015) gf_dens(~theta_ch5 , data = enem_2015, color = ~ as.factor(TP_SEXO))
t.test(~theta_ch5 | TP_SEXO, data = enem_2015)## theta_ch5 ~ TP_SEXO##
## Welch Two Sample t-test
##
## data: theta_ch5 by TP_SEXO
## t = -52.752, df = 103870, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.2227422 -0.2067833
## sample estimates:
## mean in group F mean in group M
## 0.2367979 0.4515606 cor(enem_2015$theta_ch5, as.numeric(as.factor(enem_2015$TP_SEXO)), use = "pair")## [1] 0.1517769Exercício 5
- Faça as mesmas análises acima com a prova de matemática