Hands-on Task 1 Wu, Tang & Jen (2018)

Simula dados de dois testes usando o sirt

  library(sirt)

## Warning: package 'sirt' was built under R version 3.5.2

## - sirt 3.6-21 (2019-08-01 18:42:53)

  set.seed(8484)
  N <- 500    # number of persons
  I <- 30     # number of items
  b_easy <- seq( -3 , 0.5 , length=I )
  b_hard <- seq( -.5 , 3 , length=I )
  t <- rnorm( N )
  
  df_easy <- sirt::sim.raschtype(theta =  t,b =  b_easy )
  df_hard<- sirt::sim.raschtype( t, b_hard )

Calcula os escores e cria um dataframe

  library(psych)

## Warning: package 'psych' was built under R version 3.5.2

  psicom_easy <-  alpha(df_easy, cumulative = TRUE)
  psicom_hard <-  alpha(df_hard, cumulative = TRUE)
  
  df <- cbind(theta = t, scr_easy = psicom_easy$scores, scr_hard = psicom_hard$scores)
  df <- as.data.frame(df)
  
  library(tidyverse)

## ── Attaching packages ──────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──

## ✔ ggplot2 3.1.1       ✔ purrr   0.3.2  
## ✔ tibble  2.1.1       ✔ dplyr   0.8.0.1
## ✔ tidyr   0.8.3       ✔ stringr 1.4.0  
## ✔ readr   1.3.1       ✔ forcats 0.4.0

## Warning: package 'ggplot2' was built under R version 3.5.2

## Warning: package 'tibble' was built under R version 3.5.2

## Warning: package 'tidyr' was built under R version 3.5.2

## Warning: package 'purrr' was built under R version 3.5.2

## Warning: package 'stringr' was built under R version 3.5.2

## Warning: package 'forcats' was built under R version 3.5.2

## ── Conflicts ─────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ ggplot2::%+%()   masks psych::%+%()
## ✖ ggplot2::alpha() masks psych::alpha()
## ✖ dplyr::filter()  masks stats::filter()
## ✖ dplyr::lag()     masks stats::lag()

  df <-df %>% mutate(
    odds_easy = log( (scr_easy/30) / (1- (scr_easy/30) ) ),
    odds_hard = log((scr_hard/30) / (1- (scr_hard/30)) )
  )

Figuras

  df %>% ggplot(aes(y = scr_hard, x = scr_easy)) + geom_point() + theme_light() + geom_smooth()

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

  df %>% ggplot(aes(y = odds_hard, x = odds_easy)) + geom_point() + theme_light() +  geom_smooth()

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## Warning: Removed 13 rows containing non-finite values (stat_smooth).

  df %>% ggplot(aes(y =  scr_hard, x = t)) + geom_point() + theme_light() +  geom_smooth()

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

   df %>% ggplot(aes(y =  scr_easy, x = t)) + geom_point() + theme_light() +  geom_smooth()

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'