sooyongl / BMIMIC

BMIMIC

Overview

This package is for generating example simulation data for BMIMIC model which is introduced in Bayesian MIMIC for DIF Detection under Violation of Equal Variance Assumption. More information can be found in Bayesian MIMIC for DIF Detection under Violation of Equal Variance Assumption.

Install

devtools::install_github("sooyongl/BMIMIC")

Generate Data

library(BMIMIC)
library(rstan)

generated_data <-
  mkData(N1         = 500,
         N2         = 500,
         nitem      = 10,
         mu_2       = 0.2,
         var_2      = 2,
         uni_dif    = c(0,0,0,0,0.2,0.2,0.2,0,0,0),
         nonuni_dif = c(0,0,0,0,0,0,0,0.2,0.2,0.2),
         anchor_n   = 4)

Generated data

Item parameters

generated_data$ipars

Item response

generated_data$response

Group assignments

generated_data$group

Run BMIMIC model via rstan

stan code

#> data{
#>   //Data size
#>   int<lower=1> nitemWorked;
#>   int<lower=1> nstud;
#>   int<lower=1> nitem;
#>   
#>   // DIF Index
#>   int<lower=0, upper=1> unidif_idx [nitem];
#>   int<lower=0> unidifeffect_idx [nitem];
#>   int<lower=0, upper=1> nondif_idx [nitem];
#>   int<lower=0> nondifeffect_idx [nitem];
#> 
#>   // number of DIF
#>   int<lower=0> unidif_n;
#>   int<lower=0> nondif_n;
#>   
#>   // indices
#>   int<lower=1,upper=nstud> studIdx[nitemWorked];
#>   int<lower=1,upper=nitem> itemIdx[nitemWorked];
#> 
#>   // index for first item
#>   int<lower=0, upper=1> firstitem[nitem];
#> 
#>   // data
#>   int<lower=0,upper=1> group[nstud];
#>   int<lower=0,upper=1> response[nitemWorked];
#> }
#> 
#> parameters{
#>   // IRT model parameters
#>   vector[nstud] eta;               // individual latent traits
#>  
#>   real<lower=0> lambda_free[nitem]; // item slope
#>   real tau_free[nitem];             // item intercept 
#> 
#>   // Impact parameters
#>   real impact0;       // intercept in latent mean
#>   real impact;        // difference in latent mean
#>   real impactv0;      // intercept in latent variance
#>   real impactv;       // difference in latent variance
#>  
#>   // DIF effect parameters
#>   vector[unidif_n] difeffect ;
#>   vector[nondif_n] nondifeffect; 
#>   
#> }
#> 
#> transformed parameters {
#>   real<lower=0> lambda[nitem];
#>   real tau[nitem];
#>  
#>   // Factor loading constraints
#>   for(jj in 1:nitem) {
#>     if(firstitem[jj] == 1) { // first loading per factor constrained to 1.
#>        lambda[jj] = 1;
#>     tau[jj] = 0;
#>     } else {
#>        lambda[jj] = lambda_free[jj];
#>       tau[jj] = tau_free[jj];
#>     }      
#>   };
#> }
#> 
#> model{
#>   real linPred[nitemWorked];
#>   vector[nstud] muEta;
#>   vector[nstud] sigEta;
#> 
#>   for(i in 1:nstud){
#>     muEta[i] = impact0 + group[i]*impact; 
#>  sigEta[i] = sqrt(exp(impactv0 + group[i]*impactv));
#>   };
#> 
#>    eta ~ normal(muEta, sigEta);
#> 
#> //MIMIC
#>   for(j in 1:nitemWorked) {
#>     linPred[j] = tau[itemIdx[j]] + lambda[itemIdx[j]] * eta[studIdx[j]];
#>    if( unidif_idx[itemIdx[j]] == 1 && nondif_idx[itemIdx[j]] == 0 ) {
#>      // Uniform DIF
#>      linPred[j] = linPred[j] + group[studIdx[j]]*difeffect[itemIdx[j]-unidifeffect_idx[itemIdx[j]]];
#>      
#>    } else if(unidif_idx[itemIdx[j]] == 0 && nondif_idx[itemIdx[j]] == 1 ) {
#>      // non Uniform DIF
#>      linPred[j] = linPred[j] + eta[studIdx[j]]*group[studIdx[j]]*nondifeffect[itemIdx[j]-nondifeffect_idx[itemIdx[j]]];
#>    
#>    } else if(unidif_idx[itemIdx[j]] == 1 && nondif_idx[itemIdx[j]] == 1 ) {
#>      // uni + non
#>         linPred[j] = linPred[j] + group[studIdx[j]]*difeffect[itemIdx[j]-unidifeffect_idx[itemIdx[j]]] + eta[studIdx[j]]*group[studIdx[j]]*nondifeffect[itemIdx[j]-nondifeffect_idx[itemIdx[j]]];    
#>      
#>    }
#>    
#>  response[j] ~ bernoulli_logit(linPred[j]);
#>   }
#>   
#> //priors
#>   tau_free ~ normal(0, 1);
#>   for(i in 1:nitem) {
#>     lambda_free[i] ~ lognormal(0, 1);
#>   };
#> 
#>   impact0 ~ normal(0, 1);
#>   impact ~ normal(0, 1.44);
#>   impactv0 ~ normal(0, 0.1);
#>   impactv ~ normal(0, 1.44);
#>   
#>   difeffect ~ normal(0, 1);
#>   nondifeffect  ~ normal(0, 1);
#> }
#> // last line blank

Run stan

stan_fit <-
  rstan::stan(
    file = file.path(system.file("stan", package = "BMIMIC"),
                     "BMIMIC_example.stan"),
    data   = generated_data$stan_data
  )

summary(stan_fit)