conv.rt: Estimating IRT Item Parameters with Small Samples via...

In ConvertPar: Estimating IRT Parameters via Machine Learning Algorithms

Estimating IRT Item Parameters with Small Samples via Regression Trees

Description

This function can be used to estimate IRT item parameters (2 PL) using CTT-based item statistics from small samples via Regression Trees.

Usage

conv.rt(small.data, train.data, model="2PL",pruned=TRUE,min.inst=10)

Arguments

small.data	matrix or data frame: contains small sample dichotomous participant response matrix.
train.data	matrix or data frame: contains a dichotomous response matrix to use training of ANN model. This matrix should be contain as much as possible participants for more accurate estimations.The "gen.data" function can be used to obtain a simulative response matrix.
model	string: option for desired IRT model. 'Rasch' or '2PL' ('2PL' is default)
pruned	a logical: Use unpruned tree/rules. Default is TRUE
min.inst	numeric: Minimum number of items per leaf (Default 10).

Value

This function returns a list including following:

• a matrix: Predicted IRT Parameters

• a matrix: Item Parameters of Training Data

• a list: Tree Models and Regression Equations

Examples

  ## Genarating item and ability parameters (1000 participants, 100 items)

  a <- rlnorm(100,0,0.3)
  b <- rnorm(100,0,1)
  responses <- matrix(NA, nrow=1000, ncol=100)
  theta <- rnorm(1000, 0,1)

 ### Defining Response Function (2 PL)

  pij <- function(a,b,theta) {
      1/(1+exp(-1*a*(theta-b)))
    }

 ### Creating Response Matrix and column names.

   for( i in 1:1000 ) {
    for( j in 1:100 ) {
      responses[i,j]<-ifelse(pij(a=a[j], b=b[j], theta[i]) < runif(1) , 0 ,1)

    }
  }

  names<-paste("i",1:ncol(responses),sep = "_")

  colnames(responses)<-names
  train<-as.data.frame(responses)

  small.index<-sample(1:nrow(train),100,replace=FALSE)

  small<-train[small.index,]


  ### Conducting Function

  conv.rt(small.data=small,
  train.data=train,
  model="2PL",
  pruned=TRUE,
  min.inst=10)

ConvertPar documentation built on March 18, 2022, 7:07 p.m.