Type: Package
Title: Estimating IRT Parameters via Machine Learning Algorithms
Version: 0.1
Maintainer: Eda Akdogdu Yildiz <akdogdueda@gmail.com>
Description: A tool to estimate IRT item parameters (2 PL) using CTT-based item statistics from small samples via artificial neural networks and regression trees.
Imports: neuralnet, mirt, RWeka, stats
License: GPL (≥ 3)
Encoding: UTF-8
NeedsCompilation: no
Packaged: 2022-03-12 12:14:00 UTC; husey
Author: Eda Akdogdu Yildiz ORCID iD [aut, cre], Huseyin Yıldız ORCID iD [aut], Kubra Atalay Kabasakal ORCID iD [aut]
Repository: CRAN
Date/Publication: 2022-03-14 19:20:05 UTC

Estimating IRT Item Parameters with Small Samples via Artificial Neural Networks

Description

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

Usage

conv.ann(small.data, train.data, model="2PL",layers=1,learningrate=NULL,treshold=0.01)

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)

layers

vector: a vector of integers specifying the number of hidden neurons (vertices) in each layer.

learningrate

numeric: a numeric value specifying the learning rate.

treshold

numeric: a numeric value specifying the threshold for the partial derivatives of the error function as stopping criteria.

Value

This function returns a list including following:

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.ann(small.data=small, train.data=train, model="2PL",layers=c(2,2),
  learningrate=NULL,treshold=0.01)

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:

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)

Generating Dichotomous Data Sets based on Logistic IRT Models (Rasch, 2PL, 3PL).

Description

This function can be used for generating dichotomous response matrices based on Logistic IRT Models. Sample size, item number, parameter distributions can be specified.

Usage

gen.data(model="2PL",samplesize=1000,itemsize=100,
theta.mean=0,theta.sd=1, a.mean=0, a.sd=0.2,b.mean=0,
b.sd=1, c.min=0, c.max=0.25)

Arguments

model

string: option for desired IRT model. 'Rasch', '2PL' or '3PL' ('2PL' is default)

samplesize

numeric: Desired Sample size (Default 1000).

itemsize

numeric: Desired item number (Default 100).

theta.mean

numeric: mean value of theta normal distribution (Default 0).

theta.sd

numeric: standart deviation of theta normal distribution (Default 1).

a.mean

numeric: mean value of a parameters log normal distribution (Default 0).

a.sd

numeric: standart deviation of a parameters log normal distribution (Default 0.2).

b.mean

numeric: mean value of b parameters normal distribution (Default 0).

b.sd

numeric: standart deviation of b parameters normal distribution (Default 1).

c.min

numeric: minimum value of c parameters uniform distribution (Default 0).

c.max

numeric: maximum value of c parameters uniform distribution (Default 0.25).

Value

This function returns a a data frame containing simulated dichotomous response matrix.

Examples


 gen.data(model="2PL",
 samplesize=1000,
 itemsize=100,
 theta.mean=0,
 theta.sd=1,
 a.mean=0,
 a.sd=0.2,
 b.mean=0,
 b.sd=1,
 c.min=0,
 c.max=0.25)

mirror server hosted at Truenetwork, Russian Federation.