din.deterministic: Deterministic Classification and Joint Maximum Likelihood Estimation of the Mixed DINA/DINO Model

Description

This function allows the estimation of the mixed DINA/DINO model by joint maximum likelihood and a deterministic classification based on ideal latent responses.

Usage

din.deterministic(dat, q.matrix, rule="DINA", method="JML", conv=0.001,
    maxiter=300, increment.factor=1.05, progress=TRUE)

Value

A list with following entries

attr.est: Estimated attribute patterns
criterion: Criterion of the classification function. For joint maximum likelihood it is the deviance.
guess: Estimated guessing parameters
slip: Estimated slipping parameters
prederror: Average individual prediction error
q.matrix: Used Q-matrix
dat: Used data frame

Arguments

dat: Data frame of dichotomous item responses
q.matrix: Q-matrix with binary entries (see din).
rule: The condensation rule (see din).
method: Estimation method. The default is joint maximum likelihood estimation (JML). Other options include an adaptive estimation of guessing and slipping parameters (adaptive) while using these estimated parameters as weights in the individual deviation function and classification based on the Hamming distance (hamming) and the weighted Hamming distance (weighted.hamming) (see Chiu & Douglas, 2013).
conv: Convergence criterion for guessing and slipping parameters
maxiter: Maximum number of iterations
increment.factor: A numeric value of at least one which could help to improve convergence behavior and decreases parameter increments in every iteration. This option is disabled by setting this argument to 1.
progress: An optional logical indicating whether the function should print the progress of iteration in the estimation process.

References

Chiu, C. Y., & Douglas, J. (2013). A nonparametric approach to cognitive diagnosis by proximity to ideal response patterns. Journal of Classification, 30, 225-250.

Examples

Run this code

#############################################################################
# EXAMPLE 1: 13 items and 3 attributes
#############################################################################

set.seed(679)
N <- 3000
# specify true Q-matrix
q.matrix <- matrix( 0, 13, 3 )
q.matrix[1:3,1] <- 1
q.matrix[4:6,2] <- 1
q.matrix[7:9,3] <- 1
q.matrix[10,] <- c(1,1,0)
q.matrix[11,] <- c(1,0,1)
q.matrix[12,] <- c(0,1,1)
q.matrix[13,] <- c(1,1,1)
q.matrix <- rbind( q.matrix, q.matrix )
colnames(q.matrix) <- paste0("Attr",1:ncol(q.matrix))

# simulate data according to the DINA model
dat <- CDM::sim.din( N=N, q.matrix)$dat

# Joint maximum likelihood estimation (the default: method="JML")
res1 <- CDM::din.deterministic( dat, q.matrix )

# Adaptive estimation of guessing and slipping parameters
res <- CDM::din.deterministic( dat, q.matrix, method="adaptive" )

# Classification using Hamming distance
res <- CDM::din.deterministic( dat, q.matrix, method="hamming" )

# Classification using weighted Hamming distance
res <- CDM::din.deterministic( dat, q.matrix, method="weighted.hamming" )

if (FALSE) {
#********* load NPCD library for JML estimation
library(NPCD)

# DINA model
res <- NPCD::JMLE( Y=dat[1:100,], Q=q.matrix, model="DINA" )
as.data.frame(res$par.est )   # item parameters
res$alpha.est                 # skill classifications

# RRUM model
res <- NPCD::JMLE( Y=dat[1:100,], Q=q.matrix, model="RRUM" )
as.data.frame(res$par.est )
}