Deterministic Classification and Joint Maximum Likelihood Estimation of the Mixed DINA/DINO Model

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

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

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.

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

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.

See also

For estimating the mixed DINA/DINO model using marginal maximum likelihood estimation see din.

See also the NPCD::JMLE function in the NPCD package for joint maximum likelihood estimation of the DINA or the DINO model.

Examples

#############################################################################
# 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 )
}