CDL {NPCD}

Log-likelihood for cognitive diagnostic models

Description

This function returns the log-likelihood of a particular examinee's responses to a set of cognitive diagnostic items. Currently supported cognitive diagnostic models include the DINA model, DINO model, NIDA model, G-NIDA model, and R-RUM model. This function is called by the AlphaMLE function and the JMLE function in the package.

Usage

CDL(Y, Q, par, alpha, model = c("DINA", "DINO", "NIDA", "GNIDA", "RRUM"), 
undefined.flag)

Arguments

Y

A vector of binary examinee responses. 1=correct, 0=incorrect.

Q

The Q-matrix of the test. Rows represent items and columns represent attributes. 1=attribute required by the item, 0=attribute not required by the item.

par

A list of parameters. DINA & DINO — par$slip: a vector of slipping parameters for each item; par$guess: a vector of guessing parameters for each item. NIDA — par$slip: a vector of slipping parameters for each attribute; par$guess: a vector of guessing parameters for each attribute. GNIDA — par$slip: a matrix (items by attributes) of slipping parameters; par$guess: a matrix (items by attributes) of guessing parameters. RRUM — par$pi: a vector of pi parameters for each item; par$r: a matrix (items by attributes) of r parameters.

alpha

A vector of examinee ability profile. 1=examinee masters the attribute, 0=examinee does not master the attribute.

model

Currently supports five models: "DINA", "DINO", "NIDA", "GNIDA", and "RRUM". The default is "DINA".

undefined.flag

A binary vector indicating whether the parameters of each item are undefined. 1=undefined, 0=defined.

Value

loglike

The log likelihood function value for the given data.

See Also

AlphaMLE, JMLE

Examples

# Generate item and examinee profiles

nitem <- 4
Q <- rbind(c(1, 0, 0), c(0, 1, 0), c(0, 0, 1), c(1, 1, 1))
alpha <- c(1, 0, 0)

# Generate DINA model-based response data

slip <- rep(0.1, nitem)
guess <- rep(0.1, nitem)
my.par <- list(slip=slip, guess=guess)

data <- NA
eta <- NA

for (i in 1:nitem) {
  eta[i] <- prod(alpha ^ Q[i, ])
  P <- (1 - slip[i]) ^ eta[i] * guess[i] ^ (1 - eta[i])
  u <- runif(1)
  data[i] <- as.numeric(u < P)
}

# Using the function to compute the log-likelihood of the given data

CDL(data, Q, my.par, alpha, model="DINA", undefined.flag=rep(0, nitem))