llla: Fit Log Linear by Linear Association Models

Description

This function fits log linear by linear association models using pseudolikelihood method.

Usage

llla(data, item.mtx=rep(1, ncol(data)), trait.mtx=1, useMLE=FALSE, uncorrected=FALSE)

Arguments

data

is a data frame or matrix with rows indicating individuals and columns indicating items and the values indicating the choices.

item.mtx

is the adjacency matrix between items and the latent traits

trait.mtx

is the adjacency matrix for latent traits

useMLE

inidicates whether maximum likelihood estimation is used

uncorrected

if the value is TRUE, calculate the uncorrected standard errors

Value

coefficients: the parameter estimates in the LLLA model
se: the standard error of coefficient esimates(sandwich estimator)
covb: the covariance matrix of the coefficient esimates
se.uncorrected: the standard error not corrected
ncat: number of categories
nexaminee: number of examinees
nitem: number of items

References

Anderson, C.J., Li, Z., & Vermunt, J.K. (2007). Estimation of models in the Rasch family for polytomous items and multiple latent variables. Journal of Statistical Software, 20.

Examples

Run this code

NCAT <- 2;
NITEM <- 4;
NEXAMINEE <- 50;
BETA <- c(-1, 0, 0.5, 1)
set.seed(1);
rasch.sim <- simRasch(ncat=NCAT, nitem=NITEM, nexaminee=NEXAMINEE, beta=BETA)
sim.data <- rasch.sim$data
colnames(sim.data) <- paste("I", 1:NITEM, sep='')

## The model item adjacency matrix and the latent trait adjacency matrix
item.mtx <- rep(1, NITEM);
trait.mtx <- 1;

### MLE of log-multiplicative Assoc. Model
mlfit <- llla(sim.data, item.mtx, trait.mtx, useMLE=TRUE)
mlfit

#### PLE of log-multiplicative Assoc. Model
plfit <- llla(sim.data, item.mtx, trait.mtx)
plfit