rpf (version 0.5)

multinomialFit: Multinomial fit test

Description

For degrees of freedom, we use the number of observed statistics (incorrect) instead of the number of possible response patterns (correct) (see Bock, Giibons, & Muraki, 1998, p. 265). This is not a huge problem because this test is becomes poorly calibrated when the multinomial table is sparse. For more accurate p-values, you can conduct a Monte-Carlo simulation study (see examples).

Usage

multinomialFit(grp, independenceGrp, ..., method = "lr", log = TRUE,
  .twotier = TRUE)

Arguments

grp

a list with the spec, param, mean, and cov describing the group

independenceGrp

a list with the spec, param, mean, and cov describing the independence group

...

Not used. Forces remaining arguments to be specified by name.

method

lr (default) or pearson

log

whether to report p-value in log units

.twotier

whether to use the two-tier optimization (default TRUE)

Details

Rows with missing data are ignored.

The full information test is described in Bartholomew & Tzamourani (1999, Section 3).

For CFI and TLI, you must provide an independence model.

References

Bartholomew, D. J., & Tzamourani, P. (1999). The goodness-of-fit of latent trait models in attitude measurement. Sociological Methods and Research, 27(4), 525-546.

Bock, R. D., Gibbons, R., & Muraki, E. (1988). Full-information item factor analysis. Applied Psychological Measurement, 12(3), 261-280.

Examples

# Create an example IFA group
grp <- list(spec=list())
grp$spec[1:10] <- rpf.grm()
grp$param <- sapply(grp$spec, rpf.rparam)
colnames(grp$param) <- paste("i", 1:10, sep="")
grp$mean <- 0
grp$cov <- diag(1)
grp$uniqueFree <- sum(grp$param != 0)
grp$data <- rpf.sample(1000, grp=grp)

# Monte-Carlo simulation study
mcReps <- 3    # increase this to 10,000 or so
stat <- rep(NA, mcReps)
for (rx in 1:mcReps) {
   t1 <- grp
   t1$data <- rpf.sample(grp=grp)
   stat[rx] <- multinomialFit(t1)$statistic
}
sum(multinomialFit(grp)$statistic > stat)/mcReps   # better p-value