uniquenessPrior: Uniqueness prior to assist in item factor analysis

In ifaTools: Toolkit for Item Factor Analysis with 'OpenMx'

Description

To prevent Heywood cases, Bock, Gibbons, & Muraki (1988) suggested a beta prior on the uniqueness (Equations 43-46). The analytic gradient and Hessian are included for quick optimization using Newton-Raphson.

Usage

uniquenessPrior(model, numFactors, strength = 0.1, name = "uniquenessPrior")

Arguments

model	an mxModel
numFactors	the number of factors. All items are assumed to have the same number of factors.
strength	the strength of the prior
name	the name of the mxModel that is returned

Details

To reproduce these derivatives in maxima for the case of 2 slopes (c and d), use the following code:

f(c,d) := -p*log(1-(c^2 / (c^2+d^2+1) + (d^2 / (c^2+d^2+1))));

diff(f(c,d), d),radcan;

diff(diff(f(c,d), d),d),radcan;

The general pattern is given in Bock, Gibbons, & Muraki.

Value

an mxModel that evaluates to the prior density in deviance units

References

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

Examples

numItems <- 6
spec <- list()
spec[1:numItems] <- list(rpf.drm(factors=2))
names(spec) <- paste0("i", 1:numItems)
item <- mxMatrix(name="item", free=TRUE,
                 values=mxSimplify2Array(lapply(spec, rpf.rparam)))
item$labels[1:2,] <- paste0('p',1:(numItems * 2))
data <- rpf.sample(100, spec, item$values)  # use a larger sample size
m1 <- mxModel(model="m1", item,
              mxData(observed=data, type="raw"),
              mxExpectationBA81(spec),
              mxFitFunctionML())
up <- uniquenessPrior(m1, 2)
container <- mxModel("container", m1, up,
                     mxFitFunctionMultigroup(c("m1", "uniquenessPrior")),
                     mxComputeSequence(list(
                       mxComputeOnce('fitfunction', c('fit','gradient')),
                       mxComputeReportDeriv())))
container <- mxRun(container)
container$output$fit
container$output$gradient

ifaTools documentation built on Jan. 20, 2022, 1:08 a.m.