ifaTools: uniquenessPrior – R documentation

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uniquenessPrior

Uniqueness prior to assist in item factor analysis

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

Toolkit for Item Factor Analysis with 'OpenMx'

v0.22

AGPL (>= 3)

Authors

Joshua N. Pritikin [cre, aut]

Initial release

2020-09-15