Linear Approximation of a Confirmatory Factor Analysis

This function approximates a fitted item response model by a linear confirmatory factor analysis. I.e., given item response functions, the expectation \(E(X_i | \theta_1, \ldots, \theta_D)\) is linearly approximated by \(a_{i1} \theta _1 + \ldots + a_{iD} \theta_D\). See Vermunt and Magidson (2005) for details.

IRT.linearCFA( object, group=1)

# S3 method for IRT.linearCFA
summary(object,  ...)

Arguments

object

Fitted item response model for which the IRT.expectedCounts method is defined.

group

Group identifier which defines the selected group.

...

Further arguments to be passed.

Value

A list with following entries

loadings

Data frame with factor loadings. Mlat and SDlat denote the model-implied item mean and standard deviation. The values ResidVar and h2 denote residual variances and item communality.

stand.loadings

Data frame with standardized factor loadings.

M.trait

Mean of factors

SD.trait

Standard deviations of factors

References

Vermunt, J. K., & Magidson, J. (2005). Factor Analysis with categorical indicators: A comparison between traditional and latent class approaches. In A. Van der Ark, M.A. Croon & K. Sijtsma (Eds.), New Developments in Categorical Data Analysis for the Social and Behavioral Sciences (pp. 41-62). Mahwah: Erlbaum

See also

See tam.fa for confirmatory factor analysis in TAM.

Examples