rxx.NL: Non-linear SEM composite reliability coefficient

In sjpierce/piercer: Functions for Research and Statistical Computing

Non-linear SEM composite reliability coefficient

Description

Computes a reliability estimate for a latent factor measured by ordinal indicator items from confirmatory factor analysis (CFA) parameter estimates.

Usage

rxx.NL(lambda, tau, fcor = matrix(1, ncol = 1), digits = NULL)

Arguments

lambda	A factor loading matrix (items x factors). See details below.
tau	A threshold matrix (items x thresholds, same set for all items).
fcor	A latent factor correlation matrix (factors x factors), which defaults to a 1 x 1 matrix: [cor = 1]
digits	An integer specifying the number of decimal places to used when rounding the result. Defaults to NULL, which does not round the result.

Details

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This function computes Green & Yang's (2009) nonlinear SEM reliability coefficient from CFA with ordinal indicators (Equation 21). The code was adapted from Yang & Green's (2015) SAS macro, found online at http://myweb.fsu.edu/yyang3/files/examplecodes.txt. Note that Green & Yang's (2009) Equation 21 matches Yang & Green's (2015) Equation 9.

This code was written assuming one would use Mplus to estimate the CFA, so some terminology here reflects that. If you are using WLSMV estimation with latent variance fixed to 1 and all indicator loadings freely estimated, then unstandardized & standardized estimates are identical (you can use either one as the lambda input to this function). However, if you are using Bayesian estimation with PX parameterization, use the STDYX estimates.

Value

A numeric value for the reliability.

References

Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74(1), 155-167. doi:10.1007/s11336-008-9099-3

Yang, Y., & Green, S. B. (2015). Evaluation of structural equation modeling estimates of reliability for scales with ordered categorical items. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 11(1), 23-34. doi:10.1027/1614-2241/a000087

sjpierce/piercer documentation built on Dec. 30, 2024, 3:28 p.m.