With gratitude Kit Baum, we have made available a software update to
-swain-, which corrects the SEM chi-square overidentification test in
small sample sizes or complex models.
The package now includes -swaini- an immediate version of the
postestimation test, which calculates the corrected chi-square statistic
using fit data entered manually by the user (i.e., no. of vars, df,
n-size, and chi-square value). We have also updated the help file.
Here is a description of the command:
swain and swaini correct the chi-square overidentification test
(i.e., likelihood ratio test of fit) for structural equation
models whether with or without latent variables. The chi-square
statistic is asymptotically correct; however, it does not behave
as expected in small samples and/or when the model is complex
(cf. Herzog, Boomsma, & Reinecke, 2007). Thus, particularly in
situations where the ratio of sample size to the number of
parameters estimated is relatively small, the chi-square test
will tend to overreject correctly specified models. To obtain a
closer approximation to the distribution of the chi-square
statistic, Swain (1975) developed a correction; this scaling
factor, which converges to 1 asymptotically, is multiplied with
the chi-square statistic. The correction better approximates the
chi-square distribution resulting in more appropriate Type 1
reject error rates (see Herzog & Boomsma, 2009; Herzog, et al.,
2007).
To install swain simply type -ssc install swain- from the Stata command
line.
