*! version 1.0, 04May2018

Title

jrule - Stata module to detect model misspecifications in SEM

Syntax

jrule [, options]

delta(#) Standardized size of misspecification to detect; default (.10)

power(#) Threshold for 'high' power values; default (.80)

minchi(#) Minimum MI displayed; default is only significant MI (3.841)

calpha(#) Critical alpha level for power calculation; default (.05)

dftest(#) Changing d.f. for power calculation; default (1)

Description

jrule is a postestimation tool for the sem command, using stored results from
estat mindices. It provides judgement rules for potential misspecifications based
on the power of the Modification Index (MI) or score test in combination with the
Expected Parameter Change (EPC). jrule makes use of the recommendations and formulae
provided by Saris et al. (2009) and Van der Veld et al. (2008). The jrule command
prints decision rules on possible misspecifications following their scheme.

Several judgement rules can be set in the jrule command: delta specifies the minimum
size of the misspecification that one would like to detect by the test with a certain
power and critical alpha-level (calpha) of the test. As the default, only significant
MI values (minchi) are shown.

The default size for detecting misspecifications (Delta) is .10, whereas Van der Veld
et al. (2008) further suggest:
misspecifications >=.10 for correlations/(causal) effects
misspecifications >=.40 for factor loadings
misspecifications >=.05 for means/intercepts.

Because the unstandardized EPC is dependent upon the scaling of the variables in the
model (Chou & Bentler, 1993), jrule uses an unstandardized Delta (dw) for all the
computations, identical to the LISREL add-on JRule (Van der Veld et al., 2008). In
fact, the size of a misspecification thus refers to the standardized EPC (StdYX_EPC).
A ratio of |EPC|/dw => 1 would then suggest a relevant misspecification, whereas in
case of a small ratio (< 1) there is likely no serious misspecification.

Notes

The parameters are computed as follows:
dw is the original Delta times EPC scaling weight (StdYX_EPC/EPC; Chou & Bentler, 1993):
dw = (Delta*EPC)/StdYX_EPC; where Delta = .10 as default
The noncentrality parameter: ncp = (MI/EPC^2)*dw^2
Power = nchi2tail(d.f., ncp, chi2-critical); where d.f. = 1 and chi2 = 3.841 as default

Authors

Julian Aichholzer, University of Vienna (julian.aichholzer@univie.ac.at)

Recommended citation:
Aichholzer, J. (2018). JRULE: Stata module to detect model misspecifications in SEM (v1.0).
Boston College Department of Economics: Statistical Software Components (SSC) Archive.

References

Chou, C. P., & Bentler, P. M. (1993).
Invariant standardized estimated parameter change for model modification in covariance structure analysis.
Multivariate Behavioral Research, 28(1), 97-110.

Saris, W. E., Satorra, A., & Van der Veld, W. M. (2009).
Testing structural equation models or detection of misspecifications?
Structural Equation Modeling, 16(4), 561-582.

Van der Veld, W. M., Saris, W. E., & Satorra, A. (2008).
JRule 3.0: User's Guide.