Tests of Structural Equation Models
The first tool that was developed for testing structural equation models (SEM) was a procedure to determine the power of the commonly used chi2 test (Satorra and Saris 1985). The procedure to determine the power was rather cumbersome and research showed that the power of the test was different for different parameters in the model and depended on different characteristics of the model, the strength of the relationships, the measurement errors in the indicators and of course the sample size (Saris and Satorra 1988). Therefore we later concluded that global model tests were not possible. Therefore we later concentrated on statistics that could indicate whether restricted parameters in the models were seriously misspecified or not.
In this context we present:
1. Two statistics to detect misspecifications: MI and EPC. The Modification index (MI) was the first statistic introduced to detect misspecified restrictions in SEM. We suggested as an additional statistic the Expected parameeter change or EPC. Both measures are introduced here (Saris and Satorra 1987).
2. The power of the test for misspecifications is the test whether the EPC was significiantly different from zero (Saris, Satorra and Van der Veld 2009)
3. Jrule a procedure and program to determine whether a restricted parameter in a model is misspecified or not or that there is not enough information for this decision (Saris, Satorra and Van der Veld 2009).
In this context we present:
1. Two statistics to detect misspecifications: MI and EPC. The Modification index (MI) was the first statistic introduced to detect misspecified restrictions in SEM. We suggested as an additional statistic the Expected parameeter change or EPC. Both measures are introduced here (Saris and Satorra 1987).
2. The power of the test for misspecifications is the test whether the EPC was significiantly different from zero (Saris, Satorra and Van der Veld 2009)
3. Jrule a procedure and program to determine whether a restricted parameter in a model is misspecified or not or that there is not enough information for this decision (Saris, Satorra and Van der Veld 2009).
