estimates. All variances estimated with positive values and all correlations estimated below 1.00.
See Time 1 measurement model diagram in Figure 4-7 and fit indices in Table 4-19.
Estimation of longitudinal (three-occasion) measurement models. Following
estimation of the initial single occasion measurement models, full 3-occasion measurement
models (with loading paths as previously described) were specified for each pain outcome
construct: physical, emotional, and social functioning. All exogenous (control) variables were
specified to correlate with all endogenous constructs and variables. All endogenous constructs
were specified to correlate within each time of measurement and longitudinally across the three
time periods. In addition, all uniquenesses of the endogenous indicators were correlated
longitudinally. The goal of these model specifications is to achieve an identified model, the
greatest reduction in the Chi-square value, and a good model fit.
A three-step variance-invariance test involving a series of nested models was performed
for each of the three specified full models in order to identify the strongest and most
parsimonious model for analysis. Both standardized and un-standardized estimates were
requested. In Step 1, three invariance measurement models (Measurement-1) (physical,
emotional, and social) were scaled such that both the factor loadings and factor variances were
constrained to be equal across the three occasions of measurement. All models estimated and the
results indicated that all three models had good fit, as evidenced by incremental fit indices >.9
and absolute fit indexes <.05. In step 2, invariance models (Measurement-2) were specified such
that only the factor loadings were constrained to be equal across all occasions, while the
constraints on the factor variances were free. All three models estimated with good incremental
and absolute fit indices. In Step 3, the invariance model (Measurement-3) analyses were
specified such that no constraints were placed on either the factor loadings or the factor variances