Correcting for Unreliability and Partial Invariance: A Two-Stage Path Analysis Approach

In path analysis, using composite scores without adjustment for measurement unreliability and violations of factorial invariance across groups lead to biased estimates of path coefficients. Although joint modeling of measurement and structural models can theoretically yield consistent structural association estimates, estimating a model with many variables is often impractical in small samples. A viable alternative is two-stage path analysis (2S-PA), where researchers first obtain factor scores and the corresponding individual-specific reliability coefficients, and then use those factor scores to analyze structural associations while accounting for their unreliability. The current paper extends 2S-PA to also account for partial invariance. Two simulation studies show that 2S-PA outperforms joint modeling in terms of model convergence, the efficiency of structural parameter estimation, and confidence interval coverage, especially in small samples and with categorical indicators. We illustrate 2S-PA by reanalyzing data from a multiethnic study that predicts drinking problems using college-related alcohol beliefs.

Automated summary

In path analysis, using composite scores without adjustment for measurement unreliability and violations of factorial invariance can result in biased estimations. Two-stage path analysis (2S-PA), which involves obtaining factor scores and reliability coefficients before analyzing structural associations, is a practical alternative. The method outperforms joint modeling in terms of model convergence, efficiency of parameter estimation, and confidence interval coverage, especially in small samples and with categorical indicators.