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

Abstract

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.

Keywords:

• Factor scores
• measurement error
• partial factorial invariance
• two-stage path analysis
• reliability adjustment

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Simulation codes and data are openly available on the project’s GitHub page (github.com/marklhc/2spa-inv-supp).

Notes

1 Note that we could allow $\mathbf{B}$ to be group-specific to represent $G\times$ $\eta$ interactions; however, based on our small literature review (described later in the paper), researchers rarely specified such an interaction, so in the current paper we mainly focus on analyses with a common $\mathbf{B}.$

2 The composite reliability for sum scores is computed using the same formula as presented in Table 1 (see also Raykov, 1997).

3 As reported in Lui (2019), items 4–10 of AUDIT measure drinking problems; items 4, 6, and 8 are on a scale of 0–4, items 5 and 7 are on a scale of 0–3, and items 9 and 10 consists of three response categories (0, 2, and 4).

4 This is commonly done when computing Cohen’s d effect size.

Additional information

Funding

This research is based on work supported by the National Science Foundation under Grant No. 2141790.