Power analyses for measurement model misspecification and response shift detection with structural equation modeling

Statistical power for response shift detection with structural equation modeling (SEM) is currently underreported. The present paper addresses this issue by providing worked-out examples and syntaxes of power calculations relevant for the statistical tests associated with the SEM approach for response shift detection.

Power calculations and related sample-size requirements are illustrated for two modelling goals: (1) to detect misspecification in the measurement model, and (2) to detect response shift. Power analyses for hypotheses regarding (exact) overall model fit and the presence of response shift are demonstrated in a step-by-step manner. The freely available and user-friendly R-package lavaan and shiny-app 'power4SEM' are used for the calculations.

Using the SF-36 as an example, we illustrate the specification of null-hypothesis (H₀) and alternative hypothesis (H₁) models to calculate chi-square based power for the test on overall model fit, the omnibus test on response shift, and the specific test on response shift. For example, we show that a sample size of 506 is needed to reject an incorrectly specified measurement model, when the actual model has two-medium sized cross loadings. We also illustrate power calculation based on the RMSEA index for approximate fit, where H₀ and H₁ are defined in terms of RMSEA-values.

By providing accessible resources to perform power analyses and emphasizing the different power analyses associated with different modeling goals, we hope to facilitate the uptake of power analyses for response shift detection with SEM and thereby enhance the stringency of response shift research.