Adjusting for Measurement Noninvariance with Alignment in Growth Modeling

Longitudinal measurement invariance-the consistency of measurement in data collected over time-is a prerequisite for any meaningful inferences of growth patterns. When one or more items measuring the construct of interest show noninvariant measurement properties over time, it leads to biased parameter estimates and inferences on the growth parameters. In this paper, I extend the recently developed alignment-within-confirmatory factor analysis (AwC) technique to adjust for measurement biases for growth models. The proposed AwC method does not require a priori knowledge of noninvariant items and the iterative searching of noninvariant items in typical longitudinal measurement invariance research. Results of a Monte Carlo simulation study comparing AwC with the partial invariance modeling method show that AwC largely reduces biases in growth parameter estimates and gives good control of Type I error rates, especially when the sample size is at least 1,000. It also outperforms the partial invariance method in conditions when all items are noninvariant. However, all methods give biased growth parameter estimates when the proportion of noninvariant parameters is over 25%. Based on the simulation results, I conclude that AO is a viable alternative to the partial invariance method in growth modeling when it is not clear whether longitudinal measurement invariance holds. The current paper also demonstrates AwC in an example modeling neuroticism over three time points using a public data set, which shows how researchers can compute effect size indices for noninvariance in AwC to assess to what degree invariance holds and whether AwC results are trustworthy.