Adjusting for Measurement Noninvariance With Alignment Optimization 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 shift its measurement properties over time, it leads to biased parameter estimates and inferences on the growth parameters. In this paper, we extended the recently-developed alignment optimization (AO) technique to adjust for measurement biases for growth models. The proposed AO method does not require identification of noninvariant items, and it can adjust for measurement biases even when all items are mild to moderately biased. We demonstrate how the proposed method can be implemented in the R statistical language using a textbook example, and conduct a Monte Carlo simulation study to compare its performance with the partial invariance modeling method. The simulation results show that alignment largely reduces biases in growth parameters and gives better 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. Based on the simulation results, we 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. Future research can further explore the potential of AO in other longitudinal models, such as alternative growth shapes and change score models.