Sample Size Planning for Detecting Cross-lag Effects in Longitudinal Studies with Ordinal Outcomes

In this article, we examine the importance of temporal changes in psychological studies by focusing on the usage of multilevel models (MLMs) for analyzing longitudinal data. To address the correlations among longitudinal observations within each individual, researchers commonly include a lagged outcome variable. A lagged outcome variable is a predictor which uses the value from the previous time point of the same outcome variable to predict the value in the current time point through an autoregressive coefficient. This approach allows researchers to capture the potential causal effect of the same variable across time and examine the effect of lagged predictors on the outcome while controlling for the autoregressive effect on the outcome variable. It is crucial to perform sample size planning for MLMs, and power analysis can help determine the necessary sample sizes. However, few studies have investigated sample size planning for MLMs with ordinal data when the ordinal outcomes are correctly specified. Meanwhile, researchers' interest often lies on the cross-lag effect, which refers to the effect of a predictor from the previous time point on the outcome in the next time point. To investigate the effect of different factors on sample size planning, we conducted a simulation study on how various aspects including sample size, the autoregressive effect, and the cross-lag effect can influence power in the multilevel autoregressive model. Additionally, we developed an easy-to-use R package, OrdPower, for researchers using MLM with ordinal outcomes to conduct sample size planning when the cross-lag effect is of interest.