Score limitation at the top of a scale is commonly termed “ceiling effect.” Ceiling effects can lead to serious artifactual parameter estimates in most data analysis. This study examines the consequences of ceiling effects in longitudinal data analysis and investigates several methods of dealing with ceiling effects through Monte Carlo simulations and empirical data analyses. Data were simulated based on a latent growth curve model with T = 5 occasions. The proportion of the ceiling data [10%–40%] was manipulated by using different thresholds, and estimated parameters were examined for R = 500 replications. The results showed that ceiling effects led to incorrect model selection and biased parameter estimation (shape of the curve and magnitude of the changes) when regular growth curve models were applied. The Tobit growth curve model, instead, performed very well in dealing with ceiling effects in longitudinal data analysis. The Tobit growth curve model was then applied in an empirical cognitive aging study and the results were discussed.

Cronbach’s coefficient alpha is a widely used reliability measure in social, behavioral, and education sciences. It is reported in nearly every study that involves measuring a construct through multiple items. With non-tau-equivalent items, McDonald’s omega has been used as a popular alternative to alpha in the literature. Traditional estimation methods for alpha and omega often implicitly assume that data are complete and normally distributed. This study proposes robust procedures to estimate both alpha and omega as well as corresponding standard errors and confidence intervals from samples that may contain potential outlying observations and missing values. The influence of outlying observations and missing data on the estimates of alpha and omega is investigated through two simulation studies. Results show that the newly developed robust method yields substantially improved alpha and omega estimates as well as better coverage rates of confidence intervals than the conventional nonrobust method. An R package coefficientalpha is developed and demonstrated to obtain robust estimates of alpha and omega.

Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data from the National Longitudinal Survey of Youth. This step-by-step example illustrates how to analyze data using both noninformative and informative priors. The results show that in addition to being an alternative to the maximum likelihood estimation (MLE) method, Bayesian methods also have unique strengths, such as the systematic incorporation of prior information from previous studies. These methods are more plausible ways to analyze small sample data compared with the MLE method.