Investigation of Parameter Estimation Accuracy for Growth Curve Modeling With Categorical Indicators: Impact of Number of Measurement Occasions and Number of Categories

Growth curve modeling (GCM) is an important and commonly used methodology in the social sciences for examining change over time in a variable value. While much of the empirical research examining the performance of various estimators under a variety of conditions has focused on continuous (and typically normally distributed) observed indicators, in practice researchers frequently make use of categorical indicators with anywhere from two to as many as seven categories. Given the popularity of GCMs, along with the frequent use of categorical indicators, and the relative dearth of simulation research focusing on estimation of these models with such variables, the current study focused on the issue of parameter estimation accuracy as related to the number of categorical indicators, and the number of categories per indicator. Results of this research found that for models with only a linear component, parameter estimation was very accurate for as few as four indicators with two categories each and a sample size of 200. On the other hand, when the underlying model included both linear and quadratic terms, parameter estimation accuracy suffered for a small number of dichotomous indicators unless the sample size was 1,000 or more. However, with six or more indicator variables, and/or at least three categories, parameter estimation accuracy remained high.