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.

中文翻译：

---

具有分类指标的增长曲线建模参数估计精度的研究

增长曲线建模（GCM）是社会科学中一种重要且常用的方法，用于检查可变值随时间的变化。尽管在各种条件下检查各种估计量的绩效的许多实证研究都集中在连续（通常呈正态分布）的观测指标上，但实际上，研究人员经常使用分类指标，范围从两个到多达七个类别。鉴于GCM的普及，分类指标的频繁使用以及相对缺乏针对这类变量的模型估计的仿真研究，当前的研究重点是与分类数量相关的参数估计精度问题。指标，以及每个指标的类别数。这项研究的结果发现，对于仅具有线性成分的模型，参数估计非常准确，仅需四个指标，每个指标有两个类别，样本量为200。另一方面，当基础模型同时包含线性和二次方时术语，除非样本大小为1,000或更大，否则少数二分指标会影响参数估计的准确性。但是，在具有六个或更多指标变量和/或至少三个类别的情况下，参数估计精度仍然很高。除非样本大小为1,000或更大，否则少数二分指标会影响参数估计的准确性。然而，在具有六个或更多指示符变量和/或至少三个类别的情况下，参数估计精度仍然很高。除非样本大小为1,000或更大，否则少数二分指标会影响参数估计的准确性。然而，在具有六个或更多指示符变量和/或至少三个类别的情况下，参数估计精度仍然很高。