Concomitant-Variable Latent-Class Models
提出一种新的潜在类别模型，其中类别成员概率与已知分布的伴随变量函数相关，可用于更简洁地表示数据或处理参数过多问题，并用算术测试数据演示模型拟合与比较。
Abstract This article introduces and illustrates a new type of latent-class model in which the probability of latent-class membership is functionally related to concomitant variables with known distribution. The function (or so-called submodel) may be logistic, exponential, or another suitable form. Concomitant-variable models supplement latent-class models incorporating grouping by providing more parsimonious representations of data for some cases. Also, concomitant-variable models are useful when grouping models involve a greater number of parameters than can be meaningfully fit to existing data sets. Although parameter estimates may be calculated using standard iterative procedures such as the Newton—Raphson method, sample analyses presented here employ a derivative-free approach known as the simplex method. A general procedure for imposing linear constraints on the parameter estimates is introduced. A data set involving arithmetic test items in a mastery testing context is used to illustrate fitting and comparison of concomitant-variable models.