Measuring Change in Latent Subgroups Using Dichotomous Data: Unconditional, Conditional, and Semiparametric Maximum Likelihood Estimation
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用二元数据测量潜在子群变化：无条件、条件与半参数极大似然估计
- 研究问题
- 二元响应数据中，如何识别不可直接观测、对处理反应不同的个体类型，并比较潜在变化类型模型的估计与检验方法？
- 方法与思路
- 作者将放宽假设的线性 Logistic 模型扩展为混合模型，用不同个体异质性的模拟比较无条件、条件与半参数似然方法。
- 材料陈述的贡献
- 摘要称模拟中半参数方法较受推荐，常规拟合检验对错设潜类数不敏感，而 BCVL 准则在部分估计方法下作出正确判断。
- 阅读关注点
- 应核对个体附带参数、混合类型的识别、异质性设置及潜类数选择，并区分估计偏差、拟合检验功效和分类决策表现。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要，不能推断刊本变化；模拟结果依赖所设模型与样本量，处理反应建模本身不足以确认因果识别。
原文摘要
Changes in dichotomous data caused by treatments can be analyzed by means of the so-called linear logistic model with relaxed assumptions (LLRA). In contrast to models of the Rasch type, the LLRA allows incidental multidimensional parameters describing the response behavior of the subjects so that each observable criterion used for assessing the changes is governed by its own subject parameter. Because generalizability of the treatment effects over subjects and criteria is scientifically desirable, statistical tests for this desideratum play an important role in practical situations. Whereas generalizability over the criteria can easily be tested, generalizability over subjects can be tested only by stratifying the sample according to some further observable subject variables. However, one cannot be sure to detect nongeneralizability over the subjects by this method with certainty. Therefore, the mixture LLRA is proposed that allows directly unobservable types of subjects reacting differently on the treatments. Three maximum likelihood (ML) methods for estimating the parameters of this mixture model are investigated (unconditional ML, partial- and full-information conditional ML, and semiparametric ML) with respect to some properties of their parameter estimates and their power against falsely specified number of latent change-types using simulated data sets of varying heterogeneity of the subject parameters. Because the unconditional ML method gives estimates that become the more biased the more the subjects are heterogeneous, and the conditional ML estimates always seem to be slightly biased, the semiparametric ML method, even if somewhat harder to apply, is favored. For all three methods, the usual goodness-of-fit tests contrasting the respective model to the unconstrained multinomial have shown to be insensitive against falsely specified number of change-types for the sample size being equal to 500. Contrary to this, even then the BCVL criterion (i.e., posterior probabilities for the numbers of change-types) resulted in correct decisions for the unconditional and semiparametric ML methods.