Measuring Change in Latent Subgroups Using Dichotomous Data: Unconditional, Conditional, and Semiparametric Maximum Likelihood Estimation
研究了用混合线性逻辑模型分析二分数据中治疗引起的子群变化，比较了三种最大似然估计方法，发现半参数法在参数偏差和检测变化类型数量方面表现更优。
Abstract 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.