稀少和非稀少的潛在類別迴歸模型之適合度檢定

Abstract

潛在類別迴歸( latent class regression ) 模型被廣泛利用在先前的許多文獻裡，這種模型能將多重指標的共同特徵整合成基本的類別變數。這篇論文中我們將提出ㄧ個潛在類別迴歸模型的適合度檢定，此檢定的基礎是由所有可能回答的選項以及相伴變數分群所組成的列聯表，這個概念是由Hosmer與Lemeshow 在邏輯斯迴歸中所提出來的。而當列聯表有稀少情形發生時，我們將用一階和二階邊際來取代並且修正檢定統計量。我們在不同的條件下作模擬，來測試所提出的適合度檢定表現。

Latent class regression (LCR) models have been utilized previously in many literatures. Such models can summarize shared features of the multiple indicators as an underlying categorical variable. In this paper, we propose a goodness-of-fit for the LCR model. The basis of the proposed test is a contingency table, which groups the population through all possible response patterns and concomitant covariates. The idea is from Hosmer-Lemeshow statistic for the multiple logistic regression model. When the contingency table is sparse, we replace it with the first- and second-order marginals and modify the test statistic. A simulation study is carried out to examine the behavior of the proposed goodness-of-fit test under different situations.