潛在類別迴歸模型之適合度檢定

Abstract

生物醫學以及社會心理方面的研究近來越來越常使用潛在類別迴歸(latent class regression)模型來分析多重類別資料與有興趣的共變數之間的關係。在潛在類別迴歸模型中多重類別資料會被整合摘要，而與風險因子之間的關係也會藉由模型中的線性迴歸方法整理出來。這些模型較於精簡並且能夠將多重類別資料的一些分析方法的理論基礎整合起來，然而這些優點卻是伴隨著一些很強的模型假設而來，這些假設有可能會對分析結果造成嚴重的影響，因此評估這些模型是否很適當的被使用是必須的。這篇論文中我們將簡介應用在logistic regression中Hosmer與Lemeshow提出的統計量並且將之延伸到潛在類別迴歸模型之中來做適合度檢定。

Biomedical and psychosocial researchers increasingly utilize latent class regression (LCR) models to analyze relationships between measured multiple categorical outcomes and covariates of interest. In LCR, the multiple outcomes are summarized and their associations with risk factors are determined in a single modeling step. These models are parsimonious and can incorporate theory underlying the multiple response choices. However, these advantages come at the price of strong modeling assumptions which may critically influence analytic findings. Careful evaluation of model appropriateness is necessary. In this thesis, we first introduced Hosmer-Lemeshow statistic for multiple logistic regression model and then extended the method to LCR model to assess overall fit of the LCR model. An analysis of how measured health impairments affect older persons' functioning is used for illustration.

KEY WORDS: categorical data; goodness-of-fit test; latent class regression; chi-square distribution.