插補缺失伴隨變數之比例勝算比模型參數估計

在醫學及社會科學的調查研究上，在收集資料時經常遭遇一些變數之資料有部份缺失的情況，本文將在反應變數為順序尺度下，探討有部份伴隨變數缺失時，比例勝算比模型的參數估計。我們使用Wang and Chen（2009）提供條件經驗分配來生成插補缺失之變數，並提供兩種多重插補之參數估計方法。一種是用Rubin（1987）提出一次插補代入原估計方程式求解，反覆多次再求平均值法求得參數估計。另外，我們也提供多次插補值代入估計函數求其平均後，再求解以獲得參數的估計。文中將用統計模擬來比較此兩種多重插補法的估計表現，並與Hsieh et al.（2011）所提出確認條件估計法比較。最後以99年彰化縣民眾對腎臟病認知的問卷調查結果，調查受訪者其對男性、女性腰圍的認知做為實例，以比較各種估計方法的表現。

關鍵字

比例勝算比模型；多重插補法；隨機化缺失；完整資料分析法；確認條件估計

並列摘要

Missing data routinely occur in medical or social science studies, and need to be appropriately dealt with in regression analysis. We consider the estimation problem of a proportional odds model for an ordinal response variable with covariates missing at random, and present two multiple imputation methods using the empirical likelihood idea of Wang and Chen (2009). The first method is built upon Rubin (1987)'s imputation method and uses non-parametric conditional distribution techniques to non-parametrically impute the missing covariate data. This method imputes the missing covariate data several times to generate many imputed data sets. Also, it estimates the parameter of interest by the average of the estimates obtained from standard estimation methods using the imputed data sets. The second imputation method uses similar techniques, but directly imputes the missing values of the estimating score function rather than the covariate values. The performances of the two methods are compared through a simulation study. Moreover, both methods are illustrated using real data arising from a cognitive investigation of a kidney disease in Changhua county, Taiwan in 2010.

並列關鍵字

conditional estimation method ； missing at random ； ordinal categorical data ； proportional odds model

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插補缺失伴隨變數之比例勝算比模型參數估計

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