缺失資料對潛在類別迴歸模式參數估計之影響

Parameter Estimates in Latent Class Regression Model with Missing Data

林定香(Ting-Hsiang Lin) ； 藍信龍(Sin-Long Lan)

《中國統計學報》 46卷3期 (2008/09) Pp. 197-212

https://doi.org/10.29973/JCSA.200809.0003

摘要

潛在類別分析(latent class analysis, LCA)在考慮共變數(covariates)的影響後，即形成潛在類別迴歸模式(latent class regression model, LCR)。一般而言，潛在類別迴歸模式的參數估計比潛在類別分析的結果較爲精確，亦即使用潛在類別迴歸模式會得到較小的估計信賴區間。
在潛在類別分析下處理缺失值的問題已有許多相關的研究，然而在潛在類別迴歸模式下處理缺失值問題的文獻並不多；本研究探討樣本數、潛在類別比例、條件機率、主要缺失變數及次要缺失變數缺失值比例對潛在類別迴歸模式參數估計之影響。本文主要比較在單調缺失的資料下，鑑別函數(discriminant function)和羅吉斯迴歸(logistic regression)兩種插補方法的表現，並評估上述因子對參數估計的精準度的影響。
研究結果顯示，當樣本數增加、主要缺失變數的比例較低、潛在類別比例相等時，估計參數會有較精凖的效果，次要缺失變數的缺失比例對估計影響並不顯著。條件機率對潛在類別比例有反向作用，亦即條件機率差異較大時，估計偏誤愈低但對潛在類別比例的估計並無影響。插補方法則對條件機率的比例亦有所影響，鑑別函數插補後的估計偏誤愈高，但插補方法對潛在類別比例並無影響。

關鍵字

缺失資料 ； 潛在類別迴歸模式 ； 鑑别函數 ； 羅吉斯迴歸 ； 插補

並列摘要

Latent class analysis (LCA) can be extended to latent class regression (LCR) model after including the effect of covariates. In general, parameter estimates in latent class regression model is more accurate than latent class analysis due to the covariates, i.e., the parameters are estimated with more precise confidence intervals.
Many studies have discussed various methods to handle missing data in latent class analysis, but there is little research on missing data in latent class regression models. This study examined the effect of sample sizes, latent class proportions, conditional probabilities, missing data rates of major and minor missing variables on parameter estimations. We are particularly interested in monotone missing data, and compared the performance of discriminant function imputation and logistic regression imputation. We also investigated the impact of the factors on the accuracy of parameter estimation under different combinations.
The result showed that with larger sample size, lower missing data rates of the major missing variables, y4, and equal latent class proportions, the parameter estimation are more accurate. The influence of the minor missing variables y3 is not significant. Latent class conditional probability has an inverse effect on parameter estimation, i.e., the larger difference of the conditional probabilities, the smaller the bias. Imputation method has some differential effect on conditional probability, but not on latent class proportions. The bias is higher for discriminant function imputation than logistic regression imputation.

並列關鍵字

Missing data ； latent class regression model ； discriminant function ； logistic regression ； imputation

參考文獻

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