順序尺度依變數與自變數估計方法的再檢視

Abstract

實證研究者通常將順序尺度的依變數和自變數視為數值資料或名目尺度資料進行分析，然而這些處理方式分別高估和低估了資料所包含的資訊，因此在理論和實務上都存在一些缺陷。本研究探討順序尺度資料的分析方法，並嘗試在貝氏統計方法框架下探索更適合處理順序尺度資料的統計方法，包括累積probit模型和順序尺度自變數的單調性處理，以確保模型反映出依變數與自變數的順序尺度特性。 本研究使用「臺灣農村社會文化調查計畫分項一：人口、社會與經濟調查計畫」於2019年收集之調查資料，該調查共完成3,321份農村居民問卷調查。以順序尺度的「生活滿意程度」作為依變數，示範統計建模中切點、係數等參數的先驗分配設定，將順序尺度的自變數「家庭經濟狀況」作單調性處理，並透過模型的配適結果探討自變數對於生活滿意程度的影響。本研究透過套件brms計算不同順序尺度自變數資料處理方法下累積probit模型的配適結果，並以捨一交叉確認法比較了不同模型的適合度。 本文最後提供順序尺度依變數與順序尺度自變數在統計建模與資料處理上的建議，以及實際應用上模型比較的判斷依據。本研究還提供了使用R語言進行分析的程式碼，以便其他研究者能夠重現本文的結果，或在根據需求調整後應用於相關研究。

Researchers in empirical studies often interpret ordinal dependent and independent variables as either metric or nominal data. However, these methods are susceptible to both overestimating and underestimating the information inherent in the data, resulting in certain theoretical and practical constraints. The current study examined methods appropriate for the analysis of ordinal data and attempts to search statistical models better suited for handling ordinal data within a Bayesian framework. In line with this, I employed cumulative probit models and incorporated monotonic effects for ordinal independent variables to precisely capture the ordinal characteristics of both dependent and independent variables. This study utilized data from “A Social and Cultural Survey of Rural Taiwan: Sub-project ‘Population, Society and Economy Survey’ (2019)”, consisting of 3,321 rural residents. The dependent variables, life satisfaction, was measured on an ordinal scale to demonstrate the setting of prior distributions for cutpoints, coefficients, and other parameters in statistical modeling. The ordinal independent variable, family economic status, undergoes monotonicity treatment, and the fitted results of the model are used to explore the impact of independent variables on life satisfaction. The brms package in R is employed to compute the fitted results of the cumulative probit model under different data processing methods for ordinal independent variables, and model comparison is conducted using leave-one-out cross-validation. In the conclusion section, this study proposes recommendations for the statistical modeling and data processing of ordinal dependent and independent variables. It also establishes criteria for model comparison in practical applications. Furthermore, the study includes R code for analysis, allowing fellow researchers to replicate the results or modify them for similar studies according to their specific requirements.