零膨脹次數資料分析在R程式的應用

Zero-infl ated Data Analysis in R

本文旨在介紹零膨脹次數資料分析在R程式上的應用。次數資料伴隨著大量零的數據型態在社會科學及教育領域中相當常見，卻鮮少被正確地分析。我們首先概述常見的次數資料迴歸模型，其次介紹零膨脹次數資料的迴歸模型以及模型選擇的檢定方式，最後，我們使用2016年National Survey on Drug Use and Health（NSDUH）資料庫中8,931位受測者在過去一年中因為情緒、緊張或心理健康方面的理由而缺席工作的天數為例，介紹如何在R程式執行卜瓦松迴歸模型、負二項迴歸模型、零膨脹卜瓦松迴歸模型及零膨脹負二項迴歸模型的分析，並提供模型選擇及案例結果的解釋方式，以供有興趣的讀者參考。

The purpose of this paper is to introduce how count data with excessive zeros can be analyzed using R. Count data with excessive zeros is commonly seen in education research but is not regularly taught in classes. We first introduce Poisson regression and negative binomial regression, followed by zero-inflated Poisson and zero-inflated negative binomial models. Likelihood ratio tests and the Vuong test were introduced for model selection. The analyses were demonstrated using 8931 participants from 2016 National Survey on Drug Use and Health (NSDUH). The outcome variable was the number of days missed due to emotion, nervousness, and mental health, and it was analyzed using Poisson regression, negative binomial regression, zero-inflated Poisson regression, and zero-inflated negative binomial regression. The analyses were conducted using R. The R code and the interpretation of the outcome are provided in the paper.