Vijayaragunathan R, John Kishore K, Srinivasan M R
Department of Statistics, Indira Gandhi College of Arts and Science, Puducherry, India.
Department of Foreign Trade, Indira Gandhi College of Arts and Science, Puducherry, India.
Indian J Community Med. 2023 Sep-Oct;48(5):659-665. doi: 10.4103/ijcm.ijcm_119_22. Epub 2023 Sep 7.
In this article, we attempt to demonstrate the superiority of the Bayesian approach over the frequentist approaches of the multiple linear regression model in identifying the influencing factors for the response variable.
A survey was conducted among the 310 respondents from the Kathirkamam area in Puducherry. We have considered the response variable, body mass index (BMI), and the predictors such as age, weight, gender, nature of the job, and marital status of individuals were collected with the personal interview method. Jeffreys's Amazing Statistics Program (JASP) software was used to analyze the dataset. In the conventional multiple linear regression model, the single value of regression coefficients is determined, while in the Bayesian linear regression model, the regression coefficient of each predictor follows a specific posterior distribution. Furthermore, it would be most useful to identify the best models from the list of possible models with posterior probability values. An inclusion probability for all the predictors will give a superior idea of whether the predictors are included in the model with probability.
The Bayesian framework offers a wide range of results for the regression coefficients instead of the single value of regression coefficients in the frequentist test. Such advantages of the Bayesian approach will catapult the quality of investigation outputs by giving more reliability to solutions of scientific problems.
在本文中，我们试图证明贝叶斯方法在识别响应变量的影响因素方面优于多元线性回归模型的频率主义方法。
对来自本地治里卡特希卡马姆地区的310名受访者进行了一项调查。我们将身体质量指数（BMI）作为响应变量，并通过个人访谈的方式收集了年龄、体重、性别、工作性质和个人婚姻状况等预测变量。使用杰弗里斯神奇统计程序（JASP）软件对数据集进行分析。在传统的多元线性回归模型中，确定回归系数的单一值，而在贝叶斯线性回归模型中，每个预测变量的回归系数遵循特定的后验分布。此外，从具有后验概率值的可能模型列表中识别最佳模型将非常有用。所有预测变量的包含概率将更清楚地表明这些预测变量是否以概率形式包含在模型中。
贝叶斯框架为回归系数提供了广泛的结果，而不是频率主义检验中的回归系数单一值。贝叶斯方法的这些优势将通过提高科学问题解决方案的可靠性来提升调查结果的质量。
