| The current research in educational psychology often involves high-dimensional datasets,which contain many variables,some of which may be irrelevant to the research question.Variable selection can effectively remove irrelevant redundant variables and ensure the accuracy of model parameter estimation and testing.In some cases,empirical studies may encounter low statistical power due to small sample sizes or small effect sizes.On the other hand,exploring a large number of candidate variables may lead to the multiplicity problem,where the selected model tends to include more variables as the number of candidate variables increases.To address these issues,this study conducted research on objective Bayesian one-sided variable selection methods in regression and factor analysis models.One-sided variable selection methods predefine the direction of the variables’ effects in the candidate model,similar to one-sided hypothesis testing.One-sided variable selection can improve statistical power and has been applied to variable selection under the frequency statistics framework.In this study,based on the data information,we set an objective one-sided model variable direction in the regression and factor analysis models and used Bayesian methods to evaluate the degree of support for the one-sided candidate model by the data,addressing the issue of low statistical power in small sample sizes or small effect sizes.The core indicator of Bayesian variable selection methods is the posterior model probability,which selects the model with the maximum posterior probability.The posterior model probability consists of the Bayesian factor and the model’s prior probability.To obtain the correct and feasible Bayesian factor expression,reasonable parameter prior distributions need to be set.In this study,g-prior and fractional prior distributions were used as the parameter prior distributions for regression and factor analysis models,respectively,and the Spike-andSlab prior setting method was used to control the model’s complexity.In addition,when there are many candidate variables,this study discusses using an empirical Bayesian method to set the model’s prior probability,effectively avoiding the multiplicity problem caused by too many variables.To verify the effectiveness of the method,this study set up a simulation study to explore the performance of objective one-sided Bayesian variable selection methods for regression and factor analysis models under different effect sizes and sample sizes,as well as the performance of empirical Bayesian methods for different numbers of variables.Finally,this study demonstrated the practical application of the method through empirical data analysis.This study concludes that(1)In cases where sample size and effect size are relatively small,compared with traditional Bayesian variable selection methods,onesided Bayesian variable selection improves the probability of correctly selecting variables and the true model.(2)Using the empirical Bayesian method to adjust the model’s prior probability can effectively control the problem of multiple testing,but when there are few candidate variables,the empirical Bayesian method may lead to the selection of too many incorrect variables.(3)Although the one-sided method increases the probability of incorrectly selecting redundant variables,it still improves the probability of correctly selecting the model compared with traditional methods when the sample size is small.The innovation of this study lies in that we define the direction of variable effects based on data information and propose a completely objective Bayesian one-sided variable selection method.This method enhances the statistical power in small samples even when prior information is lacking,providing a new method for variable selection in educational psychology research.In addition,this study successfully applies the empirical Bayesian method to control the problem of multiple testing in one-sided variable selection,which is an area where previous research has been lacking.Finally,this study extends the Bayesian one-sided variable selection method to factor analysis models,which also has theoretical significance and practical value. |
