How does academic performance affect self-efficacy? Interpretable modelling through latent academic achievement

2026-07-01

AI Summary

This study investigates the mechanism through which academic performance—an ordinal variable—influences self-efficacy, a continuous outcome. To this end, the authors propose a conditional Bayesian modeling framework that introduces a latent academic achievement variable and integrates Gaussian copula regression with Bayesian variable selection to identify key covariates specific to each outcome type. Methodologically, they develop a tailored partially collapsed Gibbs sampler that substantially enhances computational efficiency in estimating integrated regression coefficients and improves the accuracy of variable selection. Simulation studies demonstrate that the proposed approach markedly outperforms existing joint modeling strategies in both sampling efficiency and variable selection performance. Application to data from the Longitudinal Study of Australian Children reveals distinct association pathways between academic achievement and self-efficacy, along with markedly different covariate structures for the two outcomes.

Abstract

There is increasing evidence of a directional relationship from academic performance to self-efficacy. We develop a Bayesian model for investigating this relationship when academic performance is measured on an ordinal scale and self-efficacy on a continuous scale. The model allows latent academic achievement to enter the self-efficacy regression as a predictor, while Bayesian variable selection identifies factors associated with either response. The resulting conditional formulation yields an interpretable regression characterisation of how latent academic achievement relates to self-efficacy. Furthermore, it enables a tailored partially collapsed Gibbs sampler that analytically integrates out the regression coefficients when updating the variable inclusion indicators. Simulation studies demonstrate that the proposed conditional formulation and tailored sampler improve sampling efficiency and variable-selection performance relative to a recent, more general joint Gaussian copula regression formulation. We apply the methodology to data from the longitudinal study of Australian children, a landmark national cohort study covering children's education, social and emotional wellbeing, health and family circumstances. The model and analysis shed light on how latent academic achievement relates to self-efficacy in Australian children, and reveal that the two outcomes differ markedly in the range of covariates associated with each outcome.

Problem

• academic performance
• self-efficacy
• latent academic achievement
• ordinal scale
• continuous scale

Innovation

• Bayesian variable selection
• latent academic achievement
• partially collapsed Gibbs sampler
• interpretable regression
• ordinal-continuous modeling