Evaluating the Impact of Model Misspecification on Statistical Inference and Predictive Model Performance

Posted: Jan 21, 2010

• Levi Johnson
• Grace Campbell
• Jack Taylor

Abstract

Model specification stands as a foundational element in statistical practice, serving as the bridge between theoretical constructs and empirical reality. The assumption of correct model specification underpins virtually all statistical inference procedures, from parameter estimation to hypothesis testing and prediction interval construction. However, in practical applications, researchers frequently operate under conditions of model misspecification, where the chosen statistical model fails to fully capture the true data-generating process. This research addresses the critical gap in understanding how various forms of misspecification simultaneously impact both inferential validity and predictive accuracy, two domains often treated separately in existing literature. Traditional approaches to model misspecification have typically focused on specific types of specification errors in isolation, such as omitted variable bias in linear regression or distributional misspecification in generalized linear models. While these focused investigations have yielded valuable insights, they fail to capture the complex reality that multiple specification errors often coexist in empirical research. Our study introduces a comprehensive framework that examines the joint effects of functional form, distributional, dependency structure, and measurement specification errors across different modeling contexts. We pose three fundamental research questions that have received limited attention in the statistical literature. First, how do different types of model misspecification interact to produce compound effects on statistical inference that differ from their individual impacts? Second, to what extent do conventional diagnostic tools reliably detect complex misspecification patterns, and what alternative approaches might offer improved detection capabilities? Third, how does the