Penalized KLIC Model Selection for the Generalized Method of Moments in Longitudinal Data with Time-Dependent Covariates

TL;DR

This paper introduces two penalized KLIC criteria for improved model selection in GMM-based longitudinal data analysis with time-dependent covariates, addressing overfitting issues.

Contribution

It proposes theoretically motivated penalized KLIC criteria that better balance model fit and complexity, enhancing model selection accuracy in longitudinal GMM models.

Findings

Proposed criteria outperform traditional KLIC in simulations.

Penalized criteria reduce over-parameterization.

Method identifies key predictors reliably.

Abstract

Model selection plays an important role in longitudinal data analysis, especially when models are estimated using the generalized method of moments (GMM) in the presence of time-dependent covariates. In this setting, the number of valid moment conditions can grow quickly and may lead to over-parameterized models. The Kullback--Leibler Information Criterion (KLIC) has been proposed as a model-selection tool for this framework; however, the original KLIC criterion may favor overly complex models when the number of parameters or valid moment conditions increases. To address this limitation, this study proposes two penalized versions of KLIC that incorporate penalties based on both the number of model parameters and the number of valid moment conditions. The proposed criteria are referred to as the Moment--Parameter Product Penalty KLIC (MPPP--KLIC) and the Logarithmic Penalty KLIC (LP--KLIC). These criteria provide a theoretically motivated mechanism for balancing model fit and model complexity in GMM-based longitudinal models. Through an extensive simulation study involving both binary and continuous response settings, the proposed criteria are shown to improve the ability of KLIC to distinguish among competing models and to reduce the selection of over-parameterized models. The performance of the proposed methods is further illustrated using the Filipino Child Morbidity dataset, a longitudinal study of child health in the Philippines. The results show that the proposed penalized criteria provide stable and interpretable model rankings and consistently identify age as the most important predictor of child morbidity. Overall, the proposed penalized KLIC criteria offer practical and theoretically grounded tools for model selection in GMM-based longitudinal data analysis with time-dependent covariates.