Abstract
Generalized Information Matrix Tests (GIMTs) have recently been used for detecting the presence of misspecification in regression models in both randomized controlled trials and observational studies. In this paper, a unified GIMT framework is developed for the purpose of identifying, classifying, and deriving novel model misspecification tests for finite-dimensional smooth probability models. These GIMTs include previously published as well as newly developed information matrix tests. To illustrate the application of the GIMT framework, we derived and assessed the performance of new GIMTs for binary logistic regression. Although all GIMTs exhibited good level and power performance for the larger sample sizes, GIMT statistics with fewer degrees of freedom and derived using log-likelihood third derivatives exhibited improved level and power performance.
Highlights
If a researcher’s probability model of the observed data is not correctly specified, the interpretation of its parameter estimates may not be valid, leading to incomplete or incorrect conclusions
This paper provides a unified framework for addressing the detection of model misspecification using a variety of Generalized Information Matrix Tests (GIMTs) statistics for a large class of finite-dimensional smooth probability models
We provide formulas for a variety of different types of non-directional GIMT covariance matrix estimators
Summary
If a researcher’s probability model of the observed data is not correctly specified, the interpretation of its parameter estimates may not be valid, leading to incomplete or incorrect conclusions. Whether a model is correctly specified must be considered when analyzing and interpreting data (e.g., [1,2]). This issue is critically important in econometrics as well as more general scientific inquiry. Model misspecification testing is essential for statistical analysis of randomized control trials [7,8] and observational studies [9,10]. For these reasons, this paper introduces a unified framework for identifying, classifying, and developing a wide range of specification tests
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