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The Role of Conditional Likelihoods in Latent Variable Modeling.

Anders Skrondal^1,2,3, Sophia Rabe-Hesketh⁴

¹CEFH, Norwegian Institute of Public Health, P.O.Box 222 Skøyen, N-0213 Oslo, Norway. anders.skrondal@fhi.no.

|January 10, 2022

Summary

This summary is machine-generated.

Conditional likelihoods offer solutions for cluster-level endogeneity in psychometrics, addressing issues like unobserved confounding and measurement error to improve estimation accuracy.

Keywords:

Conditional maximum likelihood Endogeneity Fixed effects Heteroskedasticity Informative cluster size Marginal maximum likelihood Measurement error Missing data Random effects Retrospective sampling Unobserved confounding

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Area of Science:

Psychometrics
Statistical Modeling
Measurement Theory

Background:

Conditional likelihoods are traditionally used in the Rasch model for measurement.
Cluster-level endogeneity, where explanatory and latent variables are not independent, poses challenges.
Ignoring these issues can lead to severely inconsistent estimation in psychometric models.

Purpose of the Study:

To explore the broader application of conditional likelihoods in psychometrics beyond traditional measurement models.
To address cluster-level endogeneity problems in various psychometric settings.
To highlight the impact of endogeneity on estimation and propose a robust approach.

Main Methods:

Examination of conditional likelihoods in the context of cluster-level endogeneity.
Identification of diverse settings where cluster-level endogeneity arises.
Analysis of the consequences of ignoring endogeneity in statistical estimation.

Main Results:

Conditional likelihoods can be applied to a wider range of psychometric problems involving endogeneity.
Cluster-level endogeneity manifests in issues such as unobserved confounding, measurement error, and missing data.
Failure to account for endogeneity results in significantly biased parameter estimates.

Conclusions:

Conditional likelihoods provide a valuable framework for handling cluster-level endogeneity in psychometrics.
Recognizing and addressing endogeneity is crucial for valid and reliable statistical inference.
The proposed approach enhances the robustness of psychometric measurement and modeling.