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Testing fixed and random effects in linear mixed models

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Abstract

In linear mixed models the selection of fixed and random effects using a testing hypothesis approach brings up several problems. In this paper, we consider the so called boundary problem and the confounding impact of effects from one set of coefficient in the other set. These problems are addressed by defining two test statistics based on ordinary least squares obtained by dividing two quadratic forms, one that contains the effect and another that does not. As a result, the test statistics are sufficiently general, easy to compute, with known finite sample properties. The test on randomness has a known exact distribution under the null and alternative hypothesis, the test on fixed effect is approximated by a noncentral F -distribution. Because of its importance in the selection variable approach, the goodness-of-approximation is examined in-depth in final simulations.

Suggested Citation

  • Marco Barnabani, 2020. "Testing fixed and random effects in linear mixed models," Econometrics Working Papers Archive 2020_09, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    • Handle: RePEc:fir:econom:wp2020_09
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    File URL: https://labdisia.disia.unifi.it/wp_disia/2020/wp_disia_2020_09.pdf
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    More about this item

    Keywords

    Selection procedure; Hypothesis testing; Linear Mixed Models; Generalized F -distribution;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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