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An F -type multiple testing approach for assessing randomness of linear mixed models

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Abstract

In linear mixed models the assessing of the significance of all or a subset of the random effects is often of primary interest. Many techniques have been proposed for this purpose but none of them is completely satisfactory. One of the oldest methods for testing randomness is the F -test but it is often overlooked in modern applications due to poor statistical power and non-applicability in some important situations. In this work a two-step procedure is developed for generalizing an F -test and improving its statistical power. In the first step, by comparing two covariance matrices of a least squares statistics, we obtain a "repeatable" F -type test. In the second step, by changing the projected matrix which defines the least squares statistic we apply the test repeteadly to the same data in order to have a set of correlated statistics analyzed within a multiple testing approach. The resulting test is sufficiently general, easy to compute, with an exact distribution under the null and alternative hypothesis and, perhaps more importantly, with a strong increase of statistical power with respect to the F -test.

Suggested Citation

  • Marco Barnabani, 2019. "An F -type multiple testing approach for assessing randomness of linear mixed models," Econometrics Working Papers Archive 2019_09, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    • Handle: RePEc:fir:econom:wp2019_09
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    File URL: https://labdisia.disia.unifi.it/wp_disia/2019/wp_disia_2019_09.pdf
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    References listed on IDEAS

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    1. Garrett M. Fitzmaurice & Stuart R. Lipsitz & Joseph G. Ibrahim, 2007. "A Note on Permutation Tests for Variance Components in Multilevel Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 63(3), pages 942-946, September.
    2. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    3. Hunt, Daniel L. & Cheng, Cheng & Pounds, Stanley, 2009. "The beta-binomial distribution for estimating the number of false rejections in microarray gene expression studies," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1688-1700, March.
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    More about this item

    Keywords

    Linear Mixed Models; Hypothesis testing; Comparison of matrices; F-distribution; Beta binomial distribution.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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