Correct specification of design matrices in linear mixed effects models: tests with graphical representation

Jakob Peterlin, Nataša Kejžar and Rok Blagus ()
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Jakob Peterlin: University of Ljubljana
Nataša Kejžar: University of Ljubljana
Rok Blagus: University of Ljubljana

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 1, No 7, 184-210

Abstract: Abstract Linear mixed effects models (LMMs) are a popular and powerful tool for analysing grouped or repeated observations for numeric outcomes. LMMs consist of a fixed and a random component, which are specified in the model through their respective design matrices. Verifying the correct specification of the two design matrices is important since mis-specifying them can affect the validity and efficiency of the analysis. We show how to use empirical stochastic processes constructed from appropriately ordered and standardized residuals from the model to test whether the design matrices of the fitted LMM are correctly specified. We define two different processes: one can be used to test whether both design matrices are correctly specified, and the other can be used only to test whether the fixed effects design matrix is correctly specified. The proposed empirical stochastic processes are smoothed versions of cumulative sum processes, which have a nice graphical representation in which model mis-specification can easily be observed. The amount of smoothing can be adjusted, which facilitates visual inspection and can potentially increase the power of the tests. We propose a computationally efficient procedure for estimating p-values in which refitting of the LMM is not necessary. Its validity is shown by using theoretical results and a large Monte Carlo simulation study. The proposed methodology could be used with LMMs with multilevel or crossed random effects.

Keywords: Asymptotic convergence; Correlated data; Empirical stochastic processes; Monte Carlo simulations; Sign-flipping; Wild bootstrap; 62J05; 62G09 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-022-00830-1

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