Impact of Negative Variance Component Estimates on the Kenward-Roger Test for Fixed Effects in Linear Mixed Models | ||||
| The Egyptian Statistical Journal | ||||
| Article 1, Volume 67, Issue 1, June 2023, Page 1-18 PDF (1.23 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.2023.187978.1010 | ||||
 View on SCiNiTO | ||||
| Author | ||||
Waseem Alnosaier  
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| Department of Statistics, Institute of Public Administration. | ||||
| Abstract | ||||
| A well-known procedure to make inference for fixed effects in a normal mixed linear model is the Kenward-Roger procedure (Kenward and Roger 1997), where a scaled Wald type statistic follows approximately an F distribution, and in special cases the test has an exact F test. In the procedure, the estimated denominator degrees of freedom of the F distribution, the estimated scale factor, and the scaled test statistic are calculated based on the data. The variance components of the random terms in the model are estimated by the restricted maximum likelihood (REML) method, in which sometimes the estimates produced are negative. Two methods are usually considered to resolve the issue of negative variance component estimates: to set the negative estimates as zero or to allow them remain negative. Assessing the performance of the procedure with each method based on the test level and power was done analytically and by a simulation study for four different designs. The estimates of the denominator degrees of freedom and scale factor were also calculated and compared for the procedure with each method. We showed that the Kenward-Roger procedure with the method that doesn’t constrain the variance component estimates to be non-negative was instable for some data sets with negative variance component estimates, and was excessively conservative for some designs. By setting the negative variance component estimates as zero, the procedure became stable and more adequate than with allowing the estimates remain negative for the designs considered in the simulation study. | ||||
| Keywords | ||||
| Variance components; Mixed Linear Model; Kenward Roger test; Restricted maximum likelihood estimator; Linear hypothesis | ||||
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