Should we rely on the Kenward-Roger approximation when using linear mixed models if the groups have different...

Area of Science:

• Statistics
• Statistical Modeling
• Experimental Design

Background:

• Linear mixed models are widely used for analyzing repeated-measures data.
• Split-plot designs are common in various research fields.
• The Kenward-Roger (KR) procedure is a method for analyzing such data, but its robustness to assumption violations is crucial.

Purpose of the Study:

• To evaluate the robustness of the Kenward-Roger (KR) procedure in linear mixed models for split-plot designs.
• To investigate the impact of normality and sphericity violations, specifically skewness and kurtosis, on KR procedure performance.
• To examine the influence of varying group distributions and small sample sizes on the procedure's reliability.

Main Methods:

• A Monte Carlo simulation study was employed.
• The study utilized a split-plot design with three between-subjects and four within-subjects factor levels.
• Simulations focused on varying levels of skewness and kurtosis in group distributions.

Main Results:

• The violation of sphericity assumption did not impact KR robustness when normality was violated.
• KR procedure robustness decreased with increased data skewness; kurtosis had a minor effect.
• The interaction between kurtosis and group size was significant, particularly with positive pairing.

Conclusions:

• The Kenward-Roger (KR) procedure is a viable option for analyzing repeated-measures data in split-plot designs with differing group distributions.
• Robustness is maintained with total sample sizes of 45 or more and minimal to moderate skewness.
• Researchers should consider the interplay between kurtosis and group size when applying the KR procedure.