Generating a combined analysis using linear mixed models to account for pre-history effects when a treatment factor comprises fixed and random levels

Abstract

Abstract Experimental designs involving factors with a mix of fixed and random levels have been explored by few. These designs are useful when comparing a set of new treatments (fixed levels) to a population of established treatments (random levels). This approach enables partitioning variability and testing of both fixed and random effects, leading to improved estimates and more reliable inference. However, combining analyses of variance from partitioned data poses challenges, including data rearrangement, methodology, and coding complexities. Existing statistical software does not directly support combined analyses for such designs. The current study provides guidelines for conducting combined analysis of variance in linear mixed-effects models where factors have both fixed and random levels. The approach utilises SAS PROC GLIMMIX and tools from the Comprehensive R Archive Network to compile the combined analysis of variance, followed by multiple comparisons of treatment means. The procedure is demonstrated using treatment structures in a completely randomised design, split-split-plot design, and repeated-measures design. The method can be extended to other experimental designs. This framework addresses a critical gap in existing literature by providing a practical and readily applicable analytical tool that enables integrated analysis across all factor levels within a single linear mixed-model structure, while accounting for pre-history effects associated with prior management practices in complex experimental systems.