Hello, I am doing a 4-way, full factorial ANOVA with one repeated measures factor (time, 3 samplings) and three between-subject factors (species, color, and irrigation; 2 levels of each) using the Mixed Model personality in JMP Pro 18.1.0. I'm using the AR(1) repeated covariance structure, as it provides the best fit based on AICc values. The analysis indicates I have no significant 4- or 3-way interactions, but multiple 2-way interactions (see below).
To investigate the 2-way interactions, I would like to, for example, do a Tukey's means separation for time period at each level of species and t-test for species at each time period. However, I'm not interested in all pairwise comparisons in the species x time period interaction (i.e., comparing species 1 at time 1 to species 2 at time 3 is not meaningful), and I would like to avoid diluting my statistical power if possible. The User-Defined Estimates won't work in this scenario because it requires the user to select at least one level of each factor, including those not in the interaction of interest. If I'm investigating the species x time period interaction, values should be averaged across all levels of color and irrigation. Essentially, I want to test slices, but that doesn't seem to be an option in the Mixed Model output, and I cannot analyze these data in the Standard Least Squares personality because I'm using the AR(1) structure for the repeated measures. Do you have any advice on analyzing the simple effects in this scenario?
