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%% ANOVA for Fixed-Effects in LME Model %% % Load the sample data. load(fullfile(matlabroot,'examples','stats','fertilizer.mat')) %% % The dataset array includes data from a split-plot experiment, where soil % is divided into three blocks based on the soil type: sandy, silty, and % loamy. Each block is divided into five plots, where five types of tomato % plants (cherry, heirloom, grape, vine, and plum) are randomly assigned % to these plots. The tomato plants in the plots are then divided into subplots, % where each subplot is treated by one of four fertilizers. This is simulated % data. %% % Store the data in a dataset array called |ds|, for practical purposes, % and define |Tomato|, |Soil|, and |Fertilizer| as categorical variables. ds = fertilizer; ds.Tomato = nominal(ds.Tomato); ds.Soil = nominal(ds.Soil); ds.Fertilizer = nominal(ds.Fertilizer); %% % Fit a linear mixed-effects model, where |Fertilizer| and |Tomato| are % the fixed-effects variables, and the mean yield varies by the block (soil % type) and the plots within blocks (tomato types within soil types) independently. % Use the |'effects'| contrasts when fitting the data for the type III sum % of squares. lme = fitlme(ds,'Yield ~ Fertilizer * Tomato + (1|Soil) + (1|Soil:Tomato)',... 'DummyVarCoding','effects') %% % Perform an analysis of variance to test for the fixed-effects. anova(lme) %% % The $p$-value for the constant term, 5.9086e-30, is the same as in the % coefficient table in the |lme| display. The $p$-values of 0.00018935, % 1.0024e-14, and 0.19804 for |Tomato|, |Fertilizer|, and |Tomato:Fertilizer| % represent the combined significance for all tomato coefficients, fertilizer % coefficients, and coefficients representing the interaction between the % tomato and fertilizer, respectively. The $p$-value of 0.19804 indicates % that the interaction between tomato and fertilizer is not significant.