dependent variable: 'direction' has three levels: morning, noon, night. There is no reference level for 'direction' > table(indvar_FODs_new$direction) morning noon night 1683 1432 206 fixed factor/independent variable: 'Cond' has four levels: Ay, Bi, Ci, Di. There is no reference level for 'Cond' > table(indvar_FODs$Cond) Ay Bi Ci Di 880 880 880 880 random factor: 'colours' has two levels: blue and pink. > table(indvar_FODs_new$colours) blue pink 2720 800 data is categorical data I want to statistically test if 'Cond' and 'colours', and the interaction effect between 'Cond' and 'colours' has an effect on the 'direction'.

#randomised factorial design
#https://stats.stackexchange.com/questions/83585/two-way-anova-with-random-factors
#https://stats.stackexchange.com/questions/7384/how-to-specify-random-effects-in-a-mixed-model-using-the-lmer-function?rq=1
#https://www.thertrader.com/2016/01/30/repeated-measures-anova-and-linear-mixed-effects-models-in-r/
#https://stats.stackexchange.com/questions/255888/how-to-compute-two-way-interaction-effect-in-lmer
#https://rstudio-pubs-static.s3.amazonaws.com/200194_fc1c5f5ab7a34c99b9d7d0c0faa936e1.html
#https://stackoverflow.com/questions/43821727/how-to-test-