I have a data set of repeated measurements, where I use two different species and measured their force produced on five different substrates. I want to check for differences between the two species but also difference between substrates for each species. Since I have repeated measurements I would like to use a linear mixed effects model analysis. The problem is that I cannot wrap my head around of which factors should be my fixed/random effects. If I would use two-way ANOVA (which is not possible because of repeated measures) I would consider both force and substrate effects simultaneously. Any suggestions?
This is a two-factor experiment. One factor is the species and the other factor is the substrate. Clearly the species are specifically chosen and therefore the species factor is fixed effects. I mean that your interest is in two particular species not a random selection of species. If your are interested in five particular substrate then this factor (of substrate) is fixed effects. If it is a random selection then the factor would be random effects. If one factor is fixed and the other factor is random then you have a mixed effects experiment. It depends on what you want. I hear you mention a force effect. I do not see force as a factor but as the response variable because you say that you "measured their force on five different substrates".
Thanks for your reply! What I got from your answer is that I have to take a lot at two different scenarios, one where I use species as fixed factor to see effect on the substrate and one scenario where substrate is the fixed factor and I check the dependence of the measured variable for the species. Is there a way to check for two factors a the same time?
As I understood, "force" is the response. Species and substrates should be fixed factors, so that you can model the impact of the species/substrate combination on the force. If the force changes over time, you may also have a time factor (fixed). As you have repeated measures for a sample of subjects, subject should be the random factor. The random factor can be on the intercept (assuming that each subject has its own specific "baseline" force) and/or on the slope of one (or several) the fixed factors (assuming that each subject reacts differently on the respective factor).
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