Hi
I fitted mixed effect model to my data, where I have brain response as output, 2 fixed effects: stimulus type (5 types) and stimulus intensity (3 levels) and I have some random effects included. What I am interested in is to find whether there are differences in brain responses to stimuli 2, 3, 4 and 5 compared to stimulus 1 at different intensity. So I fitted the interaction model (Respons ~Level*StimType +random effects) and then I made some post hoc analysis to find where the differences are. Post hoc analysis showed, that for intensity level 1 and 2, stimuli 4 and 5 evoke larger response compared to stimuli 1, no differences between the stimuli 1 and 2 as well as 1 and 3. However, for intensity level 3, both stimuli 2 and 3 as well as 4 and 5 evoked larger response compared to stimulus 1. And this was actually also my hypothesis before I started with measurements. Then I was following the guidelines for mixed effect model and tried to reduce the model to the additive model (Respons ~Level +StimType +random effects), anova test did not show the difference between these two models. And post hoc analysis on the additive model did not show the differences between stim 1 and 2 as well as stim 1 and 3. The differences were only between 1 and 4, and 1 and 5. And this applies to all levels, of course. The question is: is it always necessary to test the model reduction? Or if I just interested in the interaction effects, so I can stop at the interaction model?
Thanks for advance
Best regards
Anna
The model ~ Level * StimType assumes that the effects of StimType depend on the values of Level. The post hoc tests of differences between StimType refer to a particular value of Level. The statistical significance depends on the value of Level. It is the key feature of such a model to say: it makes no sense to ask for a general difference between StimTypes; the value of Level must be considered.
The model ~ Level + StimType allows a different mean response depending on the value of Level, and the effects of StimType are modeled independent of that. This model asks for the general difference between StimTypes, disregarding that these differences might depend on the value of Level. If they do, the model will just see more noise (unexplained variance) and it's less likely to get low p-values.
Which model makes sense depends on your understanding of the connection of Level and StimType. If you think there can be an interaction, then use the model including this interaction - and interpret the results appropriately. Use the simpler model only if you are sure that the (possible) interactions can not be relevant.
I italicazed a part of the sentence because your conclusions about the differences between the stimuli were just disregarding the interaction (at least how you wrote it in your question). If the interaction is the relevant research question, then you should evaluate how the differences between the StimTypes change with (or depend on) the value of Level.
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