I am using brm() in R to fit a multilevel model for repeated measures data. The two predictors are both categorical. One is `Task` with two levels (`LO` and `ID`), another one is `Condition` with four levels (AD_p, AU_p, AD_a, and AU_a). The output is as follows.
It seems the model set a baseline level for each predictor, for `Task` it's ID, and for `Condition` it's AD_a. In the outputs, the effect of TaskLO is -0.037 and it's not significant. How should I interpret the effect of Condition? Specifically, how to interpret -0.098 under ConditionAD_p, -0.017 under ConditionAU_a and so on?
The interpretation of the fixed part estimates is similar to standard single level regression - this should help
https://stats.idre.ucla.edu/spss/seminars/introduction-to-regression-with-spss/introreg-lesson3/
- 3.1 Regression with a 0/1 (dummy) variable
- 3.2 Regression with a 1/2 variable
- 3.3 Regression with a 1/2/3 (multicategory) variable
- 3.4 Regression with two categorical predictors (main effects model)
- 3.5 Regression with the interaction of two categorical predictors
- 3.6 Summary
On multilevel models see
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html
especially http://www.bristol.ac.uk/cmm/learning/online-course/
The interpretation of the fixed part estimates is similar to standard single level regression - this should help
https://stats.idre.ucla.edu/spss/seminars/introduction-to-regression-with-spss/introreg-lesson3/
- 3.1 Regression with a 0/1 (dummy) variable
- 3.2 Regression with a 1/2 variable
- 3.3 Regression with a 1/2/3 (multicategory) variable
- 3.4 Regression with two categorical predictors (main effects model)
- 3.5 Regression with the interaction of two categorical predictors
- 3.6 Summary
On multilevel models see
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html
especially http://www.bristol.ac.uk/cmm/learning/online-course/
With brm it is probably helpful to plot the marginal effects using something like sjplot's plot_model() function. Plotting the marginal effects for the task by condition interaction should help interpret what's going on.
The emmeans package now works with brms I think, so that can also be used for comparing conditions and exploring interactions.
https://cran.r-project.org/web/packages/emmeans/vignettes/interactions.html
You can also get ANOVA-like 'tests' by comparing models using LOOIC or WAIC. For example the difference in LOOIC between a model with and without the interaction indicates whether there is evidence of a two-way interaction. (As it is a 2x4 design you can't easily use the CIs etc for individual effects).
You can also use hypothesis() to flexibly test any contrast, though it is a bit fiddly. This gives interval estimates and Bayes factors potentially.
For more fancy stuff you can use posterior draws to show uncertainty and to get visualisations:
https://gist.github.com/jebyrnes/d1bdea4ad4c8736c4b9e7ac290e8c940
I do not fully understand your research question. You probably have a binary dependent variable, since you used the brm R Package. In my opinion you could also use a Mantel-Heanszel analysis, followed by simple chi-squared tests. In attachment an R script for such an analysis. It includes the odd ratios.
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