Mixed-design experiment with non-binary non-ordinal response variable

[f.damore]

Hi Henrik, I really need to start with a big thank you for your afex package, which is great… 🙂

Online I have found a 2016 presentation where you showed how to implement a GLMM with the mixed() function for a mixed-design experiment with a binary response variable.

Here is the question: is it possible to do the same for a mixed-design experiment with a non-binary non-ordinal response variable?

Francesco

[henrik]

I am not sure I fully understand the question, but I guess the simple answer is yes. The question of how to map aspects of your design onto the random-effects part of the model (i.e., for which grouping-factors to you want to have random intercepts and for which fixed factors random slopes) is independent of the choice of the family or link function. So you can easily do this for a response variable that is assumed to have a conditional normal distribution.

For an introduction to this topics see our chapter:

[f.damore]

Thank you for replying so quickly! 🙂

I try to explain my problem better.

I ran a mixed-design experiment with one between-subject factor (biological sex: two levels) and two within-subject factors (four levels each). I measured several continuous response variables, which I have already analysed with a standard anova, and a nominal (non-ordinal) categorical response variable. This response variable has five possible outcomes (which would be even more, if I used the raw data without any kind of grouping).

Statistical analysis of this categorical response variable is not crucial for the study. What is more, I have realised that the needed statistical tools go beyond my current knowledge. Basically, I am exploring the viability of such analysis. For this purpose, I was wondering whether and how I could adapt this line of code from your 2016 presentation

m2 <- mixed(resp2 ~ cond * validity * believability + (believability * validity|id) + (1|content),
             d, family = binomial, method = "LRT")

when the reponse variable is categorical, non-ordinal, and non-binary.

Unfortunately, my knowledge of GLMMs is still superficial (cheeky understatement). It is not clear to me whether your answer implies that I can just replace resp2 in the code above with a response variable such as mine.

Francesco

[henrik]

If the DV is categorical with five levels, you cannot use such a mixed model. Binomial models only support categorical data with two categories. For more categories you need to use multinomial logistic models. I find these model quite advanced and their results are not easy to interpret.

You can however split your categories in what is called nested dichotomies and analyse each of these with a binomial model. The theory is described in the books by John Fox.

Let’s say you only have three categories, A, B, C. Then you first pick one category of interest, such as A. You then make a binary variable with A versus the rest (i.e., B and C). You analyse this with a binomial model. In the next step you discard all observations in which the response is A and only analyse the remaining data with a new binomial variable B versus C. We did exactly this in one paper once: http://singmann.org/download/publications/Douven_Elqayam_Singmann_Wijnbergen-Huitink-HIT_in_press.pdf

[f.damore]

What you said confirms my initial impression that this is quite advanced stuff.

I will start having a look at the book you suggested.

Thank you again 🙂

Francesco

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