I'm new to Linear Mixed Models and I'm not sure if I'm specifying the right model. I'd appreciate any feedback that confirms / disproves my model. Here's some background about my data:

I have a list of subjects. Each subject is partially crossed with an "App" group. This means that some of the "Apps" may share the same subject.

For each app, the subjects in that app answer three values on a Likert scale (AppTrust, AppImportance, AppFrequency), and two on a continuous scale (Security *Comfort*, and Non-security *Comfort*).

The question I'm trying to answer is: What is the difference in Comfort of the subjects down to?

Given this, I'm trying to model Comfort using the following model:

comfort ~  AppImportance + AppTrust + AppFrequency + AgeOfSubject + 
           GenderOfSubject + ComfortType + (1 | SubjectID) + (1 | App)

Here, ComfortType is either "Security" or "Non-security".

Is my model correctly specified? Am I correct to consider AppImportance, AppTrust and AppFrequency as fixed effects?


It looks right to me. The main question seems to be, "Do I specify the model the same as if it were a fully crossed design, or do I need to do something different to account for the fact that the crossing is only partial?" The answer to that is that you can specify the model the same as if it were a fully crossed design.

One other comment is that you should strongly consider adding random AppImportance, AppTrust, and AppFrequency slopes across subjects, since they are the fixed predictors of interest. Two readings on the problem of omitting potentially important random terms from the model are Schielzeth and Forstmeier (2008) and Barr, Levy, Scheepers, and Tily (2013).

  • $\begingroup$ Thank you, Jake! I'll go through the readings. That makes sense intuitively, that the difference in Importance, Trust and Frequency across the subjects should lead to varying slopes across subjects. Would I do that using: (AppTrust | SubjectID)? $\endgroup$ – Mark Newman May 22 '16 at 19:43
  • $\begingroup$ @MarkNewman Right, and for all three, it would be (AppImportance + AppTrust + AppFrequency | SubjectID). Technically these slopes could also vary across Apps. Although if you have only a small number of apps, such a model could be computationally difficult to estimate. $\endgroup$ – Jake Westfall May 22 '16 at 19:53
  • $\begingroup$ So the final equation is: (AppImportance + AppTrust + AppFrequency | SubjectID) + AgeOfSubject + GenderOfSubject + ComfortType + (1 | SubjectID) + (1 | App). Why would I have to remove the main effects of AppImportance, AppTrust and AppFrequency? $\endgroup$ – Mark Newman May 22 '16 at 19:56
  • $\begingroup$ @MarkNewman No, the final equation would be comfort ~ AppImportance + AppTrust + AppFrequency + AgeOfSubject + GenderOfSubject + ComfortType + (AppImportance + AppTrust + AppFrequency | SubjectID) + (1 | App). With the theoretical possibility of going even further by replacing (1 | App) with (AppImportance + AppTrust + AppFrequency | App). $\endgroup$ – Jake Westfall May 22 '16 at 20:05
  • $\begingroup$ Ah, I see - thanks! Also, my dependent variable is a score between 0-100 - what kind of a model would suit this? I'vm currently using the beta regression mixed model from the glmmADMB package. $\endgroup$ – Mark Newman May 22 '16 at 20:54

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