# Mixed effects model for group differences in R

I'm trying to run a mixed-effects analysis on some data that I have, but cannot determine if I am using the correct model.

First, I am trying to determine if there are between-group difference in 5 independent variables. My data consists of a number of participants who performed 31 different tasks (we'll call them Items), during which these 5 variables were measured. I would like to test for differences in these variables, not necessarily in relation to each other, but I would like to keep them in one model so as to avoid excessive testing. I would, however, like to control for the variance between these items, and if possible also between participants.

I currently am using the lme4 package to run a logistic regression:

glmer(Group~Var1+Var2+Var3+Var4+Var5 + (1|item),family=binomial)


My thinking here is that if there are group differences, then the variables should also predict group membership, effectively testing my hypothesis, if in an indirect way. Please correct me if this assumption is incorrect.

Ideally I would like to run this with Participant as an addition random factor, but I don't think that makes sense in a model testing for group differences.

The alternative is to run separate regression models for each of my independent variables, with Group, Item, and Participant as random effects. However, as I said before, I don't want to over-test the data, so I'm not sure if this is an advisable way to go about it.

Can anyone let me know if my current setup is a valid way to test for significant differences of multiple variables between 2 groups?

EDIT: If the above is NOT valid, and the test should be the other way around, lmer(Var1 ~ Group + (1|item)), is it then recommended to also model participants as random variables, or will this interfere with the fixed effect of Group?

• (Note that you haven't specified family=binomial, so I think you may be getting a linear mixed model.) – gung Jun 13 '17 at 13:02
• Thanks for the catch, gung. I had it specified when I ran the model, but I forgot to type it out here. – James Trujillo Jun 13 '17 at 13:07
• This is not appropriate if you are not interested in the relationship between the variables—in this model they will each be adjusted or "controlled" for the others. This has a fundamentally different interpretation than doing 5 independent tests. Also, adding them all into one model does not remove the multiple comparison problem. If the 5 variables are different in context and have their own hypotheses, then you could justify not adjusting for multiple comparisons. On the other hand, if you are just throwing things against a wall to see what sticks, then you should adjust for this. – Moose Jun 13 '17 at 13:32
• @Moose so if I understand correctly, my model works to test the hypothesis that the variables differ between the two groups, but are also hypothesized to have some relationship among themselves as well. However, it requires correction for multiple comparisons. On the other hand, if we assume the 5 variables are completely independent, the more valid model is to run something like Var1~Group+(1|item)+(1|participant), for each of the 5 variables. – James Trujillo Jun 13 '17 at 13:40
• I'll add a complete answer. If it's sufficient, please indicate it as so :) Also, you first refer to the 5 variables as "independent" when, in the experimental sense, they are the dependent variables (you measured them in response to item). – Moose Jun 14 '17 at 12:08

In the model that you specified in your initial question,

glmer(Group~Var1+Var2+Var3+Var4+Var5 + (1|item),family=binomial)


you would be asking the following question: which variables, measured across a number of items, are independent predictors of group assignment/membership?

If this was a test to try and diagnose a pathology, then it might make sense. However, it sounds more like an experimental design with treatment assignment. In this case, each response should be tested separately. The model you left in the comments section would be correct:

lmer(Var1 ~ Group + (1|item) + (1|participant), data=data)


This design would be considered a crossed random effects model. You can confirm that you specified it correctly as a similar design is shown here.

Regarding multiple testing, one cannot add many terms to a model to try and avoid the multiple comparisons problem because: 1) there are no tricks to avoid multiple testing if you do in fact make multiple tests and 2) because the tests would have a different interpretation in a full model since their estimates are controlled for the values of the other variables. There are certainly situations where one would want to do this, especially in observational studies, but for experimental designs, it would be pretty unusual.

My two cents on whether you should adjust for multiple comparisons or not will depend on the context. If each response has its own pre-specified hypothesis, are frequently tested together or if some are more like positive controls (we expect them to change, but it is not the main hypothesis of interest), then you could justify using the unadjusted p-values. However, if you don't have clearly defined hypotheses or if you take "a significant result, any significant result", then you should adjust the p-values to maintain your confidence at the nominal level.

• Thank you! This is very clear. I have just one question for clarification: does adding the (1 | participant) term interfere with Group being the main predictor? As the participants are spread across two groups. To be more specific, does adding this extra term require extra large sample size, more robust (hypothesized) effect, etc? – James Trujillo Jun 14 '17 at 13:28
• No problem for the group effect. I don't think sample size should be a problem either since you have so many tasks in each person (the person-specific intercept will be well-estimated) and I presume that you have quite complete/balanced data. And please "accept" the answer if it is satisfactory :) – Moose Jun 15 '17 at 7:59