I have calculated a particular parameter y in each subject our of 3 studies (each 15-30 subjects). In study #3, the subjects have been measured twice (with 2 different treatments, M and P), and therefore I calculated this variable twice for those subjects. Subjects of the other two studies didn't get any treatment (therefore Treatment = NA), and the treatment is not important to me.

I want to predict an overall significant difference of this parameter y from zero. Therefore, I was told to use HLM/MLM because this data is hierarchical because of the 2 treatments in study #3.

So my idea is to model something like:

y ~ Study + Subject + Treatment

As far as I understood, I want to look at the intercept of the model, to know if the parameter is statistically significant different from zero. I am not interested in the effect of Treatment, or Study, however.

Which of those parameters of the model should I now treat as fixed or random effect? And do I need to mean-center some variable to be able to interpret the intercept correctly?

Any help in a direction would be highly appreciated.

Thanks so much!


1 Answer 1


Welcome to the site, roman. I would suggest filtering out the individuals who were not in study #3. Assuming that study is coded 1, 2, or 3, I would first narrow down your data to just those subjects in study 3. You can use dplyr for this:

study3 <- original.data %>% filter(study==3) 

Now that you have a data frame with only study 3 participants, you can run your model. You should code your treatment variable such that one or the other treatments is 0 and the other is 1. If you coded treatment such that M==0 and P==1, and ran the following model:

m <- lmer(y ~ 1 + Treatment + (1|Subject), data=study3) 

This will give you two fixed effect coefficients, the intercept, which is the mean value of y in Treatment==0 and Treatment, the difference in the mean value of y for Treatment==1 relative to Treatment==0. You will also get a random effect estimate for Subject and the residual. Respectively, these tell you the variance in y that is between Subjects and within Subjects.

It is unclear to me why you want to know the mean of y irrespective of the treatment. However, you could get this by estimating a so-called "empty" model that ignores the effect of treatment:

emptym <- lmer(y ~ 1 + (1|Subject), data=study3) 

Here the fixed intercept gives you the mean value of y, while accounting for the correlation in y that is due to repeated measures of subjects. This will be slightly different than the mean you get from mean(study3$y).

Edit: Based on roman's desire to include participants from all 3 studies, one suggestion would be to recode treatment to be 0, 1, or 2, corresponding to the NA condition in studies 1 and 2, and the M and P conditions in study 3.

original.data <- original.data %>% replace_na(treatment=0) #change treatment=NA to treatment=0

Make sure that the treatment variable is a factor variable (original.data$treatment <- as.factor(original.data$treatment). Then you can run your model with treatment and study as fixed effect predictors.

m1 <- lmer(y ~ treatment + study + (1|Subject), data=original.data)

If you get any weird warnings about this, it could be because treatment and study are highly collinear and you may want to just include treatment as your fixed effect covariate.

  • $\begingroup$ My intention was to include subjects of all 3 studies. The subjects of study 3 became treament "M" or "P" (treatment is of no interest, but I want to account for this variance in my model). Subjects of Study 1&2 got no treatment (Treatment = "NA"). The only thing I want to now about is the parameter "y". So my idea was to include "study" (each was conducted independently), "subject" (bc. in study 3 most the subjects have been measured twice, with different treatments), and "treatment", to account for variance explained by this treatments. How could I include all these effects in one model? $\endgroup$
    – roman
    Feb 2, 2020 at 13:20
  • $\begingroup$ I see. Updated my post to reflect this approach. $\endgroup$
    – Erik Ruzek
    Feb 2, 2020 at 15:04
  • $\begingroup$ Superb ! Thanks a lot Erik. I dismissed one of the treatments, to account for that collinearity. So for the interpretation: the intercept would now be the "mean" of my parameter for group 1. If I want to have the intercept as a mean of that parameter across studies, I could kind of center the value of the "Study" (i.e. the number of the study), Am I right? $\endgroup$
    – roman
    Feb 2, 2020 at 19:36
  • $\begingroup$ Glad that worked for you! The intercept is the mean value of the outcome when all fixed effect predictors are at 0. If your predictors do not have a meaningful 0 value, then this mean is nonsensical. In terms of Study, depending on how many studies are in the data, you could code it so that 0 represents the mean across all studies. See pagepiccinini.com/2016/03/18/… $\endgroup$
    – Erik Ruzek
    Feb 2, 2020 at 20:26
  • $\begingroup$ Thanks a lot, Erik! This tutorial explains the contrasting very well! $\endgroup$
    – roman
    Feb 3, 2020 at 18:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.