lme4 in R (taking into account covariates)?

Question

Previously I was looking for between-group differences in response rates (controlling for baseline values) for 4 incentive groups (there is a within-subjects factor and a between-subjects factor, and it is the group*round interaction that I am interested in, and I used this code:

lmer(response_rate ~ Round + Group + Round*Group + (1|ID), data=data)

My data looks like this:

Now, I would like to extend the above analysis by taking into account for other covariates (e.g. Sex, faculty and household income). Could I just check if the code used would be like this?

lmer(response_rate ~ Round + Group + Round*Group + Sex + faculty + householdincome + (1|ID), data=data)

Based on a paper that I read, the code should follow this format: lmer(Response ~ Condition + (1 + Condition | Subject) + (1 + Condition | Item), data=data)

However, i'm abit confused as to what my 'condition' and 'item' should be. As I need to take into account the group*time interaction but account for other covariates (sex, faculty, household income).

Thank you! :)

Answer 1

Now, I would like to extend the above analysis by taking into account for other covariates (e.g. Sex, faculty and household income)

lmer(response_rate ~ Round + Group + Round*Group + Sex + faculty + householdincome + (1|ID), data=data)

Yes, that is correct. The other formula:

lmer(Response ~ Condition + (1 + Condition | Subject) + (1 + Condition | Item), data=data)

would be for crossed random effects where you have two grouping variables Item and Condition. You only have ID and you just need to add the covariates as fixed effects.