How to specify random effects for panel/longitudinal data with level 2 predictor?

Question

In the study of tweets pre- and post- metoo (set as Nov 2017), we are looking at whether there is gender differences in the use of masculine language in tweets for male and female social media users.

We have tweets collected for the period 2008-23 for 400 users. Some of these users were only active on Twitter before metoo and some only after metoo. But a majority of them have tweets in both the pre- and post- metoo period.

We are currently specifying the model as follows:

M1 = lmer(masculine_lang ~ gender * post_metoo + tweet_created_year + (1|user_id)

Where tweet_created_year is a factor variable.

We are not sure if this is a correct specification.

We have two major concerns.

• One, should we be using tweet_created_year as factor or as numeric (with year 2008 coded as 0, 2009 as 1, and so on)?
• Two, should we include tweet_created_year as random effect as follows:

M2 = lmer(masculine_lang ~ gender * post_metoo + tweet_created_year + (1 + tweet_created_year|user_id)

Alternatively, should we have the following specification?

M3 = lmer(masculine_lang ~ gender * post_metoo + (1|user_id) + (1|user_id:tweet_created_year)

We are confused what is the right approach as each one gives a different result for test of interaction hypothesis that gender * post_metoo is significant.

Also, if we are interested in seeing how the trajectories of masculine language use of men and women users change post_metoo (i.e., in the years 2018-23), how should we go about it?

Much appreciated.

Answer 1

ORIGINAL ANSWER

Without knowing much about this (interesting!) subject, I'm not sure you need the year in the model at all. Perhaps you need it for some other reason, but not to investigate gender differences in the use of masculine language or in gender differences in the pre-post metoo change in the use of masculine language. So, I think the following model would work (I assume "post_metoo" is a two-level categorical variable indicating whether the tweet was posted prior to or after metoo):

mod<-lmer(masculine_lang ~ (1|user_id)+gender*post_metoo)

When it comes to trajectories, I'd suggest using latent (growth) curve models with gender as a time-invariant covariate. See for instance this and this resource.

EDITED IN: I see you do need the year. I suppose you can enter it as a categorical predictor with each year as level. Or if you believe year can be considered as a continuous predictor, you can enter it as numeric too.