Interpreting a time variant covariate in a linear mixed effects model

[Sean Browning]

Hello,

I am looking for some help with interpreting the coefficients in a linear mixed effects model for a time varying variable (c.lonescale_UCLA_##time). All the other covariates are time invariant.

There are only two time points. Time is coded 1 = survey1 and 2 = survey2

The dependent variable is depression symptoms coded from less to more symptoms.

Lonescale_UCLA is also coded from less to more loneliness.

mi estimate: xtmixed dep_cesd9_ i.AgeSES_fu1_recode##time clsa_cohort_fu1##time c.education_bl_recode##time i.regionprv_fu1_recode##time urban_rural_2_fu1##time immigrant_status_bl##time c.chronicconditions_10_fu1##time alone2_covid_recode##time alone3_covid_recode##time bhv_selfq_covid##time i.exp_pand_se_covid_recode2##time bhv_spbg_covid_recode##time c.lonescale_UCLA_##time|| entity_id:, pweight(wghts_analytic_bl) pwscale(size)

This is limited output just for the time varying variable I need help interpreting:

dep_cesd9_               Coef.      Std. Err.      t         P>|t|       [95% Conf. Interval]

lonescale_UCLA_             .9578595   .0439655    21.79   0.000     .8716886     1.04403
                                 
time#c.lonescale_UCLA_
                    2       .3917519   .0524694     7.47   0.000     .2889137      .49459

For lonescale_UCLA_: would the correct interpretation for the coefficient be "those with more loneliness also had more depressive symptoms at time 1".

For time#c.lonescale_UCLA_: would the correct interpretation for the coefficient be "increased loneliness from time 1 to time 2 is associated with a greater increase in depressive symptoms from time 1 to time 2."

Thanks,
Sean

[Clyde Schechter]

For lonescale_UCLA_: would the correct interpretation for the coefficient be "those with more loneliness also had more depressive symptoms at time 1".

This is correct as far as it goes.

For time#c.lonescale_UCLA_: would the correct interpretation for the coefficient be "increased loneliness from time 1 to time 2 is associated with a greater increase in depressive symptoms from time 1 to time 2."

This also.

But I think the language you are using is vague and relatively uninformative. I would put it more specifically:

At time 1, each unit increase on the UCLA Loneliness score is associated with 0.96 (95% CI 0.87, 1.04) more symptoms endorsed on the CESD-9 depression scale, adjusted for the other model variables. At time 2, the increase in endorsements rises by an additional 0.39 (95% CI 0.29, 0.49).

But to be even clearer and to spare the reader the burden of adding up 0.96 and 0.39, I would get the actual CESD-9:Loneliness slope by running

lincom _b[lonescale_UCLA_] + _b[2.time#c.lonescale_UCLA_]

and change the second sentence I have proposed to: And at time 2, the increase in endorsements rises by X.XX (95% CI Y.YY Z.ZZ), filling in the appropriate numbers from the -lincom- output.

[Sean Browning]

Thank you very much Clyde. I appreciate the more succinct interpretation. I've heard of but never used the lincom command. I'll have to see if I can get a sense of whether the journal we send this to prefers them separate and/or combined.