# Interpretation of linear mixed effects model for longitudinal data with lmer

Thank you for any help. I am looking at the interaction of time with plasma biomarkers in the brain. Here is the code that I ran:

    test = lmer(precuneus.dvr ~ Cage*time + sex*time + race_binary*time + NFLz*time + (1|idno),
data = testDFlong30,
na.action = na.omit)


precuneus.dvr: is measured in this unit called DVR,

race: 0 = White and 1 = non-White,

sex: 0 = Female and 1 = male,

time: time between visits for each participant for a brain scan.

My output is here in the image below. How would I interpret the results I see and especially the ones with a time interaction?

• What values can Cage and NFLz take? Commented Mar 27, 2023 at 14:45
• Please refrain from making substantial edits to a post after it's received an answer, because doing so destroys the work of people who have taken the time to understand & answer your question. If you still have outstanding questions, then you can ask a new Question.
– Sycorax
Commented Mar 28, 2023 at 18:23

Start with time and sex. Ignoring the other variables for now, your line of best fit is

precuneus.dvr = 1.148 + 0.00222 * time + 0.03073 * sex + 0.00417 * time * sex + ...


The more time between visits, the higher the predicted value of precuneus.dvr, but the line for female participants (sex = 0) is

1.148 + 0.00222 * time


whereas for male participants (sex = 1) it is

(1.148 + 0.03073) + (0.00222 + 0.00417) * time


i.e. the two lines have different intercepts and different slopes. Males start from a higher level and the line is steeper (bigger effect as time increases).

You can interpret the interaction of race_binary and time in a similar way.

The variables Cage and NFLz are not binary, so we interpret their interaction with time a little differently, but the idea is the same. For example, the older the participant, the steeper the slope of time.

Centering the variable the way you did (so that Cage = 0 corresponds to average) is a sensible idea, as we can then interpret the value of 2.224e-02 as the slope of time for a participant of average age.