'How to interpret the fixed effects in relation to random effects in mixed effects model?
This is a small subset of my data to show what it looks like because my data set is too large:
I want to compare the long-term effect of two types of surgery on weight loss.
In my real data set 285 people get treatment B and 49 people get treatment A.
The patients are followed for a maximum of 10 years, they do not have the same follow-up time, I decide to do a linear mixed effect model. With this subset, the model does not seem to converge. But it does converge with my whole (real) data set. And the result I present is the result of my data set.
The outcome is BMI (body mass index), the predictor is treatment. I adjust for gender.
The individual will be in the random effect (ID).
I set the random intercept and slope.
I wonder if I should put the time effect in my model or not? Why do people put the time effect in their model? And what is the underlying assumption?
Here is how I implement my model. Is it correct?
lmer.bmi <- lmer(BMI ~ Treatment + Gender +
(1 + Treatment|ID),
data =mydataBMIsample)
Below are the results:
Linear mixed model fit by REML ['lmerMod']
Formula: BMI ~ Treatment + Gender + (1 +
Treatment | ID)
Data: mydataBMI
REML criterion at convergence: 12636.9
Scaled residuals:
Min 1Q Median 3Q Max
-1.9505 -0.6039 -0.2686 0.1999 4.4135
Random effects:
Groups Name Variance Std.Dev. Corr
ID (Intercept) 30.84 5.554
TreatmentB 48.97 6.998 -0.90
Residual 34.63 5.885
Number of obs: 1926, groups: ID, 334
Fixed effects:
Estimate Std. Error t value
(Intercept) 34.7613 0.8879 39.152
TreatmentB -3.2226 0.9160 -3.518
GenderMale -0.4578 0.5679 -0.806
Correlation of Fixed Effects:
(Intr) TrtmnB
TreatmentB -0.957
GenderMale -0.092 -0.040
I have some difficulty interpreting the results of the mixed effects model.
I know from the fixed effects that patients with treatment B have a lower BMI.
Is it correct to say that people with treatment B have a BMI 3 points lower than those with treatment A? If I understand correctly, the fixed effect should be interpreted in relation to the random effect.
But what will the random effect change in the interpretation of the effect size of the treatment (the fixed effect) if only to give an indication of the veracity of that effect size ?
Here below reproducible and subset of dataset:
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Sources
This article follows the attribution requirements of Stack Overflow and is licensed under CC BY-SA 3.0.
Source: Stack Overflow
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