2
$\begingroup$

I have a large database with repeated measures of Y at various times. Y is continuous, and I know that its evolution is usually modified by numerous baseline confounders.

I am trying to fit a mixed model. Here is a little reprex in R. I hope that the question won't be too much R-driven.

My actual dataset is much larger (300k+ lines in long) and confounders can be continuous or categorical, but the spirit is the same. In this example, let's say X1 is the variable I hypothesize is influencing the evolution of Y over time, and X2 is a confounder.

library(dplyr)
library(lme4)

df.long = data.frame(
  id=c(rep(c("A", "B", "C"), each=5)),
  time=c(1,2,3,4,5,10,11,12,13,14,5,6,7,8,9),
  y=c(25,32,35,37,40,55,51,59,57,60,10,15,20,30,45)
)    
df.baseline = data.frame(
  id=c("A", "B", "C"),
  x1=c(98, 42, 23),
  x2=c(250,390,527)
)

df = df.long %>% left_join(df.baseline, by="id")
df
#    id time  y x1  x2
# 1   A    1 25 98 250
# 2   A    2 32 98 250
# 3   A    4 35 98 250
# 4   A    7 37 98 250
# 5   A    8 40 98 250
# 6   B   10 55 42 390
# 7   B   12 51 42 390
# 8   B   16 59 42 390
#...

I've seen a whole lot of ressources, but very few talks about specific times and even less about adjusting for confounding variables.

In my notebook, there is a small paragraph about the time, saying you should set a specific covariance matrix Toeplitz-like since time3 is more associated to time2 than to time1.

But since I don't have time1 and time3, but a huge set of different times, with unequal delta between them, how can I build such a covariance matrix? And then how can I apply it to my model ?

Also, how should I put confounders in my model? Some talks about interaction on time (time*x1*x2), but with many confounders it makes little sense to me.

For the record, the best model I've made up so far (based on this answer) is :

lmeModel = lmer(y ~ time + x1 + x2 + (1+ time|id), data=df)

For what I understand, it has random effect on id and should account for the effect of time for each id. But it is not clear if I should keep time as standalone, neither as if the covariance matrix is OK.

DISCLAIMER: this may be a confusing question, but please help me to improve it if you think so.

$\endgroup$

1 Answer 1

2
$\begingroup$

A couple of points:

  • A general model-building strategy for mixed models is that you start with an elaborate/flexible specification of the fixed-effects part, including nonlinear and interactions terms. Then keeping this elaborate fixed-effects structure you build your random-effects part. Typically, you start with a random intercept (that corresponds to constant correlation over time), and you move to random slopes and possibly also higher-order terms, such as nonlinear random slopes. Also, depending on the features of your study it may be required to included random effects for other grouping factors (e.g., in a multilevel design). After you selected your random effects, you can return to the fixed-effects part and try to simplify your model, starting from seeing if you need the complex nonlinear/interaction terms. For more on this, you can have a look at Sections 3.1, 3.2 (also useful 2.4) and 3.9 of my course notes.

  • When you include random slopes in your random-effects part, you indeed assume that measurements that are closer in time are more strongly correlated than measurements that are further apart. To get a better intuition on how random effects capture correlations, you can have a look at Section 3.3 of my shiny app for my course mentioned above.

  • Indeed including three-way interactions of time with x1 and x2 can make interpretation difficult. Typically, I only consider interactions of time with other variables for longitudinal data. See again Section 2.4 and 3.2.

$\endgroup$
1
  • $\begingroup$ This is a pretty awesome GitHub app, kudos and thanks for sharing it, I've learn a lot ! $\endgroup$ Commented Sep 18, 2018 at 10:02

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.