Residuals look "mirrored" when using lmer with imputed data

Sun, Aug 6, 2017 6:00 AM

Uh ... part of my problem is the term "AUC". Without some very explicit
note to the contrary, AUC on a stats forum often refers to a cumulative
probability or the Receiver Operating Characteristic (ROC AUC).
Remember, we're doing this in our free time, so I am often quick and
don't read every line of code ....

You're effectively using a rectangular approximation for your integral
and that's something else to be careful with in terms of approximation.
But why impute separately here? You might be able to use a suitable
integral approximation to skip imputation:

group_by(ID, treatment) %>%??mutate(AUC =
sum(diff(sampleNum)*rollmean(value,2)))

yields similarly flat tails on the qqplot. (Okay, maybe don't use the
rectangular approximation without proper imputation; this didn't work
as well as I'd hoped.)

In both cases, the residual plot looks not horrible to me, but the
qqnorm plot suggests some issues with bounding -- those flat tails look
you're running into some minimal/maximal value. At the lower end, the
obvious answer is "zero"; at the upper end, maybe you're hitting the
limits of your measurement device? We see which values actually occur,
both with the imputed data and the implicit-imputation-via-integral-
approximation data:

In both cases, we see that the data only take on a relatively small
number of values and indeed there are lots of repetitions at the
bounds.

Phillip

On Sat, 2017-08-05 at 17:59 +0200, Jo?o C P Santiago wrote:

I'm sorry I may be misunderstanding, but why do you say my data
is??
bounded between 0 and 1? The data I shared is from multiple??
measurements of a blood hormone, which can be 0, but is certainly
not??
bounded at 1. Next I calculated the AUC i.e. the "total exposure"
of??
that hormone. X is time and y is the value of the hormone at each
time??
point. The AUC is also not bounded at 0 and 1.

Am I missing something?

Thanks for your reply!
Santiago


Quoting "Alday, Phillip" <Phillip.Alday at mpi.nl>:


You're fitting a normal/Gaussian LMM to data bounded on [0, 1].
The
model assumptions about the residuals simply won't hold for
bounded,
binomial-like values.?

Why not fit a binomial model to the data and then use
fitted(model)
to
compute AUC of the entire model??

Phillip ?

On Fri, 2017-08-04 at 08:52 +0200, Jo?o C P Santiago wrote:


I'm trying to assess if a treatment had any effect on the
levels
of
a??
hormone. To do this I need to calculate the area under the
curve
and??
then adjust it for sex (a known confounder) and smoking status
(not??
included in the demo data below to keep things simpler).

Here's a dput of the data: https://pastebin.com/VYcQGkwb

There's some missing values, so first step is to impute them
using
the??
mice package, then calculate AUC and finally fit the model:

library(dplyr)
library(lme4)
library(mice)
library(zoo)

## Impute missing values
dfMids <- mice(df, m = 10, maxit = 15, seed = 2535)
dfImp??<- complete(dfMids)

## Calculate AUC
dfImpAUC <- dfImp %>%
???arrange(sampleNum) %>%
???group_by(ID, treatment) %>%
???mutate(AUC = sum(diff(sampleNum)*rollmean(value,2)))

## Fit model
fit <- lmer(AUC ~ sex * treatment + (1|ID), data = dfImpAUC)

## Plot residuals
plot(fit)??# output: https://imgur.com/a/vfL1R
qqnorm(resid(fit))



I know it's possible to fit a model to each iteration of mids
model,??
but then I can't calculate the AUC, which is what I actually
need.
Any??
ideas why the residuals look like that?

Best
Santiago