Level 2 outcome and 'Downdated VtV' error

Agreed with the others. Chiming in only because I've recently been
doing research on such aggregation and I can say the consensus seems
to be it doesn't introduce bias (with the possible exception of very
small clusters, which you don't have).

On Tue, Jul 7, 2020 at 6:40 AM Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

Hi Matt,

What you are trying to do (i.e., use a level 2 variable as the outcome)

can and should not be done. The outcome in a multilevel model needs to be
measured at the lowest level.

In your model (A1), we know a priori that there is 0 within-station

variability. Hence, the ICC is exactly equal to 1 in that model, but trying
to fit such a model pushes the optimization routines into a situation that
leads to degeneracies.

The only way to get around this is to aggregate the data to the level of

the outcome (i.e., use PopCov as the outcome and aggregate all other level
1 predictors to level 2 means).

Best,
Wolfgang

-----Original Message-----
From: R-sig-mixed-models [mailto:

r-sig-mixed-models-bounces at r-project.org]

On Behalf Of Matthew Boden
Sent: Tuesday, 07 July, 2020 0:19
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] Level 2 outcome and 'Downdated VtV' error

Good afternoon,

I am looking for advice regarding a multi-level model I am trying to
implement using lme4. My two-level random-effects model won?t run,

perhaps

due to one or two issues.

Background: Level 1 is patients, which are clustered in healthcare
facilities (?Station?). The outcome is a continuous variable (?PopCov?)
that is calculated at the facility-level, and is thus a Level 2 variable
that does not vary at the patient level.

The aim of this analysis is to examine whether PopCov is predicted by

(a)

patient-level (e.g., race/ethnicity, age, symptom severity), and (b)
facility-level variables (e.g., overall racial/ethnic composition,

average

age). It is important to examine factors such as race/ethnicity at both
patient and facility-levels because patients with different

racial/ethnic

backgrounds tend to differ in terms of age, symptom severity, etc.

Each record/row in my data is a patient, with facility-level variables
(including PopCov) having identical values among patients within a given
facility.

An error is thrown when I run a basic model.

A1 <-lmer(PopCov ~ (1 | Station), data = DISP)

*Error in fn9nM$xeval()) : Downdated VtV is not positive definite

I obtain the same error when I add to the model either a patient-level

or

facility level predictor.

An internet search suggested that I have complete separation of my data
and/or poorly scaled variables.

I assume this issue has to do with the fact that the outcome is a level

2

variable. Perhaps compounding the issue is the large and unbalanced

nature

of the data. I have ~6 million patients clustered in ~1000 healthcare
facilities. Individual facilities have anywhere from 100 to 30000

patients

clustered in them.

I could use some advice regarding how to specify the model to predict a
facility-level variable (level 2) from both patient (level 1) and
facility-level (level 2) variables with these data.

Thank you in advance.

Matt

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