Command for a (longitudinal) multilevel model where the outcome is a proportion (aggregated binary data)

[Sid Molloy]

Hi:

I have a query on multi-level modelling for an outcome that is a proportion. Here are some details -

The outcome is a proportion (i.e. aggregated binary outcome) at country-level, for which I have a short time-series of data for a number of countries. I want to fit a (multi-level) longitudinal ‘growth curve’ model (i.e. principle predictor is year of observation), where level 1 is occasion (i.e. year) of observation and level 2 is country.

As a prelim, I’ve fitted the model assuming the outcome is continuous:

mixed x y || country:

where x is the outcome, y is year of measurement, and country is country id. (The model includes other predictors but I have left them out for simplicity).

But, it’s preferable to fit the model so the outcome is a proportion (using a binomial distribution) rather than as a continuous variable. However, I’ve been unable to find out what the correct Stata command is…

Apparently a single-level model where the outcome is a proportion would be of the form:

binreg x y, n(z)

where x is the outcome specified as a count (i.e. as the numerator of the proportion rather than a proportion), y is year, and z is the denominator of the proportion.

And, a multilevel model where the binary outcome is specified at the individual level would be of the form:

xtmelogit x y || country:

But I’m not sure what command I should use when the outcome is a proportion and I require a multilevel model. (I guess I could arbitrarily disaggregate the data to the individual level but this would be messy and I assume there’s an easier way).

If anyone is able to offer any advice I’d be grateful.

Thanks.

[Carlo Lazzaro]

Sid:
Volume 2, Chapter 5 of http://www.stata.com/bookstore/multi...ata/index.html covers what you're after.

[Sid Molloy]

Thanks for the response Carlo. I've got the two volumes by Rabe-Hesketh, but they don't seem to spend much time on what I'm looking for. Vol II p687 very briefly discusses counts vs proportions in MLMs. It suggests I could use 'xtmelogit' with the binomial option to specify the denominator. The chapter doesn't discuss proportions any further.

Maybe this is all the info I need though. But I don't want to mess this up. Is any one able to confirm that it would be correct to use a model of the form:

xtmelogit x y || country: , binomial ( ...)

where x is the outcome of interest specified as the numerator of the proportion, y is year of observation, country is country id, and binomial specifies the variable holding the denominator of the proportion.

Thanks for the help.

[Marcos Almeida]

Hello Sid,

Besides Carlo's advice, you could also check these texts:


http://www.ats.ucla.edu/stat/stata/faq/proportion.htm

http://www.theanalysisfactor.com/pro...type-of-model/


Best,

Marcos

[Marcos Almeida]

Hello Sid,

I was about to "test" if what happens with - glm - would "work" (I mean, provide reliable results) with - meglm - in your specific case when, lo and behold, I came across this thread (http://www.statalist.org/forums/foru...lts-of-melogit).


Best,

Marcos

[Sid Molloy]

Thanks a lot for this Marcos - much appreciated. I'll check it out.