Re: st: Multilevel longitudinal analysis with censored data

[Gordon Hughes <G.A.Hughes@ed.ac.uk>]

Just to be clear about the problem.  You refer to longitudinal 
achievement as measured by letters in the alphabet but I assume that 
these have some kind of ordinal significance, otherwise you are just 
dealing with a set of categories.  So suppose that you have measured 
the reading age of each child on a standard scale from 5 to 15 in 
which category 15 means a reading age of >= 15.

In that case, I don't think that you will find a pre-packaged routine 
to carry out multi-level analysis.  You should look at the 
user-written package -gllamm- which is documented in a manual and 
book by Rabe-Hesketh et al (the manual is available via the UC 
Berkeley website and there is a paper in the Journal of Econometrics 
2005).  Also, note the double "l" and double "m".  It can be 
installed from SSC : use -ssc describe gllamm- or -ssc install 
gllamm-. This does not have a multi-level version of tobit but it 
does have other specifications which might be adapted to your purpose.

However, before committing yourself to elaborate and quite time 
consuming methods of analysis, you should think about the 
specification of your model.

A.  You have only 4 observations over time.  This is very small for a 
development path with 26 different categories.

B.  Actually, you don't have 4 observations on every child since you 
say that you have used imputation to fill in gaps, which would worry 
me even more.

C.  Many multi-level models can be re-written mathematically as 
conventional panel data models, in which case you could use 
-xttobit-.  It really depends upon what assumptions you want to make 
about the structure of the random coefficients in the model.

D.  Anyway, is the top-level censoring (assuming that is what it is) 
really significant, given the other limitations of your data and 
model?  If there is a lot of censoring, then why not think about use 
of -xtmelogit- to examine who reach the highest level of achievement?

Gordon Hughes
g.a.hughes@ed.ac.uk


Date: Tue, 22 Feb 2011 13:40:24 -0500
> From: Bernadette Puckett <puckett.bernadette@gmail.com>
> Subject: st: Multilevel longitudinal analysis with censored data
>
> Dear Stata list,
> I am currently conducting an analysis on the relation between school
> quality and academic growth across 4 time points. Time point is
> clustered in children and children are clustered in school. I also
> include fixed effects for district (i.district). I have imputed the
> data to account for missingness across time periods within children
> (there is no missing data are the school level).
>
> The issue is that the longitudinal achievement has an upper limit
> (e.g. cannot exceed 26 letters in the alphabet).
> This is my current model without accounting for the ceiling effects:
> mi estimate: xtmixed achievement time quality##time i.district ||
> school: || child_id: time, variance cov(un) mle
>
> My question is how to conduct a multilevel longitudinal analysis with
> censoring (similar to a tobit, using imputed data),
>
> Thank you,
> Bernadette
> *

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