R help - Mar 2008 - [follow-up] "Longitudinal" with binary covariates and outcome

Hi again!
Following up my previous posting below (to which no response
as yet), I have located a report which situates this type
of question in a longitudinal modelling context.

http://www4.stat.ncsu.edu/~dzhang2/paper/glm.ps
Generalized Linear Models with Longitudinal Covariates
Daowen Zhang & Xihong Lin

(This work seems to originally date from around 1999).

They consider an outcome Y, with a fixed covariate [vector] Z
and a longitudinal covariate [vector] X observed at n time
points t1,...,tn; the outcome Y is observed only at the end
of the sequence. They model Y with a GLM in which Z and
subject-specific random effects U are predictors in the GLM,
where U satisfies a linear mixed model X = T'*U + error
and is normally distributed.

However, in view of the fact that the longitudinal covariates
X in my query below are binary, there cannot be a linear
mixed model for them; there would have to be a generalised
linear mixed model.

I have had a good poke around in the R resources, and have
failed to find anything which directly addresses this question
(nor which addresses Zhang & Lin's original question).

So, if anyone has done R work in this kind of context,
I'd be most grateful for any suggestions (including worked
examples of datasets) arising from it!

With thanks again, and best wishes to all,
Ted.


-----FW: <XFMail.080311001718.Ted.Harding at manchester.ac.uk>-----
Date: Tue, 11 Mar 2008 00:17:18 -0000 (GMT)
From: (Ted Harding) <Ted.Harding at manchester.ac.uk>
To: r-help at stat.math.ethz.ch
Subject: "Longitudinal" with binary covariates and outcome

Hi Folks,
I'd be grateful for suggestions about approaching the
following kind of data. I'm not sure what general class of
models it is best situated in (that's just my ignorance),
and in particular if anyone could point me to case studies
associated with an R approach that would be most useful.

Suppose I have data of the following kind. Each "subject"
is observed at say 4 time-points T2, T2, T3, T4, yielding
values of binary (0/1) variables X1, X2, X3, X4. At time T4
is also observed a binary variable Y. The objective is to
study the predictive power of (X1, X2, X3, X4) for the
outcome "Y=1".

A useful model should take account of the possibility
that more "recent" X's are likely to be better predictors
than less "recent" so that, say, P(Y=1|X4=1) is likely to
be larger than P(Y=1|X1=1), and also that the more X's
are 1, the more likely it is that Y=1.

Any suggestions or comments and, as I say, pointers to
an R treatment of similar problems would be most welcome.

With thanks,
Ted.
--------------End of forwarded message-------------------------

--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 12-Mar-08                                       Time: 14:35:59
------------------------------ XFMail ------------------------------

Ted,

What you have can be rendered as a 2^5 (X1 by X2 by X3 by X4 by Y) table 
of counts, right?

Why isn't this a vanilla log-linear modelling (as in loglin() ) problem?

It seems to me that the temporal aspect you describe suggests a sequence 
of margins that could be studied, viz

 	list( 1:4, c(4,5) )
 	list( 1:4, c(3,5), c(4,5) )
 	list( 1:4, c(2,5), c(3,5), (4,5) )
 	list( 1:4, c(1,5, c(2,5), c(3,5), (4,5) )

(taking X1 is the first and Y as the last slice in the table)

and perhaps intercalating higher order effects involving slice 5 amongst 
those.

??

Chuck

On Wed, 12 Mar 2008, Ted.Harding at manchester.ac.uk wrote:
> Hi again!
> Following up my previous posting below (to which no response
> as yet), I have located a report which situates this type
> of question in a longitudinal modelling context.
>
> http://www4.stat.ncsu.edu/~dzhang2/paper/glm.ps
> Generalized Linear Models with Longitudinal Covariates
> Daowen Zhang & Xihong Lin
>
> (This work seems to originally date from around 1999).
>
> They consider an outcome Y, with a fixed covariate [vector] Z
> and a longitudinal covariate [vector] X observed at n time
> points t1,...,tn; the outcome Y is observed only at the end
> of the sequence. They model Y with a GLM in which Z and
> subject-specific random effects U are predictors in the GLM,
> where U satisfies a linear mixed model X = T'*U + error
> and is normally distributed.
>
> However, in view of the fact that the longitudinal covariates
> X in my query below are binary, there cannot be a linear
> mixed model for them; there would have to be a generalised
> linear mixed model.
>
> I have had a good poke around in the R resources, and have
> failed to find anything which directly addresses this question
> (nor which addresses Zhang & Lin's original question).
>
> So, if anyone has done R work in this kind of context,
> I'd be most grateful for any suggestions (including worked
> examples of datasets) arising from it!
>
> With thanks again, and best wishes to all,
> Ted.
>
>
> -----FW: <XFMail.080311001718.Ted.Harding at manchester.ac.uk>-----
> Date: Tue, 11 Mar 2008 00:17:18 -0000 (GMT)
> From: (Ted Harding) <Ted.Harding at manchester.ac.uk>
> To: r-help at stat.math.ethz.ch
> Subject: "Longitudinal" with binary covariates and outcome
>
> Hi Folks,
> I'd be grateful for suggestions about approaching the
> following kind of data. I'm not sure what general class of
> models it is best situated in (that's just my ignorance),
> and in particular if anyone could point me to case studies
> associated with an R approach that would be most useful.
>
> Suppose I have data of the following kind. Each "subject"
> is observed at say 4 time-points T2, T2, T3, T4, yielding
> values of binary (0/1) variables X1, X2, X3, X4. At time T4
> is also observed a binary variable Y. The objective is to
> study the predictive power of (X1, X2, X3, X4) for the
> outcome "Y=1".
>
> A useful model should take account of the possibility
> that more "recent" X's are likely to be better predictors
> than less "recent" so that, say, P(Y=1|X4=1) is likely to
> be larger than P(Y=1|X1=1), and also that the more X's
> are 1, the more likely it is that Y=1.
>
> Any suggestions or comments and, as I say, pointers to
> an R treatment of similar problems would be most welcome.
>
> With thanks,
> Ted.
> --------------End of forwarded message-------------------------
>
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
> Fax-to-email: +44 (0)870 094 0861
> Date: 12-Mar-08                                       Time: 14:35:59
> ------------------------------ XFMail ------------------------------
>
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Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901