R help - Jan 2007 - contingency table analysis; generalized linear model

Dear List,

I would appreciate help on the following matter:

I am aware that higher dimensional contingency tables can be analysed using
either log-linear models or as a poisson regression using a generalized linear
model:

log-linear:
loglm(~Age+Site, data=xtabs(~Age+Site, data=SSites.Rev, drop.unused.levels=T))

GLM:
glm.table <- as.data.frame(xtabs(~Age+Site, data=SSites.Rev,
drop.unused.levels=T))
glm(Freq ~ Age + Site, data=glm.table, family='poisson')

where Site is a factor and Age is cast as a factor by xtabs() and treated as
such.

**Question**:
Is it acceptable to step away from contingency table analysis by recasting Age
as a numerical variable, and redoing the analysis as:

glm(Freq ~ as.numeric(Age) + Site, data=glm.table, family='poisson')

My reasons for wanting to do this are to be able to include non-linear terms in
the model, using say restricted or natural cubic splines.

Thank you in advance for your help.
Regards,
Mark Difford.


--------------------------------------------------------------- 
Mark Difford
Ph.D. candidate, Botany Department,
Nelson Mandela Metropolitan University,
Port Elizabeth, SA.

> Date: Tue, 9 Jan 2007 11:13:41 +0000 (GMT)
> From: Mark Difford <mark_difford@yahoo.co.uk>
> Subject: Re: [R] contingency table analysis; generalized linear model
>
> Dear List,
>
> I would appreciate help on the following matter:
>
> I am aware that higher dimensional contingency tables can be  
> analysed using either log-linear models or as a poisson regression  
> using a generalized linear model:
>
> log-linear:
> loglm(~Age+Site, data=xtabs(~Age+Site, data=SSites.Rev,  
> drop.unused.levels=T))
>
> GLM:
> glm.table <- as.data.frame(xtabs(~Age+Site, data=SSites.Rev,  
> drop.unused.levels=T))
> glm(Freq ~ Age + Site, data=glm.table, family='poisson')
>
> where Site is a factor and Age is cast as a factor by xtabs() and  
> treated as such.
>
> **Question**:
> Is it acceptable to step away from contingency table analysis by  
> recasting Age as a numerical variable, and redoing the analysis as:
>
> glm(Freq ~ as.numeric(Age) + Site, data=glm.table,
family='poisson')
>
> My reasons for wanting to do this are to be able to include non- 
> linear terms in the model, using say restricted or natural cubic  
> splines.
>
> Thank you in advance for your help.
> Regards,
> Mark Difford.
>
>
> ---------------------------------------------------------------
> Mark Difford
> Ph.D. candidate, Botany Department,
> Nelson Mandela Metropolitan University,
> Port Elizabeth, SA.
Yes it is, and it is often the preferred way to view the analysis.
In this case it looks like Freq is measuring something like species  
abundance,
and it is natural to model this as a Poisson count via a log-link glm.
As such you are free to include any reasonable functions of your  
predictors
in modeling the mean.

Log-linear models are typically presented as ways of  analyzing  
dependence between
categorical variables, when represented as multi-way tables. The  
appropriate multinomial
models, conditioning on certain marginals, happen to be equivalent to  
Poisson glms with
appropriate terms included.

I would suggest in your data preparation that you
glm.table[,"Age"] <- as.numeric(glm.table[,"Age"])
at the start, so that now you can think of your data in the right way.

Trevor Hastie


-------------------------------------------------------------------
   Trevor Hastie                                   hastie@stanford.edu
   Professor & Chair, Department of Statistics, Stanford University
   Phone: (650) 725-2231 (Statistics)          Fax: (650) 725-8977
   (650) 498-5233 (Biostatistics)   Fax: (650) 725-6951
   URL: http://www-stat.stanford.edu/~hastie
    address: room 104, Department of Statistics, Sequoia Hall
            390 Serra Mall, Stanford University, CA 94305-4065
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