[R] Using linear formula inside MLE

[Peter Dalgaard]

Stephen Collins wrote:
> Say I have a formula Y ~ 1 + X, where X is a categorical variable.  A 
> previous thread showed how to evaluate this model using the mle package 
> from "stats4" (see below).  But, the user had to create the data matrix, 
> X, including the column of one's for the regression constant.  Is there a 
> way to nest the linear formula in the code below, so the data matrix 
> doesn't explicitly have to be created by the user?
> 
> Y <- c(0,0,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,1) 
> X <- 
> cbind(matrix(1,21,1),matrix(c(-48.5,24.4,82.8,-24.6,-31.6,91.0,52.1,-87.7,-17.0,-51.5,
> -90.7,65.5,-44.0,-7.0,51.6,32.4,-61.8,34.0,27.9,-72.9,49.9), 21,1)) 
> 
> log.lo.like <- function(beta,Y,X) { 
> Fbetax <- 1/(1+exp(-beta%*%t(X))) 
> loglbeta <- -log(prod(Fbetax^Y*(1-Fbetax)^(1-Y))) 
> } 
> 
> #####Using MLE#####
> ll <- eval(function(beta0=0,beta1=0) 
>              log.lo.like (c(beta0,beta1),Y,X),
>            list(X=X,Y=Y))
> 
> 
> summary(mle(ll)) 
> ####Comparison using glm#####
> glm(Y~X-1,family=binomial) 
> 

You might get something out of looking at

http://staff.pubhealth.ku.dk/~pd/slides/RSS-sep08.pdf

The code on the last of the three p.12 slides (don't ask) shows how to 
go from a model formula to a likelihood function for a GLM in a fairly 
automatic way.

-- 
    O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
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