[R] Analysing ordinal/nominal data

[Piotr Majdak]

Prof Brian Ripley wrote:

> You have still not defined v' and w', nor the scores (are they estimated 
> or not).  But the model I suggested is such a model with scores 1,2,...

Sorry for that, here it is:
scores v and w: integer scores, reflecting the ordering of columns/rows. 
Agresti suggests to use 1,2,3,... as you did.
v' and w': mean of v and w, respectively

 > As I suggested before, a binomial logistic model is appropriate here,
 > not a Poisson log-linear one.  (They are equivalent, but the binomial
 > version is easier to interpret and less wasteful to fit.)

After your suggestions I've read the logit-Chapter in Agresti (1984) and 
tried to fit a logit model to my data:

log(m_ij2/m_ij1) = intercept + beta^PR_i(u_i-u') +
                    beta^ENV_j(v_j-v')

with:
mijk: expected frequencies for cell with indicies i,j,k
u_i: scores of PR with u={0,1,2,3}
v_j: scores of ENV with v={0,1,2}
beta^PR: association parameter for PR with responses
beta^ENV: association parameter for ENV with responses

I wrote in R:

count=c(250,274,285,241,279,299,247,246,255,280,355,362,
         230,207,195,239,200,181,233,235,224,200,125,118)
PR=as.integer(gl(4,3,12))-1
ENV=as.integer(gl(3,1,12))-1
countM=matrix(count,12,2)
fit=glm(countM ~ as.integer(PR)+as.integer(ENV),
	family=binomial(link=logit))
summary(fit)


R gives me:

Coefficients:
                 Estimate Std. Error z value Pr(>|z|)
(Intercept)      0.18435    0.07737   2.383 0.017179 *
as.integer(PR)  -0.10538    0.03085  -3.416 0.000635 ***
as.integer(ENV) -0.07075    0.04748  -1.490 0.136191

Looking at my data, I know that for PR=0 I have a very weak dependence 
on ENV and for PR=3 very strong dependence on ENV. How can I get this 
interpretation from the summary above? I'm new in R: is 
fit$linearpredictors what I'm looking for?




-- 
Piotr Majdak
Institut für Schallforschung
Österreichische Akademie der Wissenschaften
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E-Mail: piotr at majdak.com
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