On Jun 8, 2012, at 11:33 AM, Peter Milne wrote:
I am interested in knowing whether and how I can test the
significance of
the relationship between my continuous predictor variable (a
covariate) and
my binary response variable according to two different groups, my
categorical predictor variable, in a logistic regression model (glm).
Specifically, can I determine whether the relationships are
identical (the
hypothesis of coincidence), or whether there is a difference between
the
levels of the categorical variable, but the effect of the covariate
is the
same (hypothesis of parallelism). I have previously performed an
ANCOVA on
this data using proportions of the response variable, but I know
this is an
incorrect application of the technique since proportions (bounded by
0 and
1) violate the assumptions of linear regression.
In my ANCOVA, my model produced the equation where 'Y' is the
predicted
value for the response, 'x' is my continuous covariate and 'z' is a
dummy
term with (0,1) for the two levels of the categorical predictor.
Y = a + bx + bz + bx*z
I can test the hypothesis of coincidence (that a single regression
line
will fit all the data) by testing the terms 'z' and 'x*z'
simultaneously
using the ANOVA table to generate an F-value for these combined terms.
I can test the hypothesis of parallelism (that two intercepts are
required,
but a single slope to fit the data) by testing the term 'x*z', again
using
the ANOVA table to generate an F-value.
My logistic regression model produces the same equation, except that
'Y' is
now the logit of the response. Because I don't know all the math
behind the
technique of logistic regression, how can I evaluate the two
hypotheses?
The ANOVA table produced by glm - anova(model, test="Chisq") -
speaks about
deviances and degrees of freedom. I can see how to determine whether
each
term is predictive - 1-pchisq(deviance, df) - but how can I tell
whether
the relationship between 'z' and 'Y' is the same or different at
each level
of 'x'? ie, is the change in logodds of Y for 1z significantly
different
from the change in logodds of Y for 0z?
I have had no luck tracking this down using Google. Many thanks to
those
who take up my question!
This is the wrong forum for basic statistics questions. Another option
might be:
stats.stackexchange.com
The third hit on a Google search for logistic regression produced this
reasonably brief discussion.
www.upa.pdx.edu/IOA/newsom/da2/ho_logistic.pdf
(This material is covered in any text that deals with logistic
regression. I was going to suggest looking at the Wikipedia article,
but when I just looked my assessment of its clarity and accuracy was
not so high on either account. Harrell's text 'Regression Modeling
Strategies' on the other hand is excellent.)
Peter Milne
University of Ottawa
Department of Linguistics
[[alternative HTML version deleted]]
David Winsemius, MD
West Hartford, CT
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