[R] Testing relationships in logistic regression

[David Winsemius]

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