Regarding ways of testing the significance of log reg results you may
consult standard textbooks such as Hosmer and Lemeshow. At page 146-147 of
their book (Applied Logistic Regression, Wiley, 1989) these authors
criticise using the classification table (where an outcome is predicted
based on a cutoff point for the probability and compared to the observed
outcome for each individual case), saying that "it is easy to construct a
situation where the logistic regression model is in fact the correct model
and thus will fit, but classification will be poor" (and they give an
example). "Accurate or inaccurate classification does not address our
criteria for goodness-of-fit".
Hosmer and Lemeshow's measures rely more on the comparison of expected and
observed frequencies of the event in GROUPS of subjects with increasing
probabilities (e.g. those below 0.1, those between 0.1 and 0.2, etc.), but
not on the comparison of observed and predicted INDIVIDUAL outcomes (as in
the cross classification table).
On the frequentist (versus subjective) interpretation of probabilities there
are many references in books on the foundations of probability. An author
making much of it in the context of "fast and frugal" decision rules is Gerd
Gigerenzer; see his main books like:
Adaptive Thinking: Rationality in the Real World (OUP,2000);
Reckoning with Risk (Penguin, 2003);
Gut Feelings: The Intelligence of the Inconscious (Viking 2007), and
G. Gigerenzer & R. Selten, Bounded Rationality: The Adaptive Toolbox (MIT
Press, 2001).
Hector
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of T K
Sent: 23 April 2009 13:32
To:
[hidden email]
Subject: Re: Logistic Regression and Unequal Distribution of Dependent
Variable
Hi Hector, your logic and explanation regarding the following matter is very
convincing. I was wondering if there is any published article or book that
can be quoted in support of this matter. It would be of great help for me.
1. Apply log reg to whatever is the event of your interest, either being or
not being tested.
2. Do not care about the cross classification of predicted and observed
outcome. It means nothing.
3. To assess the adequacy of the model use the other coefficients available
to assess goodness of fit and significance.
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