On 10 Apr 2004 at 17:37, Richard Ulrich wrote: > On 10 Apr 2004 09:37:16 -0700, [EMAIL PROTECTED] (Roger Levy) > wrote: > > [snip, earlier posts of his and mine]
... > > By a "distinct covariate vector" I mean the following: with n > > covariates (i.e., predictors) X_1,...,X_n, a covariate vector is a > > value [x_1,...,x_n] for a given data point. So, for example, if I > > have a half-dozen binary covariates, there are 2^6=64 logically > > possible covariate vectors. > > Now I wonder what computer program you are using. > > What you describe was once a concern for the packages, about > 20 years. I remember a program that wanted me to sort my > cases into order, so that each 'possible covariate vector' (as > you say) would be contiguous so the program could form the > actual groups. I do not *think* that is a concern any more, > for modern packages, even though I find an ambiguous reference > to your concern in the Garson document I cited. This does not only have to do with computation, it is also a theoretical question, although maybe not of interest with 20 covariables. If the number of distinct covariate vectors is small, much lesser than n, another asymptotics applies. Kjetil Halvorsen > > > > > Each of my covariates is three-valued. So the situation for which > > ML and exact logistic regression were giving me substantially > > different results was with a half-dozen covariates, i.e. 3^6=729 > > possible covariate vectors, and 300 datapoints, therefore the > > covariate space was sparsely populated. I was not including any > > interaction terms, and in most cases each datapoint had a unique set > > of predictor values, so there were only seven parameters in my model > > and overfitting is almost certainly not an issue. > > > > So to restate my confusion, what I don't understand is the technical > > reason why asymptotic ML estimates for parameter confidence > > intervals and p-values would be unreliable in such a situation, > > since sample size is relatively large in absolute terms. > > Well, for one thing, there are two different versions of the > p-values that are available these days. You want to look > at the tests that are defined by subtraction, rather than > the Wald test: If you have an old program, it might only > feature the Wald, which is the ratio of the coefficient divided > by the ASE. See Garson for details and commentary. > > As an alternative step, diagnosing your whole dataset and > problem, I suggest that you perform a regression > with 0/1 criterion or do two-group discriminant function. > Those OLS programs are mathematically the same as each > other, and give practically identical tests to logistic, for > most data with Ns in the hundreds. They are more robust > than logistic against overfitting, and also give better > diagnostics if that is any threat. > > -- > Rich Ulrich, [EMAIL PROTECTED] > http://www.pitt.edu/~wpilib/index.html > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: . > http://jse.stat.ncsu.edu/ . > ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
