On 25 Oct 2002 05:50:59 -0700, [EMAIL PROTECTED] (John Smith) wrote: > I have a data set comprising of real valued variables X (Range :-200 > to 200 approximately) and ordered categorical response variables Y > [1,2,3,4 or 5]. > > I want to predict the probability of getting response Yi given an > input X. > > My question concerns whether a probit or logit model is more > appropriate, i.e. on what basis(es) I should make this decision.
If you really have a heck of a lot of data, you might try to let yourself be convinced by the model that fits the data. But for most data sets, there's not much to choose between, logistic versus probit, since the CDFs are so similar if you aren't talking about the outer 5%. Then, what differs *slightly* are the extreme predictions, based on two variables or factors. Do you have a large enough sample, and multiple variables, so there will be a large number of instances with extreme-and-different predictions? Otherwise, you use logixxxx-- I mean, use one of these guides. (a) What is familiar to everyone. (b) What your audience knows, in particular. (c) What convenient software is available. (d) What fits the generation of the data: Growth models imply the logistic. Sums of small variations imply normal [probit] . > > If the log-likelihood is higher for one of the models does that imply > that it is better, or am I being too simplistic? I was thinking in terms of, the resulting model being simpler. The fitted model will seem to have fewer terms, fewer interactions (especially), and more homogeneity. > > Do I need to look at the distribution of the independent variable X? Sure. If that is not 'random' in some sense, and apparently continuous, then you might want to start over, collecting new data. > > If I introduce another input variable X2, which causes the > log-likelihood to decrease, does this imply the single variable model > is a better predictor of Y? > It can't happen. Adding another potential parameter never worsens the simple likelihood, since (at worse) you just ignore it. -- 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/ . =================================================================
