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Re: st: RE: Re: Generating predicted values for OLS with transformed dependent variables

From   Phil Schumm <[email protected]>
To   [email protected]
Subject   Re: st: RE: Re: Generating predicted values for OLS with transformed dependent variables
Date   Thu, 13 Apr 2006 07:59:13 -0500

On Apr 12, 2006, at 2:47 PM, Daniel Schneider wrote:
Just to clarify the issue: For example, the predictions based on log (E[price]) = XG with GLM should be identical to the predictions generated from E[log(price)] = XB (fit by -regress-, generating B_hat), when the later are adjusted properly?

I'm not sure what you mean by "adjusted" here, but no, the predictions will not be the same.

What would you suggest for predictions based on a box-cox (left- hand side) transformation? A two step procedure, first estimating the box-cox transformation parameter and then using that parameter in a GLM to generate predicted variables?

No, I would not suggest that. These are two different approaches to the problem. In one case, you're assuming that a single transformation will address both the mean structure of the model and the error structure. In the second (GLM), you're modeling the error structure on the raw (untransformed) scale, and using the link function merely to specify the relationship between the mean of the response and the linear predictor (i.e., XB). So no, there's no reason in general to expect that an appropriate transformation in the first case will correspond to an appropriate link function (or vice versa).

I don't mean to be rude, but if you want to understand the GLM approach, you'll need to spend some time with one of the many books which explain it. If, after that, you have a specific question about something you have read (or, better yet, how something you read translates into Stata usage), then many on this list would, I'm sure, be glad to try to answer it.

-- Phil

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