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

[Phil Schumm <pschumm@uchicago.edu>]

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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