Scale Parameters and SAVE

[Gary Rosin]

The General Linearized Model allows the use of a model-based scale parameter during estimation, and reports thevalue of scale parameter in the Parameter Estimates block. When SPSS saves the XBStandardError (the estimated standard error of the predicted value of the linear predictor, XBPredicted), does the SAVE procedure take the scale parameter into account?

 

I'm sure I must have missed something while reading the fine manual, including the algorithm description. I found lots of good stuff, but couldn't find the answer to that.

 

Gary

 

[MICHAEL J TONER]



Hello,

 

I will be out of the office Friday, May 3, and Monday, May 6. I will be back in the office Tuesday afternoon. I will not check my email while I am away. I will respond to your email after I am back in the office.

 

Best,

 

Michael Toner

 

*********************************************

Michael J. Toner, Ph.D.

Associate Director, Graduate Enrollment and Data Management

Office of the Graduate School

Temple University

1803 N. Broad St.

501 Carnell Hall

Philadelphia, PA 19122-6095

phone [phone]

fax [phone]

email [hidden email]

web www.temple.edu/grad 

[Ryan]

Responses below.

On Thu, May 2, 2013 at 7:19 PM, Gary S. Rosin <[hidden email]> wrote:

The General Linearized Model allows the use of a model-based scale parameter during estimation,

 

That is true.

 

and reports thevalue of scale parameter in the Parameter Estimates block.

 

Yes, that is correct as well. 

 

When SPSS saves the XBStandardError (the estimated standard error of the predicted value of the linear predictor, XBPredicted), does the SAVE procedure take the scale parameter into account?

 

The scale parameter has to do with dispersion in the response. So, for example, if one fits a standard Poisson model and an overdispersed Poisson model in the presence of overdispersed data, then the standard errors will certainly change across the models.

 

I'm sure I must have missed something while reading the fine manual, including the algorithm description. I found lots of good stuff, but couldn't find the answer to that.

 

 

 

Gary

 

[Ryan]

The illustration BELOW is a continuation of the Poisson example I mentioned previously. Here we see that there is a presence of overdispersion (conditional variance exceeds conditional the conditional mean).  

 

If you provide further details, I may be able to provide a more targeted response. Still, I believe examination of the illustration below should help you achieve some clarity on the matter.

 

HTH

 

Ryan

--

 

*Generate Data.
set seed 98765432.
new file.
input program.
loop ID= 1 to 100000.
   compute #b0 = 1.2.
   compute #b1 = -1.8.
   compute x = rv.normal(0,1).
   compute #lambda = exp(#b0 + #b1*x).
   compute #shape = 0.8.
   *compute dispersion = 1 / #shape.
   compute #scale = #lambda / #shape.
   compute #mean  = rv.gamma(#shape, 1/#scale).
   compute y = rv.poisson(#mean).
   end case.
 end loop.
end file.
end inp pro.
execute.

 

*Fit Standard Poisson Model.
GENLIN y WITH x
  /MODEL x INTERCEPT=YES
  DISTRIBUTION=POISSON LINK=LOG
  /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION (EXPONENTIATED)
  /SAVE XBPRED XBSTDERROR.

 

*Fit Overdispersed Poisson Model.
GENLIN y WITH x
  /MODEL x INTERCEPT=YES
  DISTRIBUTION=POISSON LINK=LOG
  /CRITERIA SCALE=PEARSON
  /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION (EXPONENTIATED)
  /SAVE XBPRED XBSTDERROR.

On Thu, May 2, 2013 at 9:27 PM, Ryan Black <[hidden email]> wrote:

Responses below.

On Thu, May 2, 2013 at 7:19 PM, Gary S. Rosin <[hidden email]> wrote:

The General Linearized Model allows the use of a model-based scale parameter during estimation,

 

That is true.

 

and reports thevalue of scale parameter in the Parameter Estimates block.

 

Yes, that is correct as well. 

 

When SPSS saves the XBStandardError (the estimated standard error of the predicted value of the linear predictor, XBPredicted), does the SAVE procedure take the scale parameter into account?

 

The scale parameter has to do with dispersion in the response. So, for example, if one fits a standard Poisson model and an overdispersed Poisson model in the presence of overdispersed data, then the standard errors will certainly change across the models.

 

I'm sure I must have missed something while reading the fine manual, including the algorithm description. I found lots of good stuff, but couldn't find the answer to that.

 

 

 

Gary