Overdispersion correction in multinomial regression

[Sarah van Mastrigt]

Hi All-

I have a question regarding the SPSS options provided to correct for over-
dispersion in the multinomial logistic regression function of SPSS 15.0. I
am using the multinomial function to run a simple binary logistic
regression (only because the regular logistic menu doesn't offer a
correction for over-dispersion). In the multinomial regression menu, under
Options - Dispersion Scale, I have selected a 'Deviance' based correction,
which I understand acts to inflate the standard errors of the parameter
estimates to account for autocorrelation. The SPSS help menu states that
the formula used to achieve this over-dispersion correction is the "ratio
of the deviance goodness of fit measure to its degrees of freedom" and the
following formula is provided by SPSS:

correction factor = Deviance/ m(k-1) - p^nr

Rather unhelpfully there is no indication in the help menu as to what k,
p, and nr refer to. Can anyone clarify what these terms refer to and how
they are related to df? More generally, I suppose my question would be: in
the context of a dichotomous outcome model, how is df for a goodness of
fit deviance test determined?

I was under the impression that df for the deviance test is equal to
(number of observations - number of fitted parameters), but this doesn't
seem to be the case from what I can gather in my corrected model as this
would produce a correction factor of 0.98, whereas my SE and Wald values
appear to be corrected by a factor of 1.4?

Any help would be greatly appreciated.

Best wishes,
Sarah

--
Sarah van Mastrigt
PhD Candidate, Institute of Criminology
University of Cambridge

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[Marta Garcia-Granero]

Hi Sarah:

If you are using SPSS 15/16, run the program and go to ? (:help)->
Algorithms.

Select NOMREG and look at the beggining ("Notation"). Yo will see a
description of what "m", k", "p^nr"... stand for.

HTH,
Marta García-Granero

PS: I remembered Richard Oliver information about the Algorithms being
available in the Help system

Sarah van Mastrigt escribió:

> Hi All-
>
> I have a question regarding the SPSS options provided to correct for over-
> dispersion in the multinomial logistic regression function of SPSS 15.0. I
> am using the multinomial function to run a simple binary logistic
> regression (only because the regular logistic menu doesn't offer a
> correction for over-dispersion). In the multinomial regression menu, under
> Options - Dispersion Scale, I have selected a 'Deviance' based correction,
> which I understand acts to inflate the standard errors of the parameter
> estimates to account for autocorrelation. The SPSS help menu states that
> the formula used to achieve this over-dispersion correction is the "ratio
> of the deviance goodness of fit measure to its degrees of freedom" and the
> following formula is provided by SPSS:
>
> correction factor = Deviance/ m(k-1) - p^nr
>
> Rather unhelpfully there is no indication in the help menu as to what k,
> p, and nr refer to. Can anyone clarify what these terms refer to and how
> they are related to df? More generally, I suppose my question would be: in
> the context of a dichotomous outcome model, how is df for a goodness of
> fit deviance test determined?
>
> I was under the impression that df for the deviance test is equal to
> (number of observations - number of fitted parameters), but this doesn't
> seem to be the case from what I can gather in my corrected model as this
> would produce a correction factor of 0.98, whereas my SE and Wald values
> appear to be corrected by a factor of 1.4?
>
> Any help would be greatly appreciated.
>
> Best wishes,
> Sarah
>
> --
> Sarah van Mastrigt
> PhD Candidate, Institute of Criminology
> University of Cambridge
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
>

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[Sarah van Mastrigt]

Thanks so much- I checked the algorithms help menu and found what I was
looking for! Also found this link to an SPSS list of algorithms that may
be of interest to some readers:

http://support.spss.com/ProductsExt/SPSS/Documentation/Statistics/algorithm
s/

If anyone is interested in the answer to my original question:

m = number of subpopulations (provided in case processing summary table)
k = number of categories of the nominal outcome variable
p^nr = number of non-redundant parameters in final model (incl. constant)

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[Zhang, Jing]

Hello,

Is anyone familiar with SPSS/Exact Test as a tool for Monte Carlo
Simulation?

Thanks

Jayson

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