Typicality Probabilities in DISCRIMINANT program in SPSS XXXX

[Dan Abner]

 

Hello,

 

SPSS has been providing
the "typicality probability" or "typicality index"
as part of its casewise output from the
DISCRIMINANT routine.  I haven't been able to find
the algorithm SPSS uses to calculate this.

Does anyone know who these are computed?

 

Thanks,

 

Dan

[Art Kendall]

I do not have SPSS available at this time.  I do not recall the terms
"typicality probability" or "typicality index".

However, SPSS does produce a score for each case on each of the retained
functions, a predicted group, the probability of a case belonging to
each group, etc.

Look under <help> <algorithms> <discriminant>.  read under the heading
CLASSIFICATION.

Art Kendall
Social Research Consultants

Dan Abner wrote:

>
> Hello,
>
>
> SPSS has been providing
> the "typicality probability" or "typicality index"
> as part of its casewise output from the
> DISCRIMINANT routine.  I haven't been able to find
> the algorithm SPSS uses to calculate this.
>
> Does anyone know who these are computed?
>
> Thanks,
>
> Dan

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[Hector Maletta]

I seem to recall that the typicality index (in discriminant and cluster analyses) is a measure of how close to the group's centroid each case is. I used once a similar measure to select a subsample of subjects more "representative" of the cluster, thus avoiding "borderline" cases and concentrating on those near the cluster. However, this makes sense only if cases are indeed abundant in the vicinity of the centroid. If cases are more or less sparsely distributed about the group space, with perhaps very few actually close to the centroid, the "typical" subject would not be indeed quite typical.

Hector


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Art Kendall
Sent: 05 January 2010 13:46
To: [hidden email]
Subject: Re: Typicality Probabilities in DISCRIMINANT program in SPSS XXXX

I do not have SPSS available at this time.  I do not recall the terms
"typicality probability" or "typicality index".

However, SPSS does produce a score for each case on each of the retained
functions, a predicted group, the probability of a case belonging to
each group, etc.

Look under <help> <algorithms> <discriminant>.  read under the heading
CLASSIFICATION.

Art Kendall
Social Research Consultants

Dan Abner wrote:

>
> Hello,
>
>
> SPSS has been providing
> the "typicality probability" or "typicality index"
> as part of its casewise output from the
> DISCRIMINANT routine.  I haven't been able to find
> the algorithm SPSS uses to calculate this.
>
> Does anyone know who these are computed?
>
> Thanks,
>
> Dan

=====================
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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[Art Kendall]

I believe that what you are calling "posterior probabilities" used to be called the probabilities that a case is a member of a given group.
I believe that what you are calling "typicality probabilities" used to be called the probability that a member of that group would be so far away from its centroid.
Unfortunately I am still waiting for an auth code from SPSS so I can neither check the documentation nor do a test run.

It is a couple decades since I worked with the details, so see if this agrees with  your results
for a given case sum the squared scores across the dimensions aka functions. (the scores are like z-scores). Take the square root of that sum of squared scores aka deviations.
The functions are orthogonal so the distance is Euclidean.
 consider that a z-score. find the associated p.
something like this if you retained 3 functions.
compute mydistance = sqrt(score1**2 + score2**2 + score3**2).
compute myprob = cdf.normal(mydistance, 0,1).
* spssprob and spssdistance are the cacasewise variables from the discriminant .
descriptives variables = myprob spssprob mydistance spssdistance /statistics = all.

also try scatterplots of the casewise variables from the discriminant by your calculated variables.

If the results are close enough to attribute differences to internal rounding error then what I recall is ok.
Otherwise, standardize mydistance and compare that to the results from SPSS.
If my memory is still off, post to the list perhaps someone else has a better memory or documentation.  If it is critical, also post to SPSS.com/support.


Art Kendall
Social Research Consultants

Dan Abner wrote:

Hi Art,

 

SPSS provides both posterior probabilities (labeled P(G=g|D=d) and typicality probabilities (P(D>d | G=g)
 in the DISCRIMINANT program. Only the algorithm for the posterior probs is documented on the algorithms help page. Any idea how the typicality probabilities are computed?

 

Thanks,

 

Dan

 

 

On Tue, Jan 5, 2010 at 1:46 PM, Art Kendall <[hidden email]> wrote:

I do not have SPSS available at this time.  I do not recall the terms "typicality probability" or "typicality index".

However, SPSS does produce a score for each case on each of the retained functions, a predicted group, the probability of a case belonging to each group, etc.

Look under <help> <algorithms> <discriminant>.  read under the heading CLASSIFICATION.

Art Kendall
Social Research Consultants

Dan Abner wrote:

 Hello,
 
SPSS has been providing
the "typicality probability" or "typicality index"
as part of its casewise output from the
DISCRIMINANT routine.  I haven't been able to find
the algorithm SPSS uses to calculate this.

Does anyone know who these are computed?
 Thanks,
 Dan

===================== 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