Include Missings in Cluster analysis

[john67]

hello everyone,

I´m trying to cluster a group of 40 countries by approval to
democratic values. I have a total of 20 variables.
The countries should be clusterd in 4 cluster analysis, with each analysis
clustering the countries at 5 of the 20 variables. By comparing the cluster
i´d like to find out if the clusters are congruent and if not so why.

CLUSTER  [variables.....]
/METHOD WAVERAGE
/MEASURE=SEUCLID
/ID=countryname
/PRINT SCHEDULE CLUSTER(2,6)
/PLOT DENDROGRAM HICICLE.

my problem is that if i rum this syntax, spss kicks out like 24 countries because within that 24 countries i have at a minimum one missing value, maximum is 3 (of total 20)
How can i indluce cases that have missing values, if i don´t want to replace the missing value with the mean?

how can i implemt adapted clustering concepts like the nearest prototype strategy or partial distance strategy?

anyone knwos the syntax, or if that is possible with SPSS Version 20, or do i have to use R?

how many missings can i accept?


thanks a lot!

[Tom1234]

Not sure I've got the right end of the stick here but you could always recode the sysmis into the same variable as a number i.e. 99 and then set the value label as 'Missing' that way you'd include it in your findings.
Visual help:

[john67]

thanks for the reply, but unfortunately that is not what i meant. i am looking for a way to include the cases that have missing values and a way how i can compute values for the missings.
i read that one method is to replace the missing value by the mean value, but that´s hardly acceptable.

eventually what i´m seraching is a proper way to compute values for the missings and i read something about adapted clustering with the possibilities a) whole data strategy b) partial distance ~ and c) nearest prototype ~. but unfortunately it is not explained how to wirk with this strategys. and i can´t find any further literature.

[David Marso]

AFAIK SPSS Cluster assumes LISTWISE deletion -but I may be wrong about that-  Looks like Quick Cluster permits Pairwise but I'm not a big fan of K-Means.  CLUSTER and TWOSTEP have EXCLUDE or INCLUDE and I *REALLY* wonder *WHY* anyone would *EVER* use INCLUDE!!!!!
--
I built something like that for a client about 10 years ago using the MATRIX language and defining my own [*Sorry proprietary!!!*] (in retrospect rather flaky) adjusted distance calculations -OTOH: CLIENT WAS VERY HAPPY with results so I obviously didn't have my head completely in the wrong spot.  

[john67]

hey thanks for the reply.....

quick cluster permits pairwise, but i neither want to use K-means. the function with *include* ore *exclude* as u say, don´t really tend to be usefull.

what did u do with matrix langaugae? did u estimate the distances? or how where u able to copute vectors?

[David Marso]

Rather expensively (both computationally and billing wise for the client), somewhat experimental and a very LONG time ago in a land far far away (i.e. Today I would likely do it somewhat differently but AFAIK it is still in use by the client).
You would probably be better off trying to find some explicit algorithm for the methods you previously stated.
You can pretty much do anything achievable with Linear Algebra and more with the MATRIX language.
OTOH: Maybe you can spin something out of Multiple Imputation but I have *NO* idea how that would fly WRT a CLUSTER analysis ;-(
--

john67 wrote

hey thanks for the reply.....

quick cluster permits pairwise, but i neither want to use K-means. the function with *include* ore *exclude* as u say, don´t really tend to be usefull.

what did u do with matrix langaugae? did u estimate the distances? or how where u able to copute vectors?

[john67]

maybe i should specify my question:

i´m looking for a way to estimate / compute values for the missing values.
in my textbook (which is written in german by Prof. Backhaus, so probably
no one will know it) they guess that i can
replace the missing values by the mean value. But that far to inaccurate,
i think.

an other way that i found in some literature are the strategies i mentioned above.
my problem is, that i don´t knwo how to implement that straegies with
spss, if that is even possible.....

@ david marso, thanks for ur post & your help! i found the fuzzy c means algorithm, but same problem don´t how to implement these strategies in spps, without calculating each seperately  

[Poes, Matthew Joseph]

So it turns out your issue is not about cluster analysis at all, but rather, about missing value imputation.  This is just for your future reference.  It's a general statistical topic that impacts all analysis in roughly the same way.

As you have correctly noted, mean imputation is notoriously inaccurate, and creates an estimate bias.  It is far from the best approach.  Some people prefer predictive imputations such as regression, but this too is just another form of mean imputation, when it comes right down to it, so it too tends to be inaccurate.  Instead, the preferred approach involves first analyzing the missing data to determine if the data is missing at random, missing completely at random, or not missing at random.  To do this, go to Analyze->Multiple Imputation->analyze patterns, or under Analyze->Missing value analysis.  Both of these lead to the same program.  In terms of the goal, if no patterns can reasonably be detected, data can be inferred as missing at random, and either listwise deletion or multiple imputation can be used without issue.  If, however, the data is not missing at random, then you have a different problem, and a different solution should be utilized.

Let's assume that no pattern or rather, no meaningful patterns are generated in your missing data, and you believe it to be missing at random.  Go through with multiple imputation, its also under the multiple imputation procedures.  You will then input all the variables you intend to use for the Mi.  This uses various predictive models (inferential statistics) based on known data to impute a best guess value for the unknown value.  However, since this, in and of itself, gives a single value when the true value is a range, MI does this iteratively within the possible range.  The typical approach is 5 times, and each of the 5 iterations will impute values such that it isn't the same kind of shift across each variable or cases missing values (i.e. it doesn't shift all the values to the high end of the CI or low end of the CI, but more randomly).  These 5 versions are then split (automatically) with the split file command, and every analysis is run as many times as there are iterations, and then combined in the end.  Again, SPSS will do all this for you.  I believe this all will work with all of the cluster analysis techniques, but I recommend reading the IBM help files associated with multiple imputation.  A nautilus like shape will show up next to every analysis capable of using the MI, once it's been run.  Again, you will really want to read the documentation, as I have not given you a step by step set of directions with all pertinent details, I'll leave that up to you.

Under certain conditions, such as with large scale survey data, especially when based on multiple choice questions, an equally good technique is to use hot decking.  Hot decking uses a value from a set of possible values, chosen at random.  It's less sophisticated than MI in that it doesn't involve the iterative analysis, it only makes one draw for each missing value, but has been shown to be unbiased under certain circumstances.  Again, these circumstances require that people's responses tend to fall into typical ranges, that it's truly multiple choice, and that the data is truly missing at random.  SPSS does not natively allow for hot decking, but there are macro's floating around for it.

Matthew J Poes
Research Data Specialist
Center for Prevention Research and Development
University of Illinois
510 Devonshire Dr.
Champaign, IL 61820
Phone:� 217-265-4576
email: [hidden email]



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of john67
Sent: Wednesday, June 27, 2012 10:53 AM
To: [hidden email]
Subject: Re: Include Missings in Cluster analysis

maybe i should specify my question:

i´m looking for a way to estimate / compute values for the missing values.
in my textbook (which is written in german by Prof. Backhaus, so probably no one will know it) they guess that i can replace the missing values by the mean value. But that far to inaccurate, i think.

an other way that i found in some literature are the strategies i mentioned above.
my problem is, that i don´t knwo how to implement that straegies with spss, if that is even possible.....


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[David Marso]

"i don´t knwo how to implement that straegies with
spss, if that is even possible.."

Of course it is possible but you will want to bone up on the SPSS matrix language!!!
Briefly (and preparing to be slaughtered by the statistical purists as I have never bothered to program this exact method and don't know if others will find it acceptable or utterly naive and seat of the pants).
For simple Euclidean:
Dij=SQRT(SUM_k(Xik-Xjk)**2).
i,j=1 ..N,
k=1..p
N=number of rows in raw data
P=number of columns in raw data.

For each row i:
isolate all rows with same columns of complete data ignoring columns with missing info.
Calculate Matrix D(i) .
For each D(i),
normalize so they can be meaningfully compared (can't really compare D from 10 columns to D from <> 10).
For available pairs in complete set of normalized D matrices compute average Dij.
---
This may *NOT* be an optimal solution but will probably work pretty well.
** Note: (0-0)**2=0 (potentially useful hint for dealing with bookkeeping).
** Only compute triangles.
** Store triangles in a vectored form in a single 2 dim matrix.
eg.
1
2 3
4 5 6

1 2 3 4 5 6

(i,j)-> k

i*(i-1)/2+j
(3,2) -->(3*2)/2+2 =5.

john67 wrote

maybe i should specify my question:

i´m looking for a way to estimate / compute values for the missing values.
in my textbook (which is written in german by Prof. Backhaus, so probably
no one will know it) they guess that i can
replace the missing values by the mean value. But that far to inaccurate,
i think.

an other way that i found in some literature are the strategies i mentioned above.
my problem is, that i don´t knwo how to implement that straegies with
spss, if that is even possible.....

@ david marso, thanks for ur post & your help! i found the fuzzy c means algorithm, but same problem don´t how to implement these strategies in spps, without calculating each seperately

[Melissa Ives]

Other ways missing data are replaced are:
-->with the median instead of the mean,
-->with hot-deck imputation (sort the records by meaningful variables, and use the mean of the n records above and below the missing value)--thus replacement occurs within a smaller, more meaningful group (e.g. sort by gender, age, problem severity to replace days of problem). For SPSS details see: http://chestnut.org/LI/downloads/training_memos/index.html#DataCleaning
-->with regression using the other variables in the cluster.

Each of these would be done before running your cluster, and creating new 'missing replaced variables'.
Melissa
-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of john67
Sent: Wednesday, June 27, 2012 10:53 AM
To: [hidden email]
Subject: Re: [SPSSX-L] Include Missings in Cluster analysis

maybe i should specify my question:

i´m looking for a way to estimate / compute values for the missing values.
in my textbook (which is written in german by Prof. Backhaus, so probably no one will know it) they guess that i can replace the missing values by the mean value. But that far to inaccurate, i think.

an other way that i found in some literature are the strategies i mentioned above.
my problem is, that i don´t knwo how to implement that straegies with spss, if that is even possible.....


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[Art Kendall]

Please explain in more detail the nature of your data.
How did you gather the data? If this is aggregated data do you have access to the raw cases?

What are your variables?� What are their levels of measurement? Are there limited numbers of legitimate values for all variables? Do all of the variables have the same value labels?
Why is there missing data?� Are there different kinds?



I don't understand this.

I´m trying to cluster a group of 40 countries by approval to
democratic values. I have a total of 20 variables.
The countries should be clusterd in 4 cluster analysis, with each analysis
clustering the countries at 5 of the 20 variables. 

Do you have an a priori rationale for 4 clusters?�
Please give a more detailed explanation.
On 6/27/2012 11:53 AM, john67 wrote:

maybe i should specify my question:

i´m looking for a way to estimate / compute values for the missing values.
in my textbook (which is written in german by Prof. Backhaus, so probably
no one will know it) they guess that i can
replace the missing values by the mean value. But that far to inaccurate,
i think.

an other way that i found in some literature are the strategies i mentioned
above.
my problem is, that i don´t knwo how to implement that straegies with
spss, if that is even possible.....


--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Include-Missings-in-Cluster-analysis-tp5713829p5713843.html
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[john67]

Art Kendall wrote

 
    Please explain in more
        detail the nature of your data.
      How did you gather the data? If this
      is aggregated data do you have access to the raw cases?

My data is aggregated data from the WorldValueSurvey. I computed some macro indices on country level out of micro data from wthe WVS. Other indices
are macro indices from the world bank, and german foreign office. In the case of the WVS macro Indices are computed by myself & i have acces to the raw data
(i.e. the cases from which i calculated the macro indices. They are missing, because the specific question was not asked in the country). in the other indices from worldbank and foreign office, i have no access to the raw data.

Art Kendall wrote

      What are your variables?�  What are their levels of
        measurement? Are there limited numbers of legitimate values for
        all variables? Do all of the variables have the same value
        labels?
        Why is there missing data?�  Are there different kinds?

my variables are of the type approval to: secular leadership, ~ gender equality,  ~ democracitic institutions, ~ democratic values...and so on
most of them are measured ordinal on a 4 point scale

further more i have metric variables like GDP, GDPperSector, population composition, gini index etc....

i´m not sure if it was in the original posted syntax, but transformation / standardization of the variables is included.

about the type of the missing: i´m not really sure i got "not missing at random" (like for example in the case of saudi arabia, where certain democracy questions were not asked) as well as missing completly at random.      
       

Art Kendall wrote

       
        I don't understand this.
       
          I´m trying to cluster a group of 40 countries by approval to
democratic values. I have a total of 20 variables.
The countries should be clusterd in 4 cluster analysis, with each analysis
clustering the countries at 5 of the 20 variables.
       
        Do you have an a priori rationale for 4 clusters?�  
        Please give a more detailed explanation.
     
      Art Kendall

No i have no a priori rationale for the 4 cluster solution, i just wrote down some number, which i expect to be realstic. but i might be wrong, it was just for better reading. I want to cluster the countries by there approval to certain democratic values etc. and also cluster them by macro economic indicators and socio demogrpahic indicators

Tanks a lot!




Quoted from:
http://spssx-discussion.1045642.n5.nabble.com/Include-Missings-in-Cluster-analysis-tp5713829p5713852.html

[news]

  Change the missing value definition so that the missing becomes a
valid value.
That's it.

You may also dive into
Johann Bacher, Andreas Pöge, Knut Wenzig: Clusteranalyse. 3rd ed.
Oldenbourg 2010
And
http://www.clusteranalyse.net/
And for a first idea the 199 page lecture notes at
http://www.clusteranalyse.net/sonstiges/zaspringseminar2002/lecturenotes.pdf

HTH
Frank Thomas



Le 27/06/2012 16:55, john67 a écrit :

> thanks for the reply, but unfortunately that is not what i meant. i looking
> for a way to include the cases that have missing values and a way how i can
> compute values for the missings.
> i read that one method is to replace the missing value by the mean value,
> but that´s hardly acceptable.
>
> eventually what i´m seraching is a proper way to compute values for the
> missings and i read something about adapted clustering with the
> possibilities a) whole data strategy b) partial distance ~ and c) nearest
> prototype ~. but unfortunately it is not explained how to wirk with this
> strategys. and i cant find ana further literture.
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Include-Missings-in-Cluster-analysis-tp5713829p5713835.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
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[Poes, Matthew Joseph]

Making missing an actual value only makes sense when the variable is categorical, and if its categorical, then a specific form of cluster analysis should be done.  This is an approach I'd be cautious with.

Matthew J Poes
Research Data Specialist
Center for Prevention Research and Development
University of Illinois
510 Devonshire Dr.
Champaign, IL 61820
Phone:� 217-265-4576
email: [hidden email]


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of ftr
Sent: Thursday, June 28, 2012 8:16 AM
To: [hidden email]
Subject: Re: Include Missings in Cluster analysis

  Change the missing value definition so that the missing becomes a valid value.
That's it.

You may also dive into
Johann Bacher, Andreas Pöge, Knut Wenzig: Clusteranalyse. 3rd ed.
Oldenbourg 2010
And
http://www.clusteranalyse.net/
And for a first idea the 199 page lecture notes at http://www.clusteranalyse.net/sonstiges/zaspringseminar2002/lecturenotes.pdf

HTH
Frank Thomas



Le 27/06/2012 16:55, john67 a écrit :

> thanks for the reply, but unfortunately that is not what i meant. i
> looking for a way to include the cases that have missing values and a
> way how i can compute values for the missings.
> i read that one method is to replace the missing value by the mean
> value, but that´s hardly acceptable.
>
> eventually what i´m seraching is a proper way to compute values for
> the missings and i read something about adapted clustering with the
> possibilities a) whole data strategy b) partial distance ~ and c)
> nearest prototype ~. but unfortunately it is not explained how to wirk
> with this strategys. and i cant find ana further literture.
>
> --
> View this message in context:
> http://spssx-discussion.1045642.n5.nabble.com/Include-Missings-in-Clus
> ter-analysis-tp5713829p5713835.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
> 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
>
> __________ Information from ESET NOD32 Antivirus, version of virus
> signature database 7252 (20120627) __________
>
> The message was checked by ESET NOD32 Antivirus.
>
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>
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[Art Kendall]

it sounds like you have 3 subsets of your variables WVS, World Bank, and German.
Are there missing values in all three sets?� Are you doing 3 cluster analyses?

Are there a few variables which cause many cases to be excluded?

With the WVS, did you try clustering raw cases? Isn't it likely that countries might have a mix of value profiles?

On 6/27/2012 2:13 PM, john67 wrote:

Art Kendall wrote

    Please explain in more
        detail the nature of your data.
      How did you gather the data? If this
      is aggregated data do you have access to the raw cases?

My data is aggregated data from the WorldValueSurvey. I computed some macro
indices on country level out of micro data from wthe WVS. Other indices
are macro indices from the world bank, and german foreign office. In the
case of the WVS macro Indices are computed by myself & i have acces to the
raw data
(i.e. the cases from which i calculated the macro indices. They are missing,
because the specific question was not asked in the country). in the other
indices from worldbank and foreign office, i have no access to the raw data.



Art Kendall wrote

      What are your variables?�  What are their levels of
        measurement? Are there limited numbers of legitimate values for
        all variables? Do all of the variables have the same value
        labels?
        Why is there missing data?�  Are there different kinds?

my variables are of the type approval to: secular leadership, ~ gender
equality,  ~ democracitic institutions, ~ democratic values...and so on
most of them are measured ordinal on a 4 point scale

further more i have metric variables like GDP, GDPperSector, population
composition, gini index etc....

i´m not sure if it was in the original posted syntax, but transformation /
standardization of the variables is included.

about the type of the missing: i´m not really sure i got "not missing at
random" (like for example in the case of saudi arabia, where certain
democracy questions were not asked) as well as missing completly at random.



Art Kendall wrote

        I don't understand this.

          I´m trying to cluster a group of 40 countries by approval to
democratic values. I have a total of 20 variables.
The countries should be clusterd in 4 cluster analysis, with each analysis
clustering the countries at 5 of the 20 variables.

        Do you have an a priori rationale for 4 clusters?�
        Please give a more detailed explanation.

      Art Kendall

No i have no a priori rationale for the 4 cluster solution, i just wrote
down some number, which i expect to be realstic. but i might be wrong, it
was just for better reading.

Tanks a lot!




Quoted from:
http://spssx-discussion.1045642.n5.nabble.com/Include-Missings-in-Cluster-analysis-tp5713829p5713852.html


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[john67]

Art Kendall wrote

        Are there a few variables which cause many cases to be excluded?
       
        With the WVS, did you try clustering raw cases? Isn't it likely
        that countries might have a mix of value profiles?  
     

unfortunately not, there are several variables with 2 upt to 5 missing values, so i cannot kick out one ore two major variables that causes many missing.

I´m not sure if i got what u meant, but i might have found i solution for this myself, as i do not implement constructed indices, but the raw cases (i.e. the question aggregated on macro level) themselves.

thanks a lot for your help!!

@ FTR, just bought the book today ;)

but as Poes, Matthew Joseph mentioned, i have a mixture of categorial and metric variables, so it´s probably not the best idea

thanks everybody for ur help, i will dive into the textbook and  later try to implement your ideas!

[Art Kendall]

TWOSTEP will handle a mix of both kinds of variables.� However, you would not want to just do a hodge podge of variables.
usually there is some logic behind what variables would go into a profile, e.g., values, or economic indicators, or demographic variables, etc.

For example if you might use values as continuous dependent variables, and a nominal level cluster membership (profile type) as a predictor. ore vice versa.
On 6/28/2012 2:15 PM, john67 wrote:

Art Kendall wrote

        Are there a few variables which cause many cases to be excluded?

        With the WVS, did you try clustering raw cases? Isn't it likely
        that countries might have a mix of value profiles?

unfortunately not, there are several variables with 2 upt to 5 missing
values, so i cannot kick out one ore two major variables that causes many
missing.

I´m not sure if i got what u meant, but i might have found i solution for
this myself, as i do not implement constructed indices, but the raw cases
(i.e. the question aggregated on macro level) themselves.

thanks a lot for your help!!

@ FTR, just bought the book today ;)

but as Poes, Matthew Joseph mentioned, i have a mixture of categorial and
metric variables, so it´s probably not the best idea

thanks everybody for ur help, i will dive into the textbook and  later try
to implement your ideas!




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[David Marso]

"However, you would not want to just do a hodge podge of variables."
Otherwise you will be cast into the GIGO Abyss  (not a fun dance).

Art Kendall wrote

TWOSTEP will handle
      a mix of both kinds of variables.�  However, you would not want to
      just do a hodge podge of variables.
      usually there is some logic behind what variables would go into a
      profile, e.g., values, or economic indicators, or demographic
      variables, etc.
     
      For example if you might use values as continuous dependent
      variables, and a nominal level cluster membership (profile type)
      as a predictor. ore vice versa.
      Art Kendall
Social Research Consultants
      On 6/28/2012 2:15 PM, john67 wrote:
   
   
      Art Kendall wrote

     
       
        Are there a few variables which cause many cases to be excluded?

        With the WVS, did you try clustering raw cases? Isn't it likely
        that countries might have a mix of value profiles?



     
     
unfortunately not, there are several variables with 2 upt to 5 missing
values, so i cannot kick out one ore two major variables that causes many
missing.

I´m not sure if i got what u meant, but i might have found i solution for
this myself, as i do not implement constructed indices, but the raw cases
(i.e. the question aggregated on macro level) themselves.

thanks a lot for your help!!

@ FTR, just bought the book today ;)

but as Poes, Matthew Joseph mentioned, i have a mixture of categorial and
metric variables, so it´s probably not the best idea

thanks everybody for ur help, i will dive into the textbook and  later try
to implement your ideas!




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[bgreen]

I have run the following analysis with ALSCAL. The stimulus
configuration plot is a 2 dimensional maze. It used to be possible to
obtain a series of plots, e.g Dim 1 & 2, Dim 1 & 3, and Dime 2 & 3.
Any suggestions regarding what modification to this code is required
is much appreciated:

ALSCAL
   /MATRIX=IN('D:\userdata\greenrob\temp\spss1316\spssalsc.tmp')
   /LEVEL=ORDINAL
   /CONDITION=MATRIX
   /MODEL=EUCLID
   /CRITERIA=CONVERGE(0.001) STRESSMIN(0.005) ITER(30) CUTOFF(0) DIMENS(2,4)
   /PLOT=DEFAULT
   /PRINT=HEADER


Bob

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[Valerie Villella]

Thank you for your email.

I am out of the office on July 13 and will not be accessing my emails. I will respond to your message on my return to the office on July 16.

Have a wonderful day.

Valerie Villella
Education Coordinator &
Policy and Program Analyst

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