Discriminant function analysis

[Pete]

I've done a discriminant function analysis in SPSS intended to classify 3 types of case using 30 variables. The discriminant function coefficients and structure matrix are below. It is clear that the two functions do different things with these data. I have the following questions:
1. How do I identify what each function is doing when cases are classified?
2. I want to calculate on a case by case basis the scores for truncated forms of each discriminant function (f1 S1DUR - S3PIRANG and f2 S3INRANG -RPVIS1). I assume I generate a linear equation using these coefficients to weight each variable. Is that right?
3. Alternatively, is there a simple way of obtaining the scores from each case for each discriminant function by procedures in SPSS? On reflection, this might be the preferred option, but I will stand to be advised.

any other advice, observations would be gratefully received.
Many thanks
PH


Standardized Canonical Discriminant Function Coefficients
  Function
        1 2
S1DUR .106 -.090
S1PIRANG -.041 .074
S1INRENG .087 .009
S2DUR -.048 -.276
S2PIRANG .198 -.284
S2INRANG .211 -.113
S3DUR -1.906 .829
S3PIRANG .034 .016
S3INRANG .273 .437
S4DUR 1.546 -.843
S4PIRANG .123 .118
S4INRANG -.326 -.145
NPVIS1 -.246 -.002
NPVIS2 -.165 .343
NPVIS3 .096 -.201
RPVIS4 .253 .362
NPVIS4 .373 -.099
RPVIS1PI -.250 .234
RPVIS2PI .256 .345
RPVIS3PI .067 .107
RPVIS4PI .081 -.113
RPVIS1IN .061 .316
RPVIS2IN -.689 -.097
RPVIS3IN .640 -.269
RPVIS4IN .229 .239
RPVI1TO4 -.200 1.226
NPVI1TO4 .082 -1.588


Structure Matrix
  Function
        1 2
NPVIS4 .324 -.053
S4INRANG -.255 -.014
S2INRANG .245 .076
RPVIS3IN .230 -.029
S3DUR -.227 -.065
RPVIS3 -.227 -.065
NPVIS1 -.222 .047
S4DUR -.155 -.079
RPVIS2IN -.119 .068
S2DUR -.117 .012
RPVIS2 -.117 .012
RPVIS4PI .106 .053
RPVIS4 .103 .047
S1INRENG -.100 -.034
S3PIRANG .088 -.038
RPVI1TO4 -.077 .057
S4PIRANG .072 .049
S3INRANG .141 .354
RPVIS3PI .040 .318
RPVIS2PI .175 .313
NPVIS2 -.210 .306
RPVIS1PI -.124 .225
S2PIRANG .078 -.207
RPVIS4IN .119 .181
NPVI1TO4 -.064 -.168
NPVIS3 .111 -.167
RPVIS1IN .144 .158
S1PIRANG .069 -.082
S1DUR .033 -.062
RPVIS1 .033 -.062
Pooled within-groups correlations between discriminating variables and standardized canonical discriminant functions
 Variables ordered by absolute size of correlation within function.
* Largest absolute correlation between each variable and any discriminant function
a This variable not used in the analysis.

[Rich Ulrich]

>
> I've done a discriminant function analysis in SPSS intended to classify 3
> types of case using 30 variables. The discriminant function coefficients and
> structure matrix are below. It is clear that the two functions do different
> things with these data. I have the following questions:

The important message from *your* standardized coefficients is
that several of them are greater than 1.0; and they occur in pairs
of related variables.  Like in regression (though the standardization
is slightly different), these demonstrate that you have suppressor
variables.

> S3DUR -1.906 .829
> S4DUR 1.546 -.843

> RPVI1TO4 -.200 1.226
> NPVI1TO4 .082 -1.588

SxDUR  and xPV1TO4  comprise pairs that have similar structure
coefficients (which are correlations), but different directions (+,-)
when used in the equation.  If you want an easy interpretation,
I suggest that you redo the analysis where these variables are
replaced, each pair, by a difference and a sum (or average).


Suppressors can be created by more than two variables, and they
don't have to have the same scaling for each variable; those
conditions can make dealing with them more confusing, at the least.
Your data seems to have the simpler version, if I judge correctly
from the variable names.


> 1. How do I identify what each function is doing when cases are classified?
> 2. I want to calculate on a case by case basis the scores for truncated
> forms of each discriminant function (f1 S1DUR - S3PIRANG and f2 S3INRANG
> -RPVIS1). I assume I generate a linear equation using these coefficients to
> weight each variable. Is that right?
> 3. Alternatively, is there a simple way of obtaining the scores from each
> case for each discriminant function by procedures in SPSS? On reflection,
> this might be the preferred option, but I will stand to be advised.
>


SPSS can give you certain predicted scores, and it can list them by case.
You will have to read up on the subject, to figure out what you are
getting from "classification equations", if you use those.

I can't tell what else you are asking here.  You can also write explicit
equations in SPSS syntax, if you obtain the not-standardized coefficients.



--
Rich Ulrich



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[Swank, Paul R]

I hope you have a large sample because discriminant function analysis requires 20-30 subjects per variable per group to adequately estimate the parameters of the model. If you have a smaller sample size, multinomial logistic regression might be a better option.

Dr. Paul R. Swank,
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center-Houston


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Pete
Sent: Wednesday, April 20, 2011 3:33 AM
To: [hidden email]
Subject: Discriminant function analysis

I've done a discriminant function analysis in SPSS intended to classify 3
types of case using 30 variables. The discriminant function coefficients and
structure matrix are below. It is clear that the two functions do different
things with these data. I have the following questions:
1. How do I identify what each function is doing when cases are classified?
2. I want to calculate on a case by case basis the scores for truncated
forms of each discriminant function (f1 S1DUR - S3PIRANG and f2 S3INRANG
-RPVIS1). I assume I generate a linear equation using these coefficients to
weight each variable. Is that right?
3. Alternatively, is there a simple way of obtaining the scores from each
case for each discriminant function by procedures in SPSS? On reflection,
this might be the preferred option, but I will stand to be advised.

any other advice, observations would be gratefully received.
Many thanks
PH


Standardized Canonical Discriminant Function Coefficients
        Function
        1       2
S1DUR   .106    -.090
S1PIRANG        -.041   .074
S1INRENG        .087    .009
S2DUR   -.048   -.276
S2PIRANG        .198    -.284
S2INRANG        .211    -.113
S3DUR   -1.906  .829
S3PIRANG        .034    .016
S3INRANG        .273    .437
S4DUR   1.546   -.843
S4PIRANG        .123    .118
S4INRANG        -.326   -.145
NPVIS1  -.246   -.002
NPVIS2  -.165   .343
NPVIS3  .096    -.201
RPVIS4  .253    .362
NPVIS4  .373    -.099
RPVIS1PI        -.250   .234
RPVIS2PI        .256    .345
RPVIS3PI        .067    .107
RPVIS4PI        .081    -.113
RPVIS1IN        .061    .316
RPVIS2IN        -.689   -.097
RPVIS3IN        .640    -.269
RPVIS4IN        .229    .239
RPVI1TO4        -.200   1.226
NPVI1TO4        .082    -1.588


Structure Matrix
        Function
        1       2
NPVIS4  .324    -.053
S4INRANG        -.255   -.014
S2INRANG        .245    .076
RPVIS3IN        .230    -.029
S3DUR   -.227   -.065
RPVIS3  -.227   -.065
NPVIS1  -.222   .047
S4DUR   -.155   -.079
RPVIS2IN        -.119   .068
S2DUR   -.117   .012
RPVIS2  -.117   .012
RPVIS4PI        .106    .053
RPVIS4  .103    .047
S1INRENG        -.100   -.034
S3PIRANG        .088    -.038
RPVI1TO4        -.077   .057
S4PIRANG        .072    .049
S3INRANG        .141    .354
RPVIS3PI        .040    .318
RPVIS2PI        .175    .313
NPVIS2  -.210   .306
RPVIS1PI        -.124   .225
S2PIRANG        .078    -.207
RPVIS4IN        .119    .181
NPVI1TO4        -.064   -.168
NPVIS3  .111    -.167
RPVIS1IN        .144    .158
S1PIRANG        .069    -.082
S1DUR   .033    -.062
RPVIS1  .033    -.062
Pooled within-groups correlations between discriminating variables and
standardized canonical discriminant functions
 Variables ordered by absolute size of correlation within function.
*       Largest absolute correlation between each variable and any discriminant
function
a       This variable not used in the analysis.



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[Art Kendall]

Are your variables items from scales?  This looks like a large number
of predictors.


Art Kendall
Social Research Consultants

On 4/20/2011 4:33 AM, Pete wrote:

> I've done a discriminant function analysis in SPSS intended to classify 3
> types of case using 30 variables. The discriminant function coefficients and
> structure matrix are below. It is clear that the two functions do different
> things with these data. I have the following questions:
> 1. How do I identify what each function is doing when cases are classified?
> 2. I want to calculate on a case by case basis the scores for truncated
> forms of each discriminant function (f1 S1DUR - S3PIRANG and f2 S3INRANG
> -RPVIS1). I assume I generate a linear equation using these coefficients to
> weight each variable. Is that right?
> 3. Alternatively, is there a simple way of obtaining the scores from each
> case for each discriminant function by procedures in SPSS? On reflection,
> this might be the preferred option, but I will stand to be advised.
>
> any other advice, observations would be gratefully received.
> Many thanks
> PH
>
>
> Standardized Canonical Discriminant Function Coefficients
>          Function
>          1       2
> S1DUR   .106    -.090
> S1PIRANG        -.041   .074
> S1INRENG        .087    .009
> S2DUR   -.048   -.276
> S2PIRANG        .198    -.284
> S2INRANG        .211    -.113
> S3DUR   -1.906  .829
> S3PIRANG        .034    .016
> S3INRANG        .273    .437
> S4DUR   1.546   -.843
> S4PIRANG        .123    .118
> S4INRANG        -.326   -.145
> NPVIS1  -.246   -.002
> NPVIS2  -.165   .343
> NPVIS3  .096    -.201
> RPVIS4  .253    .362
> NPVIS4  .373    -.099
> RPVIS1PI        -.250   .234
> RPVIS2PI        .256    .345
> RPVIS3PI        .067    .107
> RPVIS4PI        .081    -.113
> RPVIS1IN        .061    .316
> RPVIS2IN        -.689   -.097
> RPVIS3IN        .640    -.269
> RPVIS4IN        .229    .239
> RPVI1TO4        -.200   1.226
> NPVI1TO4        .082    -1.588
>
>
> Structure Matrix
>          Function
>          1       2
> NPVIS4  .324    -.053
> S4INRANG        -.255   -.014
> S2INRANG        .245    .076
> RPVIS3IN        .230    -.029
> S3DUR   -.227   -.065
> RPVIS3  -.227   -.065
> NPVIS1  -.222   .047
> S4DUR   -.155   -.079
> RPVIS2IN        -.119   .068
> S2DUR   -.117   .012
> RPVIS2  -.117   .012
> RPVIS4PI        .106    .053
> RPVIS4  .103    .047
> S1INRENG        -.100   -.034
> S3PIRANG        .088    -.038
> RPVI1TO4        -.077   .057
> S4PIRANG        .072    .049
> S3INRANG        .141    .354
> RPVIS3PI        .040    .318
> RPVIS2PI        .175    .313
> NPVIS2  -.210   .306
> RPVIS1PI        -.124   .225
> S2PIRANG        .078    -.207
> RPVIS4IN        .119    .181
> NPVI1TO4        -.064   -.168
> NPVIS3  .111    -.167
> RPVIS1IN        .144    .158
> S1PIRANG        .069    -.082
> S1DUR   .033    -.062
> RPVIS1  .033    -.062
> Pooled within-groups correlations between discriminating variables and
> standardized canonical discriminant functions
>   Variables ordered by absolute size of correlation within function.
> *       Largest absolute correlation between each variable and any discriminant
> function
> a       This variable not used in the analysis.
>
>
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Discriminant-function-analysis-tp4315226p4315226.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
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