Chapter 17

Discriminant Function Analysis

Merle Canfield

The purpose of discriminant is to predict group membership (a categorical or noncontinuous DV) from a set of continuous variables.  Diagnostic groups would be the best way to think about what we are doing.  How do you diagnose people?  This statistic can be used to develop such diagnostic categories or to decide how to assign people categories.  That is diagnostic groups.

What is it that contributes to the flu?  High fever, drippy nose, runny eyes, achy muscles, and etc.  A formula can be developed that will predict whether the person might have the flu or not.

Mathematically MANOVA and discriminant analysis are the same.  Although there are some computations that each does and the other does not, the basic difference is that the DVs and IVs are reversed on the continuous and categorical variables.  When using MANOVA the IVs are the categorical variables are and the DVs are the continuous.  When using discriminant analysis the IVs are the continuous variables and the DVs are the categorical variables.  Having pointed out their similarity it should be noted that when they are used in practice the appear to be statistics of a completely different nature.

MANOVA answers the question of whether there are differences in group means of the DVs, while discriminant analysis answers the question of whether the IVs can predict group membership.  In this case the methods are still somewhat similar in their purpose.  They differ more when discriminant function provides methods of classifying subjects into groups based on the IVs.  Consequently, the goals of discriminant analysis are to predict groups and classify subjects with a minimum number of variables.  Another task for discriminant is to find the minimum number of variables that maximize the ratio of between‑groups sum of squares to within‑groups sum of squares.

On the following page is the same questionnaire that has been used throughout the manual with a few added items ‑‑ particularly items about change.  Seven subtests have been computed from the items.

Psychosocial Assessment Scale

Name:________________________________       ID #_________   Date_________

Circle the number below that is the closest to how you have felt recently.

none                         all

IN THE PAST WEEK HOW OFTEN HAVE YOU ...           of the     several  of the

time       times        time

1.  ...enjoyed your leisure hours (evenings, weekends, etc.)?             0  1  2  3  4  5  6  7  8

2.  ...felt fearful or afraid?                                                                         0  1  2  3  4  5  6  7  8

3.  ...felt sad or depressed?                                                                        0  1  2  3  4  5  6  7  8

4.  ...felt good about yourself or things you have done?                      0  1  2  3  4  5  6  7  8

5.  ...felt angry?                                                                            0  1  2  3  4  5  6  7  8

6.  ...felt mixed up or confused?                                                0  1  2  3  4  5  6  7  8

7.  ...felt like you've spent a worthwhile day?                                        0  1  2  3  4  5  6  7  8

8.  ...felt tense?                                                                             0  1  2  3  4  5  6  7  8

9.  ...felt useless?                                                                                         0  1  2  3  4  5  6  7  8

very                      very

IN THE PAST WEEK ...                                                                                                    dissatisfied      satisfied

10. ...how satisfied have you been in general (with relationships, with finances,           0  1  2  3  4  5  6  7  8

and family?)

never                often

11. ...how often did you get together with people outside of your home?                        0  1  2  3  4  5  6  7  8

all of

never            the time

12. ...did you handle the basic necessities such as paying bills, shopping and 0  1  2  3  4  5  6  7  8

and taking care of your room (home; apt.)?

none     some     much

13. ...how much time did you spend with friends & family talking or doing things        0  1  2  3  4  5  6  7  8

together?

a great

none      some      deal

14. ...how much conflict was there with the person(s) you live with?                0  1  2  3  4  5  6  7  8

15. ...have you used alcohol?                                                                                    0  1  2  3  4  5  6  7  8

16. ...have you used drugs?                                                                                                      0  1  2  3  4  5  6  7  8

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

17. How much would friends or community members support you if you were sick     0  1  2  3  4  5  6  7  8

or having problems?

not            part      full

employed  time    time

18. Are you employed (includes self-employed, housewife, student, employee)?         0  1  2  3  4  5  6  7  8

not at all    completely

19. Do you feel that you do a good job (whether self‑employed, housewife,   0  1  2  3  4  5  6  7  8

student, employee)?

20. How much do you like your work (or studies)?                                              0  1  2  3  4  5  6  7  8

21. Do emotional problems interfere with your work (or studies)?                    0  1  2  3  4  5  6  7  8

no                    enough

22. In the past month, was the amount of money you had, enough to pay the bills?      0  1  2  3  4  5  6  7  8

poor                   good

23. Do you feel that you are in good physical condition?                                    0  1  2  3  4  5  6  7  8

5-6-93

The following spss job stream is used compute the discriminant function on th  above questionnaire.

 File Name = pasdsc4.sps data list file='c:\rdda\PASALL4.TXT' free   /DIAG DISTRS QUALIT RELATE JOB CHANGE CARE ABUSE. value labels diag   1 'psychotic'   2 'affective'   3 'anxiety'   4 'sub‑abuse'   5 'adjustment'   8 'other'. DSC GROUPS=DIAG(1,9)    /VAR=DISTRS TO ABUSE    /METHOD=MINRESID    /PIN=.05    /FUNCTIONS=6,100,.05    /STATISTICS = mean univf coeff table    /plot=map.

 File Name = pasall4.txt 3,1.17,1.40,1.50,2.67,4.00,8.00,6.00   5,1.33,3.20,4.25,3.50,2.25,3.00,2.00   8,1.33,4.20,4.75,1.50,7.50,4.00,3.00   5,5.33,5.40,5.25,2.25,3.25,4.00,2.00   4,3.50,2.20,4.00,3.33,5.00,4.00,7.00   2,0.17,2.80,5.33,6.25,4.00,8.00,1.00   3,3.80,2.80,4.75,3.00,3.25,4.00,3.00   3,3.33,4.50,7.00,4.00,6.75,3.00,8.00   2,1.33,4.80,4.50,1.50,3.25,2.00,1.00   5,2.33,3.80,1.00,3.75,1.50,0.00,0.00   8,6.00,5.20,4.00,3.00,5.00,7.00,0.00   2,0.17,2.80,5.33,6.25,4.00,8.00,1.00   3,3.80,2.80,4.75,3.00,3.25,4.00,3.00   3,3.33,4.50,7.00,4.00,6.75,3.00,8.00   2,1.33,4.80,4.50,1.50,3.25,2.00,1.00   5,2.33,3.80,1.00,3.75,1.50,0.00,0.00   8,6.00,5.20,4.00,3.00,5.00,7.00,0.00   2,2.00,1.40,4.00,6.33,3.25,3.00,0.00   4,5.00,4.60,5.25,6.25,5.25,3.00,8.00   5,3.50,4.80,5.25,2.00,5.75,6.00,0.00   5,1.50,4.75,2.00,5.00,2.00,8.00,0.00   4,3.50,5.40,5.75,4.25,4.00,8.00,8.00   2,2.20,3.40,5.00,4.00,1.25,3.00,0.00   5,6.00,3.00,2.50,6.00,1.50,8.00,0.00   5,6.00,3.00,2.50,6.00,1.50,8.00,0.00   1,7.67,8.00,6.50,4.00,8.00,8.00,3.00   8,3.83,4.40,1.50,3.25,4.25,3.00,3.00   3,6.50,4.40,6.00,4.00,7.00,9.00,0.00   4,3.50,4.00,5.75,5.25,5.00,6.00,6.00   3,2.67,5.00,4.00,5.25,6.00,4.00,0.00   3,2.67,5.00,4.00,5.25,6.00,4.00,0.00   2,2.00,1.00,3.00,2.25,2.50,2.00,7.00

The variables DISTRS, QUALIT, RELATE, JOB, CHANGE, CARE, and ABUSE are subtest of the questionnaire.  Their reliability was tested in the reliability chapter.  The subtests are comprised of the items in the following manner.

DISTRS

FEARFUL, DEPRESSED; ANGRY CONFUSED; TENSE

QUALIT

LEISURE; FEEL GOOD ABOUT SELF; WORTHWILE DAY; BORED OR USELESS;

RELATE

SATISFIED; GET TOGETHER; SPEND TIME WITH FRIENDS; CONFLICT

JOB

EMPLOYED; GOOD JOB; LIKE WORK; PROBLEMS INTERFERE; AMOUNT OF MONEY

CHANGE

SENSE OF HUMOR; SEE THINGS DIFFERENT; CHANGE IN LIFE; MORE SENSE

SELCAR

HANDLE BASIC NECESSITIES

ALCDRUG

USE ALCOHOL OR DRUGS

‑ ‑ ‑ ‑ ‑ ‑ ‑   D I S C R I M I N A N T   A N A L Y S I S   ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑

On groups defined by DIAG

32 (Unweighted) cases were processed.

0 of these were excluded from the analysis.

32 (Unweighted) cases will be used in the analysis.

Number of cases by group

Number of cases

DIAG      Unweighted     Weighted  Label

1           1          1.0  psychotic

2           7          7.0  affective

3           8          8.0  anxiety

4           4          4.0  sub‑abuse

8           4          4.0  other

Total          32         32.0

Group means

DIAG         DISTRS         QUALIT         RELATE            JOB

1        7.67000        8.00000        6.50000        4.00000

2        1.31429        3.00000        4.52286        4.01143

3        3.40875        3.80000        4.87500        3.89625

4        3.87500        4.05000        5.18750        4.77000

5        3.54000        3.96875        2.96875        4.03125

8        4.29000        4.75000        3.56250        2.68750

Total        3.28500        3.94844        4.24719        3.91656

DIAG         CHANGE           CARE          ABUSE

1        8.00000        8.00000        3.00000

2        3.07143        4.00000        1.57143

3        5.37500        4.87500        3.50000

4        4.81250        5.25000        7.25000

5        2.40625        4.62500         .50000

8        5.43750        5.25000        1.50000

Total        4.14844        4.81250        2.53125

Wilks' Lambda (U‑statistic) and univariate F‑ratio

with 5 and 26 degrees of freedom

Variable   Wilks' Lambda         F         Significance

‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑‑‑‑‑

DISTRS         .54985          4.2572          .0058

QUALIT         .59531          3.5350          .0143

RELATE         .67522          2.5012          .0562

JOB            .86983           .7782          .5744

CHANGE         .40424          7.6635          .0002

CARE           .92041           .4497          .8096

ABUSE          .49453          5.3150          .0017

‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑   D I S C R I M I N A N T   A N A L Y S I S   ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑

On groups defined by DIAG

Analysis number       1

Stepwise variable selection

Selection rule:  minimize sum of unexplained variations

(residual variance)

Maximum number of steps..................      14

Minimum tolerance level..................  .00100

Maximum significance of F to enter.......  .05000

Minimum significance of F to remove...... 1.00000

Canonical Discriminant Functions

Maximum number of functions..............       5

Minimum cumulative percent of variance...  100.00

Maximum significance of Wilks' Lambda....   .0500

Prior probability for each group is  .16667

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the Analysis after Step 0 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Minimum   Signif. of

Variable  Tolerance  Tolerance  F to Enter   Residual Variance

DISTRS    1.0000000  1.0000000       .0058274   10.0912916

QUALIT    1.0000000  1.0000000       .0143077   10.2468926

RELATE    1.0000000  1.0000000       .0561791   11.7288862

JOB       1.0000000  1.0000000       .5744219   13.8239809

CHANGE    1.0000000  1.0000000       .0001538    8.9475711

CARE      1.0000000  1.0000000       .8095904   13.5391699

ABUSE     1.0000000  1.0000000       .0017044   11.1151835

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

At step 1, CHANGE   was included in the analysis.

Degrees of Freedom  Signif.   Between Groups

Wilks' Lambda         .40424        1    5       26.0

Equivalent F         7.66349             5       26.0   .0002

Residual variance    8.94757

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables in the Analysis after Step 1 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Signif. of

Variable  Tolerance  F to Remove  Residual Variance

CHANGE    1.0000000        .0002

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the Analysis after Step 1 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Minimum   Signif. of

Variable  Tolerance  Tolerance  F to Enter   Residual Variance

DISTRS     .9921191   .9921191       .0158258    7.1058353

QUALIT     .8536946   .8536946       .0578092    7.6397365

RELATE     .6238689   .6238689       .0792861    7.5457848

JOB        .9988162   .9988162       .6230502    8.2733499

CARE       .9890250   .9890250       .9547059    8.7610105

ABUSE      .9988861   .9988861       .0075100    6.8847853

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

At step 2, ABUSE    was included in the analysis.

Degrees of Freedom  Signif.   Between Groups

Wilks' Lambda         .22235        2    5       26.0

Equivalent F         5.60365            10       50.0   .0000

Residual variance    6.88479

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables in the Analysis after Step 2 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Signif. of

Variable  Tolerance  F to Remove  Residual Variance

CHANGE     .9988861        .0008    11.1151835

ABUSE      .9988861        .0075     8.9475711

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the Analysis after Step 2 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Minimum   Signif. of

Variable  Tolerance  Tolerance  F to Enter   Residual Variance

DISTRS     .9489307   .9489307       .0137434    5.3300875

QUALIT     .7733663   .7733663       .0719516    5.8123332

RELATE     .6181581   .6181581       .1260944    6.0351640

JOB        .8923964   .8923964       .2915532    6.2068628

CARE       .9211850   .9211850       .8593293    6.6430379

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

At step 3, DISTRS   was included in the analysis.

Degrees of Freedom  Signif.   Between Groups

Wilks' Lambda         .12655        3    5       26.0

Approximate F        4.95223            15       66.7   .0000

Residual variance    5.33009

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables in the Analysis after Step 3 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Signif. of

Variable  Tolerance  F to Remove  Residual Variance

DISTRS     .9489307        .0137     6.8847853

CHANGE     .9918938        .0026     7.2191285

ABUSE      .9554031        .0067     7.1058353

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the Analysis after Step 3 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Minimum   Signif. of

Variable  Tolerance  Tolerance  F to Enter   Residual Variance

QUALIT     .7657560   .7657560       .2946961    4.8957789

RELATE     .5250643   .5250643       .0319019    4.3762474

JOB        .8878955   .8647746       .3170228    4.7997273

CARE       .8863100   .8863100       .9800020    5.2671681

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

At step 4, RELATE   was included in the analysis.

Degrees of Freedom  Signif.   Between Groups

Wilks' Lambda         .07670        4    5       26.0

Approximate F        4.51397            20       77.2   .0000

Residual variance    4.37625

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables in the Analysis after Step 4 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Signif. of

Variable  Tolerance  F to Remove  Residual Variance

DISTRS     .8060229        .0034     6.0351640

RELATE     .5250643        .0319     5.3300875

CHANGE     .5619477        .0004     6.5301484

ABUSE      .9221665        .0096     5.5978973

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the Analysis after Step 4 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Minimum   Signif. of

Variable  Tolerance  Tolerance  F to Enter   Residual Variance

QUALIT     .6586641   .4516334       .1209359    3.7773653

JOB        .8848785   .5232802       .3676833    3.9752195

CARE       .8793158   .5209208       .9857679    4.3268761

F level or tolerance or VIN insufficient for further computation.

Summary Table

Action      Vars  Wilks'         Residual

Step Entered Removed   in   Lambda   Sig.  Variance    Label

1  CHANGE             1   .40424  .0002   8.94757

2  ABUSE              2   .22235  .0000   6.88479

3  DISTRS             3   .12655  .0000   5.33009

4  RELATE             4   .07670  .0000   4.37625

Classification function coefficients

(Fisher's linear discriminant functions)

DIAG    =         1              2              3              4

psychotic      affective      anxiety        sub‑abuse

DISTRS          4.2237266       .3147697      1.9540075      2.2973701

RELATE         ‑1.4717060      1.5935937      ‑.2131648      ‑.0086120

CHANGE          5.9080591       .6730551      3.3416493      2.8762865

ABUSE           1.1518138       .2313193       .8917886      1.6468356

(Constant)    ‑38.5666633     ‑6.8177778    ‑15.1438445    ‑19.1114201

Classification function coefficients

(Fisher's linear discriminant functions)

DIAG    =         5              8

DISTRS          1.5961245      2.5812427

RELATE           .1578773     ‑1.4679306

CHANGE          1.4055591      4.3107385

ABUSE            .2873630       .6623786

(Constant)     ‑6.6141529    ‑16.9303779

Canonical Discriminant Functions

Pct of   Cum  Canonical  After  Wilks'

Fcn Eigenvalue Variance  Pct     Corr      Fcn  Lambda  Chi‑square  df  Sig

:    0 .076700     66.764    20  .0000

1*    3.4442   70.76   70.76    .8803 :    1 .340871     27.983    12  .0056

2*     .9681   19.89   90.65    .7014 :    2 .670868     10.379     6  .1096

3      .3563    7.32   97.96    .5125 :    3 .909869      2.456     2  .2929

4      .0991    2.04  100.00    .3002 :

* Marks the 2 canonical discriminant functions remaining in the analysis.

Standardized canonical discriminant function coefficients

Func  1    Func  2

DISTRS        .78046    ‑.37780

RELATE       ‑.72437     .72200

CHANGE       1.09194    ‑.28892

ABUSE         .49932     .67990

Structure matrix:

Pooled within‑groups correlations between discriminating variables

and canonical discriminant functions

(Variables ordered by size of correlation within function)

Func  1    Func  2

CHANGE        .59507*    .21011

DISTRS        .41386*   ‑.33144

QUALIT        .02293*    .00838

ABUSE         .30181     .81916*

RELATE        .17047     .52429*

JOB          ‑.04750    ‑.31096*

CARE          .04567    ‑.17348*

* denotes largest absolute correlation between each variable and any

discriminant function.

Canonical discriminant functions evaluated at group means (group centroids)

Group      Func   1    Func   2

1       4.34006     ‑.65172

2      ‑2.20805      .55929

3        .97152      .29713

4       1.40209     1.56893

5      ‑1.11836     ‑.90858

8       1.67065    ‑1.16186

Symbols used in territorial map

Symbol  Group  Label

‑‑‑‑‑‑  ‑‑‑‑‑  ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

1        1  psychotic

2        2  affective

3        3  anxiety

4        4  sub‑abuse

6        8  other

*           Group centroids

Territorial Map  * indicates a group centroid

(Assuming all functions but the first two are zero)

Canonical Discriminant Function 1

‑6.0      ‑4.0      ‑2.0        .0       2.0       4.0       6.0

òôôôôôôôôôòôôôôôôôôôòôôôôôôôôôòôôôôôôôôôòôôôôôôôôôòôôôôôôôôôò

C    6.0 ò                     24                                      ò

a        ö                     24                                      ö

n        ö                      24                                     ö

o        ö                      24                                     ö

n        ö                       24                                    ö

i        ö                       24                                  44ö

c    4.0 ò          ò         ò   24    ò         ò         ò       411ò

a        ö                        24                               41  ö

l        ö                         24                             41   ö

ö                         24                           441    ö

D        ö                          24                         411     ö

i        ö                          24                        41       ö

s    2.0 ò          ò         ò     24  ò         ò         ò41        ò

c        ö                           24        *           441         ö

r        ö                           234444               411          ö

i        ö                           23333344444         41            ö

m        ö                   *       23    3333344444   41             ö

i        ö                         2253      *  333334441              ö

n     .0 ò          ò         ò  2255 53ò         333361    ò          ò

a        ö                    22255    53      333666661               ö

n        ö                  22555       53 3333666     61     *        ö

t        ö                2255    *      536666 *      61              ö

ö              2255             56            61              ö

F        ö            2255               56             61             ö

u   ‑2.0 ò         22255      ò         ò56       ò     61  ò          ò

n        ö       22555                   56             61             ö

c        ö     2255                      56              61            ö

t        ö   2255                        56              61            ö

i        ö22255                         56               61            ö

o        ö555                           56                61           ö

n   ‑4.0 ò          ò         ò         56        ò       61ò          ò

ö                              56                61           ö

2        ö                              56                61           ö

ö                              56                 61          ö

ö                              56                 61          ö

ö                             56                  61          ö

‑6.0 ò                             56                   61         ò

òôôôôôôôôôòôôôôôôôôôòôôôôôôôôôòôôôôôôôôôòôôôôôôôôôòôôôôôôôôôò

‑6.0      ‑4.0      ‑2.0        .0       2.0       4.0       6.0

Classification results ‑

No. of    Predicted Group Membership

Actual Group        Cases          1          2          3          4

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑  ‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑

Group       1              1          1          0          0          0

psychotic                         100.0%        .0%        .0%        .0%

Group       2              7          0          5          1          0

affective                            .0%      71.4%      14.3%        .0%

Group       3              8          0          0          1          2

anxiety                              .0%        .0%      12.5%      25.0%

Group       4              4          0          0          0          4

sub‑abuse                            .0%        .0%        .0%     100.0%

Group       5              8          0          1          1          0

Group       8              4          0          0          1          0

other                                .0%        .0%      25.0%        .0%

No. of    Predicted Group Membership

Actual Group        Cases          5          8

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑  ‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑

Group       1              1          0          0

psychotic                            .0%        .0%

Group       2              7          1          0

affective                          14.3%        .0%

Group       3              8          2          3

anxiety                            25.0%      37.5%

Group       4              4          0          0

sub‑abuse                            .0%        .0%

Group       5              8          6          0

Group       8              4          0          3

other                                .0%      75.0%

Percent of "grouped" cases correctly classified:  62.50%

Classification processing summary

32 (Unweighted) cases were processed.

0 cases were excluded for missing or out‑of‑range group codes.

0 cases had at least one missing discriminating variable.

32 (Unweighted) cases were used for printed output.

 File Name  =    cmpdsc1.sps data list file='c:\rdda\PASALL4.TXT' free   /DIAG DISTRS QUALIT RELATE JOB CHANGE CARE ABUSE. value labels diag   1 'psychotic'   2 'affective'   3 'anxiety'   4 'sub‑abuse'   5 'adjustment'   8 'other'. compute psychot = ( distrs*4.223727)+((‑1.471706)*relate)+(change*5.908059). compute psychot = psychot+(abuse*1.151814)+(‑38.56666). compute affecti = (distrs*.3147697)+(relate*1.593594)+(change*.6730551). compute affecti = affecti +(abuse*.2313193)+(‑6.817778). compute anxiety = ( distrs*1.954008)+((‑.1231648)*relate)+(change*3.341649). compute anxiety = anxiety+(abuse*.8917886)+(‑15.14384). compute subabus = (distrs*2.29737)+(relate*(‑.008612015))+(change*2.876287). compute subabus = subabus +(abuse*1.646836)+(‑19.11142). compute adjust = ( distrs*1.596124)+(.1578773*relate)+(change*1.405559). compute adjust = adjust+(abuse*.2873630)+(‑6.614153). compute other = (distrs*2.581243)+(relate*(‑1.467931))+(change*4.310739). compute other = other +(abuse*.6623786)+(‑16.93038). list psychot affecti anxiety subabus adjust other   /format=wrap numbered.

PSYCHOT  AFFECTI  ANXIETY  SUBABUS   ADJUST    OTHER

1    ‑5.29      .02     5.67     4.95     2.84     5.11

2   ‑23.61     2.35    ‑3.77    ‑6.33     ‑.08    ‑8.71

3     7.83     6.91    14.61    10.42     7.66    13.85

4    ‑2.28     5.88     7.27     5.73     7.86     4.46

5     7.93     5.64    14.15    14.80     8.64    12.42

6   ‑20.91     4.65    ‑1.21    ‑5.61      .41    ‑6.41

7    ‑6.85     4.83     5.23     3.87     5.63     1.90

8    14.29    11.78    20.19    21.07    11.59    15.79

9   ‑19.22     3.19    ‑1.35    ‑5.10     1.07    ‑5.43

10   ‑21.33    ‑3.48    ‑5.70    ‑9.45     ‑.63    ‑5.92

11    10.43     4.81    12.80     9.02    10.62    14.24

12   ‑20.91     4.65    ‑1.21    ‑5.61      .41    ‑6.41

13    ‑6.85     4.83     5.23     3.87     5.63     1.90

14    14.29    11.78    20.19    21.07    11.59    15.79

15   ‑19.22     3.19    ‑1.35    ‑5.10     1.07    ‑5.43

16   ‑21.33    ‑3.48    ‑5.70    ‑9.45     ‑.63    ‑5.92

17    10.43     4.81    12.80     9.02    10.62    14.24

18   ‑16.80     2.37     ‑.87    ‑5.20     1.78    ‑3.63

19    15.06     8.51    18.66    20.61    11.87    16.20

20     2.46     6.52    10.26     5.42     7.88     9.18

21   ‑23.36    ‑1.81    ‑5.78    ‑9.93    ‑1.09    ‑7.37

22      .60     7.99    11.49    13.56     7.80     6.21

23   ‑29.25     2.68    ‑7.28   ‑10.50     ‑.56   ‑13.20

24    ‑8.04      .06     1.28    ‑1.03     5.47     1.35

25    ‑8.04      .06     1.28    ‑1.03     5.47     1.35

26    34.98    12.03    28.45    26.40    18.76    29.80

27     3.97      .33     9.03     6.84     6.57    11.06

28    21.41     9.50    20.21    15.90    14.55    21.22

29     4.21     8.20    13.05    13.14     8.63     9.19

30     2.27     4.44     9.63     4.25     6.71     9.95

31     2.27     4.44     9.63     4.25     6.71     9.95

32   ‑11.70     1.89     2.99     4.18     2.58     ‑.76

Number of cases read:  32    Number of cases listed:  32

 File Name = cmpdsc2.sps data list file='c:\rdda\PASALL4.TXT' free   /DIAG DISTRS QUALIT RELATE JOB CHANGE CARE ABUSE. value labels diag   1 'psychotic'   2 'affective'   3 'anxiety'   4 'sub‑abuse'   5 'adjustment'   8 'other'. compute fun1 = ( distrs*0.4970089)+((‑.4907447)*relate)+(change*0.8215985). compute fun1 = fun1+(abuse*0.2171575)+(‑3.506419). compute fun2 = (distrs*(‑0.2405888))+(relate*0.4891394)+(change*(‑0.2173887)). compute fun2 = fun2 +(abuse*0.2956920)+(‑1.133779). list fun1 fun2   /format=wrap numbered.

FUN1     FUN2

1      .93      .22

2    ‑2.65      .73

3     1.64      .13

4     ‑.33      .04

5     1.90      .96

6    ‑2.53      .86

7     ‑.63      .46

8     2.00     2.39

9    ‑2.17      .34

10    ‑1.61    ‑1.53

11     1.62    ‑1.71

12    ‑2.53      .86

13     ‑.63      .46

14     2.00     2.39

15    ‑2.17      .34

16    ‑1.61    ‑1.53

17     1.62    ‑1.71

18    ‑1.81     ‑.36

19     2.45     1.46

20      .38     ‑.66

21    ‑2.10     ‑.95

22      .43     2.33

23    ‑3.84      .51

24     ‑.52    ‑1.68

25     ‑.52    ‑1.68

26     4.34     ‑.65

27     1.80    ‑1.36

28     2.53    ‑1.28

29      .82     1.52

30      .79    ‑1.12

31      .79    ‑1.12

32     ‑.41     1.38

Number of cases read:  32    Number of cases listed:  32

These are the discriminant scores.

This next section shows the relationship between multiple regression, MANOVA, and discriminant function.

 File Name = pasreg1.sps data list file='c:\rdda\PASALL4.TXT' free   /DIAG DISTRS QUALIT RELATE JOB CHANGE CARE ABUSE. recode diag (1,2,3=1)(4,5,8=2). value labels diag   1 'psy‑aff‑anx'   2 'abu‑adj‑oth'. REGRESSION     VARIABLES =DIAG DISTRS QUALIT RELATE JOB CHANGE CARE ABUSE     /statistics=r coeff anova outs zpp cha     /DEPENDENT=DIAG     /METHOD=STEPWISE.

* * * *   M U L T I P L E   R E G R E S S I O N   * * * *

Listwise Deletion of Missing Data

Equation Number 1    Dependent Variable..   DIAG

Block Number  1.  Method:  Stepwise     Criteria   PIN  .0500   POUT  .1000

Variable(s) Entered on Step Number

1..    RELATE

Multiple R           .35531

R Square             .12625          R Square Change    .12625

Adjusted R Square    .09712          F Change          4.33465

Standard Error       .48270          Signif F Change    .0460

Analysis of Variance

DF      Sum of Squares      Mean Square

Regression           1             1.00998          1.00998

Residual            30             6.99002           .23300

F =       4.33465       Signif F =  .0460

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables in the Equation ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Variable              B        SE B       Beta   Correl Part Cor  Partial

RELATE         ‑.109720     .052700   ‑.355313 ‑.355313 ‑.355313 ‑.355313

(Constant)     1.966003     .239541

‑‑‑‑‑‑‑‑‑‑‑ in ‑‑‑‑‑‑‑‑‑‑‑‑

Variable           T  Sig T

RELATE        ‑2.082  .0460

(Constant)     8.207  .0000

* * * *   M U L T I P L E   R E G R E S S I O N   * * * *

Equation Number 1    Dependent Variable..   DIAG

‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the Equation ‑‑‑‑‑‑‑‑‑‑‑‑‑

Variable     Beta In  Partial  Min Toler         T  Sig T

DISTRS       .348198  .366803    .969616     2.123  .0424

QUALIT       .343366  .342039    .867011     1.960  .0596

JOB         ‑.016156 ‑.017278    .999422     ‑.093  .9265

CHANGE       .029756  .024899    .611820      .134  .8942

CARE         .120990  .127067    .963723      .690  .4958

ABUSE        .106882  .106988    .875477      .579  .5667

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

Variable(s) Entered on Step Number

2..    DISTRS

Multiple R           .49377

R Square             .24381          R Square Change    .11756

Adjusted R Square    .19165          F Change          4.50835

Standard Error       .45673          Signif F Change    .0424

Analysis of Variance

DF      Sum of Squares      Mean Square

Regression           2             1.95044           .97522

Residual            29             6.04956           .20861

F =       4.67496       Signif F =  .0174

* * * *   M U L T I P L E   R E G R E S S I O N   * * * *

Equation Number 1    Dependent Variable..   DIAG

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables in the Equation ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Variable              B        SE B       Beta   Correl Part Cor  Partial

DISTRS          .091205     .042954    .348198  .275684  .342868  .366803

RELATE         ‑.128463     .050640   ‑.416007 ‑.355313 ‑.409638 ‑.426153

(Constant)     1.745999     .249215

‑‑‑‑‑‑‑‑‑‑‑ in ‑‑‑‑‑‑‑‑‑‑‑‑

Variable           T  Sig T

DISTRS         2.123  .0424

RELATE        ‑2.537  .0168

(Constant)     7.006  .0000

‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the Equation ‑‑‑‑‑‑‑‑‑‑‑‑‑

Variable     Beta In  Partial  Min Toler         T  Sig T

QUALIT       .226052  .218009    .703342     1.182  .2471

JOB         ‑.033518 ‑.038484    .967155     ‑.204  .8400

CHANGE      ‑.066398 ‑.058359    .584188     ‑.309  .7594

CARE         .011860  .012703    .867583      .067  .9469

ABUSE        .133507  .143291    .844630      .766  .4500

End Block Number   1   PIN =     .050 Limits reached.

___________________________________________________________

 File Name = pasman3.sps data list file='c:\rdda\PASALL4.TXT' free   /DIAG DISTRS QUALIT RELATE JOB CHANGE CARE ABUSE. recode diag (1,2,3=1)(4,5,8=2). value labels diag   1 'psy‑aff‑anx'   2 'abu‑adj‑oth'. manova relate distrs by diag(1,2)   /print = cellinfo(means).

‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑

The default error term in MANOVA has been changed from WITHIN CELLS to

WITHIN+RESIDUAL.  Note that these are the same for all full factorial

designs.

* * * * * * A n a l y s i s   o f   V a r i a n c e * * * * * *

32 cases accepted.

0 cases rejected because of out‑of‑range factor values.

0 cases rejected because of missing data.

2 non‑empty cells.

1 design will be processed.

‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑

Cell Means and Standard Deviations

Variable .. RELATE

FACTOR           CODE                  Mean  Std. Dev.          N

DIAG            psy‑aff‑                  4.822      1.434         16

For entire sample                          4.247      1.645         32

‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑

Variable .. DISTRS

FACTOR           CODE                  Mean  Std. Dev.          N

DIAG            psy‑aff‑                  2.759      2.040         16

For entire sample                          3.285      1.939         32

‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑

* * * * * * A n a l y s i s   o f   V a r i a n c e ‑‑ design   1 * * * * * *

EFFECT .. DIAG

Multivariate Tests of Significance (S = 1, M = 0, N = 13 1/2)

Test Name         Value    Exact F Hypoth. DF   Error DF  Sig. of F

Pillais          .24381    4.67496       2.00      29.00       .017

Hotellings       .32241    4.67496       2.00      29.00       .017

Wilks            .75619    4.67496       2.00      29.00       .017

Roys             .24381

Note.. F statistics are exact.

‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑

EFFECT .. DIAG (Cont.)

Univariate F‑tests with (1,30) D. F.

Variable   Hypoth. SS   Error SS Hypoth. MS   Error MS          F  Sig. of F

RELATE       10.59150   73.30354   10.59150    2.44345    4.33465       .046

DISTRS        8.86205  107.74115    8.86205    3.59137    2.46759       .127

‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑

 File Name = pasdsc5.sps data list file='c:\rdda\PASALL4.TXT' free   /DIAG DISTRS QUALIT RELATE JOB CHANGE CARE ABUSE. recode diag (1,2,3=1)(4,5,8=2). value labels diag   1 'psy‑aff‑anx'   2 'abu‑adj‑oth'. DSC GROUPS=DIAG(1,2)    /VAR=DISTRS TO ABUSE    /METHOD=RAO    /PIN=.05    /FUNCTIONS=1,100,.05    /STATISTICS = mean univf coeff table    /plot=map.

Since analysis= was omitted for the first analysis all variables

on the variables= list will be entered at level 1.

‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑   D I S C R I M I N A N T   A N A L Y S I S   ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑

On groups defined by DIAG

32 (Unweighted) cases were processed.

0 of these were excluded from the analysis.

32 (Unweighted) cases will be used in the analysis.

Number of cases by group

Number of cases

DIAG      Unweighted     Weighted  Label

1          16         16.0  psy‑aff‑anx

Total          32         32.0

Group means

DIAG         DISTRS         QUALIT         RELATE            JOB

1        2.75875        3.71250        4.82250        3.95313

2        3.81125        4.18437        3.67188        3.88000

Total        3.28500        3.94844        4.24719        3.91656

DIAG         CHANGE           CARE          ABUSE

1        4.53125        4.68750        2.62500

2        3.76563        4.93750        2.43750

Total        4.14844        4.81250        2.53125

Wilks' Lambda (U‑statistic) and univariate F‑ratio

with 1 and 30 degrees of freedom

Variable   Wilks' Lambda         F         Significance

‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑‑‑‑‑

DISTRS         .92400          2.4676          .1267

QUALIT         .97173           .8727          .3577

RELATE         .87375          4.3346          .0460

JOB            .99939           .0183          .8933

CHANGE         .95872          1.2916          .2647

CARE           .99761           .0720          .7903

ABUSE          .99899           .0304          .8628

‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑   D I S C R I M I N A N T   A N A L Y S I S   ‑ ‑ ‑ ‑ ‑ ‑ ‑ ‑

On groups defined by DIAG

Analysis number       1

Stepwise variable selection

Selection rule:  maximize Rao's V

Maximum number of steps..................      14

Minimum tolerance level..................  .00100

Maximum significance of F to enter.......  .05000

Minimum significance of F to remove...... 1.00000

Minimum increase in Rao's V..............  .00000

Canonical Discriminant Functions

Maximum number of functions..............       1

Minimum cumulative percent of variance...  100.00

Maximum significance of Wilks' Lambda....   .0500

Prior probability for each group is  .50000

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the Analysis after Step 0 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Minimum   Signif. of

Variable  Tolerance  Tolerance  F to Enter        Rao's V

DISTRS    1.0000000  1.0000000       .1267043    2.4675948

QUALIT    1.0000000  1.0000000       .3576717     .8726854

RELATE    1.0000000  1.0000000       .0459731    4.3346485

JOB       1.0000000  1.0000000       .8932984     .0182992

CHANGE    1.0000000  1.0000000       .2647418    1.2916472

CARE      1.0000000  1.0000000       .7903037     .0719856

ABUSE     1.0000000  1.0000000       .8627908     .0303849

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

At step 1, RELATE   was included in the analysis.

Degrees of Freedom  Signif.   Between Groups

Wilks' Lambda         .87375        1    1       30.0

Equivalent F         4.33465             1       30.0   .0460

Rao's V              4.33465             1              .0373 (Approx.)

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables in the Analysis after Step 1 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Signif. of

Variable  Tolerance  F to Remove       Rao's V

RELATE    1.0000000        .0460

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the Analysis after Step 1 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Minimum   Signif. of

Variable  Tolerance  Tolerance  F to Enter        Rao's V

DISTRS     .9081834   .9081834       .0423861    9.6723280

QUALIT     .7878493   .7878493       .0596478    8.8836833

JOB        .9997329   .9997329       .9264947    4.3449020

CHANGE     .6377659   .6377659       .8942267    4.3559486

CARE       .9504380   .9504380       .4957622    4.8981104

ABUSE      .8663327   .8663327       .5667449    4.7322067

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

At step 2, DISTRS   was included in the analysis.

Degrees of Freedom  Signif.   Between Groups

Wilks' Lambda         .75619        2    1       30.0

Equivalent F         4.67496             2       29.0   .0174

Rao's V              9.67233             2              .0079 (Approx.)

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables in the Analysis after Step 2 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Signif. of

Variable  Tolerance  F to Remove       Rao's V

DISTRS     .9081834        .0424     4.3346485

RELATE     .9081834        .0168     2.4675948

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Variables not in the Analysis after Step 2 ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

Minimum   Signif. of

Variable  Tolerance  Tolerance  F to Enter        Rao's V

QUALIT     .6894014   .6894014       .2471361   11.6519635

JOB        .9960164   .9048072       .8399925    9.7311703

CHANGE     .6072652   .6072652       .7593558    9.8079069

CARE       .8695241   .8308667       .9468797    9.6787312

ABUSE      .8540637   .7756676       .4500094   10.5039684

F level or tolerance or VIN insufficient for further computation.

Summary Table

Action      Vars  Wilks'                               Change

Step Entered Removed   in   Lambda   Sig.     Rao's V   Sig.      in V     Sig.

1  RELATE             1   .87375  .0460     4.33465  .0373     4.33465  .0373

2  DISTRS             2   .75619  .0174     9.67233  .0079     5.33768  .0209

Classification function coefficients

(Fisher's linear discriminant functions)

DIAG    =         1              2

DISTRS           .3026615       .7549487

RELATE          1.8624576      1.2254050

(Constant)     ‑5.6014819     ‑4.3815633

Canonical Discriminant Functions

Pct of   Cum  Canonical  After  Wilks'

Fcn Eigenvalue Variance  Pct     Corr      Fcn  Lambda  Chi‑square  df  Sig

:    0 .756195      8.104     2  .0174

1*     .3224  100.00  100.00    .4938 :

* Marks the 1 canonical discriminant functions remaining in the analysis.

Standardized canonical discriminant function coefficients

Func  1

DISTRS       ‑.77951

RELATE        .90564

Structure matrix:

Pooled within‑groups correlations between discriminating variables

and canonical discriminant functions

(Variables ordered by size of correlation within function)

Func  1

RELATE        .66944

DISTRS       ‑.50509

ABUSE         .32703

CHANGE        .27317

QUALIT        .07526

CARE         ‑.06228

JOB          ‑.03435

Canonical discriminant functions evaluated at group means (group centroids)

Group      Func   1

1        .54978

2       ‑.54978

Classification results ‑

No. of    Predicted Group Membership

Actual Group        Cases          1          2

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑  ‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑   ‑‑‑‑‑‑‑‑

Group       1             16         12          4

psy‑aff‑anx                        75.0%      25.0%

Group       2             16          5         11

Percent of "grouped" cases correctly classified:  71.88%

Classification processing summary

32 (Unweighted) cases were processed.

0 cases were excluded for missing or out‑of‑range group codes.

0 cases had at least one missing discriminating variable.

32 (Unweighted) cases were used for printed output.