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
5 8 8.0
adjustment
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
adjustment other
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
5 5
adjustment
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
adjustment
.0% 12.5% 12.5% .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
adjustment
75.0% .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
DIAG abu‑adj‑ 3.672
1.683 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
DIAG abu‑adj‑ 3.811 1.738 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
2 16 16.0
abu‑adj‑oth
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
psy‑aff‑anx abu‑adj‑oth
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
abu‑adj‑oth 31.3% 68.8%
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.