### 9(1) Example of Discriminant Analysis

 Research Question : Research units spent time on different activities: We assume that activity patterns may differ between two countries. Can we derive a rule for classifying research units into two groups [Country Code: 360 and on the basis 630] of their activity patterns? Methodology : Discriminant analysis, using IDAMS module DISCRAN Dataset : ICSOPRU2.DAT
##### SYNTAX
```\$RUN DISCRAN
\$FILES
PRINT = DISCRAN.LST
DICTIN = ICSOPRU2.DIC
DATAIN = ICSOPRU2.DAT
\$SETUP
INCLUDE V1=360, 638
prototype for DISCRAN program
VARS=(V22 -V30) -
MDHANDLING=(SAMPVAR,GROUPVAR,ANALVAR) -
IDVAR=V2 -
STEP=10-
PRINT=(CDICT,GROUP) -
GRVAR=V1 GR01=360 GR02=638```
##### EXTRACT FROM COMPUTER OUTPUT
 List of variables V22 V23 V24 V25 V26 V27 V28 V29 V30 After filtering      464 cases read from the input data file Valid cases processed: 464      Number of cases in samples Basic: 464    Test: 0    Anonymous: 0 Revised number of cases in samples Basic: 464    Test: 0    Anonymous: 0 Means and standard deviations (In the last column the global mean is printed) ``` Group 1 Group 2 Variable Mean S.D. Mean S.D. Mean 22 55.3972 17.0743 28.0533 12.0499 42.1377 23 5.2059 5.1370 6.8226 7.3723 5.9899 24 6.8472 4.4405 12.7442 6.4885 9.7067 25 2.1979 2.5754 13.4935 12.2004 7.6753 26 6.0667 5.1025 2.6900 2.7588 4.4293 27 2.8118 2.6504 2.7582 3.7750 2.7858 28 12.5308 11.1494 25.9432 17.8515 19.0347 29 5.7081 9.7895 2.8740 6.0661 4.3338 30 3.2399 6.4383 4.6189 8.9578 3.9086``` Step number 1 Variables entered : 22 Linear discriminant function Variable number : Constant        22 -2.829         .067 At each step, an observation is allocated : Group 1 if its value for the linear discriminant function is strictly positive Group 2 if is strictly negative No allocation if it is zero Classification table for basic sample Allocated group 1    2 Original group        1  191  48        2   32   193 % correctly classified : 82.76 Step number 2 Variables entered :    22    26   Linear discriminant function ****************************                        Variable number : Constant            22       26 -3.425               .065   .153 Classification table for basic sample Allocated group   1     2 Original group 1    205   34 2    23     202 % correctly classified : 87.72 Step number 3 Variables entered :   22   26   29   Linear discriminant function ****************************                     Variable number : Constant         22      26     29 -3.705           .068   .137  .051   Classification table for basic sample ************************************* Allocated group  1    2 Original group 1   212   27 2   23    202 % correctly classified : 89.22 Step number 4 Variables entered :   22   26   29   25   Linear discriminant function ****************************                  Variable number : Constant    22   26    29    25 -2.944     .060 .122 .042 -.038   Classification table for basic sample ************************************* Allocated group   1    2 Original group 1   218   21 2    24   201 % correctly classified : 90.30 Step number 5 Variables entered :   22   26   29   25   24   Linear discriminant function ****************************                  Variable number : Constant      22     26      29      25      24 -2.456        .055  .118   .039  -.037  -.030   Classification table for basic sample ************************************* Allocated group   1   2 Original group 1   222   17 2   23    202 % correctly classified : 91.38 The percentage of the basic sample decreases at the next step Allocation and value of the linear discriminant function for the observation in the basic sample ```Group 1 Allocation Function 101 1 1.145 108 1 .023 109 1 1.726 201 2 -.856 204 1 1.333 419 2 -.035 425 1 .034 427 2 -.910 430 1 .846 501 2 -.101 502 1 .667 503 1 1.616 504 1 1.770 505 1 2.877 506 1 .857 507 2 -.230 *****``` ```Group 2 Allocation Function 101 2 -.919 102 2 -.710 202 1 .665 301 2 -.195 302 1 1.599 303 2 -1.054 901 1 .263 902 1 1.254 1001 1 1.381 1601 1 .791 1602 1 2.289 1603 1 .233 ***** ``` Allocation and value of the linear discriminant function for the group means Group 1 : 1.267 Group 2 : -1.346
##### INTERPRETATION
 IDAMS reports analysis specifications. Variables: V22-V28 No. of Cases: ``` Basic sample: 464 Test sample : 0 Anonymous sample: 0``` No. of groups:       2 IDAMS reports descriptive statistics (mean and standard deviation) of discriminant variable for each group and means of these variable for the entire sample. These statistics give on idea of inter-group differences in the time devoted to different activities. IDAMS reports the results of stepwise discriminant analysis. At each stage the most important discriminant variable is selected and a linear discriminant function (LDF) is set up. For each object, LDF score is computed and the object is allocated to: Group – 1, if the LDF score is strictly positive Group-2, if the LDF score is strictly negative Not allocated to any group, if LDF score = 0. Step 1: At this stage, the most discriminant variable is identified, which is V22 and linear discriminant function is set up with this variable. LDF = -2.829+.067´ V22 Objects are allocated to the groups according to the classification rule mentioned above . Classification table     Alloted Actual 1.   205     34 2.    23     202 No. of objects correctly classified = 82.76%. Step 2: At this stage, the second most discriminant variable is identified, viz. V26. A linear discriminant function is computed with variables V22 (identified at Step 1) and V26. LDF = -3.425+.065V22+.153V26. Object are allocated to each group according to the LDF score using the classification rule at . No. of objects correctly classified = 87.72% Step 3: At this stage, the third most discriminant variable is identified, viz. V29. A linear discriminant function is computed with variables: V22, V26, and V29. LDF = -3.075+.068V22+.137V26+.051V29 No. of objects correctly classified = 89.29% Step 4: At this stage, variable V25 is identified as the most discriminant variable after variables V22, V26 and V29. A linear discriminant factor is computed with variables V22, V26, V29 and V25. LDF = -2.944+.060V22+.122V26+.042V29-.038V25 No. of objects correctly classified = 90.30%. Step 5: At this stage, variable V24 is identified as the most discriminant variable after V22, V26, V29 and V25. The following linear discriminant function is computed. LDF = -2.456+.055V22+.118V26+.039V29-.037V25-.030V24 No. of objects correctly classified = 91.38%. The algorithm stops at this stage, since the entry of additional variable does not improve the classification accuracy. Hence the part of the print out for subsequent stages is omitted. For each object, the value of the discriminant function is computed and the object is allocated to a group according to the allocation procedure mention at . Table of Allocation of objects belong to Group-1. To summarize the most important discriminant variables are: V22, V26, V29 and V25. and the resulting discriminant function LDF = -2.456+.055V22+.118V26+.039V29-.037V25-.030V24 achieves a classification accuracy of 91.38%.

### 9(2) Example of Discriminant Analysis

 Research Question : Research units spent time on different activities: We assume that activity patterns may differ between two countries. Can we derive a rule for classifying research units into two groups [Country Code: 360 and on the basis 630] of their activity patterns? Methodology : Discriminant analysis, using IDAMS module DISCRAN Dataset : ANJU.DAT
##### SYNTAX
```\$RUN DISCRAN
\$FILES
PRINT = SABINA1.LST
DICTIN = ANJU.DIC
DATAIN = ANJU.DAT
\$SETUP
EXCLUDE V2=0
Pototype for DISCRAN program
VARS=(V2-V8)-
MDHANDLING=(SAMPVAR,GROUPVAR,ANALVAR) -
IDVAR=V1 -
STEP=7 -
PRINT=(CDICT,DATA,GROUP) -
SAVAR=V9 BASA=(1,2) ANSA=(3) -
GRVAR=V15 GR01=1 GR02=2```
##### EXTRACT FROM COMPUTER OUTPUT

Maximum of steps to be performed: 7
List of variables
V2  V3  V4  V5  V6  V7  V8

After filtering 1063 cases read from the input data file
3 cases contained illegal characters on filter variables and were skipped
Valid cases processed: 657

Number of cases in samples
Basic: 358 Test: 0 Anonymous: 299

Revised number of cases in samples
Basic: 358 Test: 0 Anonymous: 299

Basic sample

 a ``` * 2 3 4 5 6 7 8 ******************************************************************************* 1002 * 40.00 20.00 15.00 5.00 10.00 .00 10.00 1015 * 60.00 30.00 5.00 4.00 1.00 .00 .00 1016 * 50.00 10.00 16.00 5.00 12.00 2.00 5.00 1018 * 20.00 20.00 20.00 .00 40.00 .00 .00 3199 * 30.00 30.00 20.00 10.00 10.00 .00 .00 ``` ```Anonymous sample **************** ``` b ``` * 2 3 4 5 6 7 8 ******************************************************************************* 1006 * 60.00 15.00 .00 15.00 10.00 .00 .00 1014 * 40.00 40.00 10.00 .00 5.00 5.00 .00 1020 * 50.00 40.00 .00 .00 10.00 .00 .00 1021 * 65.00 20.00 .00 .00 15.00 .00 .00 1024 * 50.00 20.00 30.00 .00 .00 .00 .00 6010 * 60.00 20.00 10.00 10.00 .00 .00 .00 9009 * 40.00 25.00 20.00 5.00 5.00 .00 .00 ```

Means and standard deviations

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

(In the last column the global mean is printed)

```                    Group  1                    Group  2
Variable       Mean        S.D.            Mean        S.D.           Mean

2        34.2300     14.2926         36.0760     17.4503       35.0447
3        23.0700     12.7850         18.8481     10.0833       21.2067
4        21.7450     11.5174         17.0063     10.5701       19.6536
5         3.6850      4.6460          6.5380      6.7305        4.9441
6        10.1500     11.4021         11.8861     11.7365       10.9162
7         1.9900      5.0110          5.7658      7.9062        3.6564
8         5.1300      4.4736          3.8797      4.6462        4.5782

******************************************************************************
```

Step number 1

Variables entered : 7

Linear discriminant function

Variable number :
Constant       7
.306       -.084

At each step, an observation is allocated :

to group 1 if its value for the linear
discriminant function is strictly positive
To group 2 if it is strictly negative
No allocation if it is zero

Classification table for basic sample
Allocated group
1    2

Original group

1   159   41
2   76   82

% correctly classified : 67.32

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

Step number 2

Variables entered : 7 5

Linear discriminant function

Variable number :
Constant      7     5
.723     -.084 -.084

Classification table for basic sample

Allocated group
1       2

Original group

1    136    64
2      48    110

% correctly classified : 68.72

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

Step number 3

Variables entered : 7 5 4

Linear discriminant function
****************************

Variable number :
Constant           7        5      4
.125             -.079 -.079 .028

Classification table for basic sample
*************************************

Allocated group
1 2

Original group

1   149   51
2    52   106

% correctly classified : 71.23

The percentage of the basic sample decreases at the next step

Allocation and value of the linear discriminant function for the observation in the basic sample (only a few cases re-listed here)

```   Group  1    Allocation      Function

1002             1             .154
1015             2            -.049
1016             1             .024
1018             1             .689
3205             2            -.240
3231             2            -.495
3233             1             .243
3235             1             .407
3245             1             .390
Group  2    Allocation      Function

1010             2            -.240
1032             2            -.381
1054             2            -.635
1115             2            -.663
1182             1             .120
1191             1             .548
1199             1             .407
3162             2            -.099
3163             2            -.752
3188             2            -.275
3195             1             .179
3199             2            -.099
```

Allocation and value of the linear discriminant function for the group means

Group 1 : .290
Group 2 : -.367

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

Allocation and value of the linear discriminant function for the anonymous observations (only a few cases re-listed here)

```  Number       Allocation      Function
1006              2          -1.058
1014              1            .011
1020              1            .125
1021              1            .125
1024              1            .971
6007              1            .689
6008              1            .013
6009              2          -1.173
6010              2           -.381
9009              1            .295
```
##### INTERPRETATION
 IDAMS reports analysis specifications Discriminant Variables: V2 V3 V4 V5 V6 V7 V8 No. of cases taken for analysis: Basic sample: 358 Anonymous sample: 299 Grouping variable: V15       No. of groups: 2 IDAMS prints the values of discriminant variables for the basic and anonymous samples perceptively.       a Basic Sample       b Anonymous Sample These tables give an idea as to which activities relatively more or less prominent compared to the global mean. Descriptive statistics of discriminant variables for each group of the anonymous sample and global mean Stepwise discriminant analysis Step 1 At this stage, the most discriminant variable is identified, which is variable V7. The linear discriminant function computed with this variable. = .306-.084V7 Classification table for basic sample Allocated group     1     2 Original group 1   159   41 2   76   82 % correctly classified : 67.32 Step 2 At this stage, the algorithm identifies V5 as the most important discriminant variable after V7. Variables V7 and V5 are used to construct the linear discriminant function LDF = .723-.084V7-.084V5 No. of cases correctly classified = 68.73% Step 3 At this stage, variable V4 is added to the linear discriminant function LDF = -.125-.079V7-.079V5+.028V4 No. of cases correctly classified = 71.23% The algorithm stops at this stage, since no others variable is able to improve the classification accuracy of the linear discriminant function. Computation of LDF scores and classification of objects for each group: Group: 1 Consider for example object Idcode: 1015. It has LDF score = -.049. Since the score is negative, this object is assigned to Group 2. Similar, interpretation for objects of Group – 2. Computation of LDF scores of objects of the anonymous sample and assignment of objects to the groups. Classification accuracy for the anonymous sample cannot be computed since their actual group membership is not known.

### 9.3 Example of Discriminant Analysis

 Research Question : Drive a rule for classifying a set of 29 countries as Western, Asian and East European on the basis of priorities given in 10 fields: subfields of Physics. Methodology : Multiple Discriminant analysis, using IDAMS module DISCRAN Dataset : PHYSICS.DAT
##### SYNTAX
```\$RUN DISCRAN
\$FILES
PRINT = PHYSICS.LST
DICTIN = PHYSICS.DIC
DATAIN = PHYSICS.DAT
\$SETUP
EXCLUDE V12=4 AND V12=5
MULTIPLE DISCRIMINANT ANALYSIS OF PHYSICS DATA
VARS=(V2-V11) -
MDHANDLING=(SAMPVAR,GROUPVAR,ANALVAR) -
IDVAR=V1 -
STEP=8 -
PRINT=(CDICT,DATA,GROUP) -
GRVAR=V12 GR01=1 GR02=2 GR03=3
```
##### EXTRACT FROM COMPUTER OUTPUT
 After filtering 36 cases read from the input data file Valid cases processed: 36      Number of cases in samples Basic: 36 Test: 0 Anonymous: 0 Revised number of cases in samples Basic: 29 Test: 0 Anonymous: 0 1Basic sample ************ Table of Means ``` Variable GR01 GR02 GR03 TOT. 2 78.4706 52.5714 111.8000 77.9655 3 93.1765 169.8571 86.8000 110.5862 4 118.7059 90.8571 109.6000 110.4138 5 73.5294 85.2857 87.6000 78.7931 6 118.8235 109.5714 115.0000 115.9310 7 116.7059 64.1429 56.4000 93.6207 8 155.6471 71.7143 95.4000 125.0000 9 100.8824 78.2857 104.6000 96.0690 10 104.2353 69.8571 142.8000 102.5862 11 87.7647 35.7143 135.2000 83.3793 Table of Standard Deviations Variable GR01 GR02 GR03 2 40.1865 37.7921 50.1733 3 21.5631 44.8344 34.9365 4 34.1015 35.2032 26.1121 5 20.9119 33.7965 59.9920 6 48.5280 47.3493 64.1685 7 57.2690 33.7107 34.0975 8 103.1184 32.7445 34.9548 9 41.2209 36.8112 53.2826 10 73.9400 32.7476 63.5591 11 45.7712 14.7039 53.7900 ``` Step number 1 Variables entered : 3   Classification table for basic sample *************************************          Allocated group       GR01 GR02 GR03 Original group GR01      10   0   7 GR02       1    6   0 GR03       1    1   3 % correctly classified : 65.52 ****************************************************************************** Step number 1 Variables entered : 3 7   Classification table for basic sample *************************************          Allocated group       GR01 GR02 GR03 Original group GR01      10   0   7 GR02       0    6   1 GR03       1    1   3 % correctly classified : 65.52 ****************************************************************************** Step number 3 Variables entered : 3  7   11   Classification table for basic sample *************************************          Allocated group       GR01 GR02 GR03 Original group GR01      10   0   6 GR02       0    7   0 GR03       2    0   3 % correctly classified : 72.41 ****************************************************************************** Step number 4 Variables entered : 3   7   11   8   Classification table for basic sample *************************************          Allocated group       GR01 GR02 GR03 Original group GR01      10   0   7 GR02       0    7   0 GR03       1    0   4 % correctly classified : 72.41 ****************************************************************************** Step number 5 Variables entered : 3   7   11   8   4     Classification table for basic sample *************************************          Allocated group       GR01 GR02 GR03 Original group GR01      12   0   5 GR02       0    7   0 GR03       1    0   4 % correctly classified : 79.31 The percentage of the basic sample decreases at the next step Allocation and distances of observations in the basic sample       (In parentheses group number under consideration) ``` Group 1 Allocation Distances to each group GR01 1 3 2.356 ( 1) 7.120 ( 2) .520 ( 3) 3 1 1.599 ( 1) 1.734 ( 2) 3.177 ( 3) 5 3 1.883 ( 1) 4.397 ( 2) 1.529 ( 3) 6 1 1.134 ( 1) 1.829 ( 2) 2.607 ( 3) 7 1 1.596 ( 1) 5.196 ( 2) 2.107 ( 3) 9 1 3.963 ( 1) 10.770 ( 2) 10.126 ( 3) 10 1 9.893 ( 1) 16.696 ( 2) 17.657 ( 3) 11 3 1.572 ( 1) 3.733 ( 2) 1.422 ( 3) 16 3 1.591 ( 1) 3.323 ( 2) 1.135 ( 3) 17 1 2.954 ( 1) 6.511 ( 2) 6.572 ( 3) 18 1 4.003 ( 1) 5.912 ( 2) 10.414 ( 3) 22 1 1.958 ( 1) 3.844 ( 2) 5.674 ( 3) 23 3 9.470 ( 1) 12.955 ( 2) 7.041 ( 3) 24 1 1.040 ( 1) 3.641 ( 2) 1.059 ( 3) 28 1 5.561 ( 1) 10.721 ( 2) 7.229 ( 3) 30 1 9.491 ( 1) 15.857 ( 2) 10.312 ( 3) 35 1 15.993 ( 1) 23.778 ( 2) 20.558 ( 3) Group 2 Allocation Distances to each group GR02 2 2 8.176 ( 1) 5.961 ( 2) 8.253 ( 3) 12 2 3.207 ( 1) .279 ( 2) 4.337 ( 3) 15 2 16.687 ( 1) 6.353 ( 2) 16.651 ( 3) 21 2 4.564 ( 1) 1.059 ( 2) 4.217 ( 3) 25 2 3.994 ( 1) 2.398 ( 2) 6.420 ( 3) 26 2 5.229 ( 1) 3.755 ( 2) 6.529 ( 3) 29 2 5.882 ( 1) 2.421 ( 2) 7.177 ( 3) Group 3 Allocation Distances to each group GR03 4 3 10.175 ( 1) 11.813 ( 2) 7.909 ( 3) 8 3 4.062 ( 1) 3.880 ( 2) 3.175 ( 3) 14 3 4.049 ( 1) 8.732 ( 2) 1.331 ( 3) 19 1 1.216 ( 1) 3.622 ( 2) 2.337 ( 3) 33 3 10.878 ( 1) 15.002 ( 2) 5.898 ( 3) ``` Discriminant factor analysis at step 5 ************************************ Sum of eigenvalues = .89884 Discriminant power of first factor : .64040 Discriminant power of second factor : .25843 Discriminant power of third factor : .00000 First eigenvector -.01455 .00635 .00644 .00251 -.00375 Second eigenvector -.00208 -.00980 .01130 -.00275 -.00943 Values of discriminant factors for all observations and group means Group GR01              Fact 1   Fact 2 Mean -.10237 -1.89252 Group GR02              Fact 1   Fact 2 Mean -1.99358 -1.63144 Group GR03              Fact 1   Fact 2 Mean -.20409 -.50127 Codes used for presentation in the graph The group near is indicated by * The overlapping of 2 observations from different groups by \$ One observation of the group GR01 is presented by 1            The overlapping of 2 observations by A One observation of the group GR02 is presented by 2           The overlapping of 2 observations by B One observation of the group GR03 is presented by 3           The overlapping of 2 observations by C
```1         -3.784    -3.314    -2.843    -2.373    -1.903    -1.432     -.962     -.491     -.021      .449      .920
+.........+.........+.........+.........+.........+.........+.........+.........+.........+.........+.
.719  .                                                                                                    .   .719
.631  .                                                                                       3            .   .631
.543  .                                                                                                    .   .543
.455  .                                                                                                    .   .455
.367  .                                                                                                    .   .367
.280  .                                                                                                    .   .280
.192  .                                                                                                    .   .192
.104  .                                                                                                    .   .104
.016  .                                                                                                    .   .016
-.072  .                                                                                                    .  -.072
-.160  .                                                                                        3           .  -.160
-.248  .                                                                                                    .  -.248
-.336  .                                                                                 1                  .  -.336
-.424  .                                                                       3  MEAN3                          .  -.424
-.512  .                                                                           *            1           .  -.512
-.600  .                                                                                                    .  -.600
-.688  .                                                                                                    .  -.688
-.776  .                                                                                                    .  -.776
-.864  .                                                                                                    .  -.864
-.952  .                                                           3                                        .  -.952
-1.040  .                                                                     1    1                         . -1.040
-1.128  .                                                                       1                            . -1.128
-1.216  .                                        2                                 1                         . -1.216
-1.304  .                                               2                                                    . -1.304
-1.392  .                                                                               1              1     . -1.392
-1.480  . 2                                                                                                  . -1.480
-1.568  .                                     MEAN2                                                               . -1.568
-1.656  .                                      *                                3                            . -1.656
-1.744  .                                         2       2           1                        1             . -1.744
-1.832  .                                      2                   1                                         . -1.832
-1.920  .                                                                             * MEAN1                     . -1.920
-2.008  .                                                                                                    . -2.008
-2.096  .                                                                                                    . -2.096
-2.184  .                                                2                                                   . -2.184
-2.272  .                                                                                                    . -2.272
-2.360  .                                                                                                    . -2.360
-2.448  .                                                                                                    . -2.448
-2.536  .                                                                  1        1                        . -2.536
-2.624  .                                                                                                    . -2.624
-2.711  .                                                                                                    . -2.711
-2.799  .                                                                                                  1 . -2.799
-2.887  .                                                                                                    . -2.887
-2.975  .                                                                                                    . -2.975
-3.063  .                                                                                                    . -3.063
-3.151  .                                                                                                    . -3.151
-3.239  .                                                                                                    . -3.239
-3.327  .                                                                                           1        . -3.327
-3.415  .                                                                                                    . -3.415
-3.503  .                                                                                                    . -3.503
-3.591  .                                                               1                                    . -3.591
-3.679  .                                                                                                    . -3.679
-3.767  .                                                                                                    . -3.767
-3.855  .                                                                                                    . -3.855
-3.943  .                                                                                         1          . -3.943
-4.031  .                                                                                                    . -4.031
+.........+.........+.........+.........+.........+.........+.........+.........+.........+.........+.
-3.784    -3.314    -2.843    -2.373    -1.903    -1.432     -.962     -.491     -.021      .449      .920

```
 Step number 6 Variables entered : 3   7   11   8   4   9   Classification table for basic sample *************************************          Allocated group       GR01 GR02 GR03 Original group GR01      11   0   6 GR02       0    7   0 GR03       1    0   4 % correctly classified : 75.86 ****************************************************************************** Step number 7 Variables entered : 3   7   11   8   4   9   2   Classification table for basic sample *************************************          Allocated group       GR01 GR02 GR03 Original group GR01      12   0   5 GR02       0    7   0 GR03       1    0   4 % correctly classified : 79.31 ****************************************************************************** Step number 8 Variables entered : 3   7   11   8   4   9   2   6   Classification table for basic sample *************************************          Allocated group       GR01 GR02 GR03 Original group GR01      12   0   5 GR02       0    7   0 GR03       1    0   4 % correctly classified : 79.31 Allocation and distances of observations in the basic sample     (In parentheses group number under consideration) ``` Group 1 Allocation Distances to each group GR01 1 3 3.712 ( 1) 9.107 ( 2) 1.991 ( 3) 3 1 3.473 ( 1) 4.135 ( 2) 5.260 ( 3) 5 3 4.951 ( 1) 7.754 ( 2) 4.380 ( 3) 6 1 1.291 ( 1) 1.934 ( 2) 3.270 ( 3) 7 1 2.714 ( 1) 5.709 ( 2) 3.670 ( 3) 9 1 5.540 ( 1) 12.311 ( 2) 12.788 ( 3) 10 1 11.016 ( 1) 18.649 ( 2) 18.901 ( 3) 11 3 2.795 ( 1) 4.652 ( 2) 2.614 ( 3) 16 3 5.507 ( 1) 8.813 ( 2) 3.904 ( 3) 17 1 8.908 ( 1) 13.420 ( 2) 10.915 ( 3) 18 1 6.774 ( 1) 8.307 ( 2) 14.724 ( 3) 22 1 5.254 ( 1) 7.595 ( 2) 7.854 ( 3) 23 3 16.312 ( 1) 19.895 ( 2) 15.910 ( 3) 24 1 7.261 ( 1) 9.272 ( 2) 7.976 ( 3) 28 1 9.260 ( 1) 13.796 ( 2) 10.494 ( 3) 30 1 12.990 ( 1) 18.726 ( 2) 14.945 ( 3) 35 1 16.070 ( 1) 24.131 ( 2) 20.797 ( 3) Group 2 Allocation Distances to each group GR02 2 2 10.159 ( 1) 7.820 ( 2) 9.653 ( 3) 12 2 6.492 ( 1) 2.407 ( 2) 9.006 ( 3) 15 2 23.166 ( 1) 14.579 ( 2) 23.009 ( 3) 21 2 7.518 ( 1) 3.288 ( 2) 7.129 ( 3) 25 2 5.451 ( 1) 3.352 ( 2) 8.440 ( 3) 26 2 7.361 ( 1) 5.925 ( 2) 8.689 ( 3) 29 2 8.778 ( 1) 5.046 ( 2) 11.636 ( 3) Group 3 Allocation Distances to each group GR03 4 3 13.573 ( 1) 14.864 ( 2) 10.981 ( 3) 8 3 5.731 ( 1) 5.106 ( 2) 4.758 ( 3) 14 3 9.590 ( 1) 16.108 ( 2) 5.891 ( 3) 19 1 6.470 ( 1) 9.831 ( 2) 6.514 ( 3) 33 3 13.243 ( 1) 17.049 ( 2) 9.708 ( 3) ``` Discriminant factor analysis at step 8 ************************************ Sum of eigenvalues = .96221 Discriminant power of first factor : .67570 Discriminant power of second factor : .28651 Discriminant power of third factor : .00000 First eigenvector -.01420 .00528 .00484 .00410 -.00687 -.00301 .00701 .00333 Second eigenvector -.00264 -.01202 .00958 -.00053 -.01130 -.00914 .00523 .00141 Values of discriminant factors for all observations and group means Group GR01              Fact 1   Fact 2 Mean .18115 -2.57679 Group GR02              Fact 1   Fact 2 Mean -1.73343 -2.22830 Group GR03              Fact 1   Fact 2 Mean .20855 -1.11043 Codes used for presentation in the graph The group near is indicated by * The overlapping of 2 observations from different groups by \$ One observation of the group GR01 is presented by 1    The overlapping of 2 observations by A One observation of the group GR02 is presented by 2    The overlapping of 2 observations by B One observation of the group GR03 is presented by 3    The overlapping of 2 observations by C
```1         -2.939    -2.516    -2.092    -1.669    -1.245     -.821     -.398      .026      .449      .873     1.296
+.........+.........+.........+.........+.........+.........+.........+.........+.........+.........+.
-.526  .                                                                                                    .  -.526
-.602  .                                                                                                  3 .  -.602
-.678  .                                                                                 3                  .  -.678
-.754  .                                                                                                    .  -.754
-.829  .                                                                                                    .  -.829
-.905  .                                                                                                    .  -.905
-.981  .                                                                 3                                  .  -.981
-1.057  .                                                                                                    . -1.057
-1.133  .                                                                          *                         . -1.133
-1.208  .                                                                                                    . -1.208
-1.284  .                                                                           1            1           . -1.284
-1.360  .                                                                                                    . -1.360
-1.436  .                                                                                                    . -1.436
-1.512  .                                                   3                                                . -1.512
-1.587  .                                                                                                    . -1.587
-1.663  .                            2           2                              1                            . -1.663
-1.739  . 2                                                               1         1                        . -1.739
-1.815  .                                                                                                    . -1.815
-1.891  .                                                                         3                          . -1.891
-1.966  .                                                                                                    . -1.966
-2.042  .                                                                1                                   . -2.042
-2.118  .                                                                                                    . -2.118
-2.194  .                            *                                         1                             . -2.194
-2.270  .                                          2                                    1                    . -2.270
-2.345  .                                                                                                    . -2.345
-2.421  .                                                      1                                             . -2.421
-2.497  .                                                      1                       1      1              . -2.497
-2.573  .                                                                         *                          . -2.573
-2.649  .                         2                                                                          . -2.649
-2.725  .                                                               1                                    . -2.725
-2.800  .                          2         2                                                               . -2.800
-2.876  .                                                                                                    . -2.876
-2.952  .                                                                                                    . -2.952
-3.028  .                                                                                                    . -3.028
-3.104  .                                                                                                    . -3.104
-3.179  .                                                                                                    . -3.179
-3.255  .                                                                                                    . -3.255
-3.331  .                                                                                                    . -3.331
-3.407  .                                                                                                    . -3.407
-3.483  .                                                                                               1    . -3.483
-3.558  .                                                                                                    . -3.558
-3.634  .                                                                                                    . -3.634
-3.710  .                                                                                                    . -3.710
-3.786  .                                                                                                    . -3.786
-3.862  .                                                                                                    . -3.862
-3.937  .                                                                                                    . -3.937
-4.013  .                                                                                                    . -4.013
-4.089  .                                                                                                    . -4.089
-4.165  .                                                                                                    . -4.165
-4.241  .                                                                                                    . -4.241
-4.316  .                                                                                    1               . -4.316
-4.392  .                                                                                                    . -4.392
-4.468  .                                                                                                    . -4.468
-4.544  .                                                   1                                    1           . -4.544
-4.620  .                                                                                                    . -4.620
+.........+.........+.........+.........+.........+.........+.........+.........+.........+.........+.
-2.939    -2.516    -2.092    -1.669    -1.245     -.821     -.398      .026      .449      .873     1.296
```

0Memory at disposal : 5000
Memory used : 932

##### INTERPRETATION
 IDAMS reports analysis specifications No. of cases read = 36 No. of cases used in the analysis = 29 (Countries of South America and Africa are omitted in this example) No. of Discriminant variables = 10 Table of means and standard deviation of variables separately for each group and for the entire sample. This table gives an idea to which fields are more or less prominent in which group. At this stage, the most important discriminant variable is identified and a linear discriminant function is computed and used for classification of countries according to their distance from the group centroids. The most important discriminant variable is V3 (condensed matter physics) Classification table shows that No. of cases correctly classified = 65.52% Group 2 (East Europe is better classified) than the other regions. Average value of V3 is higher in this group than in any other group. Step 2 At this stage the most important variable after V3 is V7 (Partial Physics) The discriminant function computed with these variables, achieves a classification accuracy is 65.52%. It is interesting to note there is no change in the overall classification accuracy, but there is a change in the classification matrix. One country from group 2 which was misclarified into Group 1 is now misclarified into Group 3 Step 3 At this stage the most important discriminant variable after V2 and V7 is V11 (Acoutics). The discriminant function set up with these three variables achieve a clarification accuracy of 72.41%. Step 4 At this stage, the most important discriminant variable is Mathematical Physics, but the overall clarification accuracy remains uncharged, but there is some adjustment is the classification matrix. At this stage the most important discriminant variable after V3, V7, V11 and V8 is V4 (Chemical Physics) The discriminant function computed with these variables achieves a classifcation accuracy of 79.35%. Note that: All East-European countries are correctly classified. 4 out of 5 Asian countries are correctly classified. 12 out of 17 Western Countries are correctly classified. Classification frequency decreases after this step. Allocation Table and distances from the centroids of each group Name of the countries in this group are misclassified 9 East-European. The following countries are Allocation Table and Distances from the centroid of each group This table provides information as to how different countries are situated from the centroids of different groups. The countries are allocated to the nearest group. The following countries of Group-1 which are allocated to Group 1 are still quite away from their centroid. Idcode        Distance from the centroid of Grouping 35                    15.999 36                    9.993 37                    9.470 38                    9.491 These countries seen to be ‘outliers’. 5 countries of this region are misclassified into Group 3 (Asia). Their idcodes are printed. Group 2. No country is misclassified Group 3 Only one country (Idcode 19) is misclassified into Group 1 (Western countries). Discriminant Function Analysis The first discriminant function is linear combination of the variables that best discriminant between the groups. The second discriminant function is orthgond to the first and is the next best combination of the variable.