Version info: Code for this page was tested in IBM SPSS 20.

Linear discriminant function analysis (i.e.,
discriminant analysis) performs a multivariate test of differences between
groups.   In addition, discriminant analysis is used to determine the
minimum number of dimensions needed to describe these differences.  A distinction is sometimes made between descriptive discriminant
analysis and predictive discriminant analysis.  We will be illustrating
predictive discriminant analysis on this page.

Please note: The purpose of this page is to show how to use various data
analysis commands.  It does not cover all aspects of the research process which
researchers are expected to do.  In particular, it does not cover data
cleaning and checking, verification of assumptions, model diagnostics or
potential follow-up analyses.

Examples of discriminant function analysis

Example 1.
A large international air carrier has collected data on employees in three different job
classifications: 1) customer service personnel, 2) mechanics and 3) dispatchers.  The director of
Human Resources wants to know if these three job classifications appeal to different personality
types.  Each employee is administered a battery of psychological test which include measures
of interest in outdoor activity, sociability and conservativeness.

Example 2.

There is Fisher’s (1936) classic example of discriminant analysis involving three
varieties of iris and
four predictor variables (petal width, petal length, sepal width, and sepal length).  Fisher not
only wanted to determine if the varieties differed significantly on the four continuous
variables, but he was also interested in predicting variety classification for unknown individual
plants.

Description of the data

Let’s pursue Example 1 from above.

We have included the data file, which can be obtained by clicking on
discrim.sav.  The dataset has 244 observations on four variables.  The psychological variables are outdoor interests, social and
conservative.  The categorical variable is job type with three
levels; 1) customer service, 2) mechanic, and 3) dispatcher.

Let’s look at the data.  It is always a good idea to start with descriptive
statistics.

get file='d:datadiscrim.sav' .

descriptives variables=outdoor social conservative. means tables=outdoor social conservative by job.correlations variables=outdoor social conservative.frequencies variables=job.

Analysis methods you might consider

Below is a list of some analysis methods you may have
encountered.  Some of the methods listed are quite reasonable, while others
have either fallen out of favor or have limitations.

Discriminant function analysis

We will run the discriminant analysis using the discriminant procedure in SPSS.

There is a lot of output so we will comment at various places
along the way.

discriminant
/groups=job(1 3)
/variables=outdoor social conservative
/analysis all
/priors equal
/statistics=boxm table
/plot=combined map
/classify=pooled.

Next, we will plot a graph of individuals on the discriminant dimensions. Due to the
large number of subjects we will shorten the labels for the job groups to make the
graph more legible. As long as we don’t save the dataset these new labels will not be
made permanent.

The discriminant functions are:

discriminant_score_1 = 0.517*conservative + 0.379*outdoor – 0.831*social.

discriminant_score_2 = 0.926*outdoor + 0.213*social – 0.291*conservative.

As you can see, the customer service employees tend to be at the more social (negative) end
of dimension 1; the dispatchers tend to be at the opposite end, with the mechanics in the middle.  On
dimension 2 the results are not as clear; however, the mechanics tend to be higher on the
outdoor dimension and customer service employees and dispatchers lower.

SPSS also produces an ASCII territorial map plot which shows the relative location of the
boundaries of the different categories.  The territorial map is shown below.

                                  Territorial Map
Canonical Discriminant
Function 2
       -6.0      -4.0      -2.0        .0       2.0       4.0       6.0
          .............................................................
     6.0 .  122                                                        .
         .   112                                                      2.
         .     12                                                   223.
         .      122                                                233 .
         .       112                                             223   .
         .         122                                          233    .
     4.0 .          112       .         .         .         . 223      .
         .            12                                     233       .
         .             122                                 223         .
         .              112                              2233          .
         .                12                            233            .
         .                 122                        223              .
     2.0 .          .       112         .         .  233    .          .
         .                    122                  223                 .
         .                     112                233                  .
         .                       12             223                    .
         .                        122    *     233                     .
         .                         112       223                       .
      .0 .          .         .      122.   233   .         .          .
         .                        *   112 223                          .
         .                              1233   *                       .
         .                              13                             .
         .                              13                             .
         .                              13                             .
    -2.0 .          .         .         13        .         .          .
         .                              13                             .
         .                              13                             .
         .                              13                             .
         .                              13                             .
         .                              13                             .
    -4.0 .          .         .         13        .         .          .
         .                              13                             .
         .                              13                             .
         .                              13                             .
         .                             13                              .
         .                             13                              .
    -6.0 .                             13                              .
          .............................................................
       -6.0      -4.0      -2.0        .0       2.0       4.0       6.0
                         Canonical Discriminant Function 1

Symbols used in territorial map

Symbol  Group  Label
------  -----  --------------------

   1        1  customer service
   2        2  mechanic
   3        3  dispatch
   *           Indicates a group centroid

Things to consider

See also

References