Disciminant analysis
Discriminant
Function Analysis (DA) undertakes the same task as multiple linear regression
by
predicting an outcome. However, multiple linear regression is limited to cases
where the
dependent
variable on the Y axis is an interval variable so that the combination of
predictors
will,
through the regression equation, produce estimated mean population numerical
Y
values for given values of weighted combinations of X values. But many
interesting
variables
are categorical, such as political party voting intention, migrant/non-migrant
status,
making
a profi t or not, holding a particular credit card, owning, renting or paying a
mortgage
for
a house, employed/unemployed, satisfi ed versus dissatisfi ed employees, which
customers are likely to buy a product or not buy.
DA
is used when:
the
dependent is categorical with the predictor IV’s at interval level such as age,
income,
attitudes,
perceptions, and years of education, although dummy variables can be used
as
predictors as in multiple regression. Logistic regression IV’s can be of any
level of
measurement.
there
are more than two DV categories, unlike logistic regression, which is limited
to a
dichotomous
dependent variable.
Assumptions
of discriminant analysis
The
major underlying assumptions of DA are:
·
The observations are a random sample
·
Each predictor variable is normally distributed
·
each of the allocations for the dependent categories in the
initial classifi cation are
·
correctly classifi ed;
·
there must be at least two groups or categories, with each
case belonging to only one
·
group so that the groups are mutually exclusive and
collectively exhaustive (all cases
·
can be placed in a group);
·
each group or category must be well defi ned, clearly differentiated
from any other
·
group(s) and natural. Putting a median split on an attitude
scale is not a natural way to
·
form groups. Partitioning quantitative variables is only
justifi able if there are easily
·
identifi able gaps at the points of division;
·
for instance, three groups taking three available levels of
amounts of housing loan;
·
the groups or categories should be defi ned before collecting
the data;
·
the attribute(s) used to separate the groups should
discriminate quite clearly between
·
the groups so that group or category overlap is clearly
non-existent or minimal;
·
group sizes of the dependent should not be grossly different
and should be at least fi ve
·
times the number of independent variables.
There are several purposes
of DA:
·
To investigate differences between groups on the basis of the
attributes of the cases,
·
indicating which attributes contribute most to group
separation. The descriptive technique successively identifi es the linear
combination of attributes known as canonical
·
discriminant functions (equations) which contribute maximally
to group separation.
·
Predictive DA addresses the question of how to assign new
cases to groups. The DA
·
function uses a person’s scores on the predictor variables to
predict the category to
·
which the individual belongs.
·
To determine the most parsimonious way to distinguish between
groups.
·
To classify cases into groups. Statistical signifi cance tests
using chi square enable you
·
to see how well the function separates the groups.
·
To test theory whether cases are classifi ed as predicted.
Steps to be followed
1 Click Analyze >>
Classify >> Discriminant.
2 Select grouping variable
and transfer to Grouping Variable box. Then click Defi ne
Range button and enter the
lowest and highest codes for your grouping variable defi ne
range.
3 Click Continue then
select predictors and enter into Independents box. Then click on
Use Stepwise Methods. This
is the important difference from the previous example
(Fig. 25.12).
4 Statistics >> Means, Univariate Anovas,
Box’s M, Unstandardized and Within Groups
Correlation.
5 Click Classify. Select
Compute From Group Sizes, Summary Table, Leave One Out
Classifi cation, Within
Groups, and all Plots.
6 Continue >> Save and select Predicted
Group Membership and Discriminant Scores.
7 OK.
- By Rachit
Team F
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