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In discriminant analysis there is one output
and it is categorical. The inputs are continuous
variables :
The purpose is to understand how to use
the input variables to differentiate between
the outputs.
For example, you may be trying to determine
the factors that make it likely that customers
will default on a loan (two categories,
default or not). The inputs might be their
annual income, length at present employment
and the amount of the loan.
Factor analysis takes a large number of
continuous factors and combines them to
form a small number of continuous factors
that explain most of the variation in the
response. These now factors are called 'eigenvectors'.
Suppose that you had the results of a questionnaire
giving the reactions of customers on a new
car. There were 100 questions in the questionnaire.
You might be able to form these questions
into three eigenvectors, 'safety', 'esteem'
and 'comfort' that explained 90% of the
variation between the respondents, and by
extension the potential customer base.
| MANOVA
(Multiple Analysis of Variance) |
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This is similar to ANOVA except
that there are several outputs. The outputs
must be correlated, if they are not you
should use a separate ANOVA analysis for
each output.
There may be one input factor
or several.
The benefit of MANOVA is that
if you carried out several ANOVA analysis,
as if the factors were not correlated, you
would increase the probability of a Type
I error. The argument is similar to the
argument for using ANOVA instead of multiple
pairwise t-tests.
Multivariate Analysis is concerned
with analyzing processes that have several
inputs and/or outputs.
| Principal
Components Analysis |
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Similar to Factor Analysis, but uses a different
method of analysis.
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