discriminant ana

7/29/2019 Discriminant Ana

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Discriminant Analysis

Discriminant analysis is a statistical techniquethat is used to classify the dependent variable

between two or more categories.

Discriminant analysis also has a regression

technique, which is used for predicting the value

of the dependent categorical variable.

In discriminant analysis, we predict the value of

two categories.

When the category of a dependent variable is

more than two, it will simply be an extension of

the simple discriminant analysis called the

multiple discriminant analysis.


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Multiple discriminant analysis and MANOVA

are considered to be similar because both tests

share many similar assumptions and tests.

The F test (Wilks' lambda) is used to test

whether or not the discriminant model is

significant as a whole.

If the F test shows the overall significance of the

model, then the individual variables are accessed

to see which variable will move the significance

from the group mean.

Discriminant analysis also assumes several

assumptions, such as multiple linear regressions,

linear relationships, homoscedastic relationships,

untruncated interval data, etc.
http://www.statisticssolutions.com/manovahttp://www.statisticssolutions.com/multiple-regressionhttp://www.statisticssolutions.com/manovahttp://www.statisticssolutions.com/multiple-regression


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Logistic regression is the alternative technique

and it is frequently used in place of discriminant

analysis when data does not meet the

assumptions.

Key Terms and Concepts:

Discriminating variables: Discriminating

variables are independent variables that are used

to predict the dependent variable. These

variables are also called the predictors.

The criterion variable: Dependent variables are

also called the criterion variables.

Discriminant function: The Linear

combination of the discriminating (independent)

variable is called the discriminant function. For

example,


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L = b1x1 + b2x2 + ... + bnxn + c

L= discriminant function

b1= discriminant coefficients

X= independents variables

C = constants

Number of discriminant functions: For the

two groups, there is one discriminant analysis

function. For multivariate discriminant analysis

there will be g-1 discriminant function.

The Eigenvalues: This is also called

characteristic root, which tells us the variance

explained by each discriminant function.

The discriminant score: By applying

discriminant formulas, the value that comes is


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called the discriminant score. This discriminant

score helps us to classify the group category.

Cutoff: This is the value which divides the

group value into two parts. When the value of

the discriminant score is at the negative side of

the cutoff point, then the group will fall into a

lower category, and when it is at the positive

side, the group will be at a higher category.

Unstandardized discriminant coefficients:

Unstandardized discriminant coefficients are

simply like the regression beta, which is used to

predict the discriminate score. Standardized

discriminant coefficients are used to compare

the relative importance of the independent

variables.

Tests of significance:

Wilks' lambda: The overall model significance

of the discriminant function is tested by the


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walks lambda test. If the overall model is

significant, than the F test is used to test whether

or not the individual variable means differ from

the group mean function.

Assumptions in Discriminant analysis:

1. Independence: Each case should be

independent of each other. Correlated data

cannot be used in discriminant analysis.

2. Adequate sample size: There must be at least

two cases for each category of the dependent

variable. However, it is recommended that there

should be at least four or five times as many

cases as independent variables.
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3. Interval data: In discriminant analysis, there

should be an interval data for independent

variable.

4. Variance: No independents have a zero

standard deviation in one or more of the groups

formed by the dependent.

5. Random error: Error terms are assumed to be

randomly distributed.

6. Homogeneity of variances: Variance with

each group of independent variables should be

equal.

7. Absence of perfect multicollinearity: There

should be no perfect multicollinearity between

the independent variables.
http://www.statisticssolutions.com/multicollinearityhttp://www.statisticssolutions.com/multicollinearity


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8. Assumes linearity: The discriminant functions

should be linear and related to each other.

9. Normally distributed: The predictor variable

should be normally distributed.

discriminant ana

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