Multiple discriminant analysis spss code

Looking at all the structure coefficients for a function allows the researcher to assign a label to the dimension it measures. The higher the value, the higher if the association between the independent variable and the dicriminant function. Structure coefficients are the correlations between a given independent variable and the discriminant scores. The standardized discriminant coefficients, like beta weights in regression, are used to assess the relative classifying importance of the independent variables. A discrminant score that belongs to a latent variable can be obtained for each case by applying the coefficients to the values in the respective independent variables. Discriminant Coefficient The discriminant function coefficients are partial coefficients that reflect the unique contribution of each variable to the classification of the groups in the dependent variable. In discriminant analysis, the first function will be the most powerful in differentiation the dimensions and the subsequent functions may or may not represent additional significant differentiation. Though mathematically different, each discriminant function is a dimension which differentiates a case into groups in the dependent variable based on its values on the independent variables. The second function is orthogonal to the first (uncorrelated with it) and maximizes the differences between the groups in the dependent variable, controlling for the first function. When there are two functions, the first function maximizes the differences between the groups in the dependent variable. That is, for two groups one function, for three groups - two functions, and so on. 29Д¤ Key Concepts and Terms Discriminant function The number of functions computed is one less than the number of groups in the dependent variable. If you have collected a large number of independent variables and want to select a useful subset for predicting the dependent variable, use Multiple Discrminant Analysis with selection methods. To test theory by observing whether cases are classified as predicted. To discard variables which are little related to group distinction. To determine the most parsimonious way to distinguish among groups. There are several purposes for MDA: To investigate differences among groups. For purposes of significance testing, the independent variables follow a multivariate normal distribution. Errors (residuals) are randomly distributed. The variance-covariance structure of the independent variables are similar within each group of the dependent variable. The number of independent variables is not more than two less than the sample size. Groups are mutually exclusive and the group sizes are not grossly different. 28ДЈ Assumptions The variables X 1, X 2, X p are independent of each other. OR simply, H 0 : i = 0, for i=1, 2, p versus H a : i 0 for at least one i. H a : Y depends on at least one of the X i s. In terms of hypothesis, it can be written as: H 0 : Y does not depend on any of the X i s. The objective discriminant analysis is to test if the classifications of groups in a variable Y depends on at least one of the X i s. The model X 1 Independent Variables (Quantitative) X 2 : Y Dependent Variable (Qualitative) X p The discriminant equation: F = X X p X p + where, F is a latent variable formed by the linear combination of the dependent variable, X 1, X 2, X p are the p independent variables, is the error term and 0, 1, 2, p are the discriminant coefficients. The weights are referred to as discriminant coefficients. The weights assigned to each independent variable are corrected for the interrelationships among all the variables. This linear combination is known as the discriminant function. Discriminant analysis derives an equation as linear combination of the independent variables that will discriminate best between the groups in the dependent variable. The choice between three candidates, A, B or C in an election is an example where the dependent variable consists of more than two groups. In most cases the dependent variable consists of two groups or classifications, like, high versus normal blood pressure, loan defaulting versus non defaulting, use versus non use of internet banking etc. The purpose of discriminant analysis is to obtain a model to predict a single qualitative variable from one or more independent variable(s). 2 MULTIPLE DISCRIMINANT ANALYSIS (MDA) In multiple linear regression, the objective is to model one quantitative variable (called the dependent variable) as a linear combination of others variables (called the independent variables).

Multiple discriminant analysis spss code