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Discriminant Analysis

Discriminant Analysis . Similar to Regression, except that criterion (or dependent variable) is categorical rather than continuous. -used to identify boundaries between groups of objects. For example: (a) does a person have the disease or not (b) Is someone a good credit risk or not?

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Discriminant Analysis

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  1. Discriminant Analysis Similar to Regression, except that criterion (or dependent variable) is categorical rather than continuous. -used to identify boundaries between groups of objects For example: (a) does a person have the disease or not (b) Is someone a good credit risk or not? (c) Should a student be admitted to college?

  2. Benefits of Discriminant Analysis • Similar to regression: • What predictor variables are related to the criterion (dependent variable) • Predict values on the criterion variable when given new values on the predictor variable

  3. A cartoon of Discriminant Analysis: showing the Discriminant Function Cutoff score to discriminate groups

  4. Cluster Analysis • Set of techniques used to partition a set of objects (people) into relatively homogenous subsets based on similarity. • Example Applications: • Psychology: classifying individuals into types • Regional Analysis: classifying cities into typology based on demographic and fiscal variables • Marketing research: classifying individuals into clusters

  5. Goal of Cluster Analysis Identify a few groups so that individuals / objects in a group are more similar than objects outside a group. Reduce the set of n objects to less than n groups. Thus it is a data reduction technique

  6. Similarity to Factor Analysis Factor Analysis and Cluster Analysis are both data reduction techniques. Goal of Factor Analysis is to reduce original set of variables to smaller set of factors. Goal of Cluster Analysis is to form groups from the people or objects, thus reducing original number of elements to fewer groups. Factor Analysis can be seen as a clustering technique than is focused on the columns of data matrix, rather than the rows.

  7. Similarity to Discriminant ANalysis In Discriminant Analysis, groups are know a priori; I.e., all the observations are supposed to be correctly classified at the outset. Objective of analysis is to predict that classification from the predictor variables. Cluster Analysis is used when the natural clusterings are not known. The objective is to discover is there are any natural groups. In cluster analysis, one begins with groups that are undifferentiated, and tries to form groups and subgroups.

  8. Types of Data Ratings of n objects on p properties

  9. Distance Data Distance of n objects from each other (can use categorical data, when you just know if two objects are in the same group)

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