MVChap05 - STA 4107/5107 Chapter 5 Multiple Discriminant...

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Unformatted text preview: STA 4107/5107 Chapter 5: Multiple Discriminant Analysis and Logistic Regression March 19, 2007 1 Key Terms Please review and learn these terms. 2 What are Discriminant Analysis and Logistic Regression? Discriminant analysis and logistic regression are dependence techniques whose goal is to classify (some refer to these techniques as classification techniques ) categorical variables based on metric variables. For both these techniques, we must have a “training set” that has the values for the class variables and predictor variables, that is, you must have a data set where you know the group (or population) memberships for all the cases. Once the discriminant function is found using the training set and either technique, you can classify an unknown case based on the values of its predictor variables. If group membership is unknown in the training set, then cluster analysis is the appropriate technique. 2.1 Examples 1. An archaeologist wishes to determine which of three possible tribes created a particular statue found in a dig. The archaeologist takes measurements from statues produced by the three tribes, as well as the unknown statue. The known statues are used to train a discriminant function and then the values from the unknown statue are plugged into the discriminant function which then classifies the statue into one of the three tribes. 2. Lubishew (1962) considers a problem of discrimination between three species of flea beetles, Chaetocnema concinna, C. heikertingeri, C heptapotamica based on various physical mea- surements. 3. The US forest service would like to identify the personal characteristics of residents near a reservoir that predict whether that person will fish as an adult, with the goal of increasing recreational fishing in the area. 4. Investigators are interested in the relationship between island size and bird extinctions. On each island they count the number of species that went extinct out of all the species on the 1 island. The investigator would like to characterize the relationship between the area of an island and the probability of extinction of birds present on the island? 5. Investigators are interested in moth coloration and natural selection. At a number of dis- tances from Liverpool they count the number of moths from each morph that were taken by predators. They would like to quantify the relationship between the distance from Liverpool, where trees are dark from industrial soot, and the probability of predation on the light and dark morphs of the moth Carbonaria? 6. Researchers are interested in survival in the Donner Party. What is the relationship between age and sex of individuals in the Donner Party and whether or not they survived?...
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MVChap05 - STA 4107/5107 Chapter 5 Multiple Discriminant...

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