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Chapter 18. Discriminant Analysis. Content. Fisher discriminant analysis Maximum likelihood method Bayes formula discriminant analysis Bayes discriminant analysis Stepwise discriminant analysis.
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Chapter 18 Discriminant Analysis
Content • Fisher discriminant analysis • Maximum likelihood method • Bayes formula discriminant analysis • Bayes discriminant analysis • Stepwise discriminant analysis
Objective：get discriminate function or probability formula (using several indicators to classify IV) • Data：IVs are classified into two or more groups; discriminate indicators are all numerical variables or categorical variables • Purpose：interpret & predict • Types： Fisher discriminant analysis & Bayes discriminant analysis
Types By data： 1.Analysis fornumerical variable：get discriminate function using numerical indicators 2. Analysis for categorical variable : get probability formula using categorical indicators
By name • Fisher discriminant analysis • Maximum likelihood method • Bayes formula discriminant analysis • Bayes discriminant analysis • Stepwise discriminant analysis
§1Fisher Discriminant Analysis Indicator: numerical indicator Discriminated into: two or more categories
I discriminate into two categories
Example18.1 Data including three indicators （X1，X2，X3）of 22 patients is displayed in table 18-1. Among them, 12 patients are declared as early stage of disease （category A）, the other 10 are terminal patients （category B）. Try to do discriminant analysis.
Table 18-1 observed values and discriminant results of 22 patients（Zc=-0.147）
（1）calculate means of every category and margins between means Dj. Showed as Table 18-2. TABLE18-2 means of every category and margins between means
（2）calculate the compounding matrices of covariance: for example: Equations: The compounding matrices of covariance
§2MAXIMUM LIKELIHOOD METHOD Indicator: qualitative indicator Discriminated into: two or more categories
1 Data：IVsare classified into two or more groups discriminate indicators are all categorical variables Principle：getdiscriminant probabilityby probability multiplicative theorem of independent event
3 application Example18.2 Someone want to use 7 indicators to diagnose 4 types of appendicitis. 5668 medical records are summed up in table 18-3.
§ 3 Bayes formula discriminance Indicator: qualitative indicator Discriminated into: two or more categories
1 Data：IVsare classified into two or more groups discriminative indicators are all qualitative or ranked data Principle：conditional probability + beforehand by probability
Rule： For Example：Example18-3
§ 4 Bayes discriminant analysis Indicator: numerical indicator Discriminated into: several categories (also two categories)
data： IVs are classified into G categoruies discriminative indicators are quantitative data principle：Bayes rule results：G discriminant functions
Decide transcendental probability: • 1. equal probability（with selection bias） • 2. frequency estimation • Rule: if the Yg is maximum, then it belongs to category g • Advantage: quick , correct
Example18-4 Use 17 medical records sorted as table18-4 to discriminate 3 diseases. Four indicators have been list out. You are suggested to set Bayes discriminant function.
Bayes discriminant function evaluation： mistake discriminant probability P is retrospective estimate ( see table18-6） jackknife
§ 5 stepwise discriminant analysis
objective：select effective indicators to establish discriminant function application：only for Bayes discriminant analysis principle：Wilks statistics ，F test。
Example18-5 make stepwise Bayes discriminant analysis on data in table 18-4. Bayes discriminant function：
Evaluation: • mistake discriminant probability P is • 1/17=5.88% retrospective estimate • ( see table18-8) • 3/17= 17.6% jackknife • Compared with example 18-4, though indicators reduced from 4 to 2, the efficiency of discriminating improved . So it is not the case that more indicators means the higher efficiency.
