Lec23.Logistic - Logistic Regression Logistic KNNL Chapter...

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Logistic Regression Logistic Regression KNNL Chapter 14 Sections 14.1-14.4,14.8,14.9 See also Lec23.Logistic.ssc
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Dengue Epidemic Dengue Epidemic Predicting Disease given age, location in city, and socioeconomic status Dante, Koopman, Addy et al. 1988. J. of Epidemiology (KNN APPENC10.txt) http://phil.cdc.gov/PHIL_Images/08051999/00004/dengue_phf/sld014.htm
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Lec23.Logistic.ssc Lec23.Logistic.ssc # disease  =  read.table("APPENC10.txt") # names(disease)  =   c("id","age","socioecon",   "sector","disease","savings") # # id # age in years # socieconomic status  1 = upper, 2 = middle, 3 = lower # sector,  location in city 1 or 2 # disease status,  1 = with disease, 0 = without disease # savings account  1 = has an account, 0 = does not have accou
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Disease Outbreak Data Disease Outbreak Data disease[1:10,]    id age socioecon sector disease  savings   1  1  33         1      1       0        1  2  2  35         1      1       0        1  3  3   6         1      1       0        0  4  4  60         1      1       0        1  5  5  18         3      1       1        0  6  6  26         3      1       0        0  7  7   6         3      1       0        0
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Age Disease 0 20 40 60 80 0.0 0.2 0.4 0.6 0.8 1.0 Disease vs. Age Disease vs. Age
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Disease vs. Age Disease vs. Age Age Disease 0 20 40 60 80 0.0 0.2 0.4 0.6 0.8 1.0
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Disease vs. Age Disease vs. Age Age Disease 0 20 40 60 80 0.0 0.2 0.4 0.6 0.8 1.0
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Problems for Standard Linear Problems for Standard Linear Regression Regression Binary Response (0, 1) Dichotomous Non-normal Errors Non-constant Error Variance E(Y) = p, V(Y)= p(1-p) Constraints on Response 0 < E(Y) < 1
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x exp(x)/(1 + exp(x)) -3 -2 -1 0 1 2 3 0.2 0.4 0.6 0.8 Sigmoid Shaped Curve Sigmoid Shaped Curve
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Three Commonly Used Sigmoid Three Commonly Used Sigmoid Models Models Logit (Logistic) Probit Log-Log )) exp( exp( 1 ) 1 ( cdf normal ) ( ) 1 ( ) exp( 1 ) exp( ) 1 ( 1 0 1 0 1 0 1 0 i i i i i i i i i i X Y P X Y P X X Y P β π + - - = = = + Φ = = = + + + = = = Log-Log aka Gumbel Error Distribution
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x exp(x)/(1 + exp(x)) -3 -2 -1 0 1 2 3 0.2 0.4 0.6 0.8 Three Sigmoid Models Three Sigmoid Models Logit Probit Log-Log
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Two Formulations for Two Formulations for Logistic Regression Logistic Regression Formulation 1: Modeling the Probability: (S-shaped) Formulation 2: Modeling the Log(Odds): (Line)
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Model vs. Data Model vs. Data How should we fit the model to the data?
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This note was uploaded on 04/17/2010 for the course STSCI 3200 taught by Professor Sullivan during the Spring '10 term at Cornell University (Engineering School).

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Lec23.Logistic - Logistic Regression Logistic KNNL Chapter...

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