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Unformatted text preview: Stat 104: Quantitative Methods for Economists Class 36: Logistic Regression 1 What is logistic regression? s There are many important research topics for which the dependent variable is "limited." s For example: voting, morbidity or mortality, and participation data is not continuous or istributed normally. distributed normally. s Binary logistic regression is a type of regression analysis where the dependent variable is a dummy variable: coded 0 (did not vote) or 1(did vote) Overview of categorical regression models Binary: Two categories s vote in last election? s patient cured after treatment? s startup failed? Ordinal: More than two categories and assume ordered s not favorable, favorable, extremely favorable s not likely, likely, very likely o coverage, partial coverage, maximum coverage in insurance s no coverage, partial coverage, maximum coverage in insurance Nominal: More than two categories but not ordered s mode of transportation bus, car or train? s employment status employed, unemployed, out of work force Count: Number of times something has happened s number of patents a company has attained s number of times a country goes to war 3 Y x x k k = + + + + 1 1 L In the usual regression model setup, we assume that Y is a linear function of k X variables, plus some random noise: Another way of stating this is E Y x x k k ( ) = + + + 1 1 L 4 Now regression works fine and well if Y is continuous (or nearly so), but things can go wrong if Y is discrete. A special case is when Y takes on only the values 0 or 1. For a 0,1 random variable Y, we have that E Y P Y P Y ( ) ( ) ( ) = = + = 1 1 Thus for a 0,1 random variable Y E Y P Y ( ) ( ) = = 1 5 P Y x x k k ( ) = = + + + 1 1 1 L If we use regression as we know it to model a 0,1, variable, our model is modeling This is sometimes called a linear probability model Why may this be a bad idea ?...
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.
 Fall '11
 MichaelParzen

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