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lec36v1_1up - Stat 104 Quantitative Methods for Economists...

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Stat 104: Quantitative Methods for Economists Class 36: Logistic Regression 1
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What is logistic regression? square4 There are many important research topics for which the dependent variable is "limited." square4 For example: voting, morbidity or mortality, and participation data is not continuous or distributed normally. square4 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)
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Overview of categorical regression models Binary: Two categories square4 vote in last election? square4 patient cured after treatment? square4 startup failed? Ordinal: More than two categories and assume ordered square4 not favorable, favorable, extremely favorable square4 not likely, likely, very likely square4 no coverage, partial coverage, maximum coverage in insurance Nominal: More than two categories but not ordered square4 mode of transportation – bus, car or train? square4 employment status – employed, unemployed, out of work force Count: Number of times something has happened square4 number of patents a company has attained square4 number of times a country goes to war 3
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Y x x k k = + + + + β β β ε 0 1 1 L In the usual regression model set-up, 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 ( ) = + + + β β β 0 1 1 L 4
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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 ( ) ( ) ( ) = = + = 0 0 1 1 Thus for a 0,1 random variable Y E Y P Y ( ) ( ) = = 1 5
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P Y x x k k ( ) = = + + + 1 0 1 1 β β β 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 ? What do we know about probabilities, i.e. what values can they take on ? 6
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Example: Failing or Passing an Exam square6 Let us define a variable ‘Outcome’ boxshadowdwn Outcome = 0 if the individual fails the exam = 1 if the individual passes the exam square6 We can reasonably assume that Failing or Passing an exam depends on the quantity of hours we use to study
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