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Week 3

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Logistic Regression Overview and applications Additional issues Select Inputs Optimize complexity Transforming Inputs

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Estimating relation between different variables dependent variables and independent variables change in DV for any change in IV Applications forecasting, healthcare, economics, finance

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Whether someone will respond or not to advertisements? Whether someone is a high default risk on a loan? Whether someone will buy or not buy? Whether the patient will responds to treatment or not? Whether a machine will fail next week?

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Regression Analysis where DV is binary (0/1) – most common case Classify a new observation into a class based on its predictors Predictors can be categorical or continuous

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Probability Odds Logit function Logistic function

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Specification

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Specify the logistic function Estimate the parameter βs Substitute the value of βs in model to estimate odds ratio = β 0 + β 1 x 1 + β 2 x 2 ·· ^ log p 1 – p () ^

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Odds ratio : Amount odds change with unit change in input. 1 odds exp(β i ) Δx i consequence... = β 0 + β 1 x 1 + β 2 x 2 ·· ^ log p 1 – p () ^

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Can the categories be correctly predicted given a set of predictors? What is the relative importance of each predictor? Which predictors have a ‘statistically significant effect’?

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Entry Cutoff Input p -value...

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Entry Cutoff Input p -value...

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Entry Cutoff Input p -value...

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Entry Cutoff Input p -value...

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Entry Cutoff Input p -value

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Stay Cutoff Input p -value...

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Stay Cutoff Input p -value...

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Stay Cutoff Input p -value...

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Stay Cutoff Input p -value...

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Stay Cutoff Input p -value...

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Stay Cutoff Input p -value...

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Stay Cutoff Input p -value...

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Stay Cutoff Input p -value

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Entry Cutoff Stay Cutoff...

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Input p -value Entry Cutoff Stay Cutoff...

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Input p -value Entry Cutoff Stay Cutoff...

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Input p -value Entry Cutoff Stay Cutoff...

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Input p -value Entry Cutoff Stay Cutoff...

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Input p -value Entry Cutoff Stay Cutoff...

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Input p -value Entry Cutoff Stay Cutoff

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1 2 3 4 5 6 Model fit statistic training validation...

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123456 Model fit statistic Evaluate each sequence step....

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high leverage points skewed input distribution standard regression true association standard regression true association Original Input Scale...

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high leverage points skewed input distribution standard regression true association standard regression true association Original Input Scale more symmetric distribution Regularized Scale...

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Original Input Scale more symmetric distribution Regularized Scale standard regression... Original Input Scale high leverage points skewed input distribution

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Regularized Scale standard regression... Original Input Scale regularized estimate

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Regularized Scale standard regression... Original Input Scale regularized estimate true association

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5.2 Input Selection 5.3 Stopped Training

5.2 Input Selection 5.3 Stopped Training

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