stat557-fall06

stat557-fall06 - Contents 1 One Dimensional Distributions 1...

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Unformatted text preview: Contents 1 One Dimensional Distributions 1 1.1 Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Multinomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Contingency Tables 3 2.1 Visualizing Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Sensitivity and Specificity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Different Types of Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 Describing Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5.1 Difference of Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5.2 Relative Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5.3 Odds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5.4 Odds Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 Odds Ratios for 2 × 2 × K Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.6.1 Excursion: Delta Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.6.2 Confidence Intervals for log odds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.6.3 Excursion: More Asymptotic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.6.4 Confidence Interval for the log odds ratio . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.7 Odds Ratios in I × J Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.8 Concordance and Discordance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.9 Testing Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 Generalized Linear Models 19 3.1 Members of the Natural Exponential Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 GLMs for Binary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3 GLM for Counts: Poisson Loglinear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Deviance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.5 A detailed Example: Moth Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.6 GLM Models with Dispersion Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.7 Residuals of GLMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.8 The Newton-Raphson Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4 Logistic Regression 37 4.1 Retrospective Study...
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This note was uploaded on 03/09/2010 for the course STAT 557 taught by Professor Staff during the Fall '08 term at Iowa State.

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stat557-fall06 - Contents 1 One Dimensional Distributions 1...

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