1 / 13

Say good things, think good thoughts, and do good deeds

Say good things, think good thoughts, and do good deeds. Categorical Data Analysis. Chapter 5 (I): Logistic Regression for Quantitative Factors. Logistic Regression. Binary response variable: Y ~ Bernoulli( p ) k quantitative/ordinal factors: x 1 , … , x k model: SAS textbook Sec 8.5.

sheadon
Download Presentation

Say good things, think good thoughts, and do good deeds

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Say good things, think good thoughts, and do good deeds

  2. Categorical Data Analysis Chapter 5 (I): Logistic Regression for Quantitative Factors

  3. Logistic Regression • Binary response variable: Y ~ Bernoulli(p) • k quantitative/ordinal factors: x1, … , xk • model: SAS textbook Sec 8.5

  4. Interpretation (for Only One Factor) • (Multiplicative effect on the odds) Increasing x by one unit is estimated to give the odds of response a increase by a factor of exp(b)— Not easy for investigators to understand

  5. Interpretation (for Only One Factor) • Interpretation of the effect of x on Y in terms of risk (or called response rate): • The bigger b (the effect of X on Y) is, the bigger the slope of a tangent line of the fitting curve (with respect to X) is: how the risk changes instantly at x

  6. LD 50 • LD50 (LD = lethal dose)= the dose level at which toxicity rate p(dose) is 50% • In the logistic regression with dose being the only x, LD50= -a/b • The instant change rate of risk (p) at LD50 is b/4

  7. Example: Insecticide vs Beetles See handout for SAS code and output

  8. Only One Factor • The estimate of b,34.27, can be interpreted as: Increasing dose by one unit is estimated to give the odds of death a increase by a factor of exp(34.27) • Interpret the effect on the risk of death at dose 1.70

  9. More than 1 Factors • The estimate of b is 34.27 can be interpreted as: Increasing x by one unit, keeping other factors fixed, is estimated to give the odds of death a increase by a factor of exp(34.27) • b1 is called the logistic regression coefficient for x1 adjusted for other factors

  10. Confidence Intervals Based on Fisher information matrix and asymptotical results of mle • Wald C.I. for bi : found by SAS • Wald C. I. for p(x): found by SAS PROC GENMOD with the OBSTATS option

  11. Significance Tests • H0: b1=0 vs. H1: b1is not zero • Wald test • LR test

  12. Examining the Fit of the Logit Model • Plot fitted and observed rates on the same plot • Residuals for logit models

  13. Grouped Data • Grouping data makes overall goodness of fit test sensible and possible • Example: Crab data grouped by the width • Ungrouped: deviance=191.7, df=165, p-value=.076 • Grouped: deviance=6.25, df=6, p-value=.40

More Related