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Binary Response
- Logistic Regression
- Inference
- Diagnostics
- Model Selection
- Goodness of Fit
- Estimation
- Prediction
-
Binomial and Proportion Responses
-
Binomial Regression
-
link
-
logit
- make retrospective equivalent to prospective
- probit
- cloglog
- cauchy
- Inference
- Goodness of Fit
-
Prediction and Effective Dose
-
prediction
- No distinction between future observation and the mean response
- effective dose
-
large deviance
- structual deviance : need transformation
- outliers
- sparse data
-
overdispersion
- causes
- dependece
- different pi
- solution
- when the covariate classes are roughly equal in size
- introduce a dispersion parameter
- estimate the dispersion parameter
- redo the test
- drop1(m1, scale = s2, test='Chisq')
- summary(m1, dispersion = s2)
- when the covariate classes are not roughly equal in size
- use dispmod package
- use F test
- check these two before trying dispersion parameter
- Beta Regression
-
Count Responses
-
Poisson Regression
-
when to use
- probability depends on the length of time
- probability small, approximates binomial
- use chisq test
-
Dispersed Poisson Model
-
when to use
- deviance is large
- no apparent outliers
- no sparsity
-
mechanism known
- negative binomial
-
mechanism unknown
- dispersion parameter
- use F test
-
Rate Model
- use log(num) as predictor
-
Negative Binomial
- can use two parameters to depict mean and variance
- glm.nb
-
Model Selection
- Cross Validation
- Stability