Dependent Variable Discrete  2 values – binomial  3 or more discrete values – multinomial  Skewed – e.g. Poisson Continuous  Non-normal

Link Function Connection between dependent variable and predictor:  Logit – ln(p/(1-p))  Probit – inverse normal  Other nonlinear connections (exponential, logarithmic, power, etc.)

Function link(y) = a + b1*x1 + b2*x2 + … + bn*xn + e) The link function should connect the (discrete) dependent observation to the linear predictor.  y = inverse-link (a + b1*x1 …)

Link Functions DistributionLink Normal, gamma, PoissonLinear, log, power BinomialLogit, probit MultinomialLog(x1/(1 – x2 - … - xn))

Solution  Requires numeric solution (rather than algebraic for traditional GLM)

Significance  Wald statistic  Likelihood Ratio statistic  Score statistic

Residuals  Pearson residuals – based on observed – predicted values  Deviance residuals – contribution to log likelihood statistic  Leverage  Studentized  Cook’s D

Models  ANOVA  Regression  ANCOVA  More complex linear models

SAS  PROC GENMOD: procedure call  CLASS: categorical (ANOVA) variables  MODEL: dependent= independent

MODEL  Model= dependent  Model = events/trials = (ratio of events divided by number of trials for summarized binomial responses)

Model Options  CORR, COVB: parameter correlations or covariances  DIST= lists the assumed distribution of the dependent variable (see SAS docs)  LINK= specifies the link function. SAS will pick a default for a DIST if you don’t  Type1 (sequential), Type3 (partial), Wald statistics  P (predicted estimates) R (residuals)