Dependent Variable

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Dependent Variable

• Discrete
• 2 values binomial
• 3 or more discrete values multinomial
• Skewed e.g. Poisson
• Continuous
• Non-normal

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Link Function

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

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Function

• link(y) a b1x1 b2x2 bnxn e)
• The link function should connect the (discrete)
  dependent observation to the linear predictor.
• y inverse-link (a b1x1 )

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Link Functions
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Solution

• Requires numeric solution (rather than algebraic
  for traditional GLM)

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Significance

• Wald statistic
• Likelihood Ratio statistic
• Score statistic

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Residuals

• Pearson residuals based on observed predicted
  values
• Deviance residuals contribution to log
  likelihood statistic
• Leverage
• Studentized
• Cooks D

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Models

• ANOVA
• Regression
• ANCOVA
• More complex linear models

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SAS

• PROC GENMOD procedure call
• CLASS categorical (ANOVA) variables
• MODEL dependent independent

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MODEL

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

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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 dont
• Type1 (sequential), Type3 (partial), Wald
  statistics
• P (predicted estimates) R (residuals)