Prev Up Next
Go backward to 5.1 Offsets
Go up to 5 Advanced Topics and Examples
Go forward to 5.3 Changing the Scale Parameter

5.2 Default Settings for Distributions

The error distribution type can be altered in glmlab via the Distributions menu item (see Section 4.2). The distributions available are: normal; inverse Gaussian; Poisson; binomial and gamma. Likewise, the type of link function used can be changed in the Link menu. The link functions available are summarised in the Table 5.2. Each distribution has a default link function and scale parameter, as summarised in Table 5.2.

ErrorDefault Link Default Scale
DistributionFunctionParameter
Normal Identity Mean Deviance
  eta=µ  
Inverse GaussianInverse QuadraticMean Deviance
  eta=1/µ2 
Poisson Logarithm Fixed (at 1)
  eta=logµ  
Binomial Logit Fixed (at 1)
  eta=log[ pi/(1-pi)]  
Gamma Reciprocal Mean Deviance
  eta=1/µ  
Default Settings for Chosen Distributions
eta is the linear predictor and µ is the mean (pi in the binomial case).  
 
Link FunctionForm
Identityeta=µ
Logarithmeta=logµ
Reciprocaleta=1/µ
Square Rooteta=sqrt(µ)
Powereta=µp (p non-zero)
Logit eta=log(pi/(1-pi) )
Complementary log-logeta=log[ -log(1-pi)]
Probiteta=Phi-1(pi)
Link Functions in glmlab
  eta is the linear predictor and µ is the mean. (pi in the binomial case).
 

Only when the binomial distribution is chosen are the logit, probit and complementary log-log links available; at all other times, they appear are unavailable and dimmed in the Link menu.


Peter Dunn

Prev Up Next