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.
Error Default Link Default Scale Distribution Function Parameter Normal Identity Mean Deviance eta=µ Inverse Gaussian Inverse Quadratic Mean 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 Function Form Identity eta=µ Logarithm eta=logµ Reciprocal eta=1/µ Square Root eta=sqrt(µ) Power eta=µp (p non-zero) Logit eta=log(pi/(1-pi) ) Complementary log-log eta=log[ -log(1-pi)] Probit eta=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.