Family Name | Family Function Name | Link | Link Function Expression | Used |
---|---|---|---|---|
Binomial or Logistic | BINOMIAL or LOGISTIC | logit (default) probit cloglog log cauchit |
log(μ/(1-μ)) Φ-μ log[-log(1-μ)] log(μ) tan(π(μ - 1/2)) |
When the dependent variable (Y) has only two possible values (0 and 1). The algorithm applies the model to the data, predicts the most likely outcome for each input, and supplies a logit (logarithm of odds) for each outcome. |
Gamma | GAMMA | inverse (default) identity log |
μ-1 μ log(μ) |
When data is continuous with constant response variance and appears to be right-skewed. |
Gaussian | GAUSSIAN | identity (default) inverse log |
μ μ-1 log(μ) |
When the data is grouped around a single mean and can be graphed in a normal or bell curve distribution. |
Inverse Gaussian | INVERSE_GAUSSIAN | inverse_mu_squared (default) identity inverse log |
μ-2 μ μ-1 log(μ) |
When the data is grouped around a single mean but the graph appears to have a right-skewed curve distribution. |
Poisson | POISSON | log (default) identity square_root |
log(μ) μ μ1/2 |
To model count data (nonnegative integers) and contingency models (matrixes of the frequency distribution of variables). The algorithm assumes that the dependent variable (Y) has a Poisson distribution (that is, that Y is segmented into intervals of, for example, time or geographic location) and then calculates the discrete probability of one or more events occurring within these segments. |
Negative Binomial | NEGATIVE_BINOMIAL | log (default) identity |
log(μ) μ |
To model count data (nonnegative integers), usually over-dispersed response variables. |
The following table shows the common link functions for the common distribution exponential families. D identifies the default link for each family.
Link | Link Descriptive | Binomial (Logistic) | Gamma | Gaussian | Inverse_Gaussian | Poisson | Negative_Binomial |
---|---|---|---|---|---|---|---|
logit | LOGIT | D | |||||
probit | PROBIT | * | |||||
cloglog | COMPLEMENTARY_LOG_LOG | * | |||||
identity | IDENTITY | * | D | * | * | * | |
inverse | INVERSE | D | * | * | |||
log | LOG | * | * | * | * | D | D |
1/μ2 | INVERSE_MU_SQUARED | D | |||||
sqrt | SQUARE_ROOT | * | |||||
cauchit | CAUCHIT | * |