# 1.1 - 8.10 - Supported Family/Link Function Combinations - Teradata Vantage

## Teradata Vantage™ - Machine Learning Engine Analytic Function Reference

Product
Release Number
1.1
8.10
Release Date
October 2019
Content Type
Programming Reference
Publication ID
B700-4003-079K
Language
English (United States)
Binomial or Logistic BINOMIAL or LOGISTIC logit (default)

probit

cloglog

log

cauchit

log(μ/(1-μ))

Φ

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.