# Background - Aster Analytics

## Teradata Aster® Analytics Foundation User GuideUpdate 2

Product
Aster Analytics
Release Number
7.00.02
Published
September 2017
Language
English (United States)
Last Update
2018-04-17
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B700-1022
Product Category
Software
Supported Family/Link Function Combinations
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

log[-log(1-μ)]

log(μ)

tan(π(μ - 1/2))

When the dependent variable (Y) has only two possible values (0 and 1, 'yes' and 'no', or 'true' and 'false').

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 (matrices 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 denotes the default link for each family.

Common Link Functions for Distribution Exponential Families
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 *