`link`

• Available in: GLM, GAM
• Hyperparameter: no

Description

GLM and GAM problems consist of three main components:

• A random component $f$ for the dependent variable $y$: The density function $f(y;\theta,\phi)$ has a probability distribution from the exponential family parametrized by $\theta$ and $\phi$. This removes the restriction on the distribution of the error and allows for non-homogeneity of the variance with respect to the mean vector.
• A systematic component (linear model) $\eta$: $\eta = X\beta$, where $X$ is the matrix of all observation vectors $x_i$.
• A link function $g$: $E(y) = \mu = {g^-1}(\eta)$ relates the expected value of the response $\mu$ to the linear component $\eta$. The link function can be any monotonic differentiable function. This relaxes the constraints on the additivity of the covariates, and it allows the response to belong to a restricted range of values depending on the chosen transformation $g$.

Accordingly, in order to specify a GLM or GAM problem, you must choose a family function $f$, link function $g$, and any parameters needed to train the model.

H2O's GLM and GAM support the following link functions: Family_Default, Identity, Logit, Log, Inverse, Tweedie, or Ologit.

The following table describes the allowed Family/Link combinations.

Family	Family_Default	Identity	Logit	Log	Inverse	Tweedie	Ologit
Binomial	X		X
Fractional Binomial	X		X
Quasibinomial	X		X
Multinomial	X
Ordinal	X						X
Gaussian	X	X		X	X
Poisson	X	X		X
Gamma	X	X		X	X
Tweedie	X					X
Negative Binomial	X	X		X
AUTO	X***	X*	X**	X*	X*

For AUTO:

• X*: the data is numeric (Real or Int) (family determined as gaussian)
• X**: the data is Enum with cardinality = 2 (family determined as binomial)
• X***: the data is Enum with cardinality > 2 (family determined as multinomial)

Refer to the Links section for more information.

Related parameters

• family

Example

R

library(h2o)
h2o.init()

# import the iris dataset:
# this dataset is used to classify the type of iris plant
# the original dataset can be found at https://archive.ics.uci.edu/ml/datasets/Iris
iris <- h2o.importFile("http://h2o-public-test-data.s3.amazonaws.com/smalldata/iris/iris_wheader.csv")

# convert response column to a factor
iris['class'] <- as.factor(iris['class'])

# set the predictor names and the response column name
predictors <- colnames(iris)[-length(iris)]
response <- 'class'

# split into train and validation
iris_splits <- h2o.splitFrame(data = iris, ratios = 0.8)
train <- iris_splits[[1]]
valid <- iris_splits[[2]]

# try using the `link` parameter:
iris_glm <- h2o.glm(x = predictors, y = response, family = 'multinomial', link = 'family_default',
                   training_frame = train, validation_frame = valid)

# print the logloss for the validation data
print(h2o.logloss(iris_glm, valid = TRUE))

Python

import h2o
from h2o.estimators.glm import H2OGeneralizedLinearEstimator
h2o.init()

# import the iris dataset:
# this dataset is used to classify the type of iris plant
# the original dataset can be found at https://archive.ics.uci.edu/ml/datasets/Iris
iris = h2o.import_file("http://h2o-public-test-data.s3.amazonaws.com/smalldata/iris/iris_wheader.csv")

# convert response column to a factor
iris['class'] = iris['class'].asfactor()

# set the predictor names and the response column name
predictors = iris.columns[:-1]
response = 'class'

# split into train and validation sets
train, valid = iris.split_frame(ratios = [.8])

# try using the `link` parameter:
# Initialize and train a GLM
iris_glm = H2OGeneralizedLinearEstimator(family = 'multinomial', link = 'family_default')
iris_glm.train(x = predictors, y = response, training_frame = train, validation_frame = valid)

# print the logloss for the validation data
iris_glm.logloss(valid = True)

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