# family¶

• Available in: GLM
• Hyperparameter: no

## Description¶

GLM 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 problem, you must choose a family function $$f$$, link function $$g$$, and any parameters needed to train the model.

You can specify one of the following family options based on the response column type:

• gaussian: The data must be numeric (Real or Int). This is the default family.
• binomial: The data must be categorical 2 levels/classes or binary (Enum or Int).
• ordinal: The data must be categorical with at least 3 levels.
• quasibinomial: The data must be numeric.
• multinomial: The data can be categorical with more than two levels/classes (Enum).
• poisson: The data must be numeric and non-negative (Int).
• gamma: The data must be numeric and continuous and positive (Real or Int).
• tweedie: The data must be numeric and continuous (Real) and non-negative.

Refer to the Families section for detailed information about each family option.

Note: If your response column is binomial, then you must convert that column to a categorical (.asfactor() in Python and as.factor() in R) and set family = binomial. The following configurations can lead to unexpected results.

• If you DO convert the response column to categorical and DO NOT to set family=binomial, then you will receive an error message.
• If you DO NOT convert response column to categorical and DO NOT set the family, then GLM will assume the 0s and 1s are numbers and will provide a Gaussian solution to a regression problem.

## Example¶

library(h2o)
h2o.init()

# import the cars dataset:
# this dataset is used to classify whether or not a car is economical based on
# the car's displacement, power, weight, and acceleration, and the year it was made
cars <- h2o.importFile("https://s3.amazonaws.com/h2o-public-test-data/smalldata/junit/cars_20mpg.csv")

# convert response column to a factor
cars["economy_20mpg"] <- as.factor(cars["economy_20mpg"])

# set the predictor names and the response column name
predictors <- c("displacement","power","weight","acceleration","year")
response <- "economy_20mpg"

# split into train and validation
cars.splits <- h2o.splitFrame(data = cars, ratios = .8)
train <- cars.splits[[1]]
valid <- cars.splits[[2]]

# try using the family parameter:
car_glm <- h2o.glm(x = predictors, y = response, family = 'binomial', training_frame = train,
validation_frame = valid)

# print the auc for your validation data
print(h2o.auc(car_glm, valid = TRUE))

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

# import the cars dataset:
# this dataset is used to classify whether or not a car is economical based on
# the car's displacement, power, weight, and acceleration, and the year it was made
cars = h2o.import_file("https://s3.amazonaws.com/h2o-public-test-data/smalldata/junit/cars_20mpg.csv")

# convert response column to a factor
cars["economy_20mpg"] = cars["economy_20mpg"].asfactor()

# set the predictor names and the response column name
predictors = ["displacement","power","weight","acceleration","year"]
response = "economy_20mpg"

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

# try using the family parameter:
# Initialize and train a GLM
cars_glm = H2OGeneralizedLinearEstimator(family = 'binomial')
cars_glm.train(x = predictors, y = response, training_frame = train, validation_frame = valid)

# print the auc for the validation data
cars_glm.auc(valid = True)