# theta¶

• Available in: GLM, GAM

• Hyperparameter: no

## Description¶

In GLM, negative binomial regression is a generalization of Poisson regression that loosens the restrictive assumption that the variance is equal to the mean. Instead, the variance of negative binomial regression is a function of its mean and parameter $$\theta$$, the dispersion parameter.

The theta parameter allows you to specify this dispersion value. This option must be > 0 and defaults to 1e-10. In addition, this option can only be used when family=negativebinomial.

Refer to the Negative Binomial Models topic for more inforamtion on how the theta value is used in negative binomial regression problems.

## Example¶

library(h2o)
h2o.init()

# Import the Swedish motor insurance dataset
h2o_df = h2o.importFile("http://h2o-public-test-data.s3.amazonaws.com/smalldata/glm_test/Motor_insurance_sweden.txt")

# Set the predictor names and the response column
predictors <- c["Payment", "Insured", "Kilometres", "Zone", "Bonus", "Make"]
response <- "Claims"

# Train the model
negativebinomial_fit <- h2o.glm(x = predictors,
y = response,
training_frame = h2o_df,
family = "negativebinomial",
theta = 0.5)

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

# Import the Swedish motor insurance dataset
h2o_df = h2o.import_file("http://h2o-public-test-data.s3.amazonaws.com/smalldata/glm_test/Motor_insurance_sweden.txt")

# Set the predictor names and the response column
predictors = ["Payment", "Insured", "Kilometres", "Zone", "Bonus", "Make"]
response = "Claims"