Discretize Continuous Distribution Family for Count Regression Models

Description

This function takes any continuous distribution family object and discretizes it, enabling it to be used for the estimation of count regression models. The discretized family can then be used in gamlss2 models that deal with count data.

Usage

discretize(family = NO)

Arguments

family

A continuous distribution family object. The family will be discretized for modeling count data, where the distribution is adapted for count outcomes.

Details

The function discretizes a continuous distribution family by converting its cumulative distribution function (CDF) into a probability mass function (PMF). This is done by computing the difference between the CDF evaluated at adjacent points. The resulting discretized distribution can be used in count regression models to estimate the relationship between count data and explanatory variables.

Value

Returns an object of class “gamlss2.family”, which is a discretized version of the input continuous family object, suitable for use in gamlss2 models for count data.

See Also

gamlss2, gamlss2.family

Examples

library("gamlss2")

## simulate count data using the Poisson distribution
set.seed(111)
y <- rpois(1000, lambda = 10)

## create a discretized family using the BCT distribution (with log link for mu)
fam <- discretize(family = BCT(mu.link = "log"))

## fit a count regression model using the discretized family
fit_family(y, family = fam)

GAMLSS-RS iteration  1: Global Deviance = 5169.4544 eps = 0.508090     
GAMLSS-RS iteration  2: Global Deviance = 5123.1813 eps = 0.008951     
GAMLSS-RS iteration  3: Global Deviance = 5121.12 eps = 0.000402     
GAMLSS-RS iteration  4: Global Deviance = 5120.9807 eps = 0.000027     
GAMLSS-RS iteration  5: Global Deviance = 5120.9196 eps = 0.000011     
GAMLSS-RS iteration  6: Global Deviance = 5120.8865 eps = 0.000006