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 = 5272.794 eps = 0.498257     
GAMLSS-RS iteration  2: Global Deviance = 5182.6298 eps = 0.017099     
GAMLSS-RS iteration  3: Global Deviance = 5169.4544 eps = 0.002542     
GAMLSS-RS iteration  4: Global Deviance = 5163.3186 eps = 0.001186     
GAMLSS-RS iteration  5: Global Deviance = 5126.728 eps = 0.007086     
GAMLSS-RS iteration  6: Global Deviance = 5123.1813 eps = 0.000691     
GAMLSS-RS iteration  7: Global Deviance = 5121.8096 eps = 0.000267     
GAMLSS-RS iteration  8: Global Deviance = 5121.3064 eps = 0.000098     
GAMLSS-RS iteration  9: Global Deviance = 5121.12 eps = 0.000036     
GAMLSS-RS iteration 10: Global Deviance = 5121.0523 eps = 0.000013     
GAMLSS-RS iteration 11: Global Deviance = 5121.012 eps = 0.000007