VGAM (version 1.1-6)

# KLD: Kullback-Leibler Divergence

## Description

Calculates the Kullback-Leibler divergence for certain fitted model objects

## Usage

```KLD(object, …)
KLDvglm(object, …)```

## Arguments

object

Some VGAM object, for example, having class `vglm-class`. Currently `object` must be intercept-only.

Other possible arguments fed into `KLDvglm` in order to compute the KLD.

## Value

Returns a numeric nonnegative value with the corresponding KLD. A 0 value means no difference between an ordinary parent or base distribution.

## Warning

Numerical problems might occur if any of the evaluated probabilities of the unscaled parent distribution are very close to 0.

## Details

The Kullback-Leibler divergence (KLD), or relative entropy, is a measure of how one probability distribution differs from a second reference probability distribution. Currently the VGAM package computes the KLD for GAITD regression models (e.g., see `gaitdpoisson` and `gaitdnbinomial`) where the reference distribution is the (unscaled) parent or base distribution. For such, the formula for the KLD simplifies somewhat. Hence one can obtain a quantitative measure for the overall effect of altering, inflating, truncating and deflating certain (special) values.

## References

Kullback, S. and Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22, 79--86.

M'Kendrick, A. G. (1925). Applications of mathematics to medical problems. Proc. Edinb. Math. Soc., 44, 98--130.

`gaitdpoisson`, `gaitdnbinomial`.

## Examples

Run this code
``````# NOT RUN {
#  McKendrick (1925): Data from 223 Indian village households
cholera <- data.frame(ncases = 0:4,  # Number of cholera cases,
wfreq  = c(168, 32, 16, 6, 1))  # Frequencies
fit7 <- vglm(ncases ~ 1, gaitdpoisson(i.mlm = 0, ilambda.p = 1),
weight = wfreq, data = cholera, trace = TRUE)
coef(fit7, matrix = TRUE)
KLD(fit7)
# }
``````

Run the code above in your browser using DataLab