R: Multinomial distribution in GAMLSS

MN3 {gamlss.dist} | R Documentation

## Multinomial distribution in GAMLSS

### Description

The set of function presented here is useful for fitting multinomial regression within gamlss.

### Usage

    MN3(mu.link = "log", sigma.link = "log")
    MN4(mu.link = "log", sigma.link = "log", nu.link = "log")
    MN5(mu.link = "log", sigma.link = "log", nu.link = "log", tau.link = "log")
    MULTIN(type = "3")
    fittedMN(model)

    dMN3(x, mu = 1, sigma = 1, log = FALSE)
    dMN4(x, mu = 1, sigma = 1, nu = 1, log = FALSE)
    dMN5(x, mu = 1, sigma = 1, nu = 1, tau = 1, log = FALSE)

    pMN3(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
    pMN4(q, mu = 1, sigma = 1, nu = 1, lower.tail = TRUE, log.p = FALSE)
    pMN5(q, mu = 1, sigma = 1, nu = 1, tau = 1, lower.tail = TRUE, log.p = FALSE)

    qMN3(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
    qMN4(p, mu = 1, sigma = 1, nu = 1, lower.tail = TRUE, log.p = FALSE)
    qMN5(p, mu = 1, sigma = 1, nu = 1, tau = 1, lower.tail = TRUE, log.p = FALSE)

    rMN3(n, mu = 1, sigma = 1)
    rMN4(n, mu = 1, sigma = 1, nu = 1)
    rMN5(n, mu = 1, sigma = 1, nu = 1, tau = 1)

### Arguments

`mu.link` | the link function for mu
`sigma.link` | the link function for sigma
`nu.link` | the link function for nu
`tau.link` | the link function for tau
`x` | the x variable
`q` | vector of quantiles
`p` | vector of probabilities
`lower.tail` | logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].
`log.p` | logical; if TRUE, probabilities p are given as log(p).
`log` | logical; if TRUE, probabilities p are given as log(p).
`n` | the number of observations
`mu` | the mu parameter
`sigma` | the sigma parameter
`nu` | the nu parameter
`tau` | the tau parameter
`type` | permitted values are 2 (Binomial), 3, 4, and 5
`model` | a gamlss multinomial fitted model

### Details

GAMLSS is in general not suitable for multinomial regression. Nevertheless multinomial regression can be fitted within GAMLSS if the response variable y has less than five categories. The function here provide the facilities to do so. The functions `MN3()`, `MN4()` and `MN5()` fit multinomial responses with 3, 4 and 5 categories respectively. The function `MULTIN()` can be used instead of codeMN3(), `MN4()` and `MN5()` by specifying the number of levels of the response. Note that `MULTIN(2)` will produce a binomial fit.

### Value

returns a `gamlss.family` object which can be used to fit a binomial distribution in the `gamlss()` function.

### Author(s)

Mikis Stasinopoulos, Bob Rigby and Vlasios Voudouris

### References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, https://www.jstatsoft.org/v23/i07.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

### See Also

`gamlss.family`, `BI`

### Examples

     dMN3(3)
     pMN3(2)
     qMN3(.6)
     rMN3(10)

[Package gamlss.dist version 5.3-2 Index]