QGglmm (version 0.8.0)

QGlink.funcs: List of functions according to a distribution and a link function

Description

Function yielding different functions (inverse-link, variance function, derivative of the inverse-link) according to a distribution and link function.

Usage

QGlink.funcs(name, n.obs = NULL, theta = NULL)

Value

This function yields a list of function:

inv.link

Inverse function of the link function. (function)

var.func

Distribution variance function. (function)

inv.link

Derivative of the inverse-link function. (function)

Arguments

name

Name of the distribution.link couple. (character) Available models are :

• "Gaussian" Gaussian distribution with identity link (e.g. LMM)

• "binom1.probit" Binomial with 1 trial (binary data) with a probit link

• "binomN.probit" Binomial with N tria with a probit link (require the parameter n.obs)

• "binom1.logit" Binomial with 1 trial (binary) with a logit link

• "binomN.logit" Binomial with N trial with a logit link (require the parameter n.obs)

• "Poisson.log" Poisson distribution with a log link

• "Poisson.sqrt" Poisson distribution with a square-root link

• "negbin.log" Negative - Binomial distribution wiht a log link (require the parameter theta)

• "negbin.sqrt" Negative - Binomial distribution with a square-root link (require the parameter theta)

• "ZIPoisson.log.logit" Zero-inflated Poisson distribution with a log link for the Poisson part and logit link for the ZI part (compound distribution)

• "HuPoisson.log.logit" Hurdle Poisson distribution with a log link for the Poisson part and logit link for the hurdle part (compound distribution)

• "ordinal" Multiple threshold model for ordinal categorical traits (require the parameter cut.points)

n.obs

Optional parameter required for "binomN" distributions (number of "trials"). See QGparams. (numeric)

theta

Optional parameter required for "negbin" distributions (dispersion parameter). See QGparams. (numeric)

Author

Pierre de Villemereuil & Michael B. Morrissey

Details

This function takes the name of a distribution.link couple and yields several important functions such as the inverse-link function and its derivative, as well as the "distribution variance function".

The inverse-link function is the inverse function of the link function. For example, if the link function is the natural logarithm (typically for a Poisson distribution), then the inverse-link function is the exponential.

The distribution variance function is a function yielding the variance of the distribution for a given latent trait. For a Poisson distribution, the variance is equal to the mean, hence the variance function is equal to the inverse-link function. For a binomial distribution, the variance is N * p(l) * (1 - p(l)), where p is the inverse-link function.

For some distributions, such as "binomN" and "negbin", some extra-parameters are required. The "compound" distributions (for now, zero-inflated and hurdle Poisson) functions take a 2-rows input instead of a vector (because they have two latent traits).

See Also

QGparams, QGmvparams

Examples

## Getting the functions for a Poisson.log model
QGlink.funcs("Poisson.log")
# Note that because the variance is equal to the mean in a Poisson distribution
# and the derivative of exp is exp
# all functions are the same!

## Getting the functions for a binom1.probit model
QGlink.funcs("binom1.probit")

## The function QGparams automatically computes these functions
QGparams(mu = 0, var.p = 2, var.a = 1, model = "binom1.logit")
# Hence this is the same as using the custom.model argument with QGlink.funcs
QGparams(mu = 0, var.p = 2, var.a = 1, custom.model = QGlink.funcs("binom1.logit"))

## We can create our own custom set of functions
# Let's create a custom model exactly identical to QGlink.funcs("binom1.logit")
custom <- list(inv.link = function(x){plogis(x)},
               var.func = function(x){plogis(x) * (1 - plogis(x))},
               d.inv.link = function(x){dlogis(x)})
    
QGparams(mu = 0, var.p = 2, var.a = 1, custom.model = custom)