Variance Functions

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Description

Compute the variance function and its derivatives with respect to regression, dispersion and power parameters.

Usage

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mc_variance_function(mu, power, Ntrial, variance, inverse,
                           derivative_power, derivative_mu)

mc_power(mu, power, inverse, derivative_power, derivative_mu)

mc_binomialP(mu, power, inverse, Ntrial,
                    derivative_power, derivative_mu)

mc_binomialPQ(mu, power, inverse, Ntrial,
                     derivative_power, derivative_mu)

Arguments

mu

a numeric vector. In general the output from mc_link_function.

power

a numeric value (power and binomialP) or a vector (binomialPQ) of the power parameters.

Ntrial

number of trials, useful only when dealing with binomial response variables.

variance

a string specifying the name (power, binomialP or binomialPQ) of the variance function.

inverse

logical. Compute the inverse or not.

derivative_power

logical if compute (TRUE) or not (FALSE) the derivatives with respect to the power parameter.

derivative_mu

logical if compute (TRUE) or not (FALSE) the derivative with respect to the mu parameter.

Details

The function mc_variance_function computes three features related with the variance function. Depending on the logical arguments, the function returns V^{1/2} and its derivatives with respect to the parameters power and mu, respectivelly. The output is a named list, completely informative about what the function has been computed. For example, if inverse = FALSE, derivative_power = TRUE and derivative_mu = TRUE. The output will be a list, with three elements: V_sqrt, D_V_sqrt_power and D_V_sqrt_mu.

Value

A list with from one to four elements depends on the arguments.

Author(s)

Wagner Hugo Bonat, wbonat@ufpr.br

Source

Bonat, W. H. and Jorgensen, B. (2016) Multivariate covariance generalized linear models. Journal of Royal Statistical Society - Series C X(X):XX–XX.

See Also

mc_link_function.

Examples

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x1 <- seq(-1, 1, l = 5)
X <- model.matrix(~x1)
mu <- mc_link_function(beta = c(1, 0.5), X = X, offset = NULL,
                       link = "logit")
mc_variance_function(mu = mu$mu, power = c(2, 1), Ntrial = 1,
                     variance = "binomialPQ", inverse = FALSE,
                     derivative_power = TRUE, derivative_mu = TRUE)

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