toufit: Touchard Estimation

In touchard: Touchard Model and Regression

Description

Maximum-likelihood and method-of-moments estimation of the Touchard model.

Usage

toufit(x, freq = NULL, start, method = c("ml", "mm", "gmm"), 
    rc = FALSE, trunc.at.zero = FALSE)

Arguments

x	either an object of class table with the observed counts as classifying factors or the observed counts (raw data) or the unique values of the observed counts in which case the observed frequencies must be given in argument freq; see example below for the three formats.
freq	unnecessary (and ignored) if x is a table or the raw data; must be provided if x is the unique values of the observed counts, in the same order.
start	starting values to be used by optimization/nonlinear solving algorithms. If missing, the default value is explained in the reference below.
method	one of 'ml' (maximum likelihood), 'mm' (method of moments based on the usual first and second moment conditions) or 'gmm' (generalized method of moments based on the first two moments and an extra condition on the first moment of log(Y+1).
rc	TRUE for right-censored data. Not implemented for methods 'mm' and 'gmm'.
trunc.at.zero	TRUE for model truncated at zero. Not implemented for methods 'mm' and 'gmm'.

Details

For method 'ml' the Touchard likelihood is numerically maximized via optim() with 'method=L-BFGS-B'. For methods 'mm' and 'gmm', the system of moment conditions is solved by calling nleqslv and numDeriv.

Value

A list with the following:

fit	a list with point estimates, standard errors and variance matrix of estimates
aic	Akaike's information criterion, -2*log-likelihood + 2*p
bic	Schwarz's Bayesian criterion, -2*log-likelihood + log(n)*p
test	a data frame with likelihood ratio and Wald test results for the Null: delta = 0 (Poisson)
method	estimation method used ('ml', 'mm' or 'gmm')
data	a list with elements x and freq

Author(s)

Bernardo Andrade and Sandro Oliveira

References

Matsushita RY, Pianto D, Andrade BB, Cancado A, Silva S (2018) The Touchard distribution, Communications in Statistics - Theory and Methods, <doi:10.1080/03610926.2018.1444177>

Andrade, BB; Matsushita, RY; Oliveira, SB (submitted) Analyzing Count Data with the Touchard Model. available upon request.

See Also

optim , rgram , Touchard , touplot

Examples

data(Epilepsy)
# 'seizures' is vector of raw data (351 counts) 
toufit( x = seizures, method = 'ml' )
toufit( x = seizures, method = 'mm' )
toufit( x = seizures, method = 'gmm' )

# suppose data were recorded as table object
TAB <- table(seizures)
TAB
toufit(TAB)  # same as above (method = 'ml') 

# suppose data were recorded as data.frame 
DF <- data.frame( y = as.numeric(names(TAB)), fr = as.numeric(TAB) )
DF
toufit(x = DF$y, freq = DF$fr) # same as above (method = 'ml') 

touchard documentation built on May 31, 2019, 5:04 p.m.