Version: 0.3-3
Date: 2020-10-09
Title: Heteroscedastic t-Regression
Author: Julian Taylor <julian.taylor@adelaide.edu.au>
Maintainer: Julian Taylor <julian.taylor@adelaide.edu.au>
Depends: R (≥ 2.0.0), MASS, lattice
Description: Functions for the fitting and summarizing of heteroscedastic t-regression.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
NeedsCompilation: no
Packaged: 2020-10-09 02:40:18 UTC; a1066967
Repository: CRAN
Date/Publication: 2020-10-13 10:50:02 UTC

Internal profile likelihood function

Description

These are internal hett functions that are not intended to be directly called by the user

Usage

dof.profile(dof, n, sqResid, orthoI, X, Z)

Author(s)

Julian Taylor

Excess returns for Martin Marietta company

Description

Data from the Martin Marietta company collected overa period of 5 years on a monthly basis

Usage

data(mm)

Format

A data frame with 60 observations on the following 4 variables.

date

the month the data was collected

am.can

a numeric vector

m.marietta

excess returns from the Martin Marietta company

CRSP

an index for the excess rate returns for the New York stock exchange

Source

Bulter et al (1990). Robust and partly adpative estimation of regression models. Review of Economic Statistics, 72, 321-327.

Examples


data(mm, package = "hett")
attach(mm)
plot(CRSP, m.marietta)
lines(CRSP, fitted(lm(m.marietta ~ CRSP)), lty = 2)

Rent for Land PLanted to Alfalfa

Description

Dataset collected in 1977 from Minnesota to study the variation in land rented for growing alfalfa

Usage

data(rent)

Format

A data frame with 67 observations on the following 5 variables.

Rent

a numeric vector average rent per acre.

AllRent

a numeric vector describing average rent paid for all tillable land.

Cows

a numeric vector describing the density of dairy cows (number per square mile).

Pasture

a numeric vector describing the proportion of farmland used as pasture.

Liming

a factor with levels No if no liming is required to grow alfalfa and Yes if it does.

Source

Weisberg, S (1985). Applied Linear Regression Wiley: New York

Examples


library(lattice)
data(rent, package = "hett")
attach(rent)
xyplot(log(Rent/AllRent) ~ sqrt(Cows), groups = Liming, panel = panel.superpose)

summary method for class "tlm"

Description

Summarizes the heteroscedastic t regression object

Usage

## S3 method for class 'tlm'
summary(object, correlation = FALSE, ...)
## S3 method for class 'summary.tlm'
print(x, ...)

Arguments

object

heteroscedastic t regression object called from tlm()

x

an object of class "summary.tlm" containing the values below

correlation

should the calaculation of the parameter correlation matrix be supressed. If the fit includes a location and a scale formula then both correlation matrices are printed. The default is FALSE.

...

arguments passed to or from other methods

Details

The table summary produced by this function should be used with caution. A more appropriate test between nested models is to use the score statistic function tscore.

Value

a list containing the following components:

loc.summary

an object containing a list of objects that summarize the location model

scale.summary

an object containing a list of objects that summarize the scale model

iter

the number of iterations of the algorithm

dof

value of the fixed or estimated degrees of freedom

dofse

the standard error associated with the degrees of freedom if estimated

logLik

the maximised log-likelihood

method

the method used to maximize the likelihood

endTime

the time taken for the algorithm to converge

Author(s)

Julian Taylor

See Also

tsum, tlm

Examples


data(mm, package = "hett")
attach(mm)

## fit a model with heteroscedasticity and estimating the degrees of freedom

tfit2 <- tlm(m.marietta ~ CRSP, ~ CRSP, data = mm, start = list(dof =
3), estDof = TRUE)
summary(tfit2)

Maximum likelihood estimation for heteroscedastic t regression

Description

Fits a heteroscedastic t regression to given data for known and unknown degrees of freedom.

Usage

tlm(lform, sform =  ~ 1, data = NULL, subset = NULL, contrasts =
    NULL, na.action = na.fail, start = NULL, control = tlm.control(...),
    obs = FALSE, estDof = FALSE, ... )

## S3 method for class 'tlm'
print(x, ...)

Arguments

x

an object of class "tlm"

lform

a formula of the type response ~ terms, where terms can be of the form, for example, first + second or first*second(see lm for details)

sform

a formula of the type ~ terms, where terms can be of the form, for example, first + second or first*second(see lm for details).

data

the data in the form of a data.frame where the column names can be matched to the variable names supplied in lform and sform

subset

numerical vector to subset the data argument

contrasts

set of contrasts for the location model (see contrasts.arg for details)

na.action

the action to proceed with in the event of NA's in the response. Currently NA's are not allowed and therefore na.fail is the sole argument.

start

is a list of possibly four named components, ("beta", "lambda", "dof", "omega"), for the location, scale, degrees of freedom parameters and random scale effects respectively. Each component must be of the appropriate length.

control

is an argument to a function that maintains the control of the algorithm. The tlm.control()function contains the arguments, epsilon to determine how small the relative difference of likelihoods should be for convergence (default is 1e-07), maxit to determine the maximum iterations required (default = 50), trace if the user requires printing of estimates etc. as algorithm runs (default = FALSE), verboseLev to determine the amount of verbose printing to the screen as the algorithm runs (verboseLev = 1 displays location scale and dof estimates and the likelihood, verboseLev = 2 displays all of 1 plus the random scale effects)

obs

should the location parameters be calculated using the observed or expected information(default = FALSE). (Note: using the observed information does not calculate the appropriate standard errors, see DETAILS)

estDof

should the degrees of freedom parameter be estimated or not. If FALSE then the value given for dof in the start argument will be the fixed value used for the algorithm. If TRUE then the value given for dof in the start argument supplies an initial value only.

...

arguments passed to tlm.control() or to the print method

Details

When the degrees of freedom is unknown the code uses the non-linear optimiser nlm. If the response (and therefore the errors) is tending toward a Gaussian this optimisation will still converge but with with very high degrees of freedom.

To obtain the appropriate standard errors from summary the user must specify the argument obs = F to ensure that the location parameter is calculated using the expected information.

Value

a list containing the following components:

loc.fit

an object containing the estimated location parameters and other elements associated with the location parameter model

scale.fit

an object containing the estimated scale parameters and other elements associated with the scale parameter model

random

the random scale effects

dof

fixed or estimated degrees of freedom

dofse

the standard error associated with the degrees of freedom

iter

the number of iterations of the algorithm

logLik

the maximised log-likelihood

endTime

the time taken for the algorithm to converge

Background

The theoretical background for this function can be found in Taylor and Verbyla (2004).

Author(s)

Julian Taylor

References

Taylor, J. D. & Verbyla, A. P (2004). Joint modelling of the location and scale parameters of the t-distribution. Statistical Modelling 4, 91-112.

See Also

summary.tlm

Examples


data(mm, package = "hett")
attach(mm)

## fit a model with no heteroscedasticity and fixed degrees of freedom

tfit <- tlm(m.marietta ~ CRSP, data = mm, start = list(dof = 3))

## fit a model with heteroscedasticity and fixed degrees of freedom

tfit1 <- tlm(m.marietta ~ CRSP, ~ CRSP, data = mm, start = list(dof = 3))

## fit a model with heteroscedasticity and estimating the degrees of freedom

tfit2 <- tlm(m.marietta ~ CRSP, ~ CRSP, data = mm,
start = list(dof = 3), estDof = TRUE)

Auxiliary for Controlling tlm Fitting

Description

Auxiliary function for fitting tlm model. Generally only used when calling tlm

Usage

tlm.control(epsilon = 1e-07, maxit = 50, trace = FALSE, verboseLev = 1)

Arguments

epsilon

positive convergence tolerance value. The iterations converge when [newlik - oldlik] < epsilon/2

maxit

integer giving the maximum iterations allowable for the routine

trace

logical. If TRUE output is printed to the screen during each iteration

verboseLev

integer. If 1 then print according to trace. If 2 then print random scale effects also.

Value

A list with the argument as values

Author(s)

Julian Taylor

See Also

tlm

Examples


data(mm, package = "hett")
attach(mm)

## change the maximum amount of iterations for the algorithm

fit1 <- tlm(m.marietta ~ CRSP, ~ 1, data = mm, start = list(dof = 3),
estDof = TRUE, control = tlm.control(maxit = 100))

Score test for heteroscedastic t models

Description

Provides a score test for the location and scale parameters of the heteroscedastic t regression model.

Usage

tscore(..., data = NULL, scale = FALSE)

Arguments

...

Any number of arguments containing nested model fits from tlm() (see Details)

data

the data used to fit the models involved

scale

logical. If TRUE the scale model is tested

Details

The user must supply nested models that test, either, the scale or the location component of the model. The model objects must be nested from left to right. Currently there are no traps if the arguments are not given in this order.

The models must also have either, all fixed degrees of freedom or estimated degrees of freedom.

Value

Output containing the hypothesis, the score statistic, degrees of freedom for the test and the p-value are printed to the screen.

Author(s)

Julian Taylor

References

Taylor, J. D. & Verbyla, A. P (2004). Joint modelling of the location and scale parameters of the t-distribution. Statistical Modelling 4, 91-112.

See Also

tlm

Examples


data(mm, package = "hett")
attach(mm)
tfit1 <- tlm(m.marietta ~ CRSP, ~ 1, data = mm, start = list(dof = 3),
estDof = TRUE)

tfit2 <- tlm(m.marietta ~ CRSP, ~ CRSP, data = mm, start = list(dof =
3), estDof = TRUE)

tscore(tfit1, tfit2, data = mm, scale = TRUE)

Summary function for the scale or location component of a heteroscedastic t model

Description

Summarizes the location or scale components of a heteroscedastic t model

Usage


tsum(object, dispersion = NULL, correlation = FALSE,
             symbolic.cor = FALSE, ...)

## S3 method for class 'tsum'
print(x, digits = max(3, getOption("digits") - 3), symbolic.cor =
      x$symbolic.cor, signif.stars = getOption("show.signif.stars"),
      scale = TRUE, ...)

Arguments

object

either the location or scale object created by fitting a heteroscedastic t object with tlm

x

an object of class "tsum"

dispersion

1 if summarizing the location model; 2 if summarizing the scale model (see Details)

correlation

logical; if TRUE, the correlation matrix of the estimated parameters is returned and printed.

digits

the number of significant digits to be printed.

symbolic.cor

logical. If TRUE, print the correlations in a symbolic form (see ‘symnum’) rather than as numbers.

signif.stars

logical. if TRUE, "significance stars" are printed for each coefficient.

scale

logical. If TRUE then the dispersion is known in advance (2), and is printed accordingly.

...

further arguments passed to or from other methods.

Details

The argument supplied to dispersion must be either 1 (location model) or 2 (scale model). The reason for this is because the fitting of the model has already scaled the covariance matrix for the location coefficients. Hence the scaled and unscaled versions of covariance matrix for the location model are identical.

This function will not be generally called by the user as it will only summarize the location or scale model but not both. Instead the user should refer to summary.tlm to print a summary of both models.

Value

tsum returns an object of class "tsum", a list with components

call

the component from object

df.residual

the component from object

coefficients

the matrix of coefficients, standard errors, z-values and p-values

dispersion

the supplied dispersion argument

df

a 2-vector of the rank of the model and the number of residual degrees of freedom

cov.unscaled

the unscaled (dispersion = 1) estimated covariance matrix of the estimated coefficients

cov.scaled

ditto, scaled by dispersion

correlation

(only if correlation is true.) The estimated correlations of the estimated coefficients

symbolic.cor

(only if correlation is true.) The value of the argument symbolic.cor

Author(s)

Julian Taylor

See Also

summary.tlm, tlm

Examples


data(mm, package = "hett")
attach(mm)
tfit <- tlm(m.marietta ~ CRSP, ~ CRSP, data = mm, start = list(dof = 3),
estDof = TRUE) 
tsum(tfit$loc.fit, dispersion = 1)

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