Package 'BSW'

Fitting a log-binomial model using the Bekhit-Schöpe-Wagenpfeil (BSW) algorithm

Description

bsw() fits a log-binomial model using a modified Newton-type algorithm (BSW algorithm) for solving the maximum likelihood estimation problem under linear inequality constraints.

Usage

bsw(formula, data, maxit = 200L)

Arguments

formula	An object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
data	A data frame containing the variables in the model.
maxit	A positive integer giving the maximum number of iterations.

Value

An object of S4 class "bsw" containing the following slots:

call	An object of class "call".
formula	An object of class "formula".
coefficients	A numeric vector containing the estimated model parameters.
iter	A positive integer indicating the number of iterations.
converged	A logical constant that indicates whether the model has converged.
y	A numerical vector containing the dependent variable of the model.
x	The model matrix.
data	A data frame containing the variables in the model.

Author(s)

Adam Bekhit, Jakob Schöpe

References

Wagenpfeil S (1996) Dynamische Modelle zur Ereignisanalyse. Herbert Utz Verlag Wissenschaft, Munich, Germany

Wagenpfeil S (1991) Implementierung eines SQP-Verfahrens mit dem Algorithmus von Ritter und Best. Diplomarbeit, TUM, Munich, Germany

Examples

set.seed(123)
x <- rnorm(100, 50, 10)
y <- rbinom(100, 1, exp(-4 + x * 0.04)) 
fit <- bsw(formula = y ~ x, data = data.frame(y = y, x = x))
summary(fit)

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S4 Class "bsw"

Description

S4 Class "bsw"

Slots

call

An object of class "call".

formula

An object of class "formula".

coefficients

A numeric vector containing the estimated model parameters.

iter

A positive integer indicating the number of iterations.

converged

A logical constant that indicates whether the model has converged.

y

A numeric vector containing the dependent variable of the model.

x

The model matrix.

data

A data frame containing the variables in the model.

Author(s)

Adam Bekhit, Jakob Schöpe

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Extracting the estimated model parameters of bsw()

Description

For objects of class "bsw", coef() extracts the estimated model parameters of bsw().

Usage

## S4 method for signature 'bsw'
coef(object)

Arguments

object

An object of class "bsw".

Value

A numeric vector containing the estimated model parameters.

Author(s)

Adam Bekhit, Jakob Schöpe

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Estimating confidence intervals of the estimated model parameters of bsw()

Description

For objects of class "bsw", confint() estimates confidence intervals of the estimated model parameters of bsw().

Usage

## S4 method for signature 'bsw'
confint(object, parm, level = 0.95, method = "wald", R = 1000L)

Arguments

object	An object of class "bsw".
parm	A specification of which model parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all model parameters are considered.
level	A numeric value that indicates the level of confidence.
method	A character giving the estimation method of the confidence intervals ("bca" or "wald").
R	A positive integer giving the number of bootstrap replicates.

Details

confint provides Wald (default) and bias-corrected accelerated bootstrap confidence intervals of the estimated model parameters of bsw().

Value

A matrix with columns giving the lower and upper confidence limits of each estimated model parameter.

Author(s)

Adam Bekhit, Jakob Schöpe

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Setting the linear inequality constraints for bsw()

Description

constr() sets the linear inequality constraints for bsw().

Usage

constr(x)

Arguments

x	A model matrix.

Value

A matrix containing the linear inequality constraints for bsw().

Author(s)

Adam Bekhit, Jakob Schöpe

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Deriving the first derivatives of the log likelihood function of the log-binomial model in bsw()

Description

gradF() derives the first derivatives of the log likelihood function of the log-binomial model.

Usage

gradF(theta, y, x)

Arguments

theta	A numeric vector containing the initial values of the model parameters.
y	A numeric vector containing the dependent variable of the model.
x	The model matrix.

Value

A numeric vector containing the first derivatives of the log likelihood function of the log-binomial model.

Author(s)

Adam Bekhit, Jakob Schöpe

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Deriving the second partial derivatives of the log likelihood function of the log-binomial model in bsw() (Hessian matrix)

Description

hess() derives the second partial derivatives of the log likelihood function of the log-binomial model.

Usage

hess(theta, y, x)

Arguments

theta	A numeric vector containing the initial values of the model parameters.
y	A numeric vector containing the dependent variable of the model.
x	The model matrix.

Value

A numeric matrix containing the second partial derivatives of the log likelihood function of the log-binomial model (Hessian matrix).

Author(s)

Adam Bekhit, Jakob Schöpe

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Summarizing the estimated model parameters of bsw()

Description

For objects of class "bsw", summary() summarizes the estimated model parameters of bsw().

Usage

## S4 method for signature 'bsw'
summary(object)

Arguments

object

An object of class "bsw".

Value

A list containing the following elements:

coefficients	A numeric vector containing the estimated model parameters.
std.err	A numeric vector containing the estimated standard errors of the model parameters.
z.value	A numeric vector containing the estimated z test statistic of the model parameters.
p.value	A numeric vector containing the estimated p values of the model parameters.

Author(s)

Adam Bekhit, Jakob Schöpe

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