Title:	Bootstrap-Based Goodness-of-Fit Tests for Parametric Regression
Version:	1.0.0
Description:	Provides statistical methods to check if a parametric family of conditional density functions fits to some given dataset of covariates and response variables. Different test statistics can be used to determine the goodness-of-fit of the assumed model, see Andrews (1997) <doi:10.2307/2171880>, Bierens & Wang (2012) <doi:10.1017/S0266466611000168>, Dikta & Scheer (2021) <doi:10.1007/978-3-030-73480-0> and Kremling & Dikta (2024) <doi:10.48550/arXiv.2409.20262>. As proposed in these papers, the corresponding p-values are approximated using a parametric bootstrap method.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.1
Suggests:	knitr, rmarkdown, testthat (≥ 3.0.0)
Config/testthat/edition:	3
Imports:	checkmate, dplyr, ggplot2, R6, survival
URL:	https://github.com/gkremling/gofreg, https://gkremling.github.io/gofreg/
BugReports:	https://github.com/gkremling/gofreg/issues
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2024-10-04 09:05:04 UTC; gitte
Author:	Gitte Kremling [aut, cre, cph]
Maintainer:	Gitte Kremling <gitte.kremling@web.de>
Repository:	CRAN
Date/Publication:	2024-10-04 10:20:17 UTC

Conditional Kolmogorov test statistic for the joint distribution of (X,Y)

Description

This class inherits from TestStatistic and implements a function to calculate the test statistic (and x-y-values that can be used to plot the underlying process).

The process underlying the test statistic is given in Andrews (1997) doi: 10.2307/2171880 and defined by

\nu_n(x,y) = \frac{1}{\sqrt{n}} \sum_{i=1}^n \left(I_{\{Y_i \le y\}} - F(y|\hat{\vartheta}_n, X_i) \right) I_{\{X_i \le x\}},\quad (x,y) \in R^{p+1}.

Super class

gofreg::TestStatistic -> CondKolmXY

Methods

Public methods

• CondKolmXY$calc_stat()

• CondKolmXY$clone()

Method calc_stat()

Calculate the value of the test statistic for given data and a model to test for.

Usage

CondKolmXY$calc_stat(data, model)

Arguments

Returns

The modified object (self), allowing for method chaining.

Method clone()

The objects of this class are cloneable with this method.

Usage

CondKolmXY$clone(deep = FALSE)

Arguments

Examples

# Create an example dataset
n <- 100
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
y <- model$sample_yx(x, params=list(beta=c(2,3), sd=1))
data <- dplyr::tibble(x = x, y = y)

# Fit the correct model
model$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts <- CondKolmXY$new()
ts$calc_stat(data, model)
print(ts)
plot(ts)

# Fit a wrong model
model2 <- NormalGLM$new(linkinv = function(u) {u+10})
model2$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts2 <- CondKolmXY$new()
ts2$calc_stat(data, model2)
print(ts2)
plot(ts2)

Conditional Kolmogorov test statistic for the marginal distribution of Y

Description

This class inherits from TestStatistic and implements a function to calculate the test statistic (and x-y-values that can be used to plot the underlying process).

The process underlying the test statistic is given in Kremling & Dikta (2024) https://arxiv.org/abs/2409.20262 and defined by

\tilde{\alpha}_n(t) = \frac{1}{\sqrt{n}} \sum_{i=1}^n \left( I_{\{Y_i \le t\}} - F(t|\hat{\vartheta}_n, X_i) \right), \quad -\infty \le t \le \infty.

Super class

gofreg::TestStatistic -> CondKolmY

Methods

Public methods

• CondKolmY$calc_stat()

• CondKolmY$clone()

Method calc_stat()

Calculate the value of the test statistic for given data and a model to test for.

Usage

CondKolmY$calc_stat(data, model)

Arguments

Returns

The modified object (self), allowing for method chaining.

Method clone()

The objects of this class are cloneable with this method.

Usage

CondKolmY$clone(deep = FALSE)

Arguments

Examples

# Create an example dataset
n <- 100
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
y <- model$sample_yx(x, params=list(beta=c(2,3), sd=1))
data <- dplyr::tibble(x = x, y = y)

# Fit the correct model
model$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts <- CondKolmY$new()
ts$calc_stat(data, model)
print(ts)
plot(ts)

# Fit a wrong model
model2 <- NormalGLM$new(linkinv = function(u) {u+10})
model2$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts2 <- CondKolmY$new()
ts2$calc_stat(data, model2)
print(ts2)
plot(ts2)

Conditional Kolmogorov test statistic for the marginal distribution of Y under random censorship

Description

This class inherits from TestStatistic and implements a function to calculate the test statistic (and x-y-values that can be used to plot the underlying process).

The process underlying the test statistic is defined by

\tilde{\alpha}_n^{KM}(t) = \sqrt{n} \left( \hat{F}^{KM}_n(t) - \frac{1}{n} \sum_{i=1}^n F(t|\hat{\vartheta}_n, X_i) \right), \quad -\infty \le t \le \infty.

Super class

gofreg::TestStatistic -> CondKolmY_RCM

Methods

Public methods

• CondKolmY_RCM$calc_stat()

• CondKolmY_RCM$clone()

Method calc_stat()

Calculate the value of the test statistic for given data and a model to test for.

Usage

CondKolmY_RCM$calc_stat(data, model)

Arguments

Returns

The modified object (self), allowing for method chaining.

Method clone()

The objects of this class are cloneable with this method.

Usage

CondKolmY_RCM$clone(deep = FALSE)

Arguments

Examples

# Create an example dataset
n <- 100
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
y <- model$sample_yx(x, params=list(beta=c(2,3), sd=1))
c <- rnorm(n, mean(y)*1.2, sd(y)*0.5)
data <- dplyr::tibble(x = x, z = pmin(y,c), delta = as.numeric(y <= c))

# Fit the correct model
model$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE, loglik = loglik_xzd)

# Print value of test statistic and plot corresponding process
ts <- CondKolmY_RCM$new()
ts$calc_stat(data, model)
print(ts)
plot(ts)

# Fit a wrong model
model2 <- NormalGLM$new(linkinv = function(u) {u+10})
model2$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE, loglik = loglik_xzd)

# Print value of test statistic and plot corresponding process
ts2 <- CondKolmY_RCM$new()
ts2$calc_stat(data, model2)
print(ts2)
plot(ts2)

Conditional Kolmogorov test statistic for the joint distribution of (beta^T X,Y)

Description

This class inherits from TestStatistic and implements a function to calculate the test statistic (and x-y-values that can be used to plot the underlying process).

The process underlying the test statistic is defined by

\bar{\alpha}_n(s,t) = \frac{1}{\sqrt{n}} \sum_{i=1}^n \left( I_{\{Y_i \le t\}} - F(t|\hat{\vartheta}_n, X_i) \right) I_{\{\hat{\beta}_n^T X_i \le s\}}, \quad (s,t) \in R^{2}.

Super class

gofreg::TestStatistic -> CondKolmbXY

Methods

Public methods

• CondKolmbXY$calc_stat()

• CondKolmbXY$clone()

Method calc_stat()

Calculate the value of the test statistic for given data and a model to test for.

Usage

CondKolmbXY$calc_stat(data, model)

Arguments

Returns

The modified object (self), allowing for method chaining.

Method clone()

The objects of this class are cloneable with this method.

Usage

CondKolmbXY$clone(deep = FALSE)

Arguments

Examples

# Create an example dataset
n <- 100
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
y <- model$sample_yx(x, params=list(beta=c(2,3), sd=1))
data <- dplyr::tibble(x = x, y = y)

# Fit the correct model
model$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts <- CondKolmbXY$new()
ts$calc_stat(data, model)
print(ts)
plot(ts)

# Fit a wrong model
model2 <- NormalGLM$new(linkinv = function(u) {u+10})
model2$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts2 <- CondKolmbXY$new()
ts2$calc_stat(data, model2)
print(ts2)
plot(ts2)

Generalized linear model with exponential distribution

Description

This class represents a generalized linear model with exponential distribution. It inherits from GLM and implements its functions that, for example, evaluate the conditional density and distribution functions.

Super classes

gofreg::ParamRegrModel -> gofreg::GLM -> ExpGLM

Methods

Public methods

• ExpGLM$fit()

• ExpGLM$f_yx()

• ExpGLM$F_yx()

• ExpGLM$F1_yx()

• ExpGLM$sample_yx()

• ExpGLM$clone()

Method fit()

Calculates the maximum likelihood estimator for the model parameters based on given data.

Usage

ExpGLM$fit(
  data,
  params_init = private$params,
  loglik = loglik_xy,
  inplace = FALSE
)

Arguments

Returns

MLE of the model parameters for the given data, same shape as params_init

Method f_yx()

Evaluates the conditional density function.

Usage

ExpGLM$f_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional density function, same shape as t

Method F_yx()

Evaluates the conditional distribution function.

Usage

ExpGLM$F_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional distribution function, same shape as t

Method F1_yx()

Evaluates the conditional quantile function.

Usage

ExpGLM$F1_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional quantile function, same shape as t

Method sample_yx()

Generates a new sample of response variables with the same conditional distribution.

Usage

ExpGLM$sample_yx(x, params = private$params)

Arguments

Returns

vector of sampled response variables, same length as nrow(x)

Method clone()

The objects of this class are cloneable with this method.

Usage

ExpGLM$clone(deep = FALSE)

Arguments

Examples

# Use the built-in cars dataset
x <- datasets::cars$speed
y <- datasets::cars$dist
data <- dplyr::tibble(x=x, y=y)

# Create an instance of ExpGLM
model <- ExpGLM$new()

# Fit an Exponential GLM to the cars dataset
model$fit(data, params_init = list(beta=3), inplace=TRUE)
params_opt <- model$get_params()

# Plot the resulting regression function
plot(datasets::cars)
abline(a = 0, b = params_opt$beta)

# Generate a sample for y for given x following the same distribution
x.new <- seq(min(x), max(x), by=2)
y.smpl <- model$sample_yx(x.new)
points(x.new, y.smpl, col="red")

# Evaluate the conditional density, distribution, quantile and regression
# function at given values
model$f_yx(y.smpl, x.new)
model$F_yx(y.smpl, x.new)
model$F1_yx(y.smpl, x.new)
y.pred <- model$mean_yx(x.new)
points(x.new, y.pred, col="blue")

Generalized linear model (abstract class)

Description

This class specializes ParamRegrModel. It is the abstract base class for parametric generalized linear model objects with specific distribution family such as NormalGLM and handles the (inverse) link function.

Super class

gofreg::ParamRegrModel -> GLM

Methods

Public methods

• GLM$new()

• GLM$mean_yx()

• GLM$clone()

Method new()

Initialize an object of class GLM.

Usage

GLM$new(linkinv = identity, params = NA)

Arguments

Returns

a new instance of the class

Method mean_yx()

Evaluates the regression function or in other terms the expected value of Y given X=x.

Usage

GLM$mean_yx(x, params = private$params)

Arguments

Returns

value of the regression function

Method clone()

The objects of this class are cloneable with this method.

Usage

GLM$clone(deep = FALSE)

Arguments

Create GLM object with specific distribution family

Description

This constructor function can be used to create an instance of a parametric GLM with specific distribution family, returning a new object of NormalGLM, ExpGLM, WeibullGLM or GammaGLM, depending on the value of distr.

Usage

GLM.new(distr, linkinv = identity, params = NA)

Arguments

Value

a new instance of a GLM-subclass

Examples

model <- GLM.new(distr = "normal")
# see examples of GLM-subclasses (e.g. NormalGLM) for how to use such models

Goodness-of-fit test for parametric regression

Description

This class implements functions to calculate the test statistic for the original data as well as the statistics for bootstrap samples. It also offers the possibility to compute the corresponding bootstrap p-value.

Methods

Public methods

• GOFTest$new()

• GOFTest$get_stat_orig()

• GOFTest$get_stats_boot()

• GOFTest$get_pvalue()

• GOFTest$plot_procs()

• GOFTest$clone()

Method new()

Initialize an instance of class GOFTest.

Usage

GOFTest$new(
  data,
  model_fitted,
  test_stat,
  nboot,
  resample = resample_param,
  loglik = loglik_xy
)

Arguments

Returns

a new instance of the class

Method get_stat_orig()

Calculates the test statistic for the original data and model.

Usage

GOFTest$get_stat_orig()

Returns

object of class TestStatistic

Method get_stats_boot()

Calculates the test statistics for the resampled data and corresponding models.

Usage

GOFTest$get_stats_boot()

Returns

vector of length nboot containing objects of class TestStatistic

Method get_pvalue()

Calculates the bootstrap p-value for the given model.

Usage

GOFTest$get_pvalue()

Returns

p-value for the null hypothesis that y was generated according to model

Method plot_procs()

Plots the processes underlying the bootstrap test statistics (gray) and the original test statistic (red)

Usage

GOFTest$plot_procs(
  title = sprintf("Test Statistic: %s, p-value: %s", class(private$test_stat)[1],
    self$get_pvalue()),
  subtitle = ggplot2::waiver(),
  color_boot = "gray40",
  color_orig = "red",
  x_lab = "plot.x",
  y_lab = "plot.y"
)

Arguments

Returns

The object (self), allowing for method chaining.

Method clone()

The objects of this class are cloneable with this method.

Usage

GOFTest$clone(deep = FALSE)

Arguments

Examples

# Create an example dataset
n <- 100
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
y <- model$sample_yx(x, params=list(beta=c(2,3), sd=1))
data <- dplyr::tibble(x = x, y = y)

# Fit the correct model
model$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Calculate the bootstrap p-value and plot the corresponding processes
goftest <- GOFTest$new(data, model, test_stat = CondKolmY$new(), nboot = 10)
goftest$get_pvalue()
goftest$plot_procs()

# Fit a wrong model
model2 <- NormalGLM$new(linkinv = function(u) {u+10})
model2$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Calculate the bootstrap p-value and plot the corresponding processes
goftest2 <- GOFTest$new(data, model2, test_stat = CondKolmY$new(), nboot = 10)
goftest2$get_pvalue()
goftest2$plot_procs()

Generalized linear model with gamma distribution

Description

This class represents a generalized linear model with Gamma distribution. It inherits from GLM and implements its functions that, for example, evaluate the conditional density and distribution functions.

Super classes

gofreg::ParamRegrModel -> gofreg::GLM -> GammaGLM

Methods

Public methods

• GammaGLM$fit()

• GammaGLM$f_yx()

• GammaGLM$F_yx()

• GammaGLM$F1_yx()

• GammaGLM$sample_yx()

• GammaGLM$clone()

Method fit()

Calculates the maximum likelihood estimator for the model parameters based on given data.

Usage

GammaGLM$fit(
  data,
  params_init = private$params,
  loglik = loglik_xy,
  inplace = FALSE
)

Arguments

Returns

MLE of the model parameters for the given data, same shape as params_init

Method f_yx()

Evaluates the conditional density function.

Usage

GammaGLM$f_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional density function, same shape as t

Method F_yx()

Evaluates the conditional distribution function.

Usage

GammaGLM$F_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional distribution function, same shape as t

Method F1_yx()

Evaluates the conditional quantile function.

Usage

GammaGLM$F1_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional quantile function, same shape as t

Method sample_yx()

Generates a new sample of response variables with the same conditional distribution.

Usage

GammaGLM$sample_yx(x, params = private$params)

Arguments

Returns

vector of sampled response variables, same length as nrow(x)

Method clone()

The objects of this class are cloneable with this method.

Usage

GammaGLM$clone(deep = FALSE)

Arguments

Examples

# Use the built-in cars dataset
x <- datasets::cars$speed
y <- datasets::cars$dist
data <- dplyr::tibble(x=x, y=y)

# Create an instance of GammaGLM
model <- GammaGLM$new()

# Fit an Gamma GLM to the cars dataset
model$fit(data, params_init = list(beta=3, shape=1), inplace=TRUE)
params_opt <- model$get_params()

# Plot the resulting regression function
plot(datasets::cars)
abline(a = 0, b = params_opt$beta)

# Generate a sample for y for given x following the same distribution
x.new <- seq(min(x), max(x), by=2)
y.smpl <- model$sample_yx(x.new)
points(x.new, y.smpl, col="red")

# Evaluate the conditional density, distribution, quantile and regression
# function at given values
model$f_yx(y.smpl, x.new)
model$F_yx(y.smpl, x.new)
model$F1_yx(y.smpl, x.new)
y.pred <- model$mean_yx(x.new)
points(x.new, y.pred, col="blue")

Marked empirical process test statistic for a given GLM

Description

This class inherits from TestStatistic and implements a function to calculate the test statistic (and x-y-values that can be used to plot the underlying process).

The process underlying the test statistic is given in Dikta & Scheer (2021) doi: 10.1007/978-3-030-73480-0 and defined by

\bar{R}^1_n(u) = \frac{1}{\sqrt{n}} \sum_{i=1}^n \left( Y_i - m(X_i, \hat{\beta}_n) \right) I_{\{\hat{\beta}_n X_i \le u\}}, \quad -\infty \le u \le \infty.

Super class

gofreg::TestStatistic -> MEP

Methods

Public methods

• MEP$calc_stat()

• MEP$clone()

Method calc_stat()

Calculate the value of the test statistic for given data and a model to test for.

Usage

MEP$calc_stat(data, model)

Arguments

Returns

The modified object (self), allowing for method chaining.

Method clone()

The objects of this class are cloneable with this method.

Usage

MEP$clone(deep = FALSE)

Arguments

Examples

# Create an example dataset
n <- 100
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
y <- model$sample_yx(x, params=list(beta=c(2,3), sd=1))
data <- dplyr::tibble(x = x, y = y)

# Fit the correct model
model$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts <- MEP$new()
ts$calc_stat(data, model)
print(ts)
plot(ts)

# Fit a wrong model
model2 <- NormalGLM$new(linkinv = function(u) {u+10})
model2$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts2 <- MEP$new()
ts2$calc_stat(data, model2)
print(ts2)
plot(ts2)

Generalized linear model with negative binomial distribution

Description

This class represents a generalized linear model with negative binomial distribution. It inherits from GLM and implements its functions that, for example, evaluate the conditional density and distribution functions.

Super classes

gofreg::ParamRegrModel -> gofreg::GLM -> NegBinomGLM

Methods

Public methods

• NegBinomGLM$fit()

• NegBinomGLM$f_yx()

• NegBinomGLM$F_yx()

• NegBinomGLM$F1_yx()

• NegBinomGLM$sample_yx()

• NegBinomGLM$clone()

Method fit()

Calculates the maximum likelihood estimator for the model parameters based on given data.

Usage

NegBinomGLM$fit(
  data,
  params_init = private$params,
  loglik = loglik_xy,
  inplace = FALSE
)

Arguments

Returns

MLE of the model parameters for the given data, same shape as params_init

Method f_yx()

Evaluates the conditional density function.

Usage

NegBinomGLM$f_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional density function, same shape as t

Method F_yx()

Evaluates the conditional distribution function.

Usage

NegBinomGLM$F_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional distribution function, same shape as t

Method F1_yx()

Evaluates the conditional quantile function.

Usage

NegBinomGLM$F1_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional quantile function, same shape as t

Method sample_yx()

Generates a new sample of response variables with the same conditional distribution.

Usage

NegBinomGLM$sample_yx(x, params = private$params)

Arguments

Returns

vector of sampled response variables, same length as nrow(x)

Method clone()

The objects of this class are cloneable with this method.

Usage

NegBinomGLM$clone(deep = FALSE)

Arguments

Examples

# Use the built-in cars dataset
x <- datasets::cars$speed
y <- datasets::cars$dist
data <- dplyr::tibble(x=x, y=y)

# Create an instance of a NegBinomGLM
model <- NegBinomGLM$new()

# Fit a Negative Binomial GLM to the cars dataset
model$fit(data, params_init = list(beta=3, shape=2), inplace=TRUE)
params_opt <- model$get_params()

# Plot the resulting regression function
plot(datasets::cars)
abline(a = 0, b = params_opt$beta)

# Generate a sample for y for given x following the same distribution
x.new <- seq(min(x), max(x), by=2)
y.smpl <- model$sample_yx(x.new)
points(x.new, y.smpl, col="red")

# Evaluate the conditional density, distribution, quantile and regression
# function at given values
model$f_yx(y.smpl, x.new)
model$F_yx(y.smpl, x.new)
model$F1_yx(y.smpl, x.new)
y.pred <- model$mean_yx(x.new)
points(x.new, y.pred, col="blue")

Generalized linear model with normal distribution

Description

This class represents a generalized linear model with normal distribution. It inherits from GLM and implements its functions that, for example, evaluate the conditional density and distribution functions.

Super classes

gofreg::ParamRegrModel -> gofreg::GLM -> NormalGLM

Methods

Public methods

• NormalGLM$fit()

• NormalGLM$f_yx()

• NormalGLM$F_yx()

• NormalGLM$F1_yx()

• NormalGLM$sample_yx()

• NormalGLM$clone()

Method fit()

Calculates the maximum likelihood estimator for the model parameters based on given data.

Usage

NormalGLM$fit(
  data,
  params_init = private$params,
  loglik = loglik_xy,
  inplace = FALSE
)

Arguments

Returns

MLE of the model parameters for the given data, same shape as params_init

Method f_yx()

Evaluates the conditional density function.

Usage

NormalGLM$f_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional density function, same shape as t

Method F_yx()

Evaluates the conditional distribution function.

Usage

NormalGLM$F_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional distribution function, same shape as t

Method F1_yx()

Evaluates the conditional quantile function.

Usage

NormalGLM$F1_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional quantile function, same shape as t

Method sample_yx()

Generates a new sample of response variables with the same conditional distribution.

Usage

NormalGLM$sample_yx(x, params = private$params)

Arguments

Returns

vector of sampled response variables, same length as nrow(x)

Method clone()

The objects of this class are cloneable with this method.

Usage

NormalGLM$clone(deep = FALSE)

Arguments

Examples

# Use the built-in cars dataset
x <- datasets::cars$speed
y <- datasets::cars$dist
data <- dplyr::tibble(x=x, y=y)

# Create an instance of a NormalGLM
model <- NormalGLM$new()

# Fit a Normal GLM to the cars dataset
model$fit(data, params_init = list(beta=3, sd=2), inplace=TRUE)
params_opt <- model$get_params()

# Plot the resulting regression function
plot(datasets::cars)
abline(a = 0, b = params_opt$beta)

# Generate a sample for y for given x following the same distribution
x.new <- seq(min(x), max(x), by=2)
y.smpl <- model$sample_yx(x.new)
points(x.new, y.smpl, col="red")

# Evaluate the conditional density, distribution, quantile and regression
# function at given values
model$f_yx(y.smpl, x.new)
model$F_yx(y.smpl, x.new)
model$F1_yx(y.smpl, x.new)
y.pred <- model$mean_yx(x.new)
points(x.new, y.pred, col="blue")

Parametric regression model (abstract class)

Description

This is the abstract base class for parametric regression model objects like NormalGLM.

Parametric regression models are built around the following key tasks:

• A method fit() to fit the model to given data, i.e. compute the MLE for the model parameters

• Methods f_yx(), F_yx() and mean_yx() to evaluate the conditional density, distribution and regression function

• A method sample_yx() to generate a random sample of response variables following the model given a vector of covariates

Methods

Public methods

• ParamRegrModel$set_params()

• ParamRegrModel$get_params()

• ParamRegrModel$fit()

• ParamRegrModel$f_yx()

• ParamRegrModel$F_yx()

• ParamRegrModel$F1_yx()

• ParamRegrModel$sample_yx()

• ParamRegrModel$mean_yx()

• ParamRegrModel$clone()

Method set_params()

Set the value of the model parameters used as default for the class functions.

Usage

ParamRegrModel$set_params(params)

Arguments

Returns

The modified object (self), allowing for method chaining.

Method get_params()

Returns the value of the model parameters used as default for the class functions.

Usage

ParamRegrModel$get_params()

Returns

model parameters used as default

Method fit()

Calculates the maximum likelihood estimator for the model parameters based on given data.

Usage

ParamRegrModel$fit(data, params_init = private$params, loglik = loglik_xy)

Arguments

Returns

MLE of the model parameters for the given data, same shape as params_init

Method f_yx()

Evaluates the conditional density function.

Usage

ParamRegrModel$f_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional density function, same shape as t

Method F_yx()

Evaluates the conditional distribution function.

Usage

ParamRegrModel$F_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional distribution function, same shape as t

Method F1_yx()

Evaluates the conditional quantile function.

Usage

ParamRegrModel$F1_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional quantile function, same shape as t

Method sample_yx()

Generates a new sample of response variables with the same conditional distribution.

Usage

ParamRegrModel$sample_yx(x, params = private$params)

Arguments

Returns

vector of sampled response variables, same length as x

Method mean_yx()

Evaluates the regression function or in other terms the expected value of Y given X=x.

Usage

ParamRegrModel$mean_yx(x, params = private$params)

Arguments

Returns

value of the regression function

Method clone()

The objects of this class are cloneable with this method.

Usage

ParamRegrModel$clone(deep = FALSE)

Arguments

Simulated integrated conditional moment test statistic

Description

This class inherits from TestStatistic and implements a function to calculate the test statistic (and x-y-values that can be used to plot the underlying process).

The process underlying the test statistic is given in Bierens & Wang (2012) doi: 10.1017/S0266466611000168 and defined by

\hat{T}_n^{(s)}(c) = \frac{1}{(2c)^{p+1}} \int_{[-c,c]^p} \int_{-c}^c \left|\frac{1}{\sqrt{n}} \sum_{j=1}^n \Big(\exp(i \tau Y_j) - \exp(i \tau \tilde{Y}_j)\Big) \exp(i \xi^T X_j)\right|^2 d\tau d\xi

Super class

gofreg::TestStatistic -> SICM

Methods

Public methods

• SICM$new()

• SICM$calc_stat()

• SICM$clone()

Method new()

Initialize an instance of class SICM.

Usage

SICM$new(
  c,
  transx = function(values) {
     tvals <- atan(scale(values))
     tvals[,
    apply(values, 2, sd) == 0] <- 0
     return(tvals)
 },
  transy = function(values, data) {
     array(atan(scale(values, center = mean(data$y),
    scale = sd(data$y))))
 }
)

Arguments

Returns

a new instance of the class

Method calc_stat()

Calculate the value of the test statistic for given data and a model to test for.

Usage

SICM$calc_stat(data, model)

Arguments

Returns

The modified object (self), allowing for method chaining.

Method clone()

The objects of this class are cloneable with this method.

Usage

SICM$clone(deep = FALSE)

Arguments

Examples

# Create an example dataset
n <- 100
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
y <- model$sample_yx(x, params=list(beta=c(2,3), sd=1))
data <- dplyr::tibble(x = x, y = y)

# Fit the correct model
model$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts <- SICM$new(c = 5)
ts$calc_stat(data, model)
print(ts)
plot(ts)

# Fit a wrong model
model2 <- NormalGLM$new(linkinv = function(u) {u+10})
model2$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts2 <- SICM$new(c = 5)
ts2$calc_stat(data, model2)
print(ts2)
plot(ts2)

Test Statistic for parametric regression models (abstract class)

Description

This is the abstract base class for test statistic objects like CondKolmY or MEP.

Test statistics are built around the key method calc_stat() which calculates the particular test statistic (and x-y-values that can be used to plot the underlying process).

Methods

Public methods

• TestStatistic$get_value()

• TestStatistic$calc_stat()

• TestStatistic$get_plot_xy()

• TestStatistic$print()

• TestStatistic$geom_ts_proc()

• TestStatistic$plot()

• TestStatistic$clone()

Method get_value()

Returns the value of the test statistic.

Usage

TestStatistic$get_value()

Returns

value of the test statistic

Method calc_stat()

Calculate the value of the test statistic for given data and a model to test for.

Usage

TestStatistic$calc_stat(data, model)

Arguments

Returns

The modified object (self), allowing for method chaining.

Method get_plot_xy()

Returns vectors of x and y that can be used to plot the process corresponding to the test statistic.

Usage

TestStatistic$get_plot_xy()

Returns

list with plot.x and plot.y being vectors of the same length

Method print()

Overrides the print-method for objects of type TestStatistic to only print its value.

Usage

TestStatistic$print()

Returns

The object (self), allowing for method chaining.

Method geom_ts_proc()

Creates a line plot showing the underlying process of the test statistic.

Usage

TestStatistic$geom_ts_proc(...)

Arguments

Returns

A ggplot2 layer representing a line plot.

Method plot()

Creates a new ggplot showing the underlying process of the test statistic.

Usage

TestStatistic$plot(...)

Arguments

Returns

A ggplot2 object representing the complete plot, including a line geometry.

Method clone()

The objects of this class are cloneable with this method.

Usage

TestStatistic$clone(deep = FALSE)

Arguments

Generalized linear model with Weibull distribution

Description

This class represents a generalized linear model with Weibull distribution. It inherits from GLM and implements its functions that, for example, evaluate the conditional density and distribution functions.

Super classes

gofreg::ParamRegrModel -> gofreg::GLM -> WeibullGLM

Methods

Public methods

• WeibullGLM$fit()

• WeibullGLM$f_yx()

• WeibullGLM$F_yx()

• WeibullGLM$F1_yx()

• WeibullGLM$sample_yx()

• WeibullGLM$clone()

Method fit()

Calculates the maximum likelihood estimator for the model parameters based on given data.

Usage

WeibullGLM$fit(
  data,
  params_init = private$params,
  loglik = loglik_xy,
  inplace = FALSE
)

Arguments

Returns

MLE of the model parameters for the given data, same shape as params_init

Method f_yx()

Evaluates the conditional density function.

Usage

WeibullGLM$f_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional density function, same shape as t

Method F_yx()

Evaluates the conditional distribution function.

Usage

WeibullGLM$F_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional distribution function, same shape as t

Method F1_yx()

Evaluates the conditional quantile function.

Usage

WeibullGLM$F1_yx(t, x, params = private$params)

Arguments

Returns

value(s) of the conditional quantile function, same shape as t

Method sample_yx()

Generates a new sample of response variables with the same conditional distribution.

Usage

WeibullGLM$sample_yx(x, params = private$params)

Arguments

Returns

vector of sampled response variables, same length as nrow(x)

Method clone()

The objects of this class are cloneable with this method.

Usage

WeibullGLM$clone(deep = FALSE)

Arguments

Examples

# Use the built-in cars dataset
x <- datasets::cars$speed
y <- datasets::cars$dist
data <- dplyr::tibble(x=x, y=y)

# Create an instance of WeibullGLM
model <- WeibullGLM$new()

# Fit an Weibull GLM to the cars dataset
model$fit(data, params_init = list(beta=3, shape=1), inplace=TRUE)
params_opt <- model$get_params()

# Plot the resulting regression function
plot(datasets::cars)
abline(a = 0, b = params_opt$beta)

# Generate a sample for y for given x following the same distribution
x.new <- seq(min(x), max(x), by=2)
y.smpl <- model$sample_yx(x.new)
points(x.new, y.smpl, col="red")

# Evaluate the conditional density, distribution, quantile and regression
# function at given values
model$f_yx(y.smpl, x.new)
model$F_yx(y.smpl, x.new)
model$F1_yx(y.smpl, x.new)
y.pred <- model$mean_yx(x.new)
points(x.new, y.pred, col="blue")

Negative log-likelihood function for a parametric regression model

Description

The log-likelihood function for a parametric regression model with data (x,y) is given by the sum of the logarithm of the conditional density of Y given X=x evaluated at y.

This function is one option that can be used to fit a ParamRegrModel. It returns the negative log-likelihood value in order for optim() to maximize (instead of minimize).

Usage

loglik_xy(data, model, params)

Arguments

Value

Value of the negative log-likelihood function

Examples

# Create an example dataset
n <- 100
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
params.true <- list(beta = c(2,3), sd = 1)
y <- model$sample_yx(x, params = params.true)
data <- dplyr::tibble(x = x, y = y)

# Compute negative log likelihood for true parameters
loglik_xy(data, model, params.true)

# Compute negative log likelihood for wrong parameters (should be higher)
loglik_xy(data, model, params = list(beta = c(1,2), sd = 0.5))

Negative log-likelihood function for a parametric regression model under random censorship

Description

The log-likelihood function for a parametric regression model under random censorship with data (x,z,delta) is given by the sum of the logarithm of the conditional density of Y given X=x evaluated at z if z was uncensored or the logarithm of the conditional survival of Y given X=x evaluated at z if z was censored.

This function is one option that can be used to fit a ParamRegrModel. It returns the negative log-likelihood value in order for optim() to maximize (instead of minimize).

Usage

loglik_xzd(data, model, params)

Arguments

Value

Value of the negative log-likelihood function

Examples

# Create an example dataset
n <- 100
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
params.true <- list(beta = c(2,3), sd = 1)
y <- model$sample_yx(x, params = params.true)
c <- rnorm(n, mean(y) * 1.2, sd(y) * 0.5)
data <- dplyr::tibble(x = x, z = pmin(y, c), delta = as.numeric(y <= c))

# Compute negative log likelihood for true parameters
loglik_xzd(data, model, params.true)

# Compute negative log likelihood for wrong parameters (should be higher)
loglik_xzd(data, model, params = list(beta = c(1,2), sd = 0.5))

Parametric resampling scheme for a parametric regression model

Description

Generate a new, resampled dataset of the same shape as data following the given model. The covariates are kept the same and the response variables are drawn according to model$sample_yx().

Usage

resample_param(data, model)

Arguments

Value

data.frame() with columns x and y containing the resampled data

Examples

# Create an example dataset
n <- 10
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
params <- list(beta = c(2, 3), sd = 1)
y <- model$sample_yx(x, params = params)
data <- dplyr::tibble(x = x, y = y)

# Fit the model to the data
model$fit(data, params_init = params, inplace = TRUE)

# Resample from the model given data
resample_param(data, model)

Parametric resampling scheme for a parametric regression model under random censorship

Description

Generate a new, resampled dataset of the same shape as data following the given model. The covariates X are kept the same. Survival times Y are drawn according to model$sample_yx() and censoring times C according to the KM estimator.

Usage

resample_param_cens(data, model)

Arguments

Value

data.frame() with columns x, z and delta containing the resampled data

Examples

# Create an example dataset
n <- 10
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
params <- list(beta = c(2, 3), sd = 1)
y <- model$sample_yx(x, params = params)
c <- rnorm(n, mean(y) * 1.2, sd(y) * 0.5)
z <- pmin(y, c)
delta <- as.numeric(y <= c)
data <- dplyr::tibble(x = x, z = z, delta = delta)

# Fit the model to the data
model$fit(data, params_init = params, inplace = TRUE, loglik = loglik_xzd)

# Resample from the model given data
resample_param_cens(data, model)

Parametric resampling scheme for a parametric regression model with resampling of covariates

Description

Generate a new, resampled dataset of the same shape as data following the given model. The covariates are resampled from data$x and the response variables are drawn according to model$sample_yx().

Usage

resample_param_rsmplx(data, model)

Arguments

Value

data.frame() with columns x and y containing the resampled data

Examples

# Create an example dataset
n <- 10
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
params <- list(beta = c(2, 3), sd = 1)
y <- model$sample_yx(x, params = params)
data <- dplyr::tibble(x = x, y = y)

# Fit the model to the data
model$fit(data, params_init = params, inplace = TRUE)

# Resample from the model given data
resample_param(data, model)