Title:  Multiple Empirical Likelihood Tests 

Description:  Performs multiple empirical likelihood tests. It offers an easytouse interface and flexibility in specifying hypotheses and calibration methods, extending the framework to simultaneous inferences. The core computational routines are implemented using the 'Eigen' 'C++' library and 'RcppEigen' interface, with 'OpenMP' for parallel computation. Details of the testing procedures are provided in Kim, MacEachern, and Peruggia (2023) <doi:10.1080/10485252.2023.2206919>. A companion paper by Kim, MacEachern, and Peruggia (2024) <doi:10.18637/jss.v108.i05> is available for further information. This work was supported by the U.S. National Science Foundation under Grants No. SES1921523 and DMS2015552. 
Authors:  Eunseop Kim [aut, cph, cre], Steven MacEachern [ctb, ths], Mario Peruggia [ctb, ths], Pierre Chausse [rev], Alex Stringer [rev] 
Maintainer:  Eunseop Kim <[email protected]> 
License:  GPL (>= 2) 
Version:  1.11.4 
Built:  20241013 07:10:49 UTC 
Source:  https://github.com/ropensci/melt 
S4 class for constrained empirical likelihood. It inherits from
EL class. Note that the optim
slot has constrained
optimization results with respect to the parameters, not the Lagrange
multiplier.
Let $l(\theta)$
denote minus twice the empirical loglikelihood
ratio function. We consider a linear hypothesis of the form
$L\theta = r,$
where the lefthandside $L$
is a $q$
by
$p$
matrix and the righthandside $r$
is a $q$
dimensional
vector. Under some regularity conditions, $l(\theta)$
converges in
distribution to $\chi^2_q$
under the constraint of hypothesis, i.e.,
$\min_{\theta: L\theta = r} l(\theta) \to_d \chi^2_q .$
Minimization of $l(\theta)$
with respect to $\theta$
is
computationally expensive since it implicitly involves the
evaluation step as described in EL. Further, depending on the
form of $g(X_i, \theta)$
and the constraint, the optimization problem
can be nonconvex and have multiple local minima. For this reason, the
package melt only considers linear hypotheses and performs local
minimization of $l(\theta)$
using projected gradient descent method.
With the orthogonal projection matrix $P$
and a step size $\gamma$
,
the algorithm updates $\theta$
as
$\theta^{(k + 1)} \leftarrow \theta^{(k)} 
\gamma P \nabla l(\theta^{(k)}),$
where $\nabla l(\theta^{(k)})$
denotes the gradient of $l$
at
$\theta^{(k)}$
. The first order optimality condition is
$P \nabla l(\theta) = 0$
, which is used as the stopping criterion.
optim
A list of the following optimization results:
par
A numeric vector of the solution to the constrained optimization
problem.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
cstr
A single logical for whether constrained EL optimization is
performed or not.
logp
A numeric vector of the log probabilities of the constrained empirical likelihood.
logl
A single numeric of the constrained empirical loglikelihood.
loglr
A single numeric of the constrained empirical loglikelihood ratio.
statistic
A single numeric of minus twice the constrained empirical loglikelihood ratio with an asymptotic chisquare distribution.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weights
A numeric vector of the rescaled weights used for the model fitting.
coefficients
A numeric vector of the maximum empirical likelihood estimates of the parameters.
method
A single character for the method dispatch in internal functions.
data
A numeric matrix of the data for the model fitting.
control
An object of class ControlEL constructed by
el_control()
.
Adimari G, Guolo A (2010). “A Note on the Asymptotic Behaviour of Empirical Likelihood Statistics.” Statistical Methods & Applications, 19(4), 463–476. doi:10.1007/s1026001001379.
Qin J, Lawless J (1995). “Estimating Equations, Empirical Likelihood and Constraints on Parameters.” Canadian Journal of Statistics, 23(2), 145–159. doi:10.2307/3315441.
showClass("CEL")
showClass("CEL")
Extracts the chisquare statistic from a model.
## S4 method for signature 'EL' chisq(object, ...) ## S4 method for signature 'ELMT' chisq(object, ...) ## S4 method for signature 'ELT' chisq(object, ...) ## S4 method for signature 'SummaryEL' chisq(object, ...) ## S4 method for signature 'SummaryELMT' chisq(object, ...) ## S4 method for signature 'SummaryELT' chisq(object, ...) ## S4 method for signature 'SummaryLM' chisq(object, ...)
## S4 method for signature 'EL' chisq(object, ...) ## S4 method for signature 'ELMT' chisq(object, ...) ## S4 method for signature 'ELT' chisq(object, ...) ## S4 method for signature 'SummaryEL' chisq(object, ...) ## S4 method for signature 'SummaryELMT' chisq(object, ...) ## S4 method for signature 'SummaryELT' chisq(object, ...) ## S4 method for signature 'SummaryLM' chisq(object, ...)
object 
An object that contains the chisquare statistic. 
... 
Further arguments passed to methods. 
The form of the value returned by chisq()
depends on the class of
its argument.
chisq(EL)
: Extracts the chisquare statistic.
chisq(ELMT)
: Extracts the vector of chisquare statistics.
chisq(ELT)
: Extracts the chisquare statistic.
chisq(SummaryEL)
: Extracts the chisquare statistic.
chisq(SummaryELMT)
: Extracts the vector of chisquare statistics.
chisq(SummaryELT)
: Extracts the chisquare statistic.
chisq(SummaryLM)
: Extracts the chisquare statistic for the overall test of
the model.
data("precip") fit < el_mean(precip, par = 40) chisq(fit)
data("precip") fit < el_mean(precip, par = 40) chisq(fit)
A dataset summarizing field experiments result of seed treatments on clothianidin concentration.
data("clothianidin")
data("clothianidin")
A data frame with 102 observations and 3 variables:
New blocks constructed from original data. The format is 'days post planting_original block_year'.
Seed treatment.
Log transformed clothianidin concentration (µg).
The original data is provided by Alford and Krupke (2017). Only some of the shoot region observations are taken from the original data and processed for illustration.
Alford A, Krupke CH (2017). “Translocation of the Neonicotinoid Seed Treatment Clothianidin in Maize.” PLOS ONE, 12(3), 1–19. doi:10.1371/journal.pone.0173836.
data("clothianidin") clothianidin
data("clothianidin") clothianidin
Extracts the maximum empirical likelihood estimates from a model.
## S4 method for signature 'EL' coef(object, ...) ## S4 method for signature 'ELMT' coef(object, ...) ## S4 method for signature 'SummaryEL' coef(object, ...) ## S4 method for signature 'SummaryLM' coef(object, ...)
## S4 method for signature 'EL' coef(object, ...) ## S4 method for signature 'ELMT' coef(object, ...) ## S4 method for signature 'SummaryEL' coef(object, ...) ## S4 method for signature 'SummaryLM' coef(object, ...)
object 
An object that contains the maximum empirical likelihood estimates. 
... 
Further arguments passed to methods. 
The form of the value returned by coef()
depends on the class of
its argument.
coef(EL)
: Extracts the numeric vector of the maximum empirical
likelihood estimates.
coef(ELMT)
: Extracts the list of numeric vectors of the maximum
empirical likelihood estimates. Each element of the list corresponds to a
distinct hypothesis.
coef(SummaryEL)
: Extracts the numeric vector of the maximum empirical
likelihood estimates.
coef(SummaryLM)
: Extracts a matrix with the results of significance tests.
data("mtcars") fit < el_lm(mpg ~ wt, data = mtcars) coef(fit)
data("mtcars") fit < el_lm(mpg ~ wt, data = mtcars) coef(fit)
Computes confidence intervals for one or more parameters in a model.
## S4 method for signature 'EL' confint(object, parm, level = 0.95, cv = NULL, control = NULL) ## S4 method for signature 'ELMT' confint(object, cv = NULL, control = NULL)
## S4 method for signature 'EL' confint(object, parm, level = 0.95, cv = NULL, control = NULL) ## S4 method for signature 'ELMT' confint(object, cv = NULL, control = NULL)
object 

parm 
A specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered. 
level 
A single numeric for the confidence level required. Defaults to

cv 
A single numeric for the critical value for calibration of
empirical likelihood ratio statistic. Defaults to 
control 
An object of class ControlEL constructed by

A matrix with columns giving lower and upper confidence limits for
each parameter. In contrast to other methods that rely on studentization,
the lower and upper limits obtained from empirical likelihood do not
correspond to the (1  level) / 2
and 1  (1  level) / 2
in %,
respectively.
Owen A (1990). “Empirical Likelihood Ratio Confidence Regions.” The Annals of Statistics, 18(1), 90–120. doi:10.1214/aos/1176347494.
EL, ELMT, confreg()
, elt()
,
el_control()
data("mtcars") fit < el_lm(mpg ~ ., data = mtcars) confint(fit, parm = c(2, 3))
data("mtcars") fit < el_lm(mpg ~ ., data = mtcars) confint(fit, parm = c(2, 3))
Computes boundary points of a twodimensional confidence region for model parameters.
## S4 method for signature 'EL' confreg(object, parm, level = 0.95, cv = NULL, npoints = 50L, control = NULL)
## S4 method for signature 'EL' confreg(object, parm, level = 0.95, cv = NULL, npoints = 50L, control = NULL)
object 
An object that inherits from EL. 
parm 
A specification of which parameters are to be given a confidence
region, either a vector of numbers or a vector of names. It must be a
vector of length two of the form 
level 
A single numeric for the confidence level required. Defaults to

cv 
A single numeric for the critical value for calibration of
empirical likelihood ratio statistic. Defaults to NULL and set to

npoints 
A single integer for the number of boundary points to compute.
Defaults to 
control 
An object of class ControlEL constructed by

An object of class ConfregEL.
Owen A (1990). “Empirical Likelihood Ratio Confidence Regions.” The Annals of Statistics, 18(1), 90–120. doi:10.1214/aos/1176347494.
EL, confint()
, elt()
, plot()
, el_control()
data("mtcars") fit < el_lm(mpg ~ wt + qsec, data = mtcars) cr < confreg(fit, parm = c(2, 3), cv = qchisq(0.90, 2)) plot(cr)
data("mtcars") fit < el_lm(mpg ~ wt + qsec, data = mtcars) cr < confreg(fit, parm = c(2, 3), cv = qchisq(0.90, 2)) plot(cr)
S4 class for confidence region. It inherits from "matrix"
.
estimates
A numeric vector of length two for the parameter estimates.
level
A single numeric for the confidence level required.
cv
A single numeric for the critical value for calibration of empirical likelihood ratio statistic.
pnames
A character vector of length two for the name of parameters.
showClass("ConfregEL")
showClass("ConfregEL")
S4 class for computational details of empirical likelihood.
maxit
A single integer for the maximum number of iterations for the
optimization with respect to $\theta$
.
maxit_l
A single integer for the maximum number of iterations for the
optimization with respect to $\lambda$
.
tol
A single numeric for the convergence tolerance denoted by
$\epsilon$
. The iteration stops when
$\P \nabla l(\theta^{(k)})\ < \epsilon.$
tol_l
A single numeric for the relative convergence tolerance denoted
by $\delta$
. The iteration stops when
$\\lambda^{(k)}  \lambda^{(k  1)}\ <
\delta\\lambda^{(k  1)}\ + \delta^2.$
step
A single numeric for the step size $\gamma$
for the projected
gradient descent method.
th
A single numeric for the threshold for the negative empirical loglikelihood ratio.
verbose
A single logical for whether to print a message on the convergence status.
keep_data
A single logical for whether to keep the data used for fitting model objects.
nthreads
A single integer for the number of threads for parallel computation via OpenMP (if available).
seed
A single integer for the seed for random number generation.
an
A single numeric representing the scaling factor for adjusted empirical likelihood calibration.
b
A single integer for the number of bootstrap replicates.
m
A single integer for the number of Monte Carlo samples.
showClass("ControlEL")
showClass("ControlEL")
Extracts the convergence status from a model.
## S4 method for signature 'CEL' conv(object, ...) ## S4 method for signature 'EL' conv(object, ...) ## S4 method for signature 'ELT' conv(object, ...) ## S4 method for signature 'SummaryEL' conv(object, ...) ## S4 method for signature 'SummaryELT' conv(object, ...) ## S4 method for signature 'SummaryLM' conv(object, ...)
## S4 method for signature 'CEL' conv(object, ...) ## S4 method for signature 'EL' conv(object, ...) ## S4 method for signature 'ELT' conv(object, ...) ## S4 method for signature 'SummaryEL' conv(object, ...) ## S4 method for signature 'SummaryELT' conv(object, ...) ## S4 method for signature 'SummaryLM' conv(object, ...)
object 
An object that contains the convergence status. 
... 
Further arguments passed to methods. 
A single logical.
conv(CEL)
: Extracts the convergence status of the model with respect to
the parameter.
conv(EL)
: Extracts the convergence status of the model with respect to
the Lagrange multiplier.
conv(ELT)
: Extracts the convergence status of the test with respect to
the parameter (or the Lagrange multiplier if the argument lhs
is NULL
).
conv(SummaryEL)
: Extracts the convergence status of the model with respect to
the Lagrange multiplier.
conv(SummaryELT)
: Extracts the convergence status of the test with respect to
the parameter (or the Lagrange multiplier if the argument lhs
is NULL
).
conv(SummaryLM)
: Extracts the convergence status of the model. See the
documentation of EL and CEL.
CEL, EL, ELT, getOptim()
## Convergence check for the overall model test data("mtcars") fit < el_lm(mpg ~ ., data = mtcars) conv(fit)
## Convergence check for the overall model test data("mtcars") fit < el_lm(mpg ~ ., data = mtcars) conv(fit)
Extracts the critical value from a model.
## S4 method for signature 'ELMT' critVal(object, ...) ## S4 method for signature 'ELT' critVal(object, ...) ## S4 method for signature 'SummaryELMT' critVal(object, ...) ## S4 method for signature 'SummaryELT' critVal(object, ...)
## S4 method for signature 'ELMT' critVal(object, ...) ## S4 method for signature 'ELT' critVal(object, ...) ## S4 method for signature 'SummaryELMT' critVal(object, ...) ## S4 method for signature 'SummaryELT' critVal(object, ...)
object 
An object that contains the critical value. 
... 
Further arguments passed to methods. 
A single numeric.
## Fcalibrated critical value data("precip") fit < el_mean(precip, 30) elt < elt(fit, rhs = 34, calibrate = "f") critVal(elt)
## Fcalibrated critical value data("precip") fit < el_mean(precip, 30) elt < elt(fit, rhs = 34, calibrate = "f") critVal(elt)
Specifies computational details of (constrained) empirical likelihood.
el_control( maxit = 200L, maxit_l = 25L, tol = 1e06, tol_l = 1e06, step = NULL, th = NULL, verbose = FALSE, keep_data = TRUE, nthreads, seed = NULL, an = NULL, b = 10000L, m = 1000000L )
el_control( maxit = 200L, maxit_l = 25L, tol = 1e06, tol_l = 1e06, step = NULL, th = NULL, verbose = FALSE, keep_data = TRUE, nthreads, seed = NULL, an = NULL, b = 10000L, m = 1000000L )
maxit 
A single integer for the maximum number of iterations for
constrained minimization of empirical likelihood. Defaults to 
maxit_l 
A single integer for the maximum number of iterations for
evaluation of empirical likelihood. Defaults to 
tol 
A single numeric for the convergence tolerance for the constrained
minimization. Defaults to 
tol_l 
A single numeric for the relative convergence tolerance for the
evaluation. Defaults to 
step 
A single numeric for the step size for projected gradient descent
method. Defaults to 
th 
A single numeric for the threshold for the negative empirical
loglikelihood ratio. The iteration stops if the value exceeds the
threshold. Defaults to 
verbose 
A single logical. If 
keep_data 
A single logical. If 
nthreads 
A single integer for the number of threads for parallel
computation via OpenMP (if available). Defaults to half the available
threads. For better performance, it is generally recommended in most
platforms to limit the number of threads to the number of physical cores.
Note that it applies to the following functions that involve multiple
evaluations or optimizations: 
seed 
A single integer for the seed for random number generation. It
only applies to 
an 
A single numeric representing the scaling factor for adjusted
empirical likelihood calibration. It only applies to 
b 
A single integer for the number of bootstrap replicates. It only
applies to 
m 
A single integer for the number of Monte Carlo samples. It only
applies to 
An object of class of ControlEL.
optcfg < el_control(maxit = 300, step = 0.01, th = 200, nthreads = 1)
optcfg < el_control(maxit = 300, step = 0.01, th = 200, nthreads = 1)
Computes empirical likelihood with general estimating functions.
el_eval(g, weights = NULL, control = el_control())
el_eval(g, weights = NULL, control = el_control())
g 
A numeric matrix, or an object that can be coerced to a numeric matrix. Each row corresponds to an observation of an estimating function. The number of rows must be greater than the number of columns. 
weights 
An optional numeric vector of weights to be used in the
fitting process. The length of the vector must be the same as the number of
rows in 
control 
An object of class ControlEL constructed by

Let $X_i$
be independent and identically distributed
$p$
dimensional random variable from an unknown distribution $P$
for $i = 1, \dots, n$
. We assume that $P$
has a positive definite
covariance matrix. For a parameter of interest
$\theta(F) \in {\rm{I\!R}}^p$
, consider a $p$
dimensional smooth
estimating function $g(X_i, \theta)$
with a moment condition
$\textrm{E}[g(X_i, \theta)] = 0.$
We assume that there exists an unique $\theta_0$
that solves the above
equation. Given a value of $\theta$
, the (profile) empirical likelihood
ratio is defined by
$R(\theta) =
\max_{p_i}\left\{\prod_{i = 1}^n np_i :
\sum_{i = 1}^n p_i g(X_i, \theta) = 0, p_i \geq 0, \sum_{i = 1}^n p_i = 1
\right\}.$
el_mean()
computes the empirical loglikelihood ratio statistic
$2\log R(\theta)$
with the $n$
by $p$
numeric matrix g
,
whose $i$
th row is $g(X_i, \theta)$
. Since the estimating function
can be arbitrary, el_eval()
does not return an object of class
EL, and the associated generics and methods are not
applicable.
A list of the following optimization results:
optim
A list with the following optimization results:
lambda
A numeric vector of the Lagrange multipliers of the dual
problem.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
logp
A numeric vector of the log probabilities of the empirical
likelihood.
logl
A single numeric of the empirical loglikelihood.
loglr
A single numeric of the empirical loglikelihood ratio.
statistic
A single numeric of minus twice the empirical loglikelihood
ratio with an asymptotic chisquare distribution.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weights
A numeric vector of the rescaled weights used for the model
fitting.
Qin J, Lawless J (1994). “Empirical Likelihood and General Estimating Equations.” The Annals of Statistics, 22(1), 300–325. doi:10.1214/aos/1176325370.
set.seed(123526) mu < 0 sigma < 1 x < rnorm(100) g < matrix(c(x  mu, (x  mu)^2  sigma^2), ncol = 2) el_eval(g, weights = rep(c(1, 2), each = 50))
set.seed(123526) mu < 0 sigma < 1 x < rnorm(100) g < matrix(c(x  mu, (x  mu)^2  sigma^2), ncol = 2) el_eval(g, weights = rep(c(1, 2), each = 50))
Fits a generalized linear model with empirical likelihood.
el_glm( formula, family = gaussian, data, weights = NULL, na.action, start = NULL, etastart = NULL, mustart = NULL, offset, control = el_control(), ... )
el_glm( formula, family = gaussian, data, weights = NULL, na.action, start = NULL, etastart = NULL, mustart = NULL, offset, control = el_control(), ... )
formula 
An object of class 
family 
A description of the error distribution and link function to be used in the model. Only the result of a call to a family function is supported. See ‘Details’. 
data 
An optional data frame, list or environment (or object coercible
by 
weights 
An optional numeric vector of weights to be used in the
fitting process. Defaults to 
na.action 
A function which indicates what should happen when the data
contain 
start 
Starting values for the parameters in the linear predictor.
Defaults to 
etastart 
Starting values for the linear predictor. Defaults to 
mustart 
Starting values for the vector of means. Defaults to 
offset 
An optional expression for specifying an a priori known
component to be included in the linear predictor during fitting. This
should be 
control 
An object of class ControlEL constructed by

... 
Additional arguments to be passed to 
Suppose that we observe $n$
independent random variables
${Z_i} \equiv {(X_i, Y_i)}$
from a common distribution, where $X_i$
is the $p$
dimensional covariate (including the intercept if any) and
$Y_i$
is the response. A generalized linear model specifies that
${\textrm{E}(Y_i  X_i)} = {\mu_i}$
,
${G(\mu_i)} = {X_i^\top \theta}$
, and
${\textrm{Var}(Y_i  X_i)} = {\phi V(\mu_i)}$
,
where $\theta = (\theta_0, \dots, \theta_{p1})$
is an unknown
$p$
dimensional parameter, $\phi$
is an optional dispersion
parameter, $G$
is a known smooth link function, and $V$
is a known
variance function.
With $H$
denoting the inverse link function, define the quasiscore
${g_1(Z_i, \theta)} =
\left\{
H^\prime(X_i^\top \theta) \left(Y_i  H(X_i^\top \theta)\right) /
\left(\phi V\left(H(X_i^\top \theta)\right)\right)
\right\}
X_i.$
Then we have the estimating equations
$\sum_{i = 1}^n g_1(Z_i, \theta) = 0$
.
When $\phi$
is known, the (profile) empirical likelihood ratio for a
given $\theta$
is defined by
$R_1(\theta) =
\max_{p_i}\left\{\prod_{i = 1}^n np_i :
\sum_{i = 1}^n p_i g_1(Z_i, \theta) = 0,\
p_i \geq 0,\
\sum_{i = 1}^n p_i = 1
\right\}.$
With unknown $\phi$
, we introduce another estimating function based on
the squared residuals. Let ${\eta} = {(\theta, \phi)}$
and
${g_2(Z_i, \eta)} =
\left(Y_i  H(X_i^\top \theta)\right)^2 /
\left(\phi^2 V\left(H(X_i^\top \theta)\right)\right)  1 / \phi.$
Now the empirical likelihood ratio is defined by
$R_2(\eta) =
\max_{p_i}\left\{\prod_{i = 1}^n np_i :
\sum_{i = 1}^n p_i g_1(Z_i, \eta) = 0,\
\sum_{i = 1}^n p_i g_2(Z_i, \eta) = 0,\
p_i \geq 0,\
\sum_{i = 1}^n p_i = 1
\right\}.$
el_glm()
first computes the parameter estimates by calling glm.fit()
(with ...
if any) with the model.frame
and model.matrix
obtained from
the formula
. Note that the maximum empirical likelihood estimator is the
same as the the quasimaximum likelihood estimator in our model. Next, it
tests hypotheses based on asymptotic chisquare distributions of the
empirical likelihood ratio statistics. Included in the tests are overall
test with
$H_0: \theta_1 = \theta_2 = \cdots = \theta_{p1} = 0,$
and significance tests for each parameter with
$H_{0j}: \theta_j = 0,\ j = 0, \dots, p1.$
The available families and link functions are as follows:
gaussian
: "identity"
, "log"
, and "inverse"
.
binomial
: "logit"
, "probit"
, and "log"
.
poisson
: "log"
, "identity"
, and "sqrt"
.
quasipoisson
: "log"
, "identity"
, and "sqrt"
.
An object of class of GLM.
Chen SX, Cui H (2003). “An Extended Empirical Likelihood for Generalized Linear Models.” Statistica Sinica, 13(1), 69–81.
Kolaczyk ED (1994). “Empirical Likelihood for Generalized Linear Models.” Statistica Sinica, 4(1), 199–218.
EL, GLM, el_lm()
, elt()
,
el_control()
data("warpbreaks") fit < el_glm(wool ~ ., family = binomial, data = warpbreaks, weights = NULL, na.action = na.omit, start = NULL, etastart = NULL, mustart = NULL, offset = NULL ) summary(fit)
data("warpbreaks") fit < el_glm(wool ~ ., family = binomial, data = warpbreaks, weights = NULL, na.action = na.omit, start = NULL, etastart = NULL, mustart = NULL, offset = NULL ) summary(fit)
Fits a linear model with empirical likelihood.
el_lm( formula, data, weights = NULL, na.action, offset, control = el_control(), ... )
el_lm( formula, data, weights = NULL, na.action, offset, control = el_control(), ... )
formula 
An object of class 
data 
An optional data frame, list or environment (or object coercible
by 
weights 
An optional numeric vector of weights to be used in the
fitting process. Defaults to 
na.action 
A function which indicates what should happen when the data
contain 
offset 
An optional expression for specifying an a priori known
component to be included in the linear predictor during fitting. This
should be 
control 
An object of class ControlEL constructed by

... 
Additional arguments to be passed to the low level regression fitting functions. See ‘Details’. 
Suppose that we observe $n$
independent random variables
${Z_i} \equiv {(X_i, Y_i)}$
from a common distribution, where $X_i$
is the $p$
dimensional covariate (including the intercept if any) and
$Y_i$
is the response. We consider the following linear model:
$Y_i = X_i^\top \theta + \epsilon_i,$
where $\theta = (\theta_0, \dots, \theta_{p1})$
is an unknown
$p$
dimensional parameter and the errors $\epsilon_i$
are
independent random variables that satisfy
$\textrm{E}(\epsilon_i  X_i)$
= 0. We assume that the errors have
finite conditional variances. Then the least square estimator of
$\theta$
solves the following estimating equations:
$\sum_{i = 1}^n(Y_i  X_i^\top \theta)X_i = 0.$
Given a value of $\theta$
, let
${g(Z_i, \theta)} = {(Y_i  X_i^\top \theta)X_i}$
and the (profile)
empirical likelihood ratio is defined by
$R(\theta) =
\max_{p_i}\left\{\prod_{i = 1}^n np_i :
\sum_{i = 1}^n p_i g(Z_i, \theta) = \theta,\
p_i \geq 0,\
\sum_{i = 1}^n p_i = 1
\right\}.$
el_lm()
first computes the parameter estimates by calling lm.fit()
(with ...
if any) with the model.frame
and model.matrix
obtained from
the formula
. Note that the maximum empirical likelihood estimator is the
same as the the quasimaximum likelihood estimator in our model. Next, it
tests hypotheses based on asymptotic chisquare distributions of the
empirical likelihood ratio statistics. Included in the tests are overall
test with
$H_0: \theta_1 = \theta_2 = \cdots = \theta_{p1} = 0,$
and significance tests for each parameter with
$H_{0j}: \theta_j = 0,\ j = 0, \dots, p1.$
An object of class of LM.
Owen A (1991). “Empirical Likelihood for Linear Models.” The Annals of Statistics, 19(4), 1725–1747. doi:10.1214/aos/1176348368.
EL, LM, el_glm()
, elt()
,
el_control()
## Linear model data("thiamethoxam") fit < el_lm(fruit ~ trt, data = thiamethoxam) summary(fit) ## Weighted data wfit < el_lm(fruit ~ trt, data = thiamethoxam, weights = visit) summary(wfit) ## Missing data fit2 < el_lm(fruit ~ trt + scb, data = thiamethoxam, na.action = na.omit, offset = NULL ) summary(fit2)
## Linear model data("thiamethoxam") fit < el_lm(fruit ~ trt, data = thiamethoxam) summary(fit) ## Weighted data wfit < el_lm(fruit ~ trt, data = thiamethoxam, weights = visit) summary(wfit) ## Missing data fit2 < el_lm(fruit ~ trt + scb, data = thiamethoxam, na.action = na.omit, offset = NULL ) summary(fit2)
Computes empirical likelihood for the mean.
el_mean(x, par, weights = NULL, control = el_control())
el_mean(x, par, weights = NULL, control = el_control())
x 
A numeric matrix, or an object that can be coerced to a numeric matrix. Each row corresponds to an observation. The number of rows must be greater than the number of columns. 
par 
A numeric vector of parameter values to be tested. The length of
the vector must be the same as the number of columns in 
weights 
An optional numeric vector of weights to be used in the
fitting process. The length of the vector must be the same as the number of
rows in 
control 
An object of class ControlEL constructed by

Let $X_i$
be independent and identically distributed
$p$
dimensional random variable from an unknown distribution $P$
for $i = 1, \dots, n$
. We assume that ${\textrm{E}[X_i]} =
{\theta_0} \in {\rm{I\!R}}^p$
and that $P$
has a positive definite
covariance matrix. Given a value of $\theta$
, the (profile) empirical
likelihood ratio is defined by
$R(\theta) =
\max_{p_i}\left\{\prod_{i = 1}^n np_i :
\sum_{i = 1}^n p_i X_i = \theta,\
p_i \geq 0,\
\sum_{i = 1}^n p_i = 1
\right\}.$
el_mean()
computes the empirical loglikelihood ratio statistic
$2\log R(\theta)$
, along with other values in EL.
An object of class EL.
Owen A (1990). “Empirical Likelihood Ratio Confidence Regions.” The Annals of Statistics, 18(1), 90–120. doi:10.1214/aos/1176347494.
EL, elt()
, el_eval()
, el_control()
## Scalar mean data("precip") fit < el_mean(precip, 30) fit summary(fit) ## Vector mean data("faithful") fit2 < el_mean(faithful, par = c(3.5, 70)) summary(fit2) ## Weighted data w < rep(c(1, 2), each = nrow(faithful) / 2) fit3 < el_mean(faithful, par = c(3.5, 70), weights = w) summary(fit3)
## Scalar mean data("precip") fit < el_mean(precip, 30) fit summary(fit) ## Vector mean data("faithful") fit2 < el_mean(faithful, par = c(3.5, 70)) summary(fit2) ## Weighted data w < rep(c(1, 2), each = nrow(faithful) / 2) fit3 < el_mean(faithful, par = c(3.5, 70), weights = w) summary(fit3)
Computes empirical likelihood for the standard deviation.
el_sd(x, mean, sd, weights = NULL, control = el_control())
el_sd(x, mean, sd, weights = NULL, control = el_control())
x 
A numeric vector, or an object that can be coerced to a numeric vector. 
mean 
A single numeric for the (known) mean value. 
sd 
A positive single numeric for the parameter value to be tested. 
weights 
An optional numeric vector of weights to be used in the
fitting process. The length of the vector must be the same as the length of

control 
An object of class ControlEL constructed by

Let $X_i$
be independent and identically random variable from an
unknown distribution $P$
for $i = 1, \dots, n$
. We assume that
${\textrm{E}[X_i]} = {\mu_0}$
is known and that $P$
has a variance
$\sigma_0^2$
. Given a value of $\sigma$
, the
(profile) empirical likelihood ratio is defined by
$R(\sigma) =
\max_{p_i}\left\{\prod_{i = 1}^n np_i :
\sum_{i = 1}^n p_i (X_i  \mu_0)^2 = \sigma^2,\
p_i \geq 0,\
\sum_{i = 1}^n p_i = 1
\right\}.$
el_sd()
computes the empirical loglikelihood ratio statistic
$2\log R(\sigma)$
, along with other values in SD.
An object of class SD.
EL, SD, el_mean()
, elt()
,
el_control()
data("women") x < women$height w < women$weight fit < el_sd(x, mean = 65, sd = 5, weights = w) fit summary(fit)
data("women") x < women$height w < women$weight fit < el_sd(x, mean = 65, sd = 5, weights = w) fit summary(fit)
S4 class for empirical likelihood.
Let $X_i$
be independent and identically distributed
$p$
dimensional random variable from an unknown distribution $P$
for $i = 1, \dots, n$
. We assume that $P$
has a positive definite
covariance matrix. For a parameter of interest
$\theta(F) \in {\rm{I\!R}}^p$
, consider a $p$
dimensional smooth
estimating function $g(X_i, \theta)$
with a moment condition
$\textrm{E}[g(X_i, \theta)] = 0.$
We assume that there exists an unique $\theta_0$
that solves the above
equation. Given a value of $\theta$
, the (profile) empirical likelihood
ratio is defined by
$R(\theta) =
\max_{p_i}\left\{\prod_{i = 1}^n np_i :
\sum_{i = 1}^n p_i g(X_i, \theta) = 0, p_i \geq 0, \sum_{i = 1}^n p_i = 1
\right\}.$
The Lagrange multiplier $\lambda \equiv \lambda(\theta)$
of the dual
problem leads to
$p_i = \frac{1}{n}\frac{1}{1 + \lambda^\top g(X_i, \theta)},$
where $\lambda$
solves
$\frac{1}{n}\sum_{i = 1}^n \frac{g(X_i, \theta)}
{1 + \lambda^\top g(X_i, \theta)} = 0.$
Then the empirical loglikelihood ratio is given by
$\log R(\theta) = \sum_{i = 1}^n
\log(1 + \lambda^\top g(X_i, \theta)).$
This problem can be efficiently solved by the NewtonRaphson method when
the zero vector is contained in the interior of the convex hull of
$\{g(X_i, \theta)\}_{i = 1}^n$
.
It is known that $2\log R(\theta_0)$
converges in
distribution to $\chi^2_p$
, where $\chi^2_p$
has a chisquare
distribution with $p$
degrees of freedom. See the references below for
more details.
optim
A list of the following optimization results:
par
A numeric vector of the specified parameters.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
cstr
A single logical for whether constrained EL optimization is
performed or not.
logp
A numeric vector of the log probabilities of the empirical likelihood.
logl
A single numeric of the empirical loglikelihood.
loglr
A single numeric of the empirical loglikelihood ratio.
statistic
A single numeric of minus twice the empirical loglikelihood ratio with an asymptotic chisquare distribution.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weights
A numeric vector of the rescaled weights used for the model fitting.
coefficients
A numeric vector of the maximum empirical likelihood estimates of the parameters.
method
A single character for the method dispatch in internal functions.
data
A numeric matrix of the data for the model fitting.
control
An object of class ControlEL constructed by
el_control()
.
Owen A (2001). Empirical Likelihood. Chapman & Hall/CRC. doi:10.1201/9781420036152.
Qin J, Lawless J (1994). “Empirical Likelihood and General Estimating Equations.” The Annals of Statistics, 22(1), 300–325. doi:10.1214/aos/1176325370.
showClass("EL")
showClass("EL")
Computes empirical likelihood displacement for model diagnostics and outlier detection.
## S4 method for signature 'EL' eld(object, control = NULL) ## S4 method for signature 'GLM' eld(object, control = NULL)
## S4 method for signature 'EL' eld(object, control = NULL) ## S4 method for signature 'GLM' eld(object, control = NULL)
object 
An object that inherits from EL. 
control 
An object of class ControlEL constructed by

Let $L(\theta)$
be the empirical loglikelihood function based
on the full sample with $n$
observations. The maximum empirical
likelihood estimate is denoted by $\hat{\theta}$
. Consider a reduced
sample with the $i$
th observation deleted and the corresponding
estimate $\hat{\theta}_{(i)}$
. The empirical likelihood displacement is
defined by
$\textrm{ELD}_i = 2\{L(\hat{\theta})  L(\hat{\theta}_{(i)})\}.$
If $\textrm{ELD}_i$
is large, then the $i$
th observation is an
influential point and can be inspected as a possible outlier. eld
computes $\textrm{ELD}_i$
for $i = 1, \dots, n$
.
An object of class ELD.
Lazar NA (2005). “Assessing the Effect of Individual Data Points on Inference From Empirical Likelihood.” Journal of Computational and Graphical Statistics, 14(3), 626–642. doi:10.1198/106186005X59568.
Zhu H, Ibrahim JG, Tang N, Zhang H (2008). “Diagnostic Measures for Empirical Likelihood of General Estimating Equations.” Biometrika, 95(2), 489–507. doi:10.1093/biomet/asm094.
EL, ELD, el_control()
, plot()
data("precip") fit < el_mean(precip, par = 30) eld < eld(fit) plot(eld)
data("precip") fit < el_mean(precip, par = 30) eld < eld(fit) plot(eld)
S4 class for empirical likelihood displacement. It inherits from "numeric"
.
showClass("ELD")
showClass("ELD")
Tests multiple linear hypotheses simultaneously.
## S4 method for signature 'EL' elmt(object, rhs = NULL, lhs = NULL, alpha = 0.05, control = NULL)
## S4 method for signature 'EL' elmt(object, rhs = NULL, lhs = NULL, alpha = 0.05, control = NULL)
object 
An object that inherits from EL. 
rhs 
A numeric vector (column matrix) or a list of numeric vectors for
the righthand sides of hypotheses. Defaults to 
lhs 
A list or a numeric matrix for the lefthand sides of hypotheses.
For a list 
alpha 
A single numeric for the overall significance level. Defaults to

control 
An object of class ControlEL constructed by

elmt()
tests multiple hypotheses simultaneously. Each hypothesis
corresponds to the constrained empirical likelihood ratio described in
CEL. rhs
and lhs
cannot be both NULL
. The righthand
side and lefthand side of each hypothesis must be specified as described
in elt()
.
For specifying linear contrasts more conveniently, rhs
and lhs
also
take a numeric vector and a numeric matrix, respectively. Each element of
rhs
and each row of lhs
correspond to a contrast (hypothesis).
The vector of empirical likelihood ratio statistics asymptotically follows
a multivariate chisquare distribution under the complete null hypothesis.
The multiple testing procedure asymptotically controls the familywise
error rate at the level alpha
. Based on the distribution of the maximum
of the test statistics, the adjusted pvalues are estimated by Monte Carlo
simulation.
An object of class of ELMT.
Kim E, MacEachern SN, Peruggia M (2023). “Empirical likelihood for the analysis of experimental designs.” Journal of Nonparametric Statistics, 35(4), 709–732. doi:10.1080/10485252.2023.2206919.
Kim E, MacEachern SN, Peruggia M (2024). “melt: Multiple Empirical Likelihood Tests in R.” Journal of Statistical Software, 108(5), 1–33. doi:10.18637/jss.v108.i05.
EL, ELMT, elt()
, el_control()
## Bivariate mean (list `rhs` & no `lhs`) set.seed(143) data("women") fit < el_mean(women, par = c(65, 135)) rhs < list(c(64, 133), c(66, 140)) elmt(fit, rhs = rhs) ## Pairwise comparison (no `rhs` & list `lhs`) data("clothianidin") fit2 < el_lm(clo ~ 1 + trt, clothianidin) lhs2 < list( "trtNaked  trtFungicide", "trtFungicide  trtLow", "trtLow  trtHigh" ) elmt(fit2, lhs = lhs2) ## Arbitrary hypotheses (list `rhs` & list `lhs`) data("mtcars") fit3 < el_lm(mpg ~ wt + qsec, data = mtcars) lhs3 < list(c(1, 4, 0), rbind(c(0, 1, 0), c(0, 0, 1))) rhs3 < list(0, c(6, 1)) elmt(fit3, rhs = rhs3, lhs = lhs3)
## Bivariate mean (list `rhs` & no `lhs`) set.seed(143) data("women") fit < el_mean(women, par = c(65, 135)) rhs < list(c(64, 133), c(66, 140)) elmt(fit, rhs = rhs) ## Pairwise comparison (no `rhs` & list `lhs`) data("clothianidin") fit2 < el_lm(clo ~ 1 + trt, clothianidin) lhs2 < list( "trtNaked  trtFungicide", "trtFungicide  trtLow", "trtLow  trtHigh" ) elmt(fit2, lhs = lhs2) ## Arbitrary hypotheses (list `rhs` & list `lhs`) data("mtcars") fit3 < el_lm(mpg ~ wt + qsec, data = mtcars) lhs3 < list(c(1, 4, 0), rbind(c(0, 1, 0), c(0, 0, 1))) rhs3 < list(0, c(6, 1)) elmt(fit3, rhs = rhs3, lhs = lhs3)
S4 class for empirical likelihood multiple tests.
estimates
A list of numeric vectors of the estimates of the linear hypotheses.
statistic
A numeric vector of minus twice the (constrained) empirical loglikelihood ratios with asymptotic chisquare distributions.
df
An integer vector of the marginal degrees of freedom of the statistic.
pval
A numeric vector for the multiplicity adjusted $p$
values.
cv
A single numeric for the multiplicity adjusted critical value.
rhs
A numeric vector for the righthand sides of the hypotheses.
lhs
A numeric matrix for the lefthand side of the hypotheses.
alpha
A single numeric for the overall significance level.
calibrate
A single character for the calibration method used.
weights
A numeric vector of the rescaled weights used for the model fitting.
coefficients
A numeric vector of the maximum empirical likelihood estimates of the parameters.
method
A single character for the method dispatch in internal functions.
data
A numeric matrix of the data for the model fitting.
control
An object of class ControlEL constructed by
el_control()
.
showClass("ELMT")
showClass("ELMT")
Tests a linear hypothesis with various calibration options.
## S4 method for signature 'EL' elt( object, rhs = NULL, lhs = NULL, alpha = 0.05, calibrate = "chisq", control = NULL )
## S4 method for signature 'EL' elt( object, rhs = NULL, lhs = NULL, alpha = 0.05, calibrate = "chisq", control = NULL )
object 
An object that inherits from EL. 
rhs 
A numeric vector or a column matrix for the righthand side of
hypothesis, with as many entries as the rows in 
lhs 
A numeric matrix or a vector (treated as a row matrix) for the
lefthand side of a hypothesis. Each row gives a linear combination of the
parameters in 
alpha 
A single numeric for the significance level. Defaults to 
calibrate 
A single character representing the calibration method. It
is caseinsensitive and must be one of 
control 
An object of class ControlEL constructed by

elt()
performs the constrained minimization of $l(\theta)$
described in CEL. rhs
and lhs
cannot be both NULL
. For
nonNULL
lhs
, it is required that lhs
have full row rank
$q \leq p$
and $p$
be equal to the number of parameters in the
object
.
Depending on the specification of rhs
and lhs
, we have the following
three cases:
If both rhs
and lhs
are nonNULL
, the constrained minimization
is performed with the righthand side $r$
and the lefthand side
$L$
as
$\inf_{\theta: L\theta = r} l(\theta).$
If rhs
is NULL
, $r$
is set to the zero vector as
$\inf_{\theta: L\theta = 0} l(\theta)$
.
If lhs
is NULL
, $L$
is set to the identity matrix and the
problem reduces to evaluating at $r$
as $l(r)$
.
calibrate
specifies the calibration method used. Four methods are
available: "ael"
(adjusted empirical likelihood calibration), "boot"
(bootstrap calibration), "chisq"
(chisquare calibration), and "f"
($F$
calibration). When lhs
is not NULL
, only "chisq"
is
available. "f"
is applicable only to the mean parameter. The an
slot in
control
applies specifically to "ael"
, while the nthreads
, seed
,
and B
slots apply to "boot"
.
An object of class of ELT. If lhs
is nonNULL
, the
optim
slot corresponds to that of CEL. Otherwise, it
corresponds to that of EL.
Adimari G, Guolo A (2010). “A Note on the Asymptotic Behaviour of Empirical Likelihood Statistics.” Statistical Methods & Applications, 19(4), 463–476. doi:10.1007/s1026001001379.
Chen J, Variyath AM, Abraham B (2008). “Adjusted Empirical Likelihood and Its Properties.” Journal of Computational and Graphical Statistics, 17(2), 426–443.
Kim E, MacEachern SN, Peruggia M (2024). “melt: Multiple Empirical Likelihood Tests in R.” Journal of Statistical Software, 108(5), 1–33. doi:10.18637/jss.v108.i05.
Qin J, Lawless J (1995). “Estimating Equations, Empirical Likelihood and Constraints on Parameters.” Canadian Journal of Statistics, 23(2), 145–159. doi:10.2307/3315441.
EL, ELT, elmt()
, el_control()
## Adjusted empirical likelihood calibration data("precip") fit < el_mean(precip, 32) elt(fit, rhs = 100, calibrate = "ael") ## Bootstrap calibration elt(fit, rhs = 32, calibrate = "boot") ## F calibration elt(fit, rhs = 32, calibrate = "f") ## Test of no treatment effect data("clothianidin") contrast < matrix(c( 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1 ), byrow = TRUE, nrow = 3) fit2 < el_lm(clo ~ 1 + trt, clothianidin) elt(fit2, lhs = contrast) ## A symbolic description of the same hypothesis elt(fit2, lhs = c( "trtNaked  trtFungicide", "trtFungicide  trtLow", "trtLow  trtHigh" ))
## Adjusted empirical likelihood calibration data("precip") fit < el_mean(precip, 32) elt(fit, rhs = 100, calibrate = "ael") ## Bootstrap calibration elt(fit, rhs = 32, calibrate = "boot") ## F calibration elt(fit, rhs = 32, calibrate = "f") ## Test of no treatment effect data("clothianidin") contrast < matrix(c( 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1 ), byrow = TRUE, nrow = 3) fit2 < el_lm(clo ~ 1 + trt, clothianidin) elt(fit2, lhs = contrast) ## A symbolic description of the same hypothesis elt(fit2, lhs = c( "trtNaked  trtFungicide", "trtFungicide  trtLow", "trtLow  trtHigh" ))
S4 class for empirical likelihood test.
optim
A list of the following optimization results:
par
A numeric vector of the solution to the (constrained) optimization
problem.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
cstr
A single logical for whether constrained EL optimization is
performed or not.
logp
A numeric vector of the log probabilities of the (constrained) empirical likelihood.
logl
A single numeric of the (constrained) empirical loglikelihood.
loglr
A single numeric of the (constrained) empirical loglikelihood ratio.
statistic
A single numeric of minus twice the (constrained) empirical loglikelihood ratio with an asymptotic chisquare distribution.
df
A single integer for the chisquare degrees of freedom of the statistic.
pval
A single numeric for the (calibrated) $p$
value of the
statistic.
cv
A single numeric for the critical value.
rhs
A numeric vector for the righthand side of the hypothesis.
lhs
A numeric matrix for the lefthand side of the hypothesis.
alpha
A single numeric for the significance level.
calibrate
A single character for the calibration method used.
control
An object of class ControlEL constructed by
el_control()
.
showClass("ELT")
showClass("ELT")
Extracts the degrees of freedom from a model.
## S4 method for signature 'EL' getDF(object) ## S4 method for signature 'ELMT' getDF(object) ## S4 method for signature 'ELT' getDF(object) ## S4 method for signature 'SummaryEL' getDF(object) ## S4 method for signature 'SummaryELMT' getDF(object) ## S4 method for signature 'SummaryLM' getDF(object)
## S4 method for signature 'EL' getDF(object) ## S4 method for signature 'ELMT' getDF(object) ## S4 method for signature 'ELT' getDF(object) ## S4 method for signature 'SummaryEL' getDF(object) ## S4 method for signature 'SummaryELMT' getDF(object) ## S4 method for signature 'SummaryLM' getDF(object)
object 
An object that contains the degrees of freedom. 
An integer vector.
getDF(EL)
: Extracts the degrees of freedom.
getDF(ELMT)
: Extracts the vector of marginal degrees of freedom.
getDF(ELT)
: Extracts the (chisquare) degrees of freedom.
getDF(SummaryEL)
: Extracts the degrees of freedom.
getDF(SummaryELMT)
: Extracts the vector of marginal degrees of freedom.
getDF(SummaryLM)
: Extracts the degrees of freedom.
data("faithful") fit < el_mean(faithful, par = c(3.5, 70)) getDF(fit)
data("faithful") fit < el_mean(faithful, par = c(3.5, 70)) getDF(fit)
Extracts the optimization results from a model.
## S4 method for signature 'EL' getOptim(object, ...) ## S4 method for signature 'ELT' getOptim(object, ...) ## S4 method for signature 'SummaryEL' getOptim(object, ...) ## S4 method for signature 'SummaryELT' getOptim(object, ...) ## S4 method for signature 'SummaryLM' getOptim(object, ...)
## S4 method for signature 'EL' getOptim(object, ...) ## S4 method for signature 'ELT' getOptim(object, ...) ## S4 method for signature 'SummaryEL' getOptim(object, ...) ## S4 method for signature 'SummaryELT' getOptim(object, ...) ## S4 method for signature 'SummaryLM' getOptim(object, ...)
object 
An object that contains the optimization results. 
... 
Further arguments passed to methods. 
A list with the following optimization results:
par
A numeric vector of the parameter value. See the documentation of
EL and CEL.
lambda
A numeric vector of the Lagrange multipliers.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
EL, ELT, sigTests()
data("precip") fit < el_mean(precip, par = 40) getOptim(fit)
data("precip") fit < el_mean(precip, par = 40) getOptim(fit)
S4 class for generalized linear models. It inherits from LM class.
The overall test involves a constrained optimization problem. All
the parameters except for the intercept are constrained to zero. The
optim
slot contains the results. When there is no intercept, all
parameters are set to zero, and the results need to be understood in terms
of EL class since no constrained optimization is involved.
Once the solution is found, the log probabilities (logp
) and the
(constrained) empirical likelihood values (logl
, loglr
, statistic
)
readily follow, along with the degrees of freedom (df
) and the
$p$
value (pval
). The significance tests for each parameter also
involve constrained optimization problems where only one parameter is
constrained to zero. The sigTests
slot contains the results.
family
A family
object used.
dispersion
A single numeric for the estimated dispersion parameter.
sigTests
A list of the following results of significance tests:
statistic
A numeric vector of minus twice the (constrained) empirical
loglikelihood ratios with asymptotic chisquare distributions.
iterations
An integer vector for the number of iterations performed for
each parameter.
convergence
A logical vector for the convergence status of each
parameter.
cstr
A single logical for whether constrained EL optimization is
performed or not.
call
A matched call.
terms
A terms
object used.
misc
A list of various outputs obtained from the model fitting process. They are used in other generics and methods.
optim
A list of the following optimization results:
par
A numeric vector of the solution to the (constrained) optimization
problem.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
logp
A numeric vector of the log probabilities of the (constrained) empirical likelihood.
logl
A single numeric of the (constrained) empirical loglikelihood.
loglr
A single numeric of the (constrained) empirical loglikelihood ratio.
statistic
A single numeric of minus twice the (constrained) empirical loglikelihood ratio with an asymptotic chisquare distribution.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weights
A numeric vector of the rescaled weights used for the model fitting.
coefficients
A numeric vector of the maximum empirical likelihood estimates of the parameters.
method
A single character for the method dispatch in internal functions.
data
A numeric matrix of the data for the model fitting.
control
An object of class ControlEL constructed by
el_control()
.
showClass("GLM")
showClass("GLM")
S4 class for linear models with empirical likelihood. It inherits from CEL class.
The overall test involves a constrained optimization problem. All
the parameters except for the intercept are constrained to zero. The
optim
slot contains the results. When there is no intercept, all
parameters are set to zero, and the results need to be understood in terms
of EL class since no constrained optimization is involved.
Once the solution is found, the log probabilities (logp
) and the
(constrained) empirical likelihood values (logl
, loglr
, statistic
)
readily follow, along with the degrees of freedom (df
) and the
$p$
value (pval
). The significance tests for each parameter also
involve constrained optimization problems where only one parameter is
constrained to zero. The sigTests
slot contains the results.
sigTests
A list of the following results of significance tests:
statistic
A numeric vector of minus twice the (constrained) empirical
loglikelihood ratios with asymptotic chisquare distributions.
iterations
An integer vector for the number of iterations performed for
each parameter.
convergence
A logical vector for the convergence status of each
parameter.
call
A matched call.
terms
A terms
object used.
misc
A list of various outputs obtained from the model fitting process. They are used in other generics and methods.
optim
A list of the following optimization results:
par
A numeric vector of the solution to the (constrained) optimization
problem.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
logp
A numeric vector of the log probabilities of the (constrained) empirical likelihood.
logl
A single numeric of the (constrained) empirical loglikelihood.
loglr
A single numeric of the (constrained) empirical loglikelihood ratio.
statistic
A single numeric of minus twice the (constrained) empirical loglikelihood ratio with an asymptotic chisquare distribution.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weights
A numeric vector of the rescaled weights used for the model fitting.
coefficients
A numeric vector of the maximum empirical likelihood estimates of the parameters.
method
A single character for the method dispatch in internal functions.
data
A numeric matrix of the data for the model fitting.
control
An object of class ControlEL constructed by
el_control()
.
showClass("LM")
showClass("LM")
Extracts the empirical loglikelihood from a model.
## S4 method for signature 'EL' logL(object, ...) ## S4 method for signature 'ELT' logL(object, ...) ## S4 method for signature 'SummaryEL' logL(object, ...) ## S4 method for signature 'SummaryELT' logL(object, ...) ## S4 method for signature 'SummaryLM' logL(object, ...)
## S4 method for signature 'EL' logL(object, ...) ## S4 method for signature 'ELT' logL(object, ...) ## S4 method for signature 'SummaryEL' logL(object, ...) ## S4 method for signature 'SummaryELT' logL(object, ...) ## S4 method for signature 'SummaryLM' logL(object, ...)
object 
An object that contains the empirical loglikelihood. 
... 
Further arguments passed to methods. 
A single numeric.
Baggerly KA (1998). “Empirical Likelihood as a GoodnessofFit Measure.” Biometrika, 85(3), 535–547. doi:10.1093/biomet/85.3.535.
data("precip") fit < el_mean(precip, par = 40) logL(fit)
data("precip") fit < el_mean(precip, par = 40) logL(fit)
Extracts the empirical loglikelihood ratio from a model.
## S4 method for signature 'EL' logLR(object, ...) ## S4 method for signature 'ELT' logLR(object, ...) ## S4 method for signature 'SummaryEL' logLR(object, ...) ## S4 method for signature 'SummaryELT' logLR(object, ...) ## S4 method for signature 'SummaryLM' logLR(object, ...)
## S4 method for signature 'EL' logLR(object, ...) ## S4 method for signature 'ELT' logLR(object, ...) ## S4 method for signature 'SummaryEL' logLR(object, ...) ## S4 method for signature 'SummaryELT' logLR(object, ...) ## S4 method for signature 'SummaryLM' logLR(object, ...)
object 
An object that contains the empirical loglikelihood ratio. 
... 
Further arguments passed to methods. 
A single numeric.
Baggerly KA (1998). “Empirical Likelihood as a GoodnessofFit Measure.” Biometrika, 85(3), 535–547. doi:10.1093/biomet/85.3.535.
data("precip") fit < el_mean(precip, par = 40) logLR(fit)
data("precip") fit < el_mean(precip, par = 40) logLR(fit)
Extracts log probabilities of empirical likelihood from a model.
## S4 method for signature 'EL' logProb(object, ...) ## S4 method for signature 'ELT' logProb(object, ...)
## S4 method for signature 'EL' logProb(object, ...) ## S4 method for signature 'ELT' logProb(object, ...)
object 

... 
Further arguments passed to methods. 
A numeric vector.
data("precip") fit < el_mean(precip, par = 40) logProb(fit)
data("precip") fit < el_mean(precip, par = 40) logProb(fit)
Extracts the number of observations from a model.
## S4 method for signature 'EL' nobs(object, ...) ## S4 method for signature 'SummaryEL' nobs(object, ...) ## S4 method for signature 'SummaryLM' nobs(object, ...)
## S4 method for signature 'EL' nobs(object, ...) ## S4 method for signature 'SummaryEL' nobs(object, ...) ## S4 method for signature 'SummaryLM' nobs(object, ...)
object 
An object that contains the number of observations. 
... 
Further arguments passed to methods. 
A single integer.
data("precip") fit < el_mean(precip, par = 40) nobs(fit)
data("precip") fit < el_mean(precip, par = 40) nobs(fit)
Provides plot methods for objects.
## S4 method for signature 'ConfregEL' plot(x, y, ...) ## S4 method for signature 'EL' plot(x, y, ...) ## S4 method for signature 'ELD' plot(x, y, ...)
## S4 method for signature 'ConfregEL' plot(x, y, ...) ## S4 method for signature 'EL' plot(x, y, ...) ## S4 method for signature 'ELD' plot(x, y, ...)
x 
An object to be plotted. 
y 
Not used. 
... 
Further graphical parameters (see 
No return value, called for side effects.
plot(ConfregEL)
: Plots a twodimensional confidence region for model
parameters.
plot(EL)
: Plots empirical likelihood displacement values versus
observation index. eld()
is called implicitly.
plot(ELD)
: Plots empirical likelihood displacement values versus
observation index.
ConfregEL, EL, ELD,
confreg()
, eld()
## Model data("mtcars") fit < el_lm(hp ~ wt, data = mtcars) ## Confidence region out1 < confreg(fit, npoints = 500) plot(out1) ## Empirical likelihood displacement out2 < eld(fit) plot(out2) ## A shortcut to `ELD` plot(fit)
## Model data("mtcars") fit < el_lm(hp ~ wt, data = mtcars) ## Confidence region out1 < confreg(fit, npoints = 500) plot(out1) ## Empirical likelihood displacement out2 < eld(fit) plot(out2) ## A shortcut to `ELD` plot(fit)
Provides print methods for objects.
## S4 method for signature 'EL' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'ELMT' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'ELT' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'LM' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'SummaryEL' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'SummaryELMT' print( x, digits = max(3L, getOption("digits")  3L), signif.stars = getOption("show.signif.stars"), ... ) ## S4 method for signature 'SummaryELT' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'SummaryGLM' print( x, digits = max(3L, getOption("digits")  3L), signif.stars = getOption("show.signif.stars"), ... ) ## S4 method for signature 'SummaryLM' print( x, digits = max(3L, getOption("digits")  3L), signif.stars = getOption("show.signif.stars"), ... )
## S4 method for signature 'EL' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'ELMT' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'ELT' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'LM' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'SummaryEL' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'SummaryELMT' print( x, digits = max(3L, getOption("digits")  3L), signif.stars = getOption("show.signif.stars"), ... ) ## S4 method for signature 'SummaryELT' print(x, digits = max(3L, getOption("digits")  3L), ...) ## S4 method for signature 'SummaryGLM' print( x, digits = max(3L, getOption("digits")  3L), signif.stars = getOption("show.signif.stars"), ... ) ## S4 method for signature 'SummaryLM' print( x, digits = max(3L, getOption("digits")  3L), signif.stars = getOption("show.signif.stars"), ... )
x 
An object to be printed. 
... 
Further arguments passed to methods. 
digits 
A single integer for the number of significant digits to be
passed to 
signif.stars 
A single logical. If 
The argument x
(invisibly).
data("precip") fit < el_mean(precip, par = 40) print(fit)
data("precip") fit < el_mean(precip, par = 40) print(fit)
$p$
valueExtracts the $p$
value from a model.
## S4 method for signature 'EL' pVal(object, ...) ## S4 method for signature 'ELMT' pVal(object, ...) ## S4 method for signature 'ELT' pVal(object, ...) ## S4 method for signature 'SummaryEL' pVal(object, ...) ## S4 method for signature 'SummaryELT' pVal(object, ...) ## S4 method for signature 'SummaryELMT' pVal(object, ...) ## S4 method for signature 'SummaryLM' pVal(object, ...)
## S4 method for signature 'EL' pVal(object, ...) ## S4 method for signature 'ELMT' pVal(object, ...) ## S4 method for signature 'ELT' pVal(object, ...) ## S4 method for signature 'SummaryEL' pVal(object, ...) ## S4 method for signature 'SummaryELT' pVal(object, ...) ## S4 method for signature 'SummaryELMT' pVal(object, ...) ## S4 method for signature 'SummaryLM' pVal(object, ...)
object 
An object that contains the 
... 
Further arguments passed to methods. 
The form of the value returned by pVal()
depends on the class of
its argument.
pVal(EL)
: Extracts the $p$
value.
pVal(ELMT)
: Extracts the multiplicity adjusted $p$
values.
pVal(ELT)
: Extracts the $p$
value.
pVal(SummaryEL)
: Extracts the $p$
value.
pVal(SummaryELT)
: Extracts the $p$
value.
pVal(SummaryELMT)
: Extracts the multiplicity adjusted $p$
values.
pVal(SummaryLM)
: Extracts the $p$
value.
data("precip") fit < el_mean(precip, par = 40) pVal(fit)
data("precip") fit < el_mean(precip, par = 40) pVal(fit)
S4 class for generalized linear models with quasilikelihood methods. It inherits from GLM class.
The overall test involves a constrained optimization problem. All
the parameters except for the intercept are constrained to zero. The
optim
slot contains the results. When there is no intercept, all
parameters are set to zero, and the results need to be understood in terms
of EL class since no constrained optimization is involved.
Once the solution is found, the log probabilities (logp
) and the
(constrained) empirical likelihood values (logl
, loglr
, statistic
)
readily follow, along with the degrees of freedom (df
) and the
$p$
value (pval
). The significance tests for each parameter also
involve constrained optimization problems where only one parameter is
constrained to zero. The sigTests
slot contains the results.
family
A family
object used.
dispersion
A single numeric for the estimated dispersion parameter.
sigTests
A list of the following results of significance tests:
statistic
A numeric vector of minus twice the (constrained) empirical
loglikelihood ratios with asymptotic chisquare distributions.
iterations
An integer vector for the number of iterations performed for
each parameter.
convergence
A logical vector for the convergence status of each
parameter.
cstr
A single logical for whether constrained EL optimization is
performed or not.
call
A matched call.
terms
A terms
object used.
misc
A list of various outputs obtained from the model fitting process. They are used in other generics and methods.
optim
A list of the following optimization results:
par
A numeric vector of the solution to the (constrained) optimization
problem.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
logp
A numeric vector of the log probabilities of the (constrained) empirical likelihood.
logl
A single numeric of the (constrained) empirical loglikelihood.
loglr
A single numeric of the (constrained) empirical loglikelihood ratio.
statistic
A single numeric of minus twice the (constrained) empirical loglikelihood ratio with an asymptotic chisquare distribution.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weights
A numeric vector of the rescaled weights used for the model fitting.
coefficients
A numeric vector of the maximum empirical likelihood estimates of the parameters.
method
A single character for the method dispatch in internal functions.
data
A numeric matrix of the data for the model fitting.
control
An object of class ControlEL constructed by
el_control()
.
showClass("QGLM")
showClass("QGLM")
S4 class for standard deviation. It inherits from EL class.
optim
A list of the following optimization results:
par
A numeric vector of the specified parameters.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
cstr
A single logical for whether constrained EL optimization is
performed or not.
logp
A numeric vector of the log probabilities of the empirical likelihood.
logl
A single numeric of the empirical loglikelihood.
loglr
A single numeric of the empirical loglikelihood ratio.
statistic
A single numeric of minus twice the empirical loglikelihood ratio with an asymptotic chisquare distribution.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weights
A numeric vector of the rescaled weights used for the model fitting.
coefficients
A numeric vector of the maximum empirical likelihood estimates of the parameters.
method
A single character for the method dispatch in internal functions.
data
A numeric matrix of the data for the model fitting.
control
An object of class ControlEL constructed by
el_control()
.
showClass("SD")
showClass("SD")
Extracts the results of significance tests from a model.
## S4 method for signature 'LM' sigTests(object, ...)
## S4 method for signature 'LM' sigTests(object, ...)
object 
An object that inherits from LM. 
... 
Further arguments passed to methods. 
The form of the value returned by sigTests()
depends on the
class of its argument.
sigTests(LM)
: Extracts a list with the optimization results of
significance tests.
data("mtcars") fit < el_lm(mpg ~ ., data = mtcars) sigTests(fit)
data("mtcars") fit < el_lm(mpg ~ ., data = mtcars) sigTests(fit)
Provides summary methods for objects.
## S4 method for signature 'EL' summary(object, ...) ## S4 method for signature 'ELMT' summary(object, ...) ## S4 method for signature 'ELT' summary(object, ...) ## S4 method for signature 'GLM' summary(object, ...) ## S4 method for signature 'LM' summary(object, ...) ## S4 method for signature 'QGLM' summary(object, ...)
## S4 method for signature 'EL' summary(object, ...) ## S4 method for signature 'ELMT' summary(object, ...) ## S4 method for signature 'ELT' summary(object, ...) ## S4 method for signature 'GLM' summary(object, ...) ## S4 method for signature 'LM' summary(object, ...) ## S4 method for signature 'QGLM' summary(object, ...)
object 
An object for which a summary is desired. 
... 
Further arguments passed to methods. 
The form of the value returned by summary()
depends on the class of
its argument.
summary(EL)
: Summarizes the test results of the specified parameters.
summary(ELMT)
: Summarizes the multiple testing results.
summary(ELT)
: Summarizes the hypothesis test results.
summary(GLM)
: Summarizes the results of the overall model test and the
significance tests for coefficients. The dispersion parameter is extracted
for display.
summary(LM)
: Summarizes the results of the overall model test and the
significance tests for coefficients.
summary(QGLM)
: Summarizes the results of the overall model test and the
significance tests for coefficients. The estimated dispersion parameter is
extracted for display.
data("faithful") fit < el_mean(faithful, par = c(3.5, 70)) summary(fit) data("mtcars") fit2 < el_lm(mpg ~ wt, data = mtcars) summary(fit2)
data("faithful") fit < el_mean(faithful, par = c(3.5, 70)) summary(fit) data("mtcars") fit2 < el_lm(mpg ~ wt, data = mtcars) summary(fit2)
S4 class for a summary of EL objects.
optim
A list of the following optimization results:
par
A numeric vector of the specified parameters.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
cstr
A single logical for whether constrained EL optimization is
performed or not.
logl
A single numeric of the empirical loglikelihood.
loglr
A single numeric of the empirical loglikelihood ratio.
statistic
A single numeric of minus twice the empirical loglikelihood ratio with an asymptotic chisquare distribution.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weighted
A single logical for whether the data are weighted or not.
coefficients
A numeric vector of the maximum empirical likelihood estimates of the parameters.
method
A single character for the method dispatch in internal functions.
control
An object of class ControlEL constructed by
el_control()
.
showClass("SummaryEL")
showClass("SummaryEL")
S4 class for a summary of ELMT objects.
aliased
A named logical vector showing if the original coefficients are aliased.
showClass("SummaryELMT")
showClass("SummaryELMT")
S4 class for a summary of ELT objects.
optim
A list of the following optimization results:
par
A numeric vector of the solution to the (constrained) optimization
problem.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
cstr
A single logical for whether constrained EL optimization is
performed or not.
logl
A single numeric of the (constrained) empirical loglikelihood.
loglr
A single numeric of the (constrained) empirical loglikelihood ratio.
statistic
A single numeric of minus twice the (constrained) empirical loglikelihood ratio with an asymptotic chisquare distribution.
df
A single integer for the chisquare degrees of freedom of the statistic.
pval
A single numeric for the (calibrated) $p$
value of the
statistic.
cv
A single numeric for the critical value.
rhs
A numeric vector for the righthand side of the hypothesis.
lhs
A numeric matrix for the lefthand side of the hypothesis.
alpha
A single numeric for the significance level.
calibrate
A single character for the calibration method used.
control
An object of class ControlEL constructed by
el_control()
.
showClass("SummaryELT")
showClass("SummaryELT")
S4 class for a summary of GLM objects. It inherits from SummaryLM class.
family
A family
object used.
dispersion
A single numeric for the estimated dispersion parameter.
coefficients
A numeric matrix of the results of significance tests.
intercept
A single logical for whether the given model has an intercept term or not.
na.action
Information returned by model.frame
on the special
handling of NA
s.
call
A matched call.
terms
A terms
object used.
aliased
A named logical vector showing if the original coefficients are aliased.
optim
A list of the following optimization results:
par
A numeric vector of the solution to the (constrained) optimization
problem.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
cstr
A single logical for whether constrained EL optimization is
performed or not.
logl
A single numeric of the empirical loglikelihood.
loglr
A single numeric of the empirical loglikelihood ratio.
statistic
A single numeric of minus twice the (constrained) empirical loglikelihood ratio for the overall test.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weighted
A single logical for whether the data are weighted or not.
method
A single character for the method dispatch in internal functions.
control
An object of class ControlEL constructed by
el_control()
.
showClass("SummaryGLM")
showClass("SummaryGLM")
S4 class for a summary of LM objects.
coefficients
A numeric matrix of the results of significance tests.
intercept
A single logical for whether the given model has an intercept term or not.
na.action
Information returned by model.frame
on the special
handling of NA
s.
call
A matched call.
terms
A terms
object used.
aliased
A named logical vector showing if the original coefficients are aliased.
optim
A list of the following optimization results:
par
A numeric vector of the solution to the (constrained) optimization
problem.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
cstr
A single logical for whether constrained EL optimization is
performed or not.
logl
A single numeric of the empirical loglikelihood.
loglr
A single numeric of the empirical loglikelihood ratio.
statistic
A single numeric of minus twice the (constrained) empirical loglikelihood ratio for the overall test.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weighted
A single logical for whether the data are weighted or not.
method
A single character for the method dispatch in internal functions.
control
An object of class ControlEL constructed by
el_control()
.
showClass("SummaryLM")
showClass("SummaryLM")
S4 class for a summary of QGLM objects. It inherits from SummaryGLM class.
family
A family
object used.
dispersion
A single numeric for the estimated dispersion parameter.
coefficients
A numeric matrix of the results of significance tests.
intercept
A single logical for whether the given model has an intercept term or not.
na.action
Information returned by model.frame
on the special
handling of NA
s.
call
A matched call.
terms
A terms
object used.
aliased
A named logical vector showing if the original coefficients are aliased.
optim
A list of the following optimization results:
par
A numeric vector of the solution to the (constrained) optimization
problem.
lambda
A numeric vector of the Lagrange multipliers of the dual
problem corresponding to par
.
iterations
A single integer for the number of iterations performed.
convergence
A single logical for the convergence status.
cstr
A single logical for whether constrained EL optimization is
performed or not.
logl
A single numeric of the empirical loglikelihood.
loglr
A single numeric of the empirical loglikelihood ratio.
statistic
A single numeric of minus twice the (constrained) empirical loglikelihood ratio for the overall test.
df
A single integer for the degrees of freedom of the statistic.
pval
A single numeric for the $p$
value of the statistic.
nobs
A single integer for the number of observations.
npar
A single integer for the number of parameters.
weighted
A single logical for whether the data are weighted or not.
method
A single character for the method dispatch in internal functions.
control
An object of class ControlEL constructed by
el_control()
.
showClass("SummaryQGLM")
showClass("SummaryQGLM")
A dataset on the effect of the thiamethoxam application method and plant variety on bees.
data("thiamethoxam")
data("thiamethoxam")
A data frame with 165 observations and 11 variables:
Treatment.
Variety.
Replicate.
Average fruit number per plant.
Individual Fruit mass average (g).
Fruit mass per plant (g).
Yield (4 plants).
Bee visits per plot.
Proportion of foliage consumed by striped cucumber beetle.
Striped cucumber beetle per plant.
Defoliation percentage.
Obregon D, Pederson G, Taylor A, Poveda K (2022). “The Pest Control and Pollinator Protection Dilemma: The Case of Thiamethoxam Prophylactic Applications in Squash Crops.” PLOS ONE, 17(5), 1–18. doi:10.1371/journal.pone.0267984.
data("thiamethoxam") thiamethoxam
data("thiamethoxam") thiamethoxam
Extracts weights from model objects. The weights are rescaled to up to the total number of observations in the fitting procedure.
## S4 method for signature 'EL' weights(object, ...)
## S4 method for signature 'EL' weights(object, ...)
object 
An object that inherits from EL. 
... 
Further arguments passed to methods. 
A numeric vector of the rescaled weights.
Glenn N, Zhao Y (2007). “Weighted Empirical Likelihood Estimates and Their Robustness Properties.” Computational Statistics & Data Analysis, 51(10), 5130–5141. doi:10.1016/j.csda.2006.07.032.
data("airquality") x < airquality$Wind w < airquality$Day fit < el_mean(x, par = 10, weights = w) weights(fit)
data("airquality") x < airquality$Wind w < airquality$Day fit < el_mean(x, par = 10, weights = w) weights(fit)