Type: Package
Title: Regression Coefficients Estimation Using the Generalized Cross Entropy
Version: 0.1.0
Date: 2025-07-04
Description: Estimation and inference using the Generalized Maximum Entropy (GME) and Generalized Cross Entropy (GCE) framework, a flexible method for solving ill-posed inverse problems and parameter estimation under uncertainty (Golan, Judge, and Miller (1996, ISBN:978-0471145925) "Maximum Entropy Econometrics: Robust Estimation with Limited Data"). The package includes routines for generalized cross entropy estimation of linear models including the implementation of a GME-GCE two steps approach. Diagnostic tools, and options to incorporate prior information through support and prior distributions are available (Macedo, Cabral, Afreixo, Macedo and Angelelli (2025) <doi:10.1007/978-3-031-97589-9_21>). In particular, support spaces can be defined by the user or be internally computed based on the ridge trace or on the distribution of standardized regression coefficients. Different optimization methods for the objective function can be used. An adaptation of the normalized entropy aggregation (Macedo and Costa (2019) <doi:10.1007/978-3-030-26036-1_2> "Normalized entropy aggregation for inhomogeneous large-scale data") and a two-stage maximum entropy approach for time series regression (Macedo (2022) <doi:10.1080/03610918.2022.2057540>) are also available. Suitable for applications in econometrics, health, signal processing, and other fields requiring robust estimation under data constraints.
License: GPL-3
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.3.2
Depends: R (≥ 3.5.0), zoo
Imports: downlit, data.table, rlang, lbfgs, lbfgsb3c, meboot, optimParallel, optimx, rstudioapi, stats, clusterGeneration, simstudy, pracma, pathviewr, Rsolnp, bayestestR, ggplot2, ggpubr, ggdist, latex2exp, plotly, viridis, hdrcde, shiny, miniUI, shinyWidgets, shinydashboardPlus, readxl, DT, magrittr
Suggests: knitr, rmarkdown, kableExtra
VignetteBuilder: knitr
URL: https://github.com/jorgevazcabral/GCEstim
BugReports: https://github.com/jorgevazcabral/GCEstim/issues
Config/spelling: wordlist: inst/WORDLIST
NeedsCompilation: no
Packaged: 2025-07-13 08:11:23 UTC; jorge
Author: Cabral Jorge ORCID iD [aut, cre], Macedo Pedro [ths], Afreixo Vera [ths]
Maintainer: Cabral Jorge <jorgecabral@ua.pt>
Repository: CRAN
Date/Publication: 2025-07-16 17:00:02 UTC

Entropy Ratio test

Description

The Entropy Ratio test - which corresponds to the likelihood ratio, or empirical ratio, test - measures the entropy discrepancy between the constrained and the unconstrained models.

Usage

ER.test(object)

Arguments

object

fitted lmgce object.

Value

A matrix with the X-squared statistics, degrees of freedom and p-value for each parameter.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)


ER.test(res_gce_package)

Normalized Entropy

Description

Returns the normalized entropy of the model or the normalized entropy of the predictors.

Usage

NormEnt(object, model = TRUE, parm)

Arguments

object

fitted lmgce or tsbootgce object.

model

Boolean value. if model = TRUE, the model's normalized entropy is returned. If model = FALSE the normalized entropy of each estimate is returned. The default is model = TRUE.

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.

Value

the value of the normalized entropy of the model or parameters.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)


NormEnt(res_gce_package)

Accuracy measures

Description

Function that allows to calculate different types of errors for point predictions:

  1. MAE - Mean Absolute Error,

  2. MAD - Mean Absolute Deviation,

  3. MSE - Mean Squared Error,

  4. RMSE - Root Mean Squared Error,

  5. MAPE - Mean Absolute Percentage Error,

  6. sMAPE - symmetric Mean Absolute Percentage Error,

  7. MASE - Mean Absolute Scaled Error (Hyndman & Koehler, 2006)

Usage

accmeasure(
  y_pred,
  y_true,
  which = c("RMSE", "MSE", "MAPE", "sMAPE", "MAE", "MAD", "MASE")
)

Arguments

y_pred

fitted values.

y_true

observed values.

which

one of c("RMSE", "MAPE", "sMAPE", "MAE", "MAD", "MASE")

Value

The value of the chosen error is returned.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

References

Hyndman, R. J., & Koehler, A. B. (2006) Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688. doi:10.1016/j.ijforecast.2006.03.001

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)


accmeasure(fitted(res_gce_package), dataGCE$y, which = "MSE")

Case Names of lmgce Fitted Models

Description

Simple utility returning case names.

Usage

## S3 method for class 'lmgce'
case.names(object, ...)

Arguments

object

Fitted lmgce model object.

...

Additional arguments (not used).

Value

A character vector containing the names or labels of the cases (observations) in the lmgce model object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

case.names(res_gce_package)

Change the step from lmgce object

Description

Changes the number of GCE reestimations of a lmgce object

Usage

changestep(object, twosteps.n, verbose = 0)

Arguments

object

fitted lmgce object.

twosteps.n

An integer that defines the number of GCE reestimations to be used.

verbose

An integer to control how verbose the output is. For a value of 0 no messages or output are shown and for a value of 3 all messages are shown. The default is verbose = 0.

Value

An lmgce object with the specified number of GCE reestimations

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        twosteps.n = 10,
        seed = 230676)

res_gce_package_change_step <- changestep(res_gce_package, 5)

summary(res_gce_package)

summary(res_gce_package_change_step)

Change the support from lmgce object

Description

Changes the support spaces of a lmgce object

Usage

changesupport(object, support, verbose = 0)

Arguments

object

fitted lmgce object.

support

One of c("min", "1se", "elbow") or a chosen support from object$support.ok.

verbose

An integer to control how verbose the output is. For a value of 0 no messages or output are shown and for a value of 3 all messages are shown. The default is verbose = 0.

Value

An lmgce object with the specified support spaces

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

res_gce_package_change <- changesupport(res_gce_package, "min")

summary(res_gce_package)

summary(res_gce_package_change)

Extract cv.lmgce Coefficients

Description

Extract coefficients from a cv.lmgce object

Usage

## S3 method for class 'cv.lmgce'
coef(object, ...)

Arguments

object

Fitted cv.lmgce model object.

...

Additional arguments (not used).

Value

Returns the coefficients from a cv.lmgce object. The coefficients are obtained from the lmgce object with best performance. These coefficients are stored in object$best$coefficients.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res.cv.lmgce <-
  cv.lmgce(y ~ .,
           data = dataGCE)

coef(res.cv.lmgce)

Extract lmgce Model Coefficients

Description

Extract coefficients from a lmgce object

Usage

## S3 method for class 'lmgce'
coef(object, ...)

Arguments

object

Fitted lmgce model object.

...

Additional arguments (not used).

Value

Returns the coefficients from a lmgce object

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

coef(res_gce_package)

Extract neagging Coefficients

Description

Extract coefficients from a neagging object

Usage

## S3 method for class 'neagging'
coef(object, which = which.min(object$error)[[1]], ...)

Arguments

object

Fitted neagging model object.

which

Number of aggregated models. The coefficients returned are by default the ones that produced the lowest in sample error.

...

Additional arguments.

Value

Returns the coefficients from a neagging object

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

res_neagging <- neagging(res_gce_package)
coef(res_neagging)
coef(res_neagging, which = ncol(res_neagging$matrix))

Extract ridgetrace Model Coefficients

Description

Extract coefficients from a ridgetrace object

Usage

## S3 method for class 'ridgetrace'
coef(object, which = "min.error", ...)

Arguments

object

Fitted ridgetrace model object.

which

One of c("min.error", "max.abs"). If which = "min.error", the default, the coefficients that produced the lowest error cross-validation error (cv = TRUE),or in sample error are returned (cv = FALSE). If which = "max.abs" then the maximum absolute coefficients are returned.

...

Additional arguments (not used).

Value

Returns the coefficients from a ridgetrace object

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples

res.ridgetrace <-
  ridgetrace(
    formula = y ~ X001 + X002 + X003 + X004 + X005,
    data = dataGCE)

coef(res.ridgetrace)

Extract tsbootgce Model Coefficients

Description

Extract coefficients from a tsbootgce object

Usage

## S3 method for class 'tsbootgce'
coef(object, which = NULL, seed = object$seed, ...)

Arguments

object

Fitted tsbootgce model object.

which

The default is which = NULL and returns the coefficients defined in the argument coef.method from the tsbootgce object. Can be set as "mode" or "median" and the mode and median coefficients will be computed, respectively (see hdr).

seed

A single value, interpreted as an integer, for reproducibility or NULL for randomness. The default is seed = object$seed.

...

Additional arguments.

Value

Returns the coefficients from a tsbootgce object

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res.tsbootgce <-
  tsbootgce(
    formula = CO2 ~ 1 + L(GDP, 1) + L(EPC, 1) + L(EU, 1),
    data = moz_ts)

coef(res.tsbootgce)

Extract cv.lmgce Coefficients

Description

Extract coefficients from a cv.lmgce object

Usage

## S3 method for class 'cv.lmgce'
coefficients(object, ...)

Arguments

object

Fitted cv.lmgce model object.

...

Additional arguments (not used).

Value

Returns the coefficients from a cv.lmgce object. The coefficients are obtained from the lmgce object with best performance. These coefficients are stored in object$best$coefficients.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res.cv.lmgce <-
  cv.lmgce(y ~ .,
           data = dataGCE)

coefficients(res.cv.lmgce)

Extract lmgce Model Coefficients

Description

Extract coefficients from a lmgce object

Usage

## S3 method for class 'lmgce'
coefficients(object, ...)

Arguments

object

Fitted lmgce model object.

...

Additional arguments (not used).

Value

Returns the coefficients from a lmgce object

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        seed = 230676)

coefficients(res_gce_package)

Extract neagging Coefficients

Description

Extract coefficients from a neagging object

Usage

## S3 method for class 'neagging'
coefficients(object, which = which.min(object$error)[[1]], ...)

Arguments

object

Fitted neagging model object.

which

Number of aggregated models. The coefficients returned are by default the ones that produced the lowest in sample error.

...

Additional arguments.

Value

Returns the coefficients from a neagging object

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

res_neagging <- neagging(res_gce_package)
coefficients(res_neagging)
coefficients(res_neagging, which = ncol(res_neagging$matrix))

Extract ridgetrace Model Coefficients

Description

Extract coefficients from a ridgetrace object

Usage

## S3 method for class 'ridgetrace'
coefficients(object, which = "min.error", ...)

Arguments

object

Fitted ridgetrace model object.

which

One of c("min.error", "max.abs"). If which = "min.error", the default, the coefficients that produced the lowest error cross-validation error (cv = TRUE),or in sample error are returned (cv = FALSE). If which = "max.abs" then the maximum absolute coefficients are returned.

...

Additional arguments.

Value

Returns the coefficients from a ridgetrace object

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples

res.ridgetrace <-
  ridgetrace(
    formula = y ~ X001 + X002 + X003 + X004 + X005,
    data = dataGCE)

coefficients(res.ridgetrace)

Extract tsbootgce Model Coefficients

Description

Extract coefficients from a tsbootgce object

Usage

## S3 method for class 'tsbootgce'
coefficients(object, which = NULL, seed = object$seed, ...)

Arguments

object

Fitted tsbootgce model object.

which

The default is which = NULL and returns the coefficients defined in the argument coef.method from the tsbootgce object. Can be set as "mode" or "median" and the mode and median coefficients will be computed, respectively (see hdr).

seed

A single value, interpreted as an integer, for reproducibility or NULL for randomness. The default is seed = object$seed.

...

Additional arguments.

Value

Returns the coefficients from a tsbootgce object

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res.tsbootgce <-
  tsbootgce(
    formula = CO2 ~ 1 + L(GDP, 1) + L(EPC, 1) + L(EU, 1),
    data = moz_ts)

coefficients(res.tsbootgce)

Confidence Intervals for lmgce Model Parameters and Normalized Entropy

Description

Computes confidence intervals for one or more parameters or Normalized Entropy in a lmgce fitted model.

Usage

## S3 method for class 'lmgce'
confint(
  object,
  parm,
  level = 0.95,
  which = c("estimates", "NormEnt"),
  method = {
     if (which == "estimates") {
         c("z", "percentile", "basic")
    
    }
     else {
         c("percentile", "basic")
     }
 },
  boot.B = ifelse(object$boot.B == 0, 100, object$boot.B),
  boot.method = object$boot.method,
  ...
)

Arguments

object

Fitted lmgce model 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

the confidence level required. The default is level = 0.95.

which

One of c("estimates", "NormEnt"). The default is which = "estimates".

method

method used to compute the interval. One of c("z","percentile", "basic"). The default is method = "z" and is only valid for the parameters.

boot.B

A single positive integer greater or equal to 10 for the number of bootstrap replicates for the computation of the bootstrap confidence interval(s), to be used when method = c("percentile", "basic") and when object was created with boot.B = 0. The default is boot.B = 100 when the object has no previous sampling information and boot.B = object$boot.B otherwise, which corresponds to the boot.B given to lmgce when the object was created.

boot.method

Method used for bootstrapping. One of c("residuals", "cases", "wild") which corresponds to resampling on residuals, on individual cases or on residuals multiplied by a N(0,1) variable, respectively. The default is boot.method = object$boot.method.

...

additional arguments.

Value

A matrix (or vector) with columns giving lower and upper confidence limits for each parameter. These will be labelled as (1-level)/2 and 1 - (1-level)/2 in percentage (by default 2.5 percent and 97.5 percent).

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)


confint(res_gce_package, method = "percentile")

confint(res_gce_package, which = "NormEnt", level = 0.99)

confint(res_gce_package, parm = c("X005"), level = 0.99)

Confidence Intervals for tsbootgce Model Parameters and Normalized Entropy

Description

Computes confidence intervals for one or more parameters or Normalized Entropy in a tsbootgce fitted model.

Usage

## S3 method for class 'tsbootgce'
confint(
  object,
  parm,
  level = 0.95,
  which = c("estimates", "NormEnt"),
  method = c("hdr", "percentile", "basic"),
  seed = object$seed,
  ...
)

Arguments

object

Fitted tsbootgce model 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

the confidence level required. The default is level = 0.95.

which

One of c("estimates", "NormEnt"). The default is which = "estimates".

method

method used to compute the interval. One of c("hdr", "percentile", "basic"). The default is method = "hdr" (see hdr).

seed

A single value, interpreted as an integer, for reproducibility or NULL for randomness. The default is seed = object$seed.

...

additional arguments.

Value

A matrix (or vector) with columns giving lower and upper confidence limits for each parameter. Generally, these will be labelled as (1-level)/2 and 1 - (1-level)/2 in percentage (by default 2.5 percent and 97.5 percent).

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res.tsbootgce <-
  tsbootgce(
    formula = CO2 ~ 1 + L(GDP, 1) + L(EPC, 1) + L(EU, 1),
    data = moz_ts)

confint(res.tsbootgce, method = "percentile")

confint(res.tsbootgce, which = "NormEnt", level = 0.99)

confint(res.tsbootgce, parm = c("L(GDP, 1)"), level = 0.99)

Cross-validation for lmgce

Description

Performs k-fold cross-validation for some of the lmgce parameters.

Usage

cv.lmgce(
  formula,
  data,
  subset,
  na.action,
  offset,
  contrasts = NULL,
  model = TRUE,
  x = FALSE,
  y = FALSE,
  cv = TRUE,
  cv.nfolds = 5,
  errormeasure = c("RMSE", "MSE", "MAE", "MAPE", "sMAPE", "MASE"),
  errormeasure.which = {
     if (isTRUE(cv)) 
         c("1se", "min", "elbow")
    
    else c("min", "elbow")
 },
  support.method = c("standardized", "ridge"),
  support.method.penalize.intercept = TRUE,
  support.signal = NULL,
  support.signal.vector = NULL,
  support.signal.vector.min = 0.3,
  support.signal.vector.max = 20,
  support.signal.vector.n = 20,
  support.signal.points = c(3, 5, 7, 9),
  support.noise = NULL,
  support.noise.points = c(3, 5, 7, 9),
  weight = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9),
  twosteps.n = 1,
  method = c("dual.lbfgsb3c", "dual.BFGS", "dual", "primal.solnl", "primal.solnp",
    "dual.CG", "dual.L-BFGS-B", "dual.Rcgmin", "dual.bobyqa", "dual.newuoa",
    "dual.nlminb", "dual.nlm", "dual.lbfgs", "dual.optimParallel"),
  caseGLM = c("D", "M", "NM"),
  boot.B = 0,
  boot.method = c("residuals", "cases", "wild"),
  seed = 230676,
  OLS = TRUE,
  verbose = 0,
  coef = NULL
)

Arguments

formula

An object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

A data frame (or object coercible by as.data.frame to a data frame) containing the variables in the model.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector or matrix of extents matching those of the response. One or more offset terms can be included in the formula instead or as well, and if more than one are specified their sum is used. See model.offset.

contrasts

An optional list. See the contrasts.arg of model.matrix.default.

model

Boolean value. if TRUE, the model frame used is returned. The default is model = TRUE.

x

Boolean value. if TRUE, the model matrix used is returned. The default is x = FALSE.

y

Boolean value. if TRUE, the response used is returned. The default is y = FALSE.

cv

Boolean value. If TRUE the error, errormeasure, will be computed using cross-validation. If FALSE the error will be computed in sample. The default is cv = TRUE.

cv.nfolds

number of folds used for cross-validation when cv = TRUE. The default is cv.nfolds = 5 and the smallest value allowable is cv.nfolds = 3.

errormeasure

Loss function (error) to be used for the selection of the support spaces. One of c("RMSE","MSE", "MAE", "MAPE", "sMAPE", "MASE"). The default is errormeasure = "RMSE".

errormeasure.which

Which value of errormeasure to be used for selecting a support space upper limit from support.signal.vector. One of c("min", "1se", "elbow") where "min" corresponds to the support spaces that produced the lowest error, "1se" corresponds to the support spaces such that error is within 1 standard error of the CV error for "min" and "elbow" corresponds to the elbow point of the error curve (the point that maximizes the distance between each observation, i.e, the pair composed by the upper limit of the support space and the error, and the line between the first and last observations, i.e., the lowest and the highest upper limits of the support space respectively. See find_curve_elbow). The default is errormeasure.which = "1se".

support.method

One of c("standardized", "ridge"). If support.method = "standardized}, the default, standardized coefficients are used to define the signal support spaces. If \code{support.method = "ridge the signal support spaces are define by the ridge trace.

support.method.penalize.intercept

Boolean value. if TRUE, the default, the intercept will be penalized. To be used when support.method = "ridge".

support.signal

NULL or fixed positive upper limit (L) for the support spaces (-L,L) on standardized data (when support.method = "standardized"); NULL or fixed positive factor to be multiplied by the maximum absolute value of the ridge trace for each coefficient (when support.method = "ridge"); a pair (LL,UL) or a matrix ((k+1) x 2) for the support spaces on original data. The default is support.signal = NULL.

support.signal.vector

NULL or a vector of positive values when support.signal = NULL. If support.signal.vector = NULL, the default, a vector c(support.signal.vector.min,...,support.signal.vector.max) of dimension support.signal.vector.n and logarithmically equally spaced will be generated. Each value represents the upper limits for the standardized support spaces, when support.method = "standardized" or the factor to be multiplied by the maximum absolute value of the ridge trace for each coefficient, when support.method = "ridge".

support.signal.vector.min

A positive value for the lowest limit of the support.signal.vector when support.signal = NULL and support.signal.vector = NULL. The default is support.signal.vector.min = 0.3.

support.signal.vector.max

A positive value for the highest limit of the support.signal.vector when support.signal = NULL and support.signal.vector = NULL. The default is support.signal.vector.max = 20.

support.signal.vector.n

A positive integer for the number of support spaces to be used when support.signal = NULL and support.signal.vector = NULL. The default is support.signal.vector.n = 20.

support.signal.points

A vector of positive integers defining the number of points for the signal support to be tested .The default is support.signal.points = c(3, 5, 7, 9).

support.noise

An interval, preferably centered around zero, given in the form c(LL,UL). If support.noise = NULL, the default, then a vector c(-L,L) is computed using the empirical three-sigma rule Pukelsheim (1994).

support.noise.points

A vector of positive integers defining the number of points for the noise support to be tested .The default is support.noise.points = c(3, 5, 7, 9).

weight

a vector of values between zero and one representing the prediction-precision loss trade-off. The default is weight = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9).

twosteps.n

Number of GCE reestimations using a previously estimated vector of signal probabilities.

method

Use "primal.solnl" (GCE using Sequential Quadratic Programming (SQP) method; see solnl) or "primal.solnp" (GCE using the augmented Lagrange multiplier method with an SQP interior algorithm; see solnp) for primal form of the optimization problem and "dual" (GME), "dual.CG" (GCE using a conjugate gradients method; see optim), "dual.BFGS" (GCE using Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method; see optim), "dual.L-BFGS-B" (GCE using a box-constrained optimization with limited-memory modification of the BFGS quasi-Newton method; see optim), dual.Rcgmin (GCE using an update of the conjugate gradient algorithm; see optimx), dual.bobyqa (GCE using a derivative-free optimization by quadratic approximation; see optimx and bobyqa), dual.newuoa (GCE using a derivative-free optimization by quadratic approximation; see optimx and newuoa), dual.nlminb (GCE; see optimx and nlminb), dual.nlm (GCE; see optimx and nlm), dual.lbfgs (GCE using the Limited-memory Broyden-Fletcher-Goldfarb-Shanno; see lbfgs), dual.lbfgsb3c (GCE using L-BFSC-B implemented in Fortran code and with an Rcpp interface; see lbfgsb3c) or dual.optimParallel (GCE using parallel version of the L-BFGS-B; see optimParallel) for dual form. The default is method = "dual.BFGS".

caseGLM

special cases of the generic general linear model. One of c("D", "M", "NM"), where "D" stands for data, "M" for moment and "NM" for normed-moment The default is caseGLM = "D".

boot.B

A single positive integer greater or equal to 10 for the number of bootstrap replicates to be used for the computation of the bootstrap confidence interval(s). Zero value will generate no replicate. The default is boot.B = 0.

boot.method

Method to be use for bootstrapping. One of c("residuals", "cases", "wild") which corresponds to resampling on residuals, on individual cases or on residuals multiplied by a N(0,1) variable, respectively. The default is boot.method = "residuals".

seed

A single value, interpreted as an integer, for reproducibility or NULL for randomness. The default is seed = 230676.

OLS

Boolean value. if TRUE, the default, OLS estimation is performed.

verbose

An integer to control how verbose the output is. For a value of 0 no messages or output are shown and for a value of 3 all messages are shown. The default is verbose = 0.

coef

A vector of the true coefficients, when available.

Details

The cv.lmgce function fits several linear regression models via generalized cross according to the defined arguments. In particular, support.signal.points, support.noise.points and weight can be defined as vectors.

Value

cv.lmgce returns an object of class cv.lmgce.

An object of class cv.lmgce is a list containing at least the following components:

results

a C \times 8 data.frame, where C is the number of combinations of the arguments support.signal.points, support.noise.points and weight. Contains information about the arguments, error, convergence of the optimization method and time of computation.

best

a lmgce object obtained with the combination of arguments that produced the lowest cross-validation error.

support.signal.points

a vector of the support.signal.points tested.

support.signal.points.best

the value of support.signal.points that produced the lowest cross-validation error.

support.noise.points

a vector of the support.noise.points tested.

support.noise.points.best

the value of support.noise.points that produced the lowest cross-validation error.

weight

a vector of the weight tested.

weight.best

the value of weight that produced the lowest cross-validation error.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

References

Golan, A., Judge, G. G. and Miller, D. (1996) Maximum entropy econometrics : robust estimation with limited data. Wiley.
Golan, A. (2008). Information and Entropy Econometrics — A Review and Synthesis. Foundations and Trends® in Econometrics, 2(1–2), 1–145. doi:10.1561/0800000004
Golan, A. (2017) Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information (Vol. 1). Oxford University Press. doi:10.1093/oso/9780199349524.001.0001
Pukelsheim, F. (1994) The Three Sigma Rule. The American Statistician, 48(2), 88–91. doi:10.2307/2684253

See Also

See the generic functions plot.cv.lmgce, print.cv.lmgce and coef.cv.lmgce.

Examples


res.cv.lmgce <-
  cv.lmgce(y ~ .,
           data = dataGCE)

res.cv.lmgce

Simulated data set generated with fngendata

Description

Simulated data, used to demonstrate the functions of GCEstim. The seed used is the different from the one used to generate dataGCE.test but the remaining parameters are the same.

Usage

dataGCE

Format

A data.frame containing:

X001

A N(0,1) independent variable.

X002

A N(0,1) independent variable.

X003

A N(0,1) independent variable.

X004

A N(0,1) independent variable.

X005

A N(0,1) independent variable.

y

A Dependent variable: y = 1 + 3 * X003 + 6 * X004 + 9 * X005 + error; the error follows a normal distribution with mean equal to zero and variance such that the signal to noise ratio is equal to 5.

Examples


data(dataGCE)

plot(dataGCE)

Simulated data set generated with fngendata

Description

Simulated data, used to demonstrate the functions of GCEstim. The seed used is the different from the one used to generate dataGCE but the remaining parameters are the same.

Usage

dataGCE.test

Format

A data.frame containing:

X001

A N(0,1) independent variable.

X002

A N(0,1) independent variable.

X003

A N(0,1) independent variable.

X004

A N(0,1) independent variable.

X005

A N(0,1) independent variable.

y

A Dependent variable: y = 1 + 3 * X003 + 6 * X004 + 9 * X005 + error; the error follows a normal distribution with mean equal to zero and variance such that the signal to noise ratio is equal to 5.

Examples


data(dataGCE.test)

plot(dataGCE.test)

Simulated data set generated with fngendata

Description

Simulated data, used to demonstrate the functions of GCEstim.

Usage

dataincRidGME

Format

A data.frame containing:

X001

A N(0,1) independent variable.

X002

A N(0,1) independent variable.

X003

A N(0,1) independent variable.

X004

A N(0,1) independent variable.

X005

A N(0,1) independent variable.

X006

A N(0,1) independent variable.

y

A Dependent variable: y = 2.5 - 8 * X004 + 19 * X005 - 13 * X006 + error; the error follows a normal distribution with mean equal to zero and variance such that the signal to noise ratio is equal to 1.

Examples


data(dataincRidGME)

plot(dataincRidGME)

Simulated data set generated with fngendata

Description

Simulated data, used to demonstrate the functions of GCEstim.

Usage

dataincRidGME.test

Format

A data.frame containing:

X001

A N(0,1) independent variable.

X002

A N(0,1) independent variable.

X003

A N(0,1) independent variable.

X004

A N(0,1) independent variable.

X005

A N(0,1) independent variable.

X006

A N(0,1) independent variable.

y

A Dependent variable: y = 2.5 - 8 * X004 + 19 * X005 - 13 * X006 + error; the error follows a normal distribution with mean equal to zero and variance such that the signal to noise ratio is equal to 1.

Examples


data(dataincRidGME.test)

plot(dataincRidGME.test)

Residual Degrees-of-Freedom

Description

Returns the residual degrees-of-freedom extracted from a fitted model lmgce object.

Usage

## S3 method for class 'lmgce'
df.residual(object, ...)

Arguments

object

Fitted lmgce model object.

...

additional arguments.

Value

The value of the residual degrees-of-freedom extracted from a lmgce object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

df.residual(res_gce_package)

Calculate lmgce Fitted Values

Description

The fitted values for the linear model represented by a lmgce object are extracted.

Usage

## S3 method for class 'lmgce'
fitted(object, ...)

Arguments

object

Fitted lmgce model object.

...

additional arguments.

Value

Returns a vector with the fitted values for the linear model represented by a lmgce object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

fitted(res_gce_package)

Calculate lmgce Fitted Values

Description

The fitted values for the linear model represented by a lmgce object are extracted.

Usage

## S3 method for class 'lmgce'
fitted.values(object, ...)

Arguments

object

Fitted lmgce model object.

...

additional arguments.

Value

Returns a vector with the fitted values for the linear model represented by a lmgce object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

fitted.values(res_gce_package)

Data generating function

Description

Generates data

Usage

fngendata(
  n,
  bin.k = 0,
  bin.prob = NULL,
  cont.k = 5,
  y.gen.bin.k = 0,
  y.gen.bin.beta = NULL,
  y.gen.bin.prob = NULL,
  y.gen.cont.beta = c(2, 4, 6, 8, 10),
  y.gen.cont.mod.k = 0,
  y.gen.cont.mod.beta = matrix(c(-2, 2), 1, 2, byrow = TRUE),
  y.gen.bin.mod.prob = c(0.5),
  y.gen.cont.sp.k = 0,
  y.gen.cont.sp.groups = 2,
  y.gen.cont.sp.rho = 0.2,
  y.gen.cont.sp.dif = 1,
  intercept.beta = 0,
  Xgenerator.method = "simstudy",
  corMatrix = 100,
  rho = NULL,
  corstr = NULL,
  condnumber = 1,
  mu = 0,
  muvect = NULL,
  sd = 1,
  sdvect = NULL,
  error.dist = "normal",
  error.dist.mean = 0,
  error.dist.sd = 1,
  error.dist.snr = NULL,
  error.dist.df = 2,
  dataframe = TRUE,
  seed = NULL
)

Arguments

n

Number of individuals.

bin.k

Number of binary variables not used for generating y.

bin.prob

A vector of probabilities with length equal to bin.k.

cont.k

Number of continuous variables not used for generating y.

y.gen.bin.k

Number of binary variables used for generating y.

y.gen.bin.beta

A vector of coefficients with length equal to bin.k used to generate y.

y.gen.bin.prob

A vector of probabilities with length equal to y.gen.bin.k.

y.gen.cont.beta

A vector of coefficients with length equal to cont.k used to generate y.

y.gen.cont.mod.k

Experimental

y.gen.cont.mod.beta

Experimental

y.gen.bin.mod.prob

Experimental

y.gen.cont.sp.k

Experimental

y.gen.cont.sp.groups

Experimental

y.gen.cont.sp.rho

Experimental

y.gen.cont.sp.dif

Experimental

intercept.beta

Value for the constant used to generate y.

Xgenerator.method

Method used to generate X data ( "simstudy" or "svd").

corMatrix

A positive number for alphad (see rcorrmatrix), NULL or a correlation matrix to be used when Xgenerator is "simstudy".

rho

Correlation coefficient, -1 <= rho <= 1. Use when Xgenerator is "simstudy" and corMatrix is NULL.

corstr

correlation structure ("ind", "cs" or "ar1") (see genCorData) to be used when Xgenerator is "simstudy" and corMatrix is NULL.

condnumber

A value for the condition number of the X matrix to be used when Xgenerator is "svd".

mu

The mean of the variables. To be used when all variables have the same mean.

muvect

A vector of means. To be used when variables have different means. The length of muvect must be k.

sd

Standard deviation of the variables. To be used when all variables have the same standard deviation.

sdvect

A vector of standard deviations. To be used when variables have different standard deviations. The length of sdvect must be k.

error.dist

Distribution of the error. "normal" for normal distribution or "t" for t-student distribution.

error.dist.mean

Mean value used when error.dist is "normal".

error.dist.sd

Standard deviation value used when error.dist is "normal".

error.dist.snr

Signal to noise ratio. If not NULL, the value of error.dist.sd will be ignored and it will be determined accordingly.

error.dist.df

Degrees of freedom used when error.dist is "t".

dataframe

Logical. If TRUE, the default, returns a data.frame else returns a list.

seed

A seed for reproducibility.

Value

A data.frame or a list composed of a matrix of independent variables values (X), a vector of the dependent variable values (y), a vector of coefficient values (coefficients), a vector of non-zero coefficients (y.coefficients), and a vector of the error values (epsilon).

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


dataGCEstim <- fngendata(
  n = 100, cont.k = 2,
  y.gen.cont.beta = c(3, 6, 9),
  intercept.beta = 1,
  Xgenerator.method = "svd", condnumber = 50,
  mu = 0, sd = 1,
  error.dist = "normal", error.dist.mean = 0, error.dist.snr = 5,
  dataframe = TRUE, seed = 230676)

summary(dataGCEstim)

Extract Model Formula from lmgce object

Description

Returns the model used to fit lmgce object.

Usage

## S3 method for class 'lmgce'
formula(x, ...)

Arguments

x

fitted lmgce object.

...

additional arguments.

Value

An object of class formula representing the model formula.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

formula(res_gce_package)

Generalized Cross entropy estimation

Description

This generic function fits a linear regression model via generalized cross entropy. Initial support spaces can be provided or computed.

Usage

lmgce(
  formula,
  data,
  subset,
  na.action,
  offset,
  contrasts = NULL,
  model = TRUE,
  x = FALSE,
  y = FALSE,
  cv = TRUE,
  cv.nfolds = 5,
  errormeasure = c("RMSE", "MSE", "MAE", "MAPE", "sMAPE", "MASE"),
  errormeasure.which = {
     if (isTRUE(cv)) 
         c("1se", "min", "elbow")
    
    else c("min", "elbow")
 },
  support.method = c("standardized", "ridge"),
  support.method.penalize.intercept = TRUE,
  support.signal = NULL,
  support.signal.vector = NULL,
  support.signal.vector.min = 0.3,
  support.signal.vector.max = 20,
  support.signal.vector.n = 20,
  support.signal.points = c(1/5, 1/5, 1/5, 1/5, 1/5),
  support.noise = NULL,
  support.noise.points = c(1/3, 1/3, 1/3),
  weight = 0.5,
  twosteps.n = 1,
  method = c("dual.BFGS", "dual.lbfgsb3c", "dual", "primal.solnl", "primal.solnp",
    "dual.CG", "dual.L-BFGS-B", "dual.Rcgmin", "dual.bobyqa", "dual.newuoa",
    "dual.nlminb", "dual.nlm", "dual.lbfgs", "dual.optimParallel"),
  caseGLM = c("D", "M", "NM"),
  boot.B = 0,
  boot.method = c("residuals", "cases", "wild"),
  seed = 230676,
  OLS = TRUE,
  verbose = 0
)

Arguments

formula

An object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

A data frame (or object coercible by as.data.frame to a data frame) containing the variables in the model.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector or matrix of extents matching those of the response. One or more offset terms can be included in the formula instead or as well, and if more than one are specified their sum is used. See model.offset.

contrasts

An optional list. See the contrasts.arg of model.matrix.default.

model

Boolean value. if TRUE, the model frame used is returned. The default is model = TRUE.

x

Boolean value. if TRUE, the model matrix used is returned. The default is x = FALSE.

y

Boolean value. if TRUE, the response used is returned. The default is y = FALSE.

cv

Boolean value. If TRUE the error, errormeasure, will be computed using cross-validation. If FALSE the error will be computed in sample. The default is cv = TRUE.

cv.nfolds

number of folds used for cross-validation when cv = TRUE. The default is cv.nfolds = 5 and the smallest value allowable is cv.nfolds = 3.

errormeasure

Loss function (error) to be used for the selection of the support spaces. One of c("RMSE","MSE", "MAE", "MAPE", "sMAPE", "MASE"). The default is errormeasure = "RMSE".

errormeasure.which

Which value of errormeasure to be used for selecting a support space upper limit from support.signal.vector. One of c("min", "1se", "elbow") where "min" corresponds to the support spaces that produced the lowest error, "1se" corresponds to the support spaces such that error is within 1 standard error of the CV error for "min" and "elbow" corresponds to the elbow point of the error curve (the point that maximizes the distance between each observation, i.e, the pair composed by the upper limit of the support space and the error, and the line between the first and last observations, i.e., the lowest and the highest upper limits of the support space respectively. See find_curve_elbow). The default is errormeasure.which = "1se".

support.method

One of c("standardized", "ridge"). If support.method = "standardized}, the default, standardized coefficients are used to define the signal support spaces. If \code{support.method = "ridge the signal support spaces are define by the ridge trace.

support.method.penalize.intercept

Boolean value. if TRUE, the default, the intercept will be penalized. To be used when support.method = "ridge".

support.signal

NULL or fixed positive upper limit (L) for the support spaces (-L,L) on standardized data (when support.method = "standardized"); NULL or fixed positive factor to be multiplied by the maximum absolute value of the ridge trace for each coefficient (when support.method = "ridge"); a pair (LL,UL) or a matrix ((k+1) x 2) for the support spaces on original data. The default is support.signal = NULL.

support.signal.vector

NULL or a vector of positive values when support.signal = NULL. If support.signal.vector = NULL, the default, a vector c(support.signal.vector.min,...,support.signal.vector.max) of dimension support.signal.vector.n and logarithmically equally spaced will be generated. Each value represents the upper limits for the standardized support spaces, when support.method = "standardized" or the factor to be multiplied by the maximum absolute value of the ridge trace for each coefficient, when support.method = "ridge".

support.signal.vector.min

A positive value for the lowest limit of the support.signal.vector when support.signal = NULL and support.signal.vector = NULL. The default is support.signal.vector.min = 0.3.

support.signal.vector.max

A positive value for the highest limit of the support.signal.vector when support.signal = NULL and support.signal.vector = NULL. The default is support.signal.vector.max = 20.

support.signal.vector.n

A positive integer for the number of support spaces to be used when support.signal = NULL and support.signal.vector = NULL. The default is support.signal.vector.n = 20.

support.signal.points

A positive integer, a vector or a matrix. Prior weights for the signal. If not a positive integer then the sum of weights by row must be equal to 1. The default is support.signal.points = c(1 / 5, 1 / 5, 1 / 5, 1 / 5, 1 / 5).

support.noise

An interval, preferably centered around zero, given in the form c(LL,UL). If support.noise = NULL, the default, then a vector c(-L,L) is computed using the empirical three-sigma rule Pukelsheim (1994).

support.noise.points

A positive integer, a vector or a matrix. Prior weights for the noise. If not a positive integer then the sum of weights by row must be equal to 1. The default is support.noise.points = c(1 / 3, 1 / 3, 1 / 3).

weight

a value between zero and one representing the prediction-precision loss trade-off. If weight = 0.5, the default, equal weight is placed on the signal and noise entropies. A higher than 0.5 value places more weight on the noise entropy whereas a lower than 0.5 value places more weight on the signal entropy.

twosteps.n

Number of GCE reestimations using a previously estimated vector of signal probabilities.

method

Use "primal.solnl" (GCE using Sequential Quadratic Programming (SQP) method; see solnl) or "primal.solnp" (GCE using the augmented Lagrange multiplier method with an SQP interior algorithm; see solnp) for primal form of the optimization problem and "dual" (GME), "dual.CG" (GCE using a conjugate gradients method; see optim), "dual.BFGS" (GCE using Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method; see optim), "dual.L-BFGS-B" (GCE using a box-constrained optimization with limited-memory modification of the BFGS quasi-Newton method; see optim), dual.Rcgmin (GCE using an update of the conjugate gradient algorithm; see optimx), dual.bobyqa (GCE using a derivative-free optimization by quadratic approximation; see optimx and bobyqa), dual.newuoa (GCE using a derivative-free optimization by quadratic approximation; see optimx and newuoa), dual.nlminb (GCE; see optimx and nlminb), dual.nlm (GCE; see optimx and nlm), dual.lbfgs (GCE using the Limited-memory Broyden-Fletcher-Goldfarb-Shanno; see lbfgs), dual.lbfgsb3c (GCE using L-BFSC-B implemented in Fortran code and with an Rcpp interface; see lbfgsb3c) or dual.optimParallel (GCE using parallel version of the L-BFGS-B; see optimParallel) for dual form. The default is method = "dual.BFGS".

caseGLM

special cases of the generic general linear model. One of c("D", "M", "NM"), where "D" stands for data, "M" for moment and "NM" for normed-moment The default is caseGLM = "D".

boot.B

A single positive integer greater or equal to 10 for the number of bootstrap replicates to be used for the computation of the bootstrap confidence interval(s). Zero value will generate no replicate. The default is boot.B = 0.

boot.method

Method to be use for bootstrapping. One of c("residuals", "cases", "wild") which corresponds to resampling on residuals, on individual cases or on residuals multiplied by a N(0,1) variable, respectively. The default is boot.method = "residuals".

seed

A single value, interpreted as an integer, for reproducibility or NULL for randomness. The default is seed = 230676.

OLS

Boolean value. if TRUE, the default, OLS estimation is performed.

verbose

An integer to control how verbose the output is. For a value of 0 no messages or output are shown and for a value of 3 all messages are shown. The default is verbose = 0.

Details

The lmgce function fits a linear regression model via generalized cross entropy. Models for lmgce are specified symbolically. A typical model has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. lmgce calls the lower level functions lmgce.validate, lmgce.assign.ci, lmgce.assign.noci, lmgce.sscv, lmgce.ss, lmgce.cv and lmgce.fit.

Value

lmgce returns an object of class lmgce. The function summary.lmgce is used to obtain and print a summary of the results. The generic accessory functions coef.lmgce, fitted.values.lmgce, residuals.lmgce and df.residual.lmgce, extract various useful features of the value returned by object of class lmgce.

An object of class lmgce is a list containing at least the following components:

coefficients

a named vector of coefficients.

residuals

the residuals, that is response minus fitted values.

fitted.values

the fitted mean values.

df.residual

the residual degrees of freedom.

call

the matched call.

terms

the terms object used.

contrast

(only where relevant) the contrasts used.

xlevels

(only where relevant) a record of the levels of the factors used in fitting.

offset

the offset used (missing if none were used).

y

if requested (the default), the response used.

x

if requested (the default), the model matrix used.

model

if requested (the default), the model frame used.

na.action

(where relevant) information returned by model.frame on the special handling of NAs.

boot.B

number of bootstrap replicates used.

boot.method

method used for bootstrapping.

caseGLM

case of the generic general linear model used.

convergence

an integer code. 0 indicates successful optimization completion. Other numbers indicate different errors. See optim, optimx, solnl, solnp, lbfgs) and lbfgsb3c).

error

loss function (error) used for the selection of the support spaces.

error.measure

in sample error for the selected support space.

error.measure.cv.mean

cross-validation mean error for the selected support space.

error.measure.cv.sd

standard deviation of the cross-validation error for the selected support space.

error.which

which criterion/standardized/factor support was used

support.signal.1se

upper limit of the standardized support space or factor that produced the error within one standard error from the minimum error.

support.signal.elbow

upper limit of the standardized support space or factor that produced the error correspondent to the elbow of the error curve.

support.signal.min

upper limit of the standardized support space or factor that produced the minimum error.

p0

vector of prior weights used for the signal.

p

estimated probabilities associated with the signal.

w0

vector of prior weights used for the noise.

w

estimated probabilities associated with the noise.

lambda

estimated Lagrange multipliers.

nep

normalized entropy of the signal of the model.

nep.cv.mean

cross-validation normalized entropy of the signal of the model.

nep.cv.sd

standard deviation of the cross-validation normalized entropy of the signal of the model.

nepk

normalized entropy of the signal of each coefficient.

results

results from the different support spaces with or without cross-validation, and from bootstrap replicates, namely number of attempts (if the number of attempts is greater than three times the number of bootstrap replicates the bootstrapping process stops), coefficients and normalized entropies (nep - model, and nepk - coefficients), when applicable; results from OLS estimation if OLS = TRUE; results from GCE reestimation if twosteps.n is greater than 0.

support

vector of given positive upper limits for the support spaces on standardized data or factors, when support.signal = NULL or support.signal = L, or "interval" otherwise.

support.matrix

matrix with the support spaces used for estimation on original data.

support.method

method chosen for the support's limits

support.ok

vector of successful positive upper limits for the support spaces on standardized data (support.method = "standardized") or factors (support.method = "ridge"), when support.signal = NULL or support.signal = L, or "interval" otherwise.

support.stdUL

when applicable, the upper limit of the standardized support chosen, when support.method = "standardized" or the factor used when support.method = "ridge".

vcov

variance-covariance matrix of the coefficients.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

References

Golan, A., Judge, G. G. and Miller, D. (1996) Maximum entropy econometrics : robust estimation with limited data. Wiley.
Golan, A. (2008). Information and Entropy Econometrics — A Review and Synthesis. Foundations and Trends® in Econometrics, 2(1–2), 1–145. doi:10.1561/0800000004
Golan, A. (2017) Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information (Vol. 1). Oxford University Press. doi:10.1093/oso/9780199349524.001.0001
Pukelsheim, F. (1994) The Three Sigma Rule. The American Statistician, 48(2), 88–91. doi:10.2307/2684253
Macedo, P., Cabral, J., Afreixo, V., Macedo, F., Angelelli, M. (2025) RidGME estimation and inference in ill-conditioned models. In: Gervasi O, Murgante B, Garau C, et al., eds. Computational Science and Its Applications – ICCSA 2025 Workshops. Springer Nature Switzerland; 2025:300-313. doi:10.1007/978-3-031-97589-9_21

See Also

summary.lmgce for more detailed summaries. The generic functions plot.lmgce, print.lmgce, coef.lmgce and confint.lmgce.

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)


res_gce_package

lmgce Shiny application

Description

A Shiny application to execute lmgce

Usage

lmgceAPP()

Value

NULL. This function is called for its side effect (launching the app).

Author(s)

Jorge Cabral, jorgecabral@ua.pt

An add-in to easily generate the code for a lmgce analysis

Description

Select data and choose the arguments to be used. The execution of the code is also possible within the addin.

Usage

lmgceAddin()

Details

An addin for lmgce

Value

The code to be use in the lmgce analysis.

Examples


lmgceAddin()

Extract design matrix from lmgce object

Description

Returns the design matrix used to fit lmgce object.

Usage

## S3 method for class 'lmgce'
model.matrix(object, ...)

Arguments

object

fitted lmgce object.

...

additional arguments.

Value

A numeric matrix with one row for each observation and one column for each parameter in the model.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        x = TRUE,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

model.matrix(res_gce_package)

Worldbank time series data for Mozambique

Description

Mozambique's CO2, GDP, EPC e EU time series (1991-2014) from https://databank.worldbank.org/ (Downloaded in 2024/12/03).

Usage

moz_ts

Format

A ts object containing:

year

Year to which data refers

CO2

CO2 emissions (metric tons per capita); Data from: IDA Results Measurement System, Tier I Database – WDI;

EPC

Electric power consumption (kWh per capita). Data from database: Jobs;

EU

Energy use (kg of oil equivalent per capita). Data from database: World Development Indicators;

GDP

Gross domestic product per capita (current US$); Data from: World Development Indicators.

Examples

data(moz_ts)

plot(moz_ts)

Normalized Entropy Aggregation for Inhomogeneous Large-Scale Data - Neagging

Description

Computes the estimates for the Normalized Entropy Aggregation

Usage

neagging(
  object,
  boot.B = ifelse(object$boot.B == 0, 100, object$boot.B),
  boot.method = object$boot.method,
  error = object$error
)

Arguments

object

Fitted lmgce or tsbootgce model object.

boot.B

To use with a lmgce object. A single positive integer greater or equal to 10 for the number of bootstrap replicates for the computation of the Normalized Entropy Aggregation estimate(s), to be used when object was created with boot.B = 0. The default is boot.B = 100 when the object has no previous sampling information and boot.B = object$boot.B otherwise, which corresponds to the boot.B given to lmgce when the object was created.

boot.method

To use with a lmgce object. Method used for bootstrapping. One of c("residuals", "cases", "wild") which corresponds to resampling on residuals, on individual cases or on residuals multiplied by a N(0,1) variable, respectively. The default is boot.method = object$boot.method.

error

Loss function (error) to be used for the selection of the support spaces. One of c("RMSE","MSE", "MAE", "MAPE", "sMAPE", "MASE"). The default is boot.method = object$error.

Value

An object of class neagging is a list containing at least the following components:

matrix

a matrix where each column contains sequentially the aggregated estimates.

error

a named vector with the in sample error for each aggregated set of estimates.

error.object

the in sample error of the object.

coefficients

the aggregated coefficients that produced the lowest in sample error.

coefficients.object

the coefficients of the object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

References

da Conceição Costa, M. and Macedo, P. (2019). Normalized Entropy Aggregation for Inhomogeneous Large-Scale Data. In O. Valenzuela, F. Rojas, H. Pomares, & I. Rojas (Eds.), Theory and Applications of Time Series Analysis (pp. 19–29). Springer International Publishing. doi:10.1007/978-3-030-26036-1_2

See Also

The generic functions plot.neagging and coef.neagging.

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

neagging(res_gce_package, boot.method = "cases")

res.tsbootgce <-
  tsbootgce(
    formula = CO2 ~ 1 + L(GDP, 1) + L(EPC, 1) + L(EU, 1),
    data = moz_ts)

neagging(res.tsbootgce)

Extract the Number of Observations from a lmgce model fit

Description

Extract the number of ‘observations’ from a lmgce model fit.

Usage

## S3 method for class 'lmgce'
nobs(object, ...)

Arguments

object

Fitted lmgce model object.

...

additional arguments.

Value

An integer scalar representing the number of observations (rows) used in fitting the lmgce model object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)


nobs(res_gce_package)

Plot Diagnostics for a cv.lmgce Object

Description

One plot (selectable by which) is currently available to evaluate a cv.lmgce object. The plot depicts the error change with the combination of different arguments of cv.lmgce.

Usage

## S3 method for class 'cv.lmgce'
plot(x, which = 1, ncol = 1, scales = "free", ...)

Arguments

x

Fitted cv.lmgce model object.

which

A subset of the numbers 1:1.

ncol

Number of columns of the plot (see facet_wrap).

scales

One of c("free", "fixed") (see facet_wrap).

...

additional arguments.

Value

A ggplot object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

See Also

cv.lmgce

Examples


res.cv.lmgce <-
  cv.lmgce(y ~ .,
           data = dataGCE)

plot(res.cv.lmgce)

Plot Diagnostics for a lmgce Object

Description

Seven plots (selectable by which) are currently available to evaluate a lmgce object: a plot of the Estimates and confidence intervals; four plots of supports against Prediction Error, Estimates, Normalized Entropy and Precision Error; two plots of GCE reestimation against Prediction and Precision Errors. Note that plots regarding Precision Error are only produced if the argument coef is not NULL.

Usage

## S3 method for class 'lmgce'
plot(
  x,
  type = c("ggplot2", "plotly"),
  which = 1:7,
  ci.level = 0.95,
  ci.method = c("z", "percentile", "basic"),
  boot.B = ifelse(x$boot.B == 0, 100, x$boot.B),
  boot.method = x$boot.method,
  coef = NULL,
  OLS = TRUE,
  NormEnt = TRUE,
  caption = list(paste0("Estimates (", ci.method[1], " ", ci.level * 100, "% CI)"),
    "Prediction Error vs supports", "Estimates vs supports",
    "Normalized Entropy vs supports", "Precision Error vs supports",
    "Prediction Error vs GCE reestimation", "Precision Error vs GCE reestimation"),
  ...
)

Arguments

x

Fitted lmgce model object.

type

One of c("ggplot2", "plotly"). "ggplot2" is used by default.

which

A subset of the numbers 1:7.

ci.level

the confidence level (0,1) required to compute the confidence interval.

ci.method

the method used to compute the confidence interval. One of c("z","percentile", "basic"). The default is method = "z".

boot.B

A single positive integer greater or equal to 10 for the number of bootstrap replicates for the computation of the bootstrap confidence interval(s), to be used when method = c("percentile", "basic") and when object was created with boot.B = 0. The default is boot.B = 100 when the object has no previous sampling information and boot.B = object$boot.B otherwise, which corresponds to the boot.B given to lmgce when the object was created.

boot.method

Method used for bootstrapping. One of c("residuals", "cases", "wild") which corresponds to resampling on residuals, on individual cases or on residuals multiplied by a N(0,1) variable, respectively. The default is boot.method = object$boot.method.

coef

A vector of true coefficients to be used when which = c(5,7).

OLS

Boolean value. if TRUE, the default, plots the OLS results.

NormEnt

Boolean value. if TRUE, the default, plots the normalized entropy.

caption

Captions to appear above the plots; character vector or list of valid graphics annotations, see as.graphicsAnnot, of length 7, the j-th entry corresponding to which[j]. Can be set to "" or NA to suppress all captions.

...

additional arguments.

Value

A named list of ggplot or plotly objects, each representing a separate plot.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

See Also

lmgce

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

plot(res_gce_package)

Plot Diagnostics for a neagging Object

Description

Two plots (selectable by which) are currently available to evaluate a neagging object: plots of the estimates and in sample error against the number of bootstrap samples aggregated.

Usage

## S3 method for class 'neagging'
plot(x, which = 1, ...)

Arguments

x

Fitted neagging model object.

which

Numbers 1 or 2.

...

additional arguments.

Value

A ggplot object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

See Also

lmgce, tsbootgce and neagging

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

res_neagging <- neagging(res_gce_package)

plot(res_neagging)

Plot Diagnostics for a ridgetrace Object

Description

Plot Diagnostics for a ridgetrace Object

Usage

## S3 method for class 'ridgetrace'
plot(x, coef = NULL, ...)

Arguments

x

Fitted ridgetrace model object.

coef

A vector of true coefficients if available.

...

additional arguments.

Value

Supports are returned.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

res.ridgetrace <- ridgetrace( formula = y ~ X001 + X002 + X003 + X004 + X005, data = dataGCE)

plot(res.ridgetrace)

Plot Diagnostics for a tsbootgce object

Description

Three plots (selectable by which) are currently available to evaluate a tsbootgce object.

Usage

## S3 method for class 'tsbootgce'
plot(
  x,
  which = c(1, 2),
  group = TRUE,
  group.ncol = NULL,
  group.nrow = NULL,
  ci.levels = c(0.9, 0.95, 0.99),
  ci.method = c("hdr", "basic", "percentile"),
  seed = object$seed,
  lambda = 1,
  col = NULL,
  plot.lines = TRUE,
  legend.position = "bottom",
  ...
)

Arguments

x

Fitted tsbootgce object.

which

Integers from 1 to 3. The default is which = c(1,2).

group

Boolean value. If group = TRUE, the default, plots are grouped in one image.

group.ncol

Number of columns (see ggarrange). The default is group.ncol = NULL.

group.nrow

Number of rows. (see ggarrange). The default is group.nrow = NULL.

ci.levels

the confidence levels (maximum of 4) required to compute the confidence interval. The default is ci.levels = c(0.90, 0.95, 0.99).

ci.method

One of c("hdr", "basic", "percentile"). The default is ci.method = "hdr" (see hdr).

seed

A single value, interpreted as an integer, for reproducibility or NULL for randomness. The default is seed = object$seed.

lambda

Box-Cox transformation parameter. Value between 0 and 1. The default is lambda = 1 (see hdr).

col

Vector of colors for regions. The default is col = NULL.

plot.lines

Boolean. The default is plot.lines = TRUE.

legend.position

The default is legend.position = "bottom".

...

additional arguments.

Value

A ggplot object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

See Also

tsbootgce

Examples


res.tsbootgce <-
  tsbootgce(
    formula = CO2 ~ 1 + L(GDP, 1) + L(EPC, 1) + L(EU, 1),
    data = moz_ts)

plot(res.tsbootgce, which = 2, group = TRUE)

Predict method for lmgce Linear Model Fits

Description

Predicted values based on a fitted model lmgce object.

Usage

## S3 method for class 'lmgce'
predict(
  object,
  newdata,
  interval = c("none", "confidence"),
  type = c("response", "terms"),
  level = 0.95,
  terms = NULL,
  na.action = na.pass,
  ...
)

Arguments

object

Fitted lmgce model object.

newdata

An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.

interval

One of c("none", "confidence"). Type of interval calculation. Can be abbreviated.

type

One of c("response", "terms"). Type of prediction (response or model term). Can be abbreviated.

level

Tolerance/confidence level (0,1).

terms

if type = "terms", which terms (default is all terms), a character vector.

na.action

function determining what should be done with missing values in newdata. The default is to predict NA.

...

additional arguments.

Value

predict.lmgce produces a vector of predictions.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)


predict(res_gce_package, dataGCE.test)

Print cv.lmgce object

Description

Print cv.lmgce object

Usage

## S3 method for class 'cv.lmgce'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

fitted cv.lmgce object.

digits

significant digits in printout.

...

additional print arguments.

Value

A small summary of a cv.lmgce object is returned.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res.cv.lmgce <-
  cv.lmgce(y ~ .,
           data = dataGCE)

res.cv.lmgce

Print a lmgce object

Description

Concise summary of a lmgce object

Usage

## S3 method for class 'lmgce'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

fitted lmgce object.

digits

significant digits in printout.

...

additional print arguments.

Value

A small summary of a lmgce object is returned.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

res_gce_package

Print a ridgetrace object

Description

Concise summary of a ridgetrace object

Usage

## S3 method for class 'ridgetrace'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

fitted ridgetrace object.

digits

significant digits in printout.

...

additional print arguments.

Value

A small summary of a ridgetrace object is returned.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples

res.ridgetrace <-
  ridgetrace(
    formula = y ~ X001 + X002 + X003 + X004 + X005,
    data = dataGCE)

res.ridgetrace

Print Summary of lmgce Model Fits

Description

print.summary method for class lmgce.

Usage

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

Arguments

x

an object of class summary.lmgce, usually, a result of a call to summary.lmgce.

digits

The number of significant digits to use when printing.

symbolic.cor

Boolean value. if TRUE, print the correlations in a symbolic form (see symnum) rather than as numbers.

signif.stars

Boolean value. if TRUE, ‘significance stars’ are printed for each coefficient.

...

Further arguments passed to or from other methods.

Value

The function print.summary.lmgce prints the information in a summary.lmgce object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)


summary(res_gce_package)

summary(res_gce_package, ci.level = 0.90, ci.method = "basic")

Print tsbootgce object

Description

Print tsbootgce object

Usage

## S3 method for class 'tsbootgce'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

fitted lmgce object.

digits

significant digits in printout.

...

additional print arguments.

Value

A small summary of a tsbootgce object is returned.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res.tsbootgce <-
  tsbootgce(
    formula = CO2 ~ 1 + L(GDP, 1) + L(EPC, 1) + L(EU, 1),
    data = moz_ts)

res.tsbootgce

Example 'lmgce' object

Description

An example of an object of class 'lmgce' used for demonstration.

Usage

res_gce_package

Format

An object of class '"lmgce"'.

Source

generated by the package.

Extract lmgce Model Residuals

Description

resid is a function which extracts model residuals from lmgce objects.

Usage

## S3 method for class 'lmgce'
resid(object, ...)

Arguments

object

Fitted lmgce model object.

...

additional arguments.

Value

Returns the residuals from a lmgce object

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

resid(res_gce_package)

Extract lmgce Model Residuals

Description

residuals is a function which extracts model residuals from lmgce objects. The abbreviated form resid is an alias for residuals.

Usage

## S3 method for class 'lmgce'
residuals(object, ...)

Arguments

object

Fitted lmgce model object.

...

additional arguments.

Value

Returns the residuals from a lmgce object

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

residuals(res_gce_package)

Function to obtain the ridge trace and choose the support limits given a formula

Description

Function to obtain the ridge trace and choose the support limits given a formula

Usage

ridgetrace(
  formula,
  data,
  subset,
  na.action,
  offset,
  contrasts = NULL,
  lambda = NULL,
  lambda.min = 0.001,
  lambda.max = 1,
  lambda.n = 100,
  penalize.intercept = TRUE,
  errormeasure = c("RMSE", "MSE", "MAE", "MAPE", "sMAPE", "MASE"),
  cv = TRUE,
  cv.nfolds = 5,
  seed = 230676
)

Arguments

formula

An object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

A data frame (or object coercible by as.data.frame to a data frame) containing the variables in the model.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector or matrix of extents matching those of the response. One or more offset terms can be included in the formula instead or as well, and if more than one are specified their sum is used. See model.offset.

contrasts

An optional list. See the contrasts.arg of model.matrix.default.

lambda

The default is lambda = NULL and a lambda sequence will be computed based on lambda.n, lambda.min and lambda.max. Supplying a lambda sequence overrides this.

lambda.min

Minimum value for the lambda sequence.

lambda.max

Maximum value for the lambda sequence.

lambda.n

The number of lambda values. The default is lambda.n = 100.

penalize.intercept

Boolean value. if TRUE, the default, the intercept will be penalized.

errormeasure

Loss function (error) to be used for the selection of the support spaces. One of c("RMSE","MSE", "MAE", "MAPE", "sMAPE", "MASE"). The default is errormeasure = "RMSE".

cv

Boolean value. If TRUE the error, errormeasure, will be computed using cross-validation. If FALSE the error will be computed in sample. The default is cv = TRUE.

cv.nfolds

number of folds used for cross-validation when cv = TRUE. The default is cv.nfolds = 5.

seed

A single value, interpreted as an integer, for reproducibility or NULL for randomness. The default is seed = 230676.

Value

An object of class ridgetrace is a list containing at least the following components:

lambda

the lambda sequence used

max.abs.coef

a named vector of coefficients (maximum absolute coefficients)

max.abs.residual

the maximum absolute residual

coef.lambda

a data.frame with the coefficients for each lambda tested

error.lambda

a vector with the in sample error

error.lambda.cv

a data.frame with cross-validation errors

call

the matched call

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples

res.ridgetrace <-
  ridgetrace(
    formula = y ~ X001 + X002 + X003 + X004 + X005,
    data = dataGCE)

res.ridgetrace

Scale coefficients back

Description

Given a vector of scaled (standardized) regression coefficients the function returns the unscaled (in the original scale) regression coefficients

Usage

scalebackcoef(X.scaled, y.scaled, betas.scaled, intercept = TRUE)

Arguments

X.scaled

A matrix scaled with scale.

y.scaled

A vector scaled with scale.

betas.scaled

A vector of given scaled coefficients.

intercept

logical indicating if intercept is to be calculated

Value

Returns a vector of unscaled numeric regression coefficients.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Summarise a linear regression model via generalized cross entropy fit

Description

summary method for class lmgce. Function used to produce summary information from a fitted linear regression model via generalized cross entropy as represented by object of class lmgce.

Usage

## S3 method for class 'lmgce'
summary(
  object,
  call = TRUE,
  correlation = FALSE,
  symbolic.cor = FALSE,
  ci.level = NULL,
  ci.method = c("z", "percentile", "basic"),
  boot.B = ifelse(object$boot.B == 0, 100, object$boot.B),
  boot.method = object$boot.method,
  ...
)

Arguments

object

Fitted lmgce model object.

call

Boolean value. if TRUE, the call used is returned. The default is model = TRUE.

correlation

Boolean value. if TRUE, the correlation matrix of the estimated parameters is returned and printed.

symbolic.cor

Boolean value. if TRUE, print the correlations in a symbolic form (see symnum) rather than as numbers.

ci.level

the confidence level (0,1) required to compute the confidence interval. The default is ci.level = NULL which results in the omission of the confidence interval.

ci.method

method used to compute a confidence interval. One of c("z","percentile", "basic"). The default is ci.method = "z".

boot.B

A single positive integer greater or equal to 10 for the number of bootstrap replicates for the computation of the bootstrap confidence interval(s), to be used when method = c("percentile", "basic") and when object was created with boot.B = 0. The default is boot.B = 100 when the object has no previous sampling information and boot.B = object$boot.B otherwise, which corresponds to the boot.B given to lmgce when the object was created.

boot.method

Method used for bootstrapping. One of c("residuals", "cases", "wild") which corresponds to resampling on residuals, on individual cases or on residuals multiplied by a N(0,1) variable, respectively. The default is boot.method = object$boot.method.

...

additional arguments.

Value

The function summary.lmgce computes and returns a list of summary statistics of the fitted lmgce linear model given in object, using the components (list elements) "call" and "terms" from its argument, plus

residuals

the residuals, that is response minus fitted values.

coefficients

a p \times 4 matrix, where p is the number of non-aliased coefficients, with columns for the estimated coefficient, its standard error, z-statistic and corresponding (two-sided) p-value. Aliased coefficients are omitted.

support

a p \times 3 matrix with columns for the normalized entropy (NormEnt), and lower (LL) and upper (UL) limits for each of the K+1 support spaces.

aliased

named logical vector showing if the original coefficients are aliased.

sigma

the square root of the estimated variance of the random error.

df

degrees of freedom, a 3-vector (p, n - p) the first being the number of non-aliased coefficients, the last being the p minus the number of included individuals n.

r.squared

R^2, the ‘fraction of variance explained by the model’

adj.r.squared

the above R^2 statistic ‘adjusted’, penalizing for higher p.

cov.unscaled

a p \times p matrix of covariances of the \hat \beta

support.stdUL

when applicable, the upper limit of the standardized support chosen, when support.method = "standardized" or the factor used when support.method = "ridge".

support.method

method chosen for the support's limits

nep

the normalized entropy of the model.

nep.cv.mean

the cross-validation normalized entropy of the model.

nep.cv.sd

the standard deviation of the cross-validation normalized entropy of the model.

error

the error measure chosen

error.which

which criterion/standardized/factor support was used

error.measure

the value of the error measure

error.measure.cv.mean

the cross-validation value of the error measure

error.measure.cv.sd

the standard deviation of the cross-validation value of the error measure

correlation

the correlation matrix corresponding to the above cov.unscaled, if correlation = TRUE is specified.

symbolic.cor

(only if correlation = TRUE) The value of the argument symbolic.cor.

na.action

from object, if present there.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)


sm_res_gce_package <- summary(res_gce_package)

str(sm_res_gce_package)

sm_res_gce_package$coefficients

Time series bootstrap Cross entropy estimation

Description

This generic function fits a linear regression model using bootstrapped time series via generalized cross entropy.

Usage

tsbootgce(
  formula,
  data,
  subset,
  na.action,
  offset,
  contrasts = NULL,
  trim = 0.05,
  reps = 1000,
  start = NULL,
  end = NULL,
  coef.method = c("mode", "median"),
  cv = TRUE,
  cv.nfolds = 5,
  errormeasure = c("RMSE", "MSE", "MAE", "MAPE", "sMAPE", "MASE"),
  errormeasure.which = {
     if (isTRUE(cv)) 
         c("1se", "min", "elbow")
    
    else c("min", "elbow")
 },
  support.method = c("standardized", "ridge"),
  support.method.penalize.intercept = TRUE,
  support.signal = NULL,
  support.signal.vector = NULL,
  support.signal.vector.min = 0.3,
  support.signal.vector.max = 20,
  support.signal.vector.n = 20,
  support.signal.points = c(1/5, 1/5, 1/5, 1/5, 1/5),
  support.noise = NULL,
  support.noise.points = c(1/3, 1/3, 1/3),
  weight = 0.5,
  twosteps.n = 1,
  method = c("dual.BFGS", "dual.lbfgsb3c", "dual", "primal.solnl", "primal.solnp",
    "dual.CG", "dual.L-BFGS-B", "dual.Rcgmin", "dual.bobyqa", "dual.newuoa",
    "dual.nlminb", "dual.nlm", "dual.lbfgs", "dual.optimParallel"),
  caseGLM = c("D", "M", "NM"),
  boot.B = 0,
  boot.method = c("residuals", "cases", "wild"),
  seed = 230676,
  OLS = TRUE,
  verbose = 0
)

Arguments

formula

a "formula" describing the linear model to be fit. For details see lm and dynlm.

data

A data.frame (or object coercible by as.data.frame to a data frame) or time series object (e.g., ts or zoo), containing the variables in the model.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector or matrix of extents matching those of the response. One or more offset terms can be included in the formula instead or as well, and if more than one are specified their sum is used. See model.offset.

contrasts

An optional list. See the contrasts.arg of model.matrix.default.

trim

The trimming proportion (see meboot). The default is trim = 0.05.

reps

The number of replicates to generate (see meboot). The default is reps = 1000.

start

The time of the first observation. Either a single number or a vector of two numbers (the second of which is an integer), which specify a natural time unit and a (1-based) number of samples into the time unit (see ts).

end

The time of the last observation, specified in the same way as start (see ts).

coef.method

Method used to estimate the coefficients. One of c("mode", "median"). for "mode" see hdr

cv

Boolean value. If TRUE the error, errormeasure, will be computed using cross-validation. If FALSE the error will be computed in sample. The default is cv = TRUE.

cv.nfolds

number of folds used for cross-validation when cv = TRUE. The default is cv.nfolds = 5 and the smallest value allowable is cv.nfolds = 3.

errormeasure

Loss function (error) to be used for the selection of the support spaces. One of c("RMSE","MSE", "MAE", "MAPE", "sMAPE", "MASE"). The default is errormeasure = "RMSE".

errormeasure.which

Which value of errormeasure to be used for selecting a support space upper limit from support.signal.vector. One of c("min", "1se", "elbow") where "min" corresponds to the support spaces that produced the lowest error, "1se" corresponds to the support spaces such that error is within 1 standard error of the CV error for "min" and "elbow" corresponds to the elbow point of the error curve (the point that maximizes the distance between each observation, i.e, the pair composed by the upper limit of the support space and the error, and the line between the first and last observations, i.e., the lowest and the highest upper limits of the support space respectively. See find_curve_elbow). The default is errormeasure.which = "1se".

support.method

One of c("standardized", "ridge"). If support.method = "standardized}, the default, standardized coefficients are used to define the signal support spaces. If \code{support.method = "ridge the signal support spaces are define by the ridge trace.

support.method.penalize.intercept

Boolean value. if TRUE, the default, the intercept will be penalized. To be used when support.method = "ridge".

support.signal

NULL or fixed positive upper limit (L) for the support spaces (-L,L) on standardized data (when support.method = "standardized"); NULL or fixed positive factor to be multiplied by the maximum absolute value of the ridge trace for each coefficient (when support.method = "ridge"); a pair (LL,UL) or a matrix ((k+1) x 2) for the support spaces on original data. The default is support.signal = NULL.

support.signal.vector

NULL or a vector of positive values when support.signal = NULL. If support.signal.vector = NULL, the default, a vector c(support.signal.vector.min,...,support.signal.vector.max) of dimension support.signal.vector.n and logarithmically equally spaced will be generated. Each value represents the upper limits for the standardized support spaces, when support.method = "standardized" or the factor to be multiplied by the maximum absolute value of the ridge trace for each coefficient, when support.method = "ridge".

support.signal.vector.min

A positive value for the lowest limit of the support.signal.vector when support.signal = NULL and support.signal.vector = NULL. The default is support.signal.vector.min = 0.3.

support.signal.vector.max

A positive value for the highest limit of the support.signal.vector when support.signal = NULL and support.signal.vector = NULL. The default is support.signal.vector.max = 20.

support.signal.vector.n

A positive integer for the number of support spaces to be used when support.signal = NULL and support.signal.vector = NULL. The default is support.signal.vector.n = 20.

support.signal.points

A positive integer, a vector or a matrix. Prior weights for the signal. If not a positive integer then the sum of weights by row must be equal to 1. The default is support.signal.points = c(1 / 5, 1 / 5, 1 / 5, 1 / 5, 1 / 5).

support.noise

An interval, preferably centered around zero, given in the form c(LL,UL). If support.noise = NULL, the default, then a vector c(-L,L) is computed using the empirical three-sigma rule Pukelsheim (1994).

support.noise.points

A positive integer, a vector or a matrix. Prior weights for the noise. If not a positive integer then the sum of weights by row must be equal to 1. The default is support.noise.points = c(1 / 3, 1 / 3, 1 / 3).

weight

a value between zero and one representing the prediction-precision loss trade-off. If weight = 0.5, the default, equal weight is placed on the signal and noise entropies. A higher than 0.5 value places more weight on the noise entropy whereas a lower than 0.5 value places more weight on the signal entropy.

twosteps.n

Number of GCE reestimations using a previously estimated vector of signal probabilities.

method

Use "primal.solnl" (GCE using Sequential Quadratic Programming (SQP) method; see solnl) or "primal.solnp" (GCE using the augmented Lagrange multiplier method with an SQP interior algorithm; see solnp) for primal form of the optimization problem and "dual" (GME), "dual.CG" (GCE using a conjugate gradients method; see optim), "dual.BFGS" (GCE using Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method; see optim), "dual.L-BFGS-B" (GCE using a box-constrained optimization with limited-memory modification of the BFGS quasi-Newton method; see optim), dual.Rcgmin (GCE using an update of the conjugate gradient algorithm; see optimx), dual.bobyqa (GCE using a derivative-free optimization by quadratic approximation; see optimx and bobyqa), dual.newuoa (GCE using a derivative-free optimization by quadratic approximation; see optimx and newuoa), dual.nlminb (GCE; see optimx and nlminb), dual.nlm (GCE; see optimx and nlm), dual.lbfgs (GCE using the Limited-memory Broyden-Fletcher-Goldfarb-Shanno; see lbfgs), dual.lbfgsb3c (GCE using L-BFSC-B implemented in Fortran code and with an Rcpp interface; see lbfgsb3c) or dual.optimParallel (GCE using parallel version of the L-BFGS-B; see optimParallel) for dual form. The default is method = "dual.BFGS".

caseGLM

special cases of the generic general linear model. One of c("D", "M", "NM"), where "D" stands for data, "M" for moment and "NM" for normed-moment The default is caseGLM = "D".

boot.B

A single positive integer greater or equal to 10 for the number of bootstrap replicates to be used for the computation of the bootstrap confidence interval(s). Zero value will generate no replicate. The default is boot.B = 0.

boot.method

Method to be use for bootstrapping. One of c("residuals", "cases", "wild") which corresponds to resampling on residuals, on individual cases or on residuals multiplied by a N(0,1) variable, respectively. The default is boot.method = "residuals".

seed

A single value, interpreted as an integer, for reproducibility or NULL for randomness. The default is seed = 230676.

OLS

Boolean value. if TRUE, the default, OLS estimation is performed.

verbose

An integer to control how verbose the output is. For a value of 0 no messages or output are shown and for a value of 3 all messages are shown. The default is verbose = 0.

Details

The tsbootgce function fits several linear regression models via generalized cross entropy in replicas of time series obtained using meboot. Models for tsbootgce are specified symbolically (see lm and dynlm).

Value

tsbootgce returns an object of class tsbootgce. The generic accessory functions coef.tsbootgce, confint.tsbootgce and plot.tsbootgce extract various useful features of the value returned by object of class tsbootgce.

An object of class tsbootgce is a list containing at least the following components:

call

the matched call.

coefficients

a named data frame of coefficients determined by coef.method.

data.ts

ts object.

error

loss function (error) used for the selection of the support spaces.

error.measure

in sample error for the selected support space.

fitted.values

the fitted mean values.

frequency

see link[zoo]{zoo}.

index

see link[zoo]{zoo}.

lmgce

lmgce object.

meboot

meboot replicates.

model

the model frame used.

nep

normalized entropy of the signal of the model.

nepk

normalized entropy of the signal of each coefficient.

residuals

the residuals, that is response minus fitted values.

results

a list containing the bootstrap results: "coef.matrix", a named data frame of all the coefficients; "nepk.matrix", a named data frame of all the normalized entropy values of each parameter; "nep.vector", a vector of all the normalized entropy values of the model.

seed

the seed used.

terms

the terms object used.

x

if requested (the default), the model matrix used.

xlevels

(only where relevant) a record of the levels of the factors used in fitting.

y

if requested (the default), the response used.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

References

Golan, A., Judge, G. G. and Miller, D. (1996) Maximum entropy econometrics : robust estimation with limited data. Wiley.

Golan, A. (2008) Information and Entropy Econometrics — A Review and Synthesis. Foundations and Trends® in Econometrics, 2(1–2), 1–145. doi:10.1561/0800000004

Golan, A. (2017) Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information (Vol. 1). Oxford University Press. doi:10.1093/oso/9780199349524.001.0001

Hyndman, R.J. (1996) Computing and graphing highest density regions. American Statistician, 50, 120-126. doi:10.2307/2684423

Pukelsheim, F. (1994) The Three Sigma Rule. The American Statistician, 48(2), 88–91. doi:10.2307/2684253

Vinod, H. D., & Lopez-de-Lacalle, J. (2009). Maximum Entropy Bootstrap for Time Series: The meboot R Package. Journal of Statistical Software, 29(5), 1–19. doi:10.18637/jss.v029.i05

See Also

The generic functions plot.tsbootgce, print.tsbootgce, and coef.tsbootgce.

Examples


res.tsbootgce <-
  tsbootgce(
    formula = CO2 ~ 1 + L(GDP, 1) + L(EPC, 1) + L(EU, 1),
    data = moz_ts)

res.tsbootgce

Variable Names of lmgce Fitted Models

Description

Simple utility returning variable names.

Usage

## S3 method for class 'lmgce'
variable.names(object, ...)

Arguments

object

Fitted lmgce model object.

...

additional arguments.

Value

A character vector containing the names of the variables in the lmgce model object.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)


variable.names(res_gce_package)

Extract lmgce Model's Variance-Covariance Matrix

Description

Returns the variance-covariance matrix of the main parameters of a lmgce object

Usage

## S3 method for class 'lmgce'
vcov(object, ...)

Arguments

object

Fitted lmgce model object.

...

additional arguments.

Value

A matrix of the estimated covariances between the parameter estimates in the linear predictor of the lmgce model.

Author(s)

Jorge Cabral, jorgecabral@ua.pt

Examples


res_gce_package <-
  lmgce(y ~ .,
        data = dataGCE,
        boot.B = 50,
        seed = 230676)

vcov(res_gce_package)

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