Type: Package
Title: Fits Regression & ARMA Models Subject to Constraints to the Coefficient
Version: 0.1.0
Author: Josep Puig Sallés
Maintainer: Josep Puig <puigjos@gmail.com>
Description: Fits or generalized linear models either a regression with Autoregressive moving-average (ARMA) errors for time series data. The package makes it easy to incorporate constraints into the model's coefficients. The model is specified by an objective function (Gaussian, Binomial or Poisson) or an ARMA order (p,q), a vector of bound constraints for the coefficients (i.e beta1 > 0) and the possibility to incorporate restrictions among coefficients (i.e beta1 > beta2). The references of this packages are the same as 'stats' package for glm() and arima() functions. See Brockwell, P. J. and Davis, R. A. (1996, ISBN-10: 9783319298528). For the different optimizers implemented, it is recommended to consult the documentation of the corresponding packages.
License: GPL-2 | GPL-3
Encoding: UTF-8
LazyData: true
Depends: R (≥ 3.5)
RoxygenNote: 6.1.1
BugReports: https://github.com/puigjos/ConsReg/issues
URL: https://github.com/puigjos/ConsReg
Suggests: testthat, knitr, rmarkdown
Imports: data.table (≥ 1.10), forecast (≥ 8.0), rlang (≥ 0.4), nloptr (≥ 1.2), FME (≥ 1.3), MCMCpack (≥ 1.4), Rsolnp (≥ 1.15), DEoptim (≥ 2.2), dfoptim, GA (≥ 3.0), GenSA (≥ 1.1), Metrics, ggplot2, adaptMCMC, Rcpp
VignetteBuilder: knitr
NeedsCompilation: yes
Packaged: 2020-04-03 18:54:39 UTC; jpuigsal
Repository: CRAN
Date/Publication: 2020-04-05 15:20:03 UTC

Fit a regression model with gaussian or binomial objective function

Description

ConsReg is a function that allows to estimate a regression model: linear regression (gaussian), logistic regression (binomial) or poisson regression. It allows the introduction of restrictions (both lower and upper limits) and restrictions between the coefficients (in the form, for example, of a>b).

Usage

ConsReg(...)

## Default S3 method:
ConsReg(x, y, family, optimizer, ini.pars.coef = NULL,
  constraints = NULL, LOWER = NULL, UPPER = NULL, penalty = 1000,
  ...)

## S3 method for class 'formula'
ConsReg(formula, data = list(), optimizer = "solnp",
  family = c("gaussian", "binomial"), constraints = NULL,
  LOWER = NULL, UPPER = NULL, penalty = 1000,
  na.action = "na.omit", ini.pars.coef = NULL, ...)

Arguments

...

additional parameters passed in the optimizer (number of iterations, ...)

x

matrix of predictive variables

y

vector of outcome variable

family

a description of the error distribution and link function to be used in the model. Possible values are: "gaussian" (linear regression) or "binomial" (logistic regression) and "poisson"

optimizer

Optimizer package used for fit the model (include bayesian and genetic algorithm optimization). Possible values are: "solnp" (default) (Rsolnp), "gosonlp" (Rsolnp), "optim" (stats::optim), "nloptr" (nloptr), DEoptim ("DEoptim"), "dfoptim" (dfoptim), "mcmc" (FME::modMCMC), "MCMCmetrop" (MCMCpack::MCMCmetrop1R),'adaptMCMC'(adaptMCMC::MCMC), "GA" (GA package), "GenSA" (GenSA package)

ini.pars.coef

vector of initial parameters. In case there is some constraint, then the ini.pars.coef should fulfill the constraints

constraints

vector of constraints (see details)

LOWER

(default NULL) vector of lower bounds for the coefficients. If the lenght of LOWER is not equal with the length of the coeefficients, then, the rest will be equal to -Inf

UPPER

(default NULL) vector of lower bounds for the coefficients. If the lenght of UPPER is not equal with the length of the coeefficients, then, the rest will be equal to +Inf

penalty

(default 1000) penalty to the objective function if some constraints do not fullfill

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

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called.

na.action

na.action to the data

Details

Several optimizers of various R packages are implemented, including methods typically used in Bayesian regressions like Markov Chain Monte Carlo simulation.

Constraints will be a string: For example, if x1 and x2 are two coefficient names, then a constraint could be: "x1 > x2" or "x1+x2 > 2". For some constraints, one can write: "x1+x2>2, x1 > 1". Each constraint will be separate by commas.

Important: if there are some constraints that do not fulfill in a model without those constraints, it is recommended to use ini.pars.coef parameter to set initial values that fulfill constraints. See the example

Value

An object of class "ConsReg".

coefficients

Coefficients of the regression

hessian

hessian matrix if the optimizer can return it

family

Model family function

optimizer

optimizer object return (see details of each optimization package)

optimizer.name

name of the optimizer

df

nrow(data) - number of coefficients

rank

number of coefficients

residuals

residuals of the model

fitted

fitted values of the model

metrics

Accuracy metrics of the model

call

the matched call

y

objective variable

x

regressors

formula

formula term

family.name

Name of the family used

Author(s)

Josep Puig Sallés

Examples

data('fake_data')
fit1 = ConsReg(formula = y~x1+x2+x3+ I(x3^2) + x4, family = 'gaussian',
                     optimizer = 'mcmc',
                     data = fake_data)
summary(fit1)

# We impose constraints to x3 and x3^2 and x4
fit2 = ConsReg(formula = y~x1+x2+x3+ I(x3^2) + x4, data = fake_data,
            family = 'gaussian',
            constraints = '(x3 + `I(x3^2)`) > .01, x4 < .2',
            optimizer = 'mcmc',
            ini.pars.coef = c(-1.65, .12, -.004, 0.1, 0.1, .15))

fit1$coefficients
fit2$coefficients

Fit regression model with Arma errors to univariate time series

Description

ConsRegArima is a function that allows to estimate a regression model with errors following an ARMA process (p,q). It allows the introduction of restrictions (both lower and upper limits) and restrictions between the coefficients (in the form, for example, of a>b). Largely a wrapper for the arima function in the stats package but easier to include regressors.

Usage

ConsRegArima(...)

## Default S3 method:
ConsRegArima(x, y, order, seasonal, optimizer,
  LOWER = NULL, UPPER = NULL, penalty = 1000, constraints = NULL,
  ini.pars.coef, model_fit = NULL, ...)

## S3 method for class 'formula'
ConsRegArima(formula, data = list(),
  optimizer = c("solnp"), order = c(0, 0), seasonal = list(order =
  c(0, 0), period = NA), LOWER = NULL, UPPER = NULL, penalty = 1000,
  constraints = NULL, ini.pars.coef = NULL, na.action = "na.omit",
  ...)

Arguments

...

additional parameters passed in the optimizer (number of iterations, ...)

x

matrix of predictive variables

y

vector of outcome variable

order

Arma component (p, q)

seasonal

A specification of the seasonal part of the ARMA model (P,Q), plus the period (which defaults to 1).

optimizer

Optimizer package used for fit the model (include bayesian and genetic algorithm optimization). Possible values are: "solnp" (default) (Rsolnp), "gosonlp" (Rsolnp), "optim" (stats::optim), "nloptr" (nloptr), DEoptim ("DEoptim"), "dfoptim" (dfoptim), "mcmc" (FME::modMCMC), "MCMCmetrop" (MCMCpack::MCMCmetrop1R), 'adaptMCMC'(adaptMCMC::MCMC), "GA" (GA package), "GenSA" (GenSA package)

LOWER

(default NULL) vector of lower bounds for the coefficients. If the lenght of LOWER is not equal with the length of the coeefficients, then, the rest will be equal to -Inf

UPPER

(default NULL) vector of lower bounds for the coefficients. If the lenght of UPPER is not equal with the length of the coeefficients, then, the rest will be equal to +Inf

penalty

(default 1000) penalty to the objective function if some constraints do not fullfill

constraints

vector of constraints (see details)

ini.pars.coef

vector of initial parameters. In case there is some constraint, then the ini.pars.coef should fulfill the constraints. This vector is only for regression component.

model_fit

object of class ConsRegArima to update the Arma part and fix the coefficient from a previous model

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

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called.

na.action

na.action to the data

Details

Several optimizers of various R packages are implemented, including methods typically used in Bayesian regressions like Markov Chain Monte Carlo simulation.

Constraints will be a string: For example, if x1 and x2 are two coefficient names, then a constraint could be: "x1 > x2" or "x1+x2 > 2". For some constraints, one can write: "x1+x2>2, x1 > 1". Each constraint will be separate by commas.

Important: if there are some constraints that do not fulfill in a model without those constraints, it is recommended to use ini.pars.coef parameter to set initial values that fulfill constraints. See the example

On the other hand, aic value is computed as auto.arima function computes the AIC when method == 'CSS':

AIC = n * log(sigma2) + npar * 2

Where npar I set the number of coefficients.

Value

An object of class "ConsRegArima".

coefficients

Coefficients (regression + arma errors)

hessian

hessian matrix if the optimizer can return it

optimizer

optimizer object return (see details of each optimization package)

optimizer.name

name of the optimizer

df

nrow(data) - number of coefficients

rank

number of coefficients

objective_function

objective_function used

model

A list representing the Kalman Filter used in the fitting

sigma2

the MLE of the innovations variance

residuals

residuals of the model

fitted

fitted values of the model

fitted_regression

fitted values only of the regression part

fitted_arima

fitted values only of the arma part

metrics

Accuracy metrics of the model (accuracy function of the forecast package)

call

the matched call

y

objective series

x

regressors

formula

formula term

aic

the AIC value (see details)

bic

the BIC value

aicc

the AICc value

Author(s)

Josep Puig Salles

References

Peiris, M. & Perera, B. (1988), On prediction with fractionally Hyndman RJ, Khandakar Y (2008). “Automatic time series forecasting: the forecast package for R.”

Examples

data('series')
fit1 = ConsRegArima(formula = y ~ x1+x2 +x3+x4,
                    order = c(2, 1), data = series)
summary(fit1)
fit2 = ConsRegArima(formula = y ~ x1+x2 +x3+x4, order = c(2, 1),
                    data = series, constraints = '(x3 +.1) > x1',
                    ini.pars.coef = c(.96, .2, -.8, .4), UPPER = 1, LOWER = -1)

fit1$coefficients
fit2$coefficients

Fake data for regression

Description

Fake data to show gaussian model example

Usage

fake_data

Format

data

Examples

data('fake_data')

Plot an roll object plot an roll.ConsRegArima object

Description

Plot an roll object plot an roll.ConsRegArima object

Usage

## S3 method for class 'roll.ConsRegArima'
plot(x, ...)

Arguments

x

roll.ConsRegArima object

...

Additional params passed to ggplot2::labs function

Predict or fitted values of object ConsReg

Description

Predict or fitted values of object ConsReg

Usage

## S3 method for class 'ConsReg'
predict(object, newdata = NULL, components = F, ...)

Arguments

object

object of class ConsReg

newdata

New data to predict the objective function. If is NULL (default), then the fitted values will be returned

components

if its TRUE, it will return the predictions for each regression component

...

Additional argument passed to family. In particular, at this moment, if type = 'link', then for binomial family, it will return the link values

Value

predictions

Examples

data('fake_data')
data = fake_data
data$y = 1/(1+exp(-data$y))
data$y = ifelse(data$y > .5, 1, 0)
table(data$y)

fit5 = ConsReg(y~x1+x2+x3+x4, data = data,
               family = 'binomial', penalty = 10000,
               LOWER = -.5, UPPER = .2,
               optimizer = 'gosolnp')
pr = predict(fit5, newdata = data[1:3,], type = 'probability')
pr

Predict function for ConsRegArima object

Description

Obtains predictions of ConsRegArima object

Usage

## S3 method for class 'ConsRegArima'
predict(object, h = ifelse(is.null(newdata), 1,
  nrow(newdata)), newdata = NULL, intervals = 90, origdata = NULL,
  ...)

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

## S3 method for class 'predict.ConsRegArima'
plot(x, ...)

Arguments

object

ConsRegArima object

h

horizont to predict

newdata

data frame in which to look for variables with which to predict. In case there is no regression part, this parameter could be set NULL

intervals

Confidence level for prediction intervals (default 90)

origdata

Original data (default NULL). Useful if lagged predictive variables are used in the formula

...

Additional params passed to the function ggplot2::labs

x

object of class predict.ConsRegArima

Value

Returns an object of class predict.ConsRegArima

predict

dataframe with the predictions

table

dataframe with the predictions as well as the fitted values

intervals

Interval level

object

original object

rolling: Back-test your model

Description

Function for creating rolling density forecast from ConsRegArima models with option for refitting every n periods.

Usage

rolling(object, used.sample, refit, h = 1, orig.data, ...)

Arguments

object

ConsRegArima object

used.sample

The starting point in the dataset from which to initialize the rolling forecast.

refit

Determines every how many periods the model is re-estimated. If refit=0, then no refit is doing

h

The number of periods to forecast

orig.data

data original which was used to estimate the ConsRegArima object

...

Additional params for predict function

Value

results

data.frame with Real, Prediction, Prediction_High, Prediction_Low and fitted values of the object

refitT

how many periods the model is re-estimated

metrics

Main metrics of the predictions

See Also

plot.roll.ConsRegArima

Examples

data('series')
fit1 = ConsRegArima(formula = y ~ x1+x2 +x3, order = c(2, 1),
                    optimizer = 'solnp', data = series)
roll = rolling(fit1, used.sample = 40,
               refit = 5, orig.data = series, h=3)
roll
plot(roll)

Sales data set

Description

Sales data set for time series models

Usage

sales

Format

data

Examples

data('series')

Fake data for time series

Description

Fake data to show Arima example

Usage

series

Format

data