Help for package SLRMss

Title:

Symmetric Linear Regression Models for Small Samples

Version:

1.0.0

Description:

Ordinary and modified statistics for symmetrical linear regression models with small samples. The supported ordinary statistics include Wald, score, likelihood ratio and gradient. The modified statistics include score, likelihood ratio and gradient. Diagnostic tools associated with the fitted model are implemented. For more details see Medeiros and Ferrari (2017) <doi:10.1111/stan.12107>.

License:

GPL-3

Encoding:

UTF-8

RoxygenNote:

7.3.2

Imports:

methods, normalp, ssym

NeedsCompilation:

Packaged:

2025-07-06 15:25:48 UTC; eliardocosta

Author:

Ivonaldo S. da Silva-Júnior [aut, cre], Francisco Moisés C. de Medeiros

[aut], Eliardo Costa

[aut]

Maintainer:

Ivonaldo S. da Silva-Júnior <ivosilvestresjr@gmail.com>

Depends:

R (≥ 3.5.0)

Repository:

CRAN

Date/Publication:

2025-07-09 13:20:02 UTC

Symmetric Linear Regression Models for small samples

Description

Computes Wald, Likelihood Ratio, Score, or Gradient statistics for symmetric linear regression models. Also computes modified versions of the Likelihood Ratio, Score, and Gradient tests for small sample sizes.

Usage

SLRMss(formula, family, xi, statistic, testingbeta, data)

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.

family

A description of the error distribution to be used in the model. There are four supported families, Normal, t-Student, Power Exponential and Logistic ("Normal", "Student", "Powerexp" and "Logistic", respectively)

xi

An extra parameter of some specified error distribution. For t-Student is a positive value and for Power Exponential is a real number between -1 and 1/3.

statistic

The statistic which will be used. It includes "Wald", "LR", "Score" or "Gradient".

testingbeta

A vector containing the names of the variables to be testing.

data

An optional data frame containing the variables in the model.

Value

A list with the following components

beta.coefficients

A matrix with the estimated position parameters under alternative hypothesis.

phi

A numeric value with the estimated precision paramater under alternative hypothesis.

beta.coefficients.h0

A matrix with the estimated position parameters under null hypothesis.

phi.h0

A numeric value with the estimated precision paramater under null hypothesis.

y.fitted

A vector with the fitted values of the model.

null.hypothesis

The description of the null hypothesis.

statistics

A matrix with the selected statistics and theirs p-values. The corrected statistic is marked with an asterisk.

statistic.distribution

The name of the statistics' distribution used to test null hypothesis. It always return "Chi-Squared".

df

The degrees of freedom of the statistics' distribution. It's the length of the testingbeta vector.

residuals

The difference among the real y values and the fitted y.

std.residuals

The residuals divided by the precision parameter

AICc

The corrected Akaike Information Criterion for small samples.

BIC

The Bayesian Information Criterion.

References

Medeiros, F. M. C and Ferrari, S. L. P. (2017). Small-sample testing inference in symmetric and log-symmetric linear regression models, Statistica Neerlandica. doi:10.1111/stan.12107.

Examples

data(orange)
fit1 <- SLRMss(emulsion ~ arabicgum + xanthangum + orangeoil, family="Student", 
xi=3, testingbeta="xanthangum", statistic="LR", data=orange)
print(fit1)

data(cheese)
fit2 <- SLRMss(cohe ~ fat + xangum + sodcase, family="Normal", 
testingbeta=c("xangum","sodcase"), statistic="Gradient", data=cheese)
print(fit2)

Cheese data set

Description

The Nateghi's cheese data set gives measurements of the cheddar cheese textures.

Usage

data(cheese)

Format

A data frame with 16 observations on the following 4 variables.

Details

cohe The cohesiveness.
fat The fat percentage.
xangum The xanthan gum percentage.
sodcase The sodium caseinate percentage.

Source

Nateghi, L., Roohinejad, S., Totosaus, A., Mirhosseini, H., Shuhaimi, M., Meimandipour, A., Omidizadeh, A., Manap, M.Y.A. (2012). Optimization of textural properties and formulation of reduced fat Cheddar cheeses containing fat replacers. Journal of Food, Agriculture & Environment, 10(2), 46-54.

Extract the model coefficients for a SLRMss object

Description

This function provides the coefficients of a SLRMss model.

Usage

## S3 method for class 'SLRMss'
coef(object, H0 = FALSE, ...)

Arguments

object

An object of class SLRMss.

H0

If TRUE, choose the coefficients under the null hypothesis, if FALSE, choose the coefficients under alternative hypothesis (default).

...

Currently ignored.

Value

Coefficients extracted from the SLRMss object.

Examples

data(orange)
fit <- SLRMss(emulsion ~ arabicgum + xanthangum + orangeoil, family="Student",
xi=3, testingbeta="xanthangum", statistic="LR", data=orange)
coef(fit)

Quantile-quantile plots with simulated envelope of residuals for SLRMss objects

Description

This function provides an envelope plot of a fitted SLRMss model.

Usage

envplot(
  object,
  J = 100,
  conf = 0.95,
  seed = NULL,
  H0 = FALSE,
  colors = c("red", "green"),
  pch = 16,
  lty = 2,
  xlab,
  ylab,
  main
)

Arguments

object

An object of class SLRMss.

J

The number of Monte Carlo replications. 100 by default.

conf

The confidence level. 0.95 by default.

seed

An optional seed for the simulation.

H0

If TRUE, choose the fitted values under null hypothesis, if FALSE, choose the fitted values under alternative hypothesis (default).

colors

A vector with one or two characters. If it has one character, that represents the color of the plotted points. If it has two characters, the first one represents the color of the points out of the limits and the second one represents the color of the points under the limits. Red and green by default.

pch

A vector with one or two numbers. If it has one numeric, that represents the plot pch. If it has two numbers, the first one represents the pch of the points out of the limits and the second one represents the pch of the points under the limits. 16 by default.

lty

A vector with one or two numbers. If it has one number, that represents the lty of all lines. If it has two numbers, the first one represents the lty of the middle line and the second one represents the lty of the limits line. 2 by default.

xlab

A title for the x axis.

ylab

A title for the y axis.

main

A title for the plot.

Value

Quantile-quantile plot with simulated envelope for a SLRMss object.

Examples

data(orange)
fit <- SLRMss(emulsion ~ arabicgum + xanthangum + orangeoil, family="Student",
xi=3, testingbeta="xanthangum", statistic="LR", data=orange)
envplot(fit)

Extract model fitted values for a SLRMss object

Description

This function provides the fitted values of a SLRMss model.

Usage

## S3 method for class 'SLRMss'
fitted(object, H0 = FALSE, ...)

Arguments

object

An object of class SLRMss.

H0

If TRUE, choose the fitted values under null hypothesis, if FALSE, choose the fitted values under alternative hypothesis (default).

...

Currently ignored.

Value

Fitted values extracted from the SLRMss object.

Examples

data(orange)
fit <- SLRMss(emulsion ~ arabicgum + xanthangum + orangeoil, family="Student", xi=3,
testingbeta="xanthangum", statistic="LR", data=orange)
fitted(fit)

Orange data Set

Description

The Mirhosseini's and Tan's data set gives the measurements of the physicochemical properties of emulsion in orange drinks.

Usage

data(orange)

Format

A data frame with 20 observations on the following 4 variables.

Details

emulsion The emulsion density in g/cm3.
arabicgum The arabic gum quantity in g.
xanthangum The xanthan gum quantity in g.
orangeoil The orange oil quantity in g.

Source

Mirhosseini, H., Tan, C.P. (2010). Discrimination of orange beverage emulsions with different formulations using multivariate analysis. Journal of the Science of Food and Agriculture, 90, 1308-1316.

Diagnostic plots for SLRMss objects

Description

This function provides four plot for residual analysis. The first plot shows the standardized residuals against the fitted values. The second one shows the standardized residuals against by their index. The third one presents QQ-normal plot of them and the last one shows their density estimate.

Usage

## S3 method for class 'SLRMss'
plot(
  x,
  H0 = FALSE,
  xlab = c("Fitted Values", "Index", "Theoretical Quantiles", "Standardized Residuals"),
  ylab = c("Standardized Residuals", "Standardized Residuals", "Standardized Residuals",
    "Density"),
  main = c("Residuals Against Fitted Values", " Residuals Against Index",
    "Normal Q-Q Plot", "Density Estimate"),
  ...
)

Arguments

x

An object of class SLRMss.

H0

If TRUE, plot the graphics under null hypothesis, if FALSE, plot the graphics under alternative hypothesis (default).

xlab

A vector containing the four x-axis titles.

ylab

A vector containing the four y-axis titles.

main

A vector containing the four main plot titles.

...

Currently ignored.

Value

Four diagnostic plots extracted from a SLRMss object.

Examples

data(orange)
fit <- SLRMss(emulsion ~ arabicgum + xanthangum + orangeoil, family="Student",
xi=3, testingbeta="xanthangum", statistic="LR", data=orange)
plot(fit)

Print values of a SLRMss object

Description

This function displays a succinct summary of the fitted model. It includes the mean and dispersion parameter estimates, corrected Akaike information criterion and Bayesian information criterion.

Usage

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

Arguments

x

An object of class SLRMss.

...

Currently ignored.

Value

Coefficients, AICc and BIC extracted from a SLRMss object.

Examples

data(orange)
fit <- SLRMss(emulsion ~ arabicgum + xanthangum + orangeoil, family="Student", xi=3,
testingbeta="xanthangum", statistic="LR", data=orange)
print(fit)

Extract residuals model for SLRMss objects

Description

This function provides the residuals of a SLRMss model.

Usage

## S3 method for class 'SLRMss'
residuals(object, H0 = FALSE, std = FALSE, ...)

Arguments

object

An object of class SLRMss.

H0

If TRUE, choose the residuals under null hypothesis, if FALSE, choose the residuals under alternative hypothesis (default).

std

If TRUE, choose the standardized residuals, if FALSE, choose the non-standardized residuals (default).

...

Currently ignored.

Value

Residuals extracted from a SLRMss object.

Examples

data(orange)
fit <- SLRMss(emulsion ~ arabicgum + xanthangum + orangeoil, family="Student",
xi=3, testingbeta="xanthangum", statistic="LR", data=orange)
residuals(fit)

SLRMss object summaries

Description

This function displays the summary of the fitted model. It includes parameter estimates under both, null and alternative hypothesis, corrected Akaike information criterion, bayesian information criterion and choosed statistics.

Usage

## S3 method for class 'SLRMss'
summary(object, ...)

Arguments

object

An object of class SLRMss.

...

Currently ignored.

Value

A selected components extracted from a SLRMss object.

Examples

data(orange)
fit <- SLRMss(emulsion ~ arabicgum + xanthangum + orangeoil, family="Student",
xi=3, testingbeta="xanthangum", statistic="LR", data=orange)
summary(fit)