Package 'StepBeta'

StepBeta and StepBetaBinomial internal object

Description

StepBeta and StepBetaBinomial internal object

Usage

check_formula_terms(model)

Arguments

model

Beta regression model

Value

It returns the complete formula in a standard form

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StepBetaBinomial internal object

Description

StepBetaBinomial internal object

Usage

Combination_Terms(Terms, interaction = F)

Arguments

Terms	Variables from the starting model
interaction	Parameter to define which part of linear predictor to operate

Value

The function create alle possible combination of the linear predictor

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StepBeta internal object

Description

StepBeta internal object

Usage

dispersion_formula_terms(object)

Arguments

object

full model

Value

The function updates the formula for the dispersion component of the model

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StepBeta internal object

Description

StepBeta internal object

Usage

keep_formula_terms(the_formula, var_name)

Arguments

the_formula	Formula of Beta Regression model
var_name	Names of the variables to keep

Value

The function updates the formula, it keeps the variables defined by the user

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StepBeta internal object

Description

StepBeta internal object

Usage

remove_formula_interactions(the_formula)

Arguments

the_formula

Formula of Beta Regression model

Value

The function returns a reduced form of the formula. It excludes the interactive effects.

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Stepwise model selection for Beta-Binomial and Negative Binomial Regressions from aod package

Description

This function performs a stepwise algorithm to define the best linear predictor according to an user defined criterion (defeault is the Akaike Information Criterion aka AIC, but it is also possible to perform the corrected version AICc). It works only for object from betabin function (class "glimML" from "aod" package). If the object is different from "glimMl" class, the function performs the classical step function in "stats" package.

Usage

Step_glimML(object, k = 2, overdispersion = T, correctAIC = T)

Arguments

object	Object of class "glimML". If the class is different the function apply step function in "stats" package
k	The penalty parameter used for the criterion, e.g. default is k = 2 which identify the classical AIC. BIC can be obtained as k = log(n)
overdispersion	Provide the stepwise procedure also for the overdispersion component of the model (defined as random) Default is TRUE
correctAIC	Use AICc instead of AIC. Default TRUE is for AICc

Details

Step_glimML is different from step (stats) and stepAIC (MASS) functions; for an object of class betabin is impossible to use an algorithm which uses the function extractAIC. Starting from a full model it provides a backaward procedure where the scope model is the reduced one.

First, Step_glimML operates with all the principal effects included in the model; starting from the full model, the algorithm computes all the possible models, it calculates the measure (default is AIC) and it defines as a good predictor the model with lower AIC.

Then, based on the previous results, Step_glimML operates adding all the possible interactive effects. As in the first passage, the model choosen by the algorithm is the one whose AIC is the lowest.

During the procedure, Step_glimML considers all the possible models which betabin can fit. There are many cases where betabin function falls into error, in these cases the algorithm does not consider the linear predictor which causes the error and it goes forward.

Value

The algorithm returns an object of class "glimML"

Author(s)

Sergio Garofalo

References

Crowder, M.J., 1978. Beta-binomial anova for proportions. Appl. Statist. 27, 34-37.

Lawless, J.F., 1987. Negative binomial and mixed Poisson regression. The Canadian Journal of Statistics, 15(3): 209-225.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole. (has iris3 as iris.)

Examples

## Starting from a "betabinom" model

## Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language.
## Wadsworth & Brooks/Cole. (has iris3 as iris.)

## Prepare the data

library(aod)
data(iris)

############ Beta Binomial model
## Not run: 
n <- round(runif(dim(iris)[1],1,50))
y <- round(runif(length(n), 1,n))
data <- cbind(iris,y,n)
fullModel <- betabin(cbind(y, n - y) ~ Sepal.Width * Petal.Length + Petal.Width, ~ Species,
                     data = data)
reducedModel <- Step_glimML(fullModel)
summary(reducedModel)

## End(Not run)
############ Negative Binomial model
## Not run: 
data <- iris
data$Sepal.Length <- round(Sepal.length + runif(dim(data)[1],0,1) * 100)
fullModel <- negbin(Sepal.Length ~ Sepal.Width * Petal.Length + Petal.Width, ~ Species,
                    data = data)
reducedModel <-Step_glimML(fullModel)
summary(reducedModel)

## End(Not run)

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Stepwise model selection for Beta Regression

Description

This function performs a stepwise algorithm to define the best linear predictor according to an user defined criterion (defeault is the Akaike Information Criterion aka AIC). It works for objects of class "betareg" from betareg function. If the object is different from "betareg" class, the function performs the classical step function in "stats" package.

Usage

StepBeta(object, k = 2, dispersion = T)

Arguments

object	Object of class "betareg". If the class is different the function apply the step function in "stats" package
k	The penalty parameter used for the criterion, e.g. default is k = 2 which identify the classical AIC. BIC can be obtained as k = log(n)
dispersion	Provide the stepwise procedure also for dispersion parameter. Default is TRUE

Details

StepBeta is different from step (stats) and stepAIC (MASS) functions; for an object of class "betareg" is impossible to use an algorithm which uses the function extractAIC Starting from a full model it provides a backaward procedure where the scope model is the reduced one.

First, StepBeta operates with all the principal effects included in the model; starting from the full model, the algorithm computes all the possible models, it calculates the measure (default is AIC) and it defines as a good predictor the model with lower AIC.

Then, based on the previous results, StepBeta operates adding all the possible interactive effects. As in the first passage, the model choosen by the algorithm is the one whose AIC is the lowest.

During the procedure, StepBeta considers all the possible models which betareg can fit. There are many cases where betareg function falls into error, in these cases the algorithm does not consider the linear predictor which causes the error and it goes forward.

Value

The algorithm returns an object of class "betareg"

Author(s)

Sergio Garofalo

References

Cribari-Neto, F., and Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1–24. 10.18637/jss.v034.i02

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole. (has iris3 as iris.)

Examples

## Starting from a "betareg" model

## Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language.
## Wadsworth & Brooks/Cole. (has iris3 as iris.)

## Prepare the data

library(betareg)
data <- iris
data$Sepal.Length <- data$Sepal.Length/(max(data$Sepal.Length) + 0.01)

###### Mean parameters

fullModel <- betareg(Sepal.Length ~ Sepal.Width * Petal.Length *
                                    Petal.Width * Species, data = data)
reducedModel <- StepBeta(fullModel)
summary(reducedModel)

##### Mean and precision parameters

fullModel <- betareg(Sepal.Length ~ Sepal.Width * Petal.Length *
                                    Petal.Width * Species| Sepal.Width + Petal.Length,
                                    data = data)
reducedModel <- StepBeta(fullModel, dispersion = TRUE)
summary(reducedModel)

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