Package 'BinaryEPPM'

Title: Mean and Scale-Factor Modeling of Under- And Over-Dispersed Binary Data
Description: Under- and over-dispersed binary data are modeled using an extended Poisson process model (EPPM) appropriate for binary data. A feature of the model is that the under-dispersion relative to the binomial distribution only needs to be greater than zero, but the over-dispersion is restricted compared to other distributional models such as the beta and correlated binomials. Because of this, the examples focus on under-dispersed data and how, in combination with the beta or correlated distributions, flexible models can be fitted to data displaying both under- and over-dispersion. Using Generalized Linear Model (GLM) terminology, the functions utilize linear predictors for the probability of success and scale-factor with various link functions for p, and log link for scale-factor, to fit a variety of models relevant to areas such as bioassay. Details of the EPPM are in Faddy and Smith (2012) <doi:10.1002/bimj.201100214> and Smith and Faddy (2019) <doi:10.18637/jss.v090.i08>.
Authors: David M. Smith [aut, cre], Malcolm J. Faddy [aut]
Maintainer: David M. Smith <[email protected]>
License: GPL-2
Version: 3.0
Built: 2024-11-02 06:28:04 UTC
Source: CRAN

Help Index

Mean and Scale-Factor Modeling of Under- And Over-Dispersed Binary Data

Description

Under- and over-dispersed binary data are modeled using an extended Poisson process model (EPPM) appropriate for binary data. A feature of the model is that the under-dispersion relative to the binomial distribution only needs to be greater than zero, but the over-dispersion is restricted compared to other distributional models such as the beta and correlated binomials. Because of this, the examples focus on under-dispersed data and how, in combination with the beta or correlated distributions, flexible models can be fitted to data displaying both under- and over-dispersion. Using Generalized Linear Model (GLM) terminology, the functions utilize linear predictors for the probability of success and scale-factor with various link functions for p, and log link for scale-factor, to fit a variety of models relevant to areas such as bioassay. Details of the EPPM are in Faddy and Smith (2012) and Smith and Faddy (2019). Two important changes from version 2.3 are the change to scale-factor rather than variance modeling, and the inclusion of a vignette.

Details

Index of help topics: 

BBprob                  Calculation of vector of probabilities for the
                        beta binomial distribution.
Berkshires.litters      The data are of the number of male piglets born
                        in litters of varying sizes for the Berkshire
                        breed of pigs.
BinaryEPPM              Fitting of EPPM models to binary data.
BinaryEPPM-package      Mean and Scale-Factor Modeling of Under- And
                        Over-Dispersed Binary Data
CBprob                  Calculation of vector of probabilities for the
                        correlated binomial distribution.
EPPMprob                Calculation of vector of probabilities for a
                        extended Poisson process model (EPPM).
GBprob                  Calculation of vector of probabilities for the
                        EPPM binomial distribution.
KupperHaseman.case      Kupper and Haseman example data
LL.Regression.Binary    Function called by optim to calculate the log
                        likelihood from the probabilities and hence
                        perform the fitting of regression models to the
                        binary data.
LL.gradient             Function used to calculate the first
                        derivatives of the log likelihood with respect
                        to the model parameters.
Model.BCBinProb         Probabilities for beta and correlated binomial
                        distributions given p's and scale-factors.
Model.Binary            Function for obtaining output from
                        distributional models.
Model.GB                Probabilities for binomial and EPPM extended
                        binomial distributions given p's and b.
Model.JMVGB             Probabilities for EPPM extended binomial
                        distributions given p's and scale-factors.
Parkes.litters          The data are of the number of male piglets born
                        in litters of varying sizes for the Parkes
                        breed of pigs.
Yorkshires.litters      The data are of the number of male piglets born
                        in litters of varying sizes for the Yorkshire
                        breed of pigs.
coef.BinaryEPPM         Extraction of model coefficients for BinaryEPPM
                        Objects
cooks.distance.BinaryEPPM
                        Cook's distance for BinaryEPPM Objects
doubexp                 Double exponential Link Function
doubrecip               Double reciprocal Link Function
fitted.BinaryEPPM       Extraction of fitted values from BinaryEPPM
                        Objects
hatvalues.BinaryEPPM    Extraction of hat matrix values from BinaryEPPM
                        Objects
logLik.BinaryEPPM       Extract Log-Likelihood
loglog                  Log-log Link Function
negcomplog              Negative complementary log-log Link Function
plot.BinaryEPPM         Diagnostic Plots for BinaryEPPM Objects
powerlogit              Power Logit Link Function
predict.BinaryEPPM      Prediction Method for BinaryEPPM Objects
print.BinaryEPPM        Printing of BinaryEPPM Objects
print.summaryBinaryEPPM
                        Printing of summaryBinaryEPPM Objects
residuals.BinaryEPPM    Residuals for BinaryEPPM Objects
ropespores.case         Dilution series for the presence of rope
                        spores.
ropespores.grouped      Dilution series for the presence of rope
                        spores.
summary.BinaryEPPM      Summary of BinaryEPPM Objects
vcov.BinaryEPPM         Variance/Covariance Matrix for Coefficients
waldtest.BinaryEPPM     Wald Test of Nested Models for BinaryEPPM
                        Objects
wordcount.case          Number of occurences of an article in five-word
                        and ten-word samples from two authors.
wordcount.grouped       Number of occurences of an article in five-word
                        and ten-word samples from two authors.

Further information is available in the following vignettes:

Vignette_RSP_one.pdf Mean and Scale-Factor Modeling of Under- and Overdispersed Grouped Binary Data (source, pdf)

Author(s)

David M. Smith [aut, cre], Malcolm J. Faddy [aut]

Maintainer: David M. Smith <[email protected]>

References

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

Faddy M, Smith D. (2012). Extended Poisson Process Modeling and Analysis of Grouped Binary Data. Biometrical Journal, 54, 426-435. doi:10.1002/bimj.201100214.

Grun B, Kosmidis I, Zeileis A. (2012). Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned. Journal of Statistical Software, 48(11), 1-25. doi:10.18637/jss.v048.i11.

Smith D, Faddy M. (2019). Mean and Variance Modeling of Under-Dispersed and Over-Dispersed Grouped Binary Data. Journal of Statistical Software, 90(8), 1-20. doi:10.18637/jss.v090.i08.

Zeileis A, Croissant Y. (2010). Extended Model Formulas in R: Multiple Parts and Multiple Responses. Journal of Statistical Software, 34(1), 1-13. doi:10.18637/jss.v034.i01.

See Also

CountsEPPM betareg

Examples

data("ropespores.case")
output.fn <- BinaryEPPM(data = ropespores.case,
                  number.spores / number.tested ~ 1 + offset(logdilution),
                  model.type = 'p only', model.name = 'binomial')                 
summary(output.fn)

Calculation of vector of probabilities for the beta binomial distribution.

Description

Given a vector of parameters and a scalar of the number of trials the function returns a vector of probabilities.

Usage

BBprob(twoparameter, nt)

Arguments

twoparameter

A vector of the parameters of the beta binomial distribution.

nt

The number of trials.

Value

Vector of probabilities

Author(s)

David M. Smith <[email protected]>

References

Smith D (1982). Algorithm AS189. Maximum Likelihood Estimation of the Parameters of the Beta Binomial Distribution. Applied Statistics, 32, 196-204.

Williams D (1996). "Overdispersion in Logistic Linear Models." In B Mrgan (ed.), Statistics in Toxicology, pp75-84. Oxford Science Publications.

Examples

twoparameter <- c(0.96477815,0.7561417)
names(twoparameter) <- c('p','theta')
nt <- 37
BBprob(twoparameter,nt)

The data are of the number of male piglets born in litters of varying sizes for the Berkshire breed of pigs.

Description

The data are arranged as a list of binomial frequency distributions where the listing is by litter size which is included both as a variate (vsize) and as a factor (fsize)

Usage

data("Berkshires.litters")

Format

The format is: List of 3 $ fsize : Factor w/ 7 levels " size 5"," size 6",..: 1 2 3 4 5 6 7 $ vsize : int [1:7] 5 6 7 8 9 10 11 $ number.success:List of 7 ..$ : num [1:6] 8 29 72 65 40 3 ..$ : num [1:7] 5 22 89 129 74 35 4 ..$ : num [1:8] 1 25 62 131 136 89 26 5 ..$ : num [1:9] 1 15 79 179 219 149 71 33 4 ..$ : num [1:10] 2 6 47 117 172 181 117 40 9 2 ..$ : num [1:11] 2 1 23 65 131 145 120 61 20 3 ... ..$ : num [1:12] 0 3 9 22 53 94 72 54 20 4 ...

Source

Brooks, R.J., James, W.H., Gray, E. (1993). Modelling Sub-Binomial Variation in the Frequency of Sex Combinations in Litters of Pigs. Biometrics 47, 403-417.

Examples

data("Berkshires.litters")

Fitting of EPPM models to binary data.

Description

Fits regression models to under- and over-dispersed binary data using extended Poisson process models.

Usage

BinaryEPPM(formula, data, subset = NULL, na.action = NULL, 
       weights = NULL, model.type = "p only", 
       model.name = "EPPM extended binomial", link = "cloglog", 
       initial = NULL, method = "Nelder-Mead", 
       pseudo.r.squared.type = "square of correlation", control = NULL)

Arguments

formula

Formulae for the probability of a success p and scale-factor. The object used is from the package Formula of Zeileis and Croissant (2010) which allows multiple parts and multiple responses. "formula" should consist of a left hand side (lhs) of single response variable and a right hand side (rhs) of one or two sets of variables for the linear predictors for the mean and (if two sets) the variance. This is as used for the R function "glm" and also, for example, as for the package "betareg" (Cribari-Neto and Zeileis, 2010). The function identifies from the argument data whether a data frame (as for use of "glm") or a list has been input. The list should be exactly the same as for a data frame except that the response variable is a list of vectors of frequency distributions rather than two vectors of paired counts of number responding (r) out of number tested as for the data frame. The subordinate functions fit models where the response variables are "p.obs", or "scalef.obs" according to the model type being fitted. The values for these response variables are not input as part of "data", they are calculated within the function from a list of grouped binary data input. If the "model.type" is "p only", "formula" consists of a lhs of the response variable and a rhs of the terms of the linear predictor for the mean model. If the "model.type" is "p and scale-factor" there are two sets of terms in the rhs of "formula" i.e., "p.obs" and "scalef.obs" together with the two sets of terms for the linear predictors of p and scale-factor.

data

"data" should be either a data frame (as for use of "glm") or a list. The list should be exactly the same as for a data frame except that the response variable is a list of vectors of frequency distributions rather than a vector of single counts as for the data frame. Only one list is allowed within "data" as it is identified as the dependent variable. If other lists are in "data", for example for use as weights, they should be removed from "data" prior to calling this function. The extracted list can be called using the "weights" argument to this function. Within the function a working list "listcounts" and data frames with components such as "p.obs", "scalef.obs", "covariates", "offset.mean", "offset.variance" are set up . The component "covariates" is a data frame of vectors of covariates in the model. The component "listcounts" is a list of vectors of frequency distributions, or the single pairs of r/n in grouped form if "data" is a data frame.

subset

Subsetting commands.

na.action

Action taken for NAs in data.

weights

Vector of list of lists of weights.

model.type

Takes one of two values i.e. "p only" or "p and scale-factor". The "p only" value fits a linear predictor function to the parameter a in equation (3) of Faddy and Smith (2012). If the model type being fitted is binomial, modeling a is the same as modeling the mean. For the negative binomial the mean is b exp(a)-1), b also being as in equation (3) of Faddy and Smith (2012). The "p and scale-factor" value fits linear predictor functions to both the probability of a success p and the scale-factor.

model.name

If model.type is "p only" the model being fitted is one of the four "binomial", "EPPM extended binomial", "beta binomial", "correlated binomial". If model.type is "p and scale-factor" the model being fitted is either "EPPM extended binomial" i.e. as equations (4) and (6) of Faddy and Smith (2012) or one of the two "beta binomial", "correlated binomial".

link

Takes one of nine values i.e., 'logit', 'probit', 'cloglog', 'cauchit', 'log', 'loglog', 'double exponential', 'double reciprocal', 'power logit'. The default is 'cloglog'. The 'power logit' has an attribute of 'power' for which the default is 1 i.e., a logit link.

initial

This is a vector of initial values for the parameters. If this vector is NULL then initial values based on a fitting binomial models using "glm" are calculated within the function.

method

Takes one of the two values "Nelder-Mead" or "BFGS" these being arguments of optim.

pseudo.r.squared.type

Takes one of the three values "square of correlation", "R square" or "max-rescaled R square". The "default" is as used in Cribari-Neto and Zeileis (2010) and is the square of the correlation between the observed and predicted values on the GLM linear predictor scale. The other two are as described in Cox and Snell (1989), and Nagelkerke (1991) and apply to logistic regression.

control

"control" is a list of control parameters as used in "optim". If this list is NULL the defaults for "optim" are set as "control <- list(fnscale=-1, trace=0, maxit=1000)". The control parameters that can be changed by inputting a variable length list are "fnscale, trace, maxit, abstol, reltol, alpha, beta, gamma". Details of "optim" and its control parameters are available in the online R help manuals.

Value

An object of class "BinaryEPMM" is returned. A list of object items follows.

data.type

The type of the data i.e., data frame or list
list.data

Data as a list of lists of frequency distributions
call

The call of the function
formula

The formula argument
model.type

The type of model being fitted
model.name

The model being fitted
link

The link function
covariates.matrix.p

The design matrix for the probability of a success
covariates.matrix.scalef

The design matrix for the scalefactor
offset.p

The offset vector for the probability of a success
offset.scalef

The offset vector for the scalefactor
coefficients

Estimates of model parameters
loglikelihood

Loglikelihood
vcov

The variance/covariance matrix
n

The number of observations
nobs

The number of observations
df.null

The degrees of freedom of the null model
df.residual

The degrees of freedom of the residual
vnmax

Vector of maximums of grouped count data vectors in list.counts
weights

Vector or list of weights
converged

Whether the iterative process converged, TRUE or FALSE
iterations

Number of iterations taken
method

Method for optim either Nelder-Mead or BFGS
pseudo.r.squared

Pseudo R**2 value
start

Starting values for iterative process
optim

Estimates of model parameters
control

Control parameters for optim
fitted.values

Fitted values for probability of success
y

Dependent variable
terms

Terms in model fitted

Author(s)

David M. Smith <[email protected]>

References

Cox DR, Snell EJ. (1989). Analysis of Binary Data. Second Edition. Chapman & Hall.

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

Grun B, Kosmidis I, Zeileis A. (2012). Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned. Journal of Statistical Software, 48(11), 1-25. doi:10.18637/jss.v048.i11.

Faddy M, Smith D. (2012). Extended Poisson Process Modeling and Analysis of Grouped Binary Data. Biometrical Journal, 54, 426-435. doi:10.1002/bimj.201100214.

Nagelkerke NJD. (1991). A Note on a General Definition of the Coefficient of Determination. Biometrika, 78, 691-692.

Smith D, Faddy M. (2019). Mean and Variance Modeling of Under-Dispersed and Over-Dispersed Grouped Binary Data. Journal of Statistical Software, 90(8), 1-20. doi:10.18637/jss.v090.i08.

Zeileis A, Croissant Y. (2010). Extended Model Formulas in R: Multiple Parts and Multiple Responses. Journal of Statistical Software, 34(1), 1-13. doi:10.18637/jss.v034.i01.

See Also

CountsEPPM betareg

Examples

data("ropespores.case") 
output.fn <- BinaryEPPM(data = ropespores.case,
                  number.spores / number.tested ~ 1 + offset(logdilution),
                  model.type = "p only", model.name = "binomial")   
summary(output.fn)

Calculation of vector of probabilities for the correlated binomial distribution.

Description

Given a vector of parameters and a scalar of the number of trials the function returns a vector of probabilities.

Usage

CBprob(twoparameter, nt)

Arguments

twoparameter

A vector of the parameters of the correlated binomial distribution.

nt

The number of trials.

Value

Vector of probabilities

Author(s)

David M. Smith <[email protected]>

References

Kupper L, Haseman J (1978). The Use of a Correlated Binomial Model for the Analysis of Toxicological Experiments. Biometrics, 34(1), 69-76.

Examples

twoparameter <- c(0.971242852,0.001465007)
names(twoparameter) <- c('p','rho')
nt <- 37
CBprob(twoparameter,nt)

Extraction of model coefficients for BinaryEPPM Objects

Description

Extract the regression model coefficients from models of class "BinaryEPMM".

Usage

## S3 method for class 'BinaryEPPM'
coef(object, prtpar = c("full", "p", "scale.factor"), ...)

Arguments

object

fitted model object of class "BinaryEPPM".

prtpar

character indicating coefficients of the fitted model to be output: all coefficients ("full"), coefficients of the model for probability of success ("p"), coefficients of the model for scale-factor ("scale.factor")

...

some methods for this generic function require additional arguments.

Details

One of a set of standard extractor functions for fitted model objects of class "BinaryEPPM.

Value

Vector of coefficients of fitted regression model.

Author(s)

David M. Smith <[email protected]>

See Also

betareg

Examples

data("ropespores.case")
output.fn <- BinaryEPPM(data = ropespores.case,
                  number.spores / number.tested ~ 1 + offset(logdilution))   
coef(output.fn, prtpar = "full")
coef(output.fn, prtpar = "p")
coef(output.fn, prtpar = "scale.factor")

Cook's distance for BinaryEPPM Objects

Description

Calculates Cook's distances for BinaryEPPM objects.

Usage

## S3 method for class 'BinaryEPPM'
cooks.distance(model, ...)

Arguments

model

fitted model object of class "BinaryEPPM".

...

some methods for this generic function require additional arguments.

Details

Cook's distances as in GLMs.

Value

A vector of Cook's distances.

Author(s)

David M. Smith <[email protected]>

References

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

See Also

betareg

Examples

data("ropespores.case") 
output.fn <- BinaryEPPM(data = ropespores.case,
                  number.spores / number.tested ~ 1 + offset(logdilution),
                  model.type = 'p only', model.name = 'binomial')   
cooks.distance(output.fn)

Double exponential Link Function

Description

Computes the double exponential link function, including its inverse.

Usage

doubexp()

Value

The double exponential transformation of theta.

Author(s)

David M. Smith <[email protected]>

References

Ford I, Torsney B, Wu C (1992). "The Use of a Canonical Form in the Construction of Locally Optimal Designs for Non-linear Problems." Journal of the Royal Statistical Society B, 54, 569-583. doi:10.1111/j.2517-6161.1992.tb01897.x

Double reciprocal Link Function

Description

Computes the double reciprocal link function, including its inverse.

Usage

doubrecip()

Value

The double reciprocal transformation of theta.

Author(s)

David M. Smith <[email protected]>

References

Ford I, Torsney B, Wu C (1992). "The Use of a Canonical Form in the Construction of Locally Optimal Designs for Non-linear Problems." Journal of the Royal Statistical Society B, 54, 569-583. doi:10.1111/j.2517-6161.1992.tb01897.x

Calculation of vector of probabilities for a extended Poisson process model (EPPM).

Description

Calculates a vector of probabilities given a vector of rates using the matrix exponential function from Maechler, Dutang, Goulet, Bates, Firth (2023).

Usage

EPPMprob(vlambda)

Arguments

vlambda

a vector of rates of an extended Poisson process.

Details

This is a similar function to that in Smith and Faddy (2014).

Value

The value returned is a vector of probabilities.

Author(s)

David M. Smith <[email protected]>

References

Maechler M, Dutang C, Goulet V, Bates D, Firth D. (2023). expm: Matrix Exponential. R package version 0.999-8, https://CRAN.R-project.org/package=expm.

Smith D, Faddy M (2014). CountsEPPM: Mean and Variance Modeling of Count Data. R package version 2.0, https://CRAN.R-project.org/package=CountsEPPM.

Extraction of fitted values from BinaryEPPM Objects

Description

This function is generic. Extract the fitted values from models of class "BinaryEPMM".

Usage

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

Arguments

object

fitted model object of class "BinaryEPPM".

...

currently not used.

Details

This function is included so that function lrtest from package lmtest can be used.

Value

An vector of class "numeric" of the fitted values from the object of class "BinaryEPMM".

Author(s)

David M. Smith <[email protected]>

See Also

fitted

Calculation of vector of probabilities for the EPPM binomial distribution.

Description

Given a vector of parameters and a scalar of the number of trials the function returns a vector of probabilities. The name GBprob is used to avoid confusion with EPPMprob which is the function calculating the probabilties given the constructed vector vector of lambdas.

Usage

GBprob(twoparameter, nt)

Arguments

twoparameter

A vector of the parameters of the EPPM binomial distribution.

nt

The number of trials.

Value

Vector of probabilities

Author(s)

David M. Smith <[email protected]>

References

Faddy M, Smith D. (2012). Extended Poisson Process Modeling and Analysis of Grouped Binary Data. Biometrical Journal, 54, 426-435. doi:10.1002/bimj.201100214.

Examples

twoparameter <- c(0.971242852,0.001465007)
names(twoparameter) <- c('p','b')
nt <- 37
GBprob(twoparameter,nt)

Extraction of hat matrix values from BinaryEPPM Objects

Description

Extract the values of the hat matrix from models of class "BinaryEPMM".

Usage

## S3 method for class 'BinaryEPPM'
hatvalues(model, ...)

Arguments

model

fitted model object of class "BinaryEPPM".

...

some methods for this generic function require additional arguments.

Value

The calculated hat values for the fitted model. These are used to calculate Cook's distances.

Author(s)

David M. Smith <[email protected]>

References

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

See Also

betareg

Examples

data("ropespores.case") 
output.fn <- BinaryEPPM(data = ropespores.case,
                  number.spores / number.tested ~ 1 + offset(logdilution),
                  model.type = 'p only', model.name = 'binomial')   
hatvalues(output.fn)

Kupper and Haseman example data

Description

Data of the number of deaths out of number of implants for pregnant female mice for two groups each of size 10.

Usage

data("KupperHaseman.case")

Format

A data frame with 20 observations on the following 3 variables.

Group

a factor with levels Control Treated

Number.Deaths

a numeric vector

Number.Implants

a numeric vector

Source

Kupper L, Haseman J. (1978). The Use of a Correlated Binomial Model for the Analysis of Toxicological Experiments. Biometrics, 34(1), 69-76.

Examples

data("KupperHaseman.case")

Function used to calculate the first derivatives of the log likelihood with respect to the model parameters.

Description

Function used to calculate the first derivatives of the log likelihood with respect to the model parameters. These are numerical derivatives calculated using the numerical derivative functions of Gilbert and Varadhan (2015).

Usage

LL.gradient(parameter, model.type, model.name, link, ntrials, nsuccess,
            covariates.matrix.p, covariates.matrix.scalef, 
            offset.p, offset.scalef, weights, grad.method)

Arguments

parameter

A vector of the parameters of the model which is set to initial estimates on function call.

model.type

Takes one of two values i.e. 'p only' or 'p and scale-factor'. The 'p only' value fits linear predictor functions to the probability of a success 'p' as in Faddy and Smith (2012). The 'p and scale-factor' value fits linear predictor functions to both the 'p' and the scale-factor. The default is 'p and scale-factor'.

model.name

If model.type is 'p only' the model being fitted is one of the four 'binomial', 'EPPM extended binomial', 'beta binomial' or 'correlated binomial'. If model.type is 'p and scale-factor' the model being fitted is one of the three 'EPPM extended binomial', 'beta binomial' or 'correlated binomial'. Information about these models is given in Faddy and Smith (2012). The default is 'EPPM extended binomial'.

link

Takes one of nine values i.e., 'logit', 'probit', 'cloglog', 'cauchit', 'log', 'loglog', 'double exponential', 'double reciprocal', 'power logit'. The default is 'cloglog'. The 'power logit' has an attribute of 'power' for which the default is 1 i.e., a logit link.

ntrials

A vector length 'n+1' representing the number of trials 'n' i.e., a vector with all elements equal to 'n'.

nsuccess

A vector representing the frequency distribution of the binomial distribution for fixed number of trials 'n'.

covariates.matrix.p

A matrix of covariates for the mean where rows are the number of values in list.binary and columns the covariates. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

covariates.matrix.scalef

A matrix of covariates for the variance where rows are the number of values in list.binary and columns the covariates. The default is a vector of ones. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

offset.p

An offset vector for the probability of success p. The default is a vector of ones.

offset.scalef

An offset vector for the scale-factor. The default is a vector of ones.

weights

A vector or list of weights for the modeling of probability of success. The default is a vector of ones.

grad.method

Numerical method used to calculate gradients when the optimization method for optim is BFGS either simple or Richardson. This is the grad.method attribute of argument method of BinaryEPPM. The default is simple.

Value

A vector of numerical first derivatives.

Author(s)

David M. Smith <[email protected]>

References

Gilbert P, Varadhan R. (2015). numDeriv: Accurate Numerical Derivatives. R Package version 2014.2-1, https://CRAN.R-project.org/package=numDeriv.

Examples

link <- 'cloglog'
attr(link, which="p") <- make.link(link)
nsuccess <- list(c(rep(0,5),352,479,530,291,101,17))
ntrials  <- list(c(rep(10,11)))
parameter <- c(0.06363398,-0.47085362)
LL.gradient(parameter, model.type = "p and scale-factor",
     model.name = "EPPM extended binomial", link = link, ntrials = ntrials, nsuccess = nsuccess,
     covariates.matrix.p = matrix(c(1), nrow=1),
     covariates.matrix.scalef = matrix(c(1), nrow=1), 
     offset.p = c(0), offset.scalef = c(0), weights = list(c(rep(1,11))),
     grad.method = "Richardson")

Function called by optim to calculate the log likelihood from the probabilities and hence perform the fitting of regression models to the binary data.

Description

Fits specified regression models to the data.

Usage

LL.Regression.Binary(parameter,model.type,model.name,link,ntrials,nsuccess,
                     covariates.matrix.p,covariates.matrix.scalef,
                     offset.p,offset.scalef,weights,grad.method)

Arguments

parameter

A vector of the parameters of the model which is set to initial estimates on function call.

model.type

Takes one of two values i.e. 'p only' or 'p and scale-factor'. The 'p only' value fits linear predictor functions to the probability of a success 'p' as in Faddy and Smith (2012). The 'p and scale-factor' value fits linear predictor functions to both the 'p' and the scale-factor. The default is 'p and scale-factor'.

model.name

If model.type is 'p only' the model being fitted is one of the four 'binomial', 'EPPM extended binomial', 'beta binomial' or 'correlated binomial'. If model.type is 'p and scale-factor' the model being fitted is one of the three 'EPPM extended binomial', 'beta binomial' or 'correlated binomial'. Information about these models is given in Faddy and Smith (2012). The default is 'EPPM extended binomial'.

link

Takes one of nine values i.e., 'logit', 'probit', 'cloglog', 'cauchit', 'log', 'loglog', 'double exponential', 'double reciprocal', 'power logit'. The default is 'cloglog'. The 'power logit' has an attribute of 'power' for which the default is 1 i.e., a logit link.

ntrials

A vector length 'n+1' representing the number of trials 'n' i.e., a vector with all elements equal to 'n'.

nsuccess

A vector representing the frequency distribution of the binomial distribution for fixed number of trials 'n'.

covariates.matrix.p

A matrix of covariates for the mean where rows are the number of values in list.binary and columns the covariates. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

covariates.matrix.scalef

A matrix of covariates for the variance where rows are the number of values in list.binary and columns the covariates. The default is a vector of ones. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

offset.p

An offset vector for the probability of success p. The default is a vector of ones.

offset.scalef

An offset vector for the scale-factor. The default is a vector of ones.

weights

A vector or list of weights for the modeling of probability of success. The default is a vector of ones.

grad.method

Numerical method used to calculate gradients either simple or Richardson. The default is simple.

Value

The log likelihood is returned.

Author(s)

David M. Smith <[email protected]>

References

Faddy M, Smith D. (2012). Extended Poisson Process Modeling and Analysis of Grouped Binary Data. Biometrical Journal, 54, 426-435. doi:10.1002/bimj.201100214.

Examples

link <- 'cloglog'
attr(link, which="p") <- make.link(link)
nsuccess <- list(c(rep(0,5),352,479,530,291,101,17))
ntrials  <- list(c(rep(10,11)))
parameter <- c(0.06363398,-0.47085362)
LL.Regression.Binary(parameter, model.type = "p and scale-factor",
            model.name = "EPPM extended binomial", link, ntrials, nsuccess, 
            covariates.matrix.p = matrix(c(1), nrow=1),
            covariates.matrix.scalef = matrix(c(1), nrow=1),
            offset.p = c(0), offset.scalef = c(0),
            weights = list(c(rep(1,11))))

Extract Log-Likelihood

Description

This function is generic. It is a method for extracting the log-likelihood for objects of class "BinaryEPPM".

Usage

## S3 method for class 'BinaryEPPM'
logLik(object, ...)

Arguments

object

fitted model object of class "BinaryEPPM".

...

some methods for this generic function require additional arguments

Details

logLik is most commonly used for a model fitted by maximum likelihood as is done here.

Value

The log likelihood value for the fitted model object.

Author(s)

David M. Smith <[email protected]>

See Also

betareg

Log-log Link Function

Description

Computes the loglog link function, including its inverse.

Usage

loglog()

Details

Same link function as in Cribari-Neto and Zeileis (2010).

Value

The loglog of theta where the logarithms are to base e.

Author(s)

David M. Smith <[email protected]>

References

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

Probabilities for beta and correlated binomial distributions given p's and scale-factors.

Description

Calculates the probabilities for beta and correlated binomials given values for p's and scale-factors.

Usage

Model.BCBinProb(parameter, model.type, model.name, link, ntrials, covariates.matrix.p, 
covariates.matrix.scalef = matrix(c(rep(1, nrow(covariates.matrix.p))), ncol = 1), 
offset.p = c(rep(0, length(ntrials))), offset.scalef = c(rep(0, length(ntrials))))

Arguments

parameter

A vector of the parameters of the model which is set to initial estimates on function call.

model.type

Takes one of two values i.e. 'p only' or 'p and scale-factor'. The 'p only' value fits a linear predictor function to the parameter p which is the 'm(1)' in equation (6) of Faddy and Smith (2012) divided by 'N'. The 'p and scale-factor' value fits linear predictor functions to both p and the scale-factor.

model.name

The model being fitted is one of the two 'beta binomial' or 'correlated binomial'.

link

Takes one of nine values i.e., 'logit', 'probit', 'cloglog', 'cauchit', 'log', 'loglog', 'double exponential', 'double reciprocal', 'power logit'. The default is 'cloglog'. The 'power logit' has an attribute of 'power' for which the default is 1 i.e., a logit link.

ntrials

This is a scalar representing the denominator i.e., the length of the probability mass function returned is this scalar + 1.

covariates.matrix.p

A matrix of covariates for p where rows are the number of values in listbinary and columns the covariates. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

covariates.matrix.scalef

A matrix of covariates for the scale-factor where rows are the number of values in listbinary and columns the covariates. The default is a vector of ones. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

offset.p

An offset vector for p. The default is a vector of ones.

offset.scalef

An offset vector for the scale-factor. The default is a vector of ones.

Value

List of arguments input together with a list of probabilities vectors and a data frame of values of p, theta (beta binomial) or rho (correlated binomial) and the limits for theta or rho.

model

The model is either 'beta binomial' or 'correlated binomial'.

link

The link is either 'logit' or 'cloglog'.

parameter

A vector of the parameters of the model which is set to initial estimates on function call.

probabilities

A list of the vectors of probabilities of the model.

probabilities

A data frame of values of p, theta (beta binomial) or rho (correlated binomial) and the limits for theta or rho.

Author(s)

David M. Smith <[email protected]>

References

Hughes G, Madden L (1995). Some methods allowing for aggregated patterns of disease incidence in the analysis of data from designed experiments. Plant Pathology, 44, 927-943.

Kupper L, Haseman J (1978). The use of a correlated binomial model for the analysis of toxicological epxeriments. Biometrics, 34(1), 69-76.

Examples

link <- 'cloglog'
attr(link, which="p") <- make.link(link)
parameter <- c(-0.68294630,0.03451481)
names(parameter) <- c('p','rho')
model.type <- 'p and scale-factor'
model.name <- 'correlated binomial'
ntrials    <- list(c(rep(10,11)))
Model.BCBinProb(parameter, model.type, model.name, link, ntrials,
                covariates.matrix.p = matrix(c(1),nrow=1), 
                covariates.matrix.scalef = matrix(c(1),nrow=1),
                offset.p = c(0), offset.scalef = c(0))

Function for obtaining output from distributional models.

Description

Produces output of model, parameters and probabilities from the various models.

Usage

Model.Binary(parameter, model.type, model.name, link, ntrials, covariates.matrix.p, 
covariates.matrix.scalef, offset.p, offset.scalef)

Arguments

parameter

A vector of the parameters of the model which is set to initial estimates on function call.

model.type

Takes one of two values i.e. 'p only' or 'p and scale-factor'. The 'p only' value fits a linear predictor function to the parameter p which is the 'm(1)' in equation (6) of Faddy and Smith (2012) divided by 'N'. The 'p and scale-factor' value fits linear predictor functions to both p and the scale-factor.

model.name

If model.type is 'p only' the model being fitted is one of the six 'binomial', 'over-dispersed-one', 'over-dispersed-two', 'EPPM binomial', 'beta binomial' or 'correlated binomial'. If model.type is 'p and scale-factor' the model being fitted is one of the three 'EPPM binomial', 'beta binomial' or 'correlated binomial'.

link

Takes one of nine values i.e., 'logit', 'probit', 'cloglog', 'cauchit', 'log', 'loglog', 'double exponential', 'double reciprocal', 'power logit'. The default is 'cloglog'. The 'power logit' has an attribute of 'power' for which the default is 1 i.e., a logit link.

ntrials

This is a scalar representing the denominator i.e., the length of the probability mass function returned is this scalar + 1.

covariates.matrix.p

A matrix of covariates for p where rows are the number of values in listbinary and columns the covariates. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

covariates.matrix.scalef

A matrix of covariates for the scale-factor where rows are the number of values in listbinary and columns the covariates. The default is a vector of ones. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

offset.p

An offset vector for p. The default is a vector of ones.

offset.scalef

An offset vector for the scale-factor. The default is a vector of ones.

Value

The output from either Model.BCBinProb, Model.GB, Model.Binary, Model.JMVGB, or Model.ODB.

Author(s)

David M. Smith <[email protected]>

References

Faddy M, Smith D. (2012). Extended Poisson Process Modeling and Analysis of Grouped Binary Data. Biometrical Journal, 54, 426-435. doi:10.1002/bimj.201100214.

Examples

link <- 'cloglog'
attr(link, which="p") <- make.link(link)
parameter <- c(-0.68294630,0.03451481)
names(parameter) <- c('p','rho')
model.type <- 'p and scale-factor'
model.name <- 'correlated binomial'
ntrials    <- list(c(rep(10,11)))
Model.Binary(parameter, model.type, model.name, link, ntrials,
             covariates.matrix.p = matrix(c(1),nrow=1), 
             covariates.matrix.scalef = matrix(c(1),nrow=1),
             offset.p = c(0), offset.scalef = c(0))

Probabilities for binomial and EPPM extended binomial distributions given p's and b.

Description

Calculates the probabilities for binomial and EPPM extended binomial given values for p's and b.

Usage

Model.GB(parameter, model.name, link, ntrials, covariates.matrix.p, 
         offset.p = c(rep(0, length(ntrials))))

Arguments

parameter

A vector of the parameters of the model which is set to initial estimates on function call.

model.name

The model being fitted is one of the two 'binomial' or 'EPPM extended binomial'.

link

Takes one of nine values i.e., 'logit', 'probit', 'cloglog', 'cauchit', 'log', 'loglog', 'double exponential', 'double reciprocal', 'power logit'. The default is 'cloglog'. The 'power logit' has an attribute of 'power' for which the default is 1 i.e., a logit link.

ntrials

This is a scalar representing the denominator i.e., the length of the probability mass function returned is this scalar + 1.

covariates.matrix.p

A matrix of covariates for p where rows are the number of values in listbinary and columns the covariates. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

offset.p

An offset vector for p. The default is a vector of ones.

Value

List of arguments input together with a list of probabilities vectors and a data frame of values of a and b of Equation (5) of Faddy and Smith (2012).

model

The model is either 'binomial' or 'EPPM extended binomial'.

link

The link is either 'logit' or 'cloglog'.

parameter

A vector of the parameters of the model which is set to initial estimates on function call.

probabilities

A list of the vectors of probabilities of the model.

Dparameters

A data frame of values of a and b of Equation (5) of Faddy and Smith (2012).

Author(s)

David M. Smith <[email protected]>

References

Faddy M, Smith D. (2012). Extended Poisson Process Modeling and Analysis of Grouped Binary Data. Biometrical Journal, 54, 426-435. doi:10.1002/bimj.201100214.

Examples

link <- 'cloglog'
attr(link, which="p") <- make.link(link)
parameter <- c(0.9423342,0.5846321)
names(parameter) <- c('p','b')
model.name <- 'EPPM extended binomial'
ntrials <- list(c(rep(10,11)))
Model.GB(parameter, model.name, link, ntrials, 
         covariates.matrix.p = matrix(c(1),ncol=1), 
         offset.p = c(0))

Probabilities for EPPM extended binomial distributions given p's and scale-factors.

Description

Calculates the probabilities for binomial and generalized binomial given values for p's and scale-factors.

Usage

Model.JMVGB(parameter, model.name, link, ntrials, 
            covariates.matrix.p, covariates.matrix.scalef, 
            offset.p = c(rep(0, length(ntrials))), 
            offset.scalef = c(rep(0, length(ntrials))))

Arguments

parameter

A vector of the parameters of the model which is set to initial estimates on function call.

model.name

The model being fitted is one of the two 'binomial' or 'EPPM extended binomial'.

link

Takes one of nine values i.e., 'logit', 'probit', 'cloglog', 'cauchit', 'log', 'loglog', 'double exponential', 'double reciprocal', 'power logit'. The default is 'cloglog'. The 'power logit' has an attribute of 'power' for which the default is 1 i.e., a logit link.

ntrials

This is a scalar representing the denominator i.e., the length of the probability mass function returned is this scalar + 1.

covariates.matrix.p

A matrix of covariates for p where rows are the number of values in listbinary and columns the covariates. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

covariates.matrix.scalef

A matrix of covariates for the scale-factor where rows are the number of values in listbinary and columns the covariates. The default is a vector of ones. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM.

offset.p

An offset vector for p. The default is a vector of ones.

offset.scalef

An offset vector for the scale-factor. The default is a vector of ones.

Value

List of arguments input together with a list of probabilities vectors and a data frame of values of a and b of Equation (5) of Faddy and Smith (2012).

model

The model is either 'binomial' or 'EPPM extended binomial'.

link

The link is either 'logit' or 'cloglog'.

parameter

A vector of the parameters of the model which is set to initial estimates on function call.

probabilities

A list of the vectors of probabilities of the model.

Dparameters

A data frame of values of a and b of Equation (5) of Faddy and Smith (2012).

Author(s)

David M. Smith <[email protected]>

References

Faddy M, Smith D. (2012). Extended Poisson Process Modeling and Analysis of Grouped Binary Data. Biometrical Journal, 54, 426-435. doi:10.1002/bimj.201100214.

Examples

link <- 'cloglog'
attr(link, which="p") <- make.link(link)
parameter <- c(-0.68294630,0.03451481)
names(parameter) <- c('p','scale-factor')
model.name <- 'EPPM extended binomial'
ntrials <- list(c(rep(10,11)))
Model.JMVGB(parameter, model.name, link, ntrials, 
            covariates.matrix.p = matrix(c(1),nrow=1), 
            covariates.matrix.scalef = matrix(c(1),nrow=1), 
            offset.p = c(0), offset.scalef = c(0))

Negative complementary log-log Link Function

Description

Computes the negative complementary log-log link function, including its inverse.

Usage

negcomplog()

Value

The negative complementary log-log of theta.

Author(s)

David M. Smith <[email protected]>

References

Tibshirani RJ, Ciampi A (1983). "A Family of Proportional- and Additive-Hazards Models for Survival Data". Biometrics 39(1), 141-147.

The data are of the number of male piglets born in litters of varying sizes for the Parkes breed of pigs.

Description

The data are arranged as a list of binomial frequency distributions where the listing is by litter size which is included both as a variate (vsize) and as a factor (fsize)

Usage

data("Parkes.litters")

Format

The format is: List of 3 $ fsize : Factor w/ 7 levels " size 5"," size 6",..: 1 2 3 4 5 6 7 $ vsize : int [1:7] 5 6 7 8 9 10 11 $ number.success:List of 7 ..$ : num [1:6] 2 20 41 35 14 4 ..$ : num [1:7] 3 16 53 78 53 18 0 ..$ : num [1:8] 0 21 63 117 104 46 21 2 ..$ : num [1:9] 1 8 37 81 162 77 30 5 1 ..$ : num [1:10] 0 2 23 72 101 83 46 12 7 0 ..$ : num [1:11] 0 7 8 19 79 82 48 24 10 0 ... ..$ : num [1:12] 0 1 3 15 15 33 13 12 8 1 ...

Source

Brooks, R.J., James, W.H., Gray, E. (1993). Modelling Sub-Binomial Variation in the Frequency of Sex Combinations in Litters of Pigs. Biometrics 47, 403-417.

Examples

data("Parkes.litters")

Diagnostic Plots for BinaryEPPM Objects

Description

This function is generic. Various types of standard diagnostic plots can be produced, involving various types of residuals, influence measures etc. It is a minorly modified version of the generic plot function of betareg with details of the displays given in Cribari-Neto and Zeileis (2010). The same six displays and arguments list as in Cribari-Neto and Zeileis (2010) are used. The six displays are "Residuals vs indices of obs", "Cook's distance plot", "Leverage vs predicted values", "Residuals vs linear predictor", "Normal Q-Q plot of residuals", "Predicted vs observed values".

Usage

## S3 method for class 'BinaryEPPM'
plot(x, which = 1:4,
    caption = c("Residuals vs indices of obs.", "Cook's distance plot",
    "Leverage vs predicted values", "Residuals vs linear predictor",
    "Normal Q-Q plot of residuals", "Predicted vs observed values"),
    sub.caption = " ", main = "", 
    ask = prod(par("mfcol"), 1) < length(which) && dev.interactive(),
    ..., type = "spearson")

Arguments

x

fitted model object of class "BinaryEPPM".

which

numeric. If a subset of plots is required, specify a subset of the numbers 1:6.

caption

character. Captions to appear above the plots.

sub.caption

character. Common title-above figures if there are multiple.

main

character. Title to each plot in addition to the above caption.

ask

logical. If true, the user is asked before each plot.

...

other parameters to be passed through to plotting functions.

type

character indicating type of residual to be used, see residuals.BinaryEPPM.

Details

The plot method for BinaryEPPM objects produces various plots of diagnostic plots similar to those produced by betareg. See Cribari-Neto and Zeileis (2010) for further details of the displays of betareg.

Value

No return value.

Author(s)

David M. Smith <[email protected]>

References

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

See Also

plot.betareg

Examples

data("ropespores.case") 
output.fn <- BinaryEPPM(data = ropespores.case,
                  number.spores / number.tested ~ 1 + offset(logdilution),
                  model.type = 'p only', model.name = 'binomial')  
plot.BinaryEPPM(output.fn, which = 1, type= "sdeviance")

Power Logit Link Function

Description

Computes the power logit link function, including its inverse.

Usage

powerlogit(power = 1)

Arguments

power

power value for the power logit link function.

Value

The power logit transformation of theta. All logarithms are natural ones, i.e., to base e.

Author(s)

David M. Smith <[email protected]>

References

Gaudard MA, Karson MJ, Linder E, Tse Sk (1993). Efficient Designs for Estimation in the Power Logistic Quantal Response Model." Statistica Sinica, 3, 233-243.

Prediction Method for BinaryEPPM Objects

Description

Extract various types of predictions from BinaryEPPM regression models.

Usage

## S3 method for class 'BinaryEPPM'
predict(object, newdata = NULL, type = c("response", 
     "linear.predictor.p", "linear.predictor.scale.factor",
 "p", "scale.factor", "scale.factor.limits", "mean", 
 "variance",   "distribution", "distribution.parameters"), na.action = na.pass, ...)

Arguments

object

fitted model object of class "BinaryEPPM".

newdata

optionally, a data frame in which to look for variables with which to predict. If omitted, the original observations are used.

type

character indicating type of predictions: fitted means of responses ("response"), linear predictors ("linear.predictor.p", "linear.predictor.scale.factor"), fitted value of probability of success ("p"), fitted value of scale-factor ("scale.factor"), fitted value of mean ("mean"), scale factor limits ("scale.factor.limits"), fitted value of variance ("variance"), fitted probability distribution ("distribution"), parameters of fitted distributions ("distribution.parameters")

na.action

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

...

some methods for this generic function require additional arguments.

Value

A vector or list of the predicted values from the fitted model object.

Author(s)

David M. Smith <[email protected]>

References

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

See Also

predict.betareg

Examples

data("ropespores.case")
output.fn <- BinaryEPPM(data = ropespores.case,
                  number.spores / number.tested ~ 1 + offset(logdilution),
                  model.type = 'p only', model.name = 'binomial')                 
predict(output.fn, type = "response")
predict(output.fn, type = "linear.predictor.p")

Printing of BinaryEPPM Objects

Description

Prints objects of class "BinaryEPPM".

Usage

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

Arguments

x

fitted model object of class "BinaryEPPM".

digits

digits of printed output.

...

not currently used.

Value

An object of class "BinaryEPPM" is constructed. This object has the following attributes.

data.type

Indicator of the type of data either 0 "data.frame" or 1 "list".

list.data

Regardless of the "data.type", the data in list form.

call

The "call" to the function "BinaryEPPM".

formula

The model formula in "call".

model.type

The model type in "call".

model.name

The model name in "call".

link

The link function in "call".

covariates.matrix.p

The matrix of covariates for the model for p.

covariates.matrix.scalef

The matrix of covariates for the model for scale-factor.

offset.p

The vector of offsets for the model for p.

offset.scalef

The vector of offsets for the model for scale-factor.

coefficients

The coefficients of the fitted model.

loglik

The log-likelihood of the fitted model.

vcov

The variance-covariance matrix of the fitted model.

n

The number of observations. Relabelled duplication of "nobs" needed when calling function "lrtest".

nobs

The number of observations.

df.null

The degrees of freedom of the null model.

df.residual

The degrees of freedom of the residual model.

vnmax

Vector of number of "trials" in each observation.

weights

Vector of weights for observation.

converged

Indicator of convergence.

method

Method used to calculate pseudo.r.squared.

pseudo.r.squared

The value of the coefficient of determination r squared.

start

Initial estimates.

optim

Final model fit.

control

Control parameters for optimization function "optim".

fitted.values

The fitted values.

y

The dependent variable in the model.

terms

The terms in the model.

Author(s)

David M. Smith <[email protected]>

References

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

See Also

betareg

Examples

data("ropespores.case") 
BinaryEPPM(data = ropespores.case,
           number.spores / number.tested ~ 1 + offset(logdilution),
           model.type = 'p only', model.name = 'binomial')

Printing of summaryBinaryEPPM Objects

Description

Prints the objects of class "summaryBinaryEPPM".

Usage

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

Arguments

x

object output by summary.BinaryEPPM.

...

not currently used.

Value

No return value.

Author(s)

David M. Smith <[email protected]>

References

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

See Also

betareg

Examples

data("ropespores.case") 
output.fn <- BinaryEPPM(data = ropespores.case,
                  number.spores / number.tested ~ 1 + offset(logdilution),
                  model.type = 'p only', model.name = 'binomial')   
print(summary(output.fn))

Residuals for BinaryEPPM Objects

Description

This function is generic. Extract various types of residuals from objects of class "BinaryEPPM".

Usage

## S3 method for class 'BinaryEPPM'
residuals(object, type = c("spearson", "deviance", "pearson",
        "response", "likelihood", "sdeviance"), ...)

Arguments

object

Fitted model object of class "BinaryEPPM".

type

Type of residuals wanted i.e., standardized Pearson "spearson", deviance "deviance", Pearson "pearson",response "response", likelihood "likelihood", standardized deviance "sdeviance".

...

Some methods for this generic function require additional arguments.

Details

Residuals as Cribari-Neto and Zeileis (2010).

Value

An vector of class "numeric" of residuals of a specified type from the object of class "BinaryEPMM".

Author(s)

David M. Smith <[email protected]>

References

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

See Also

residuals.betareg

Dilution series for the presence of rope spores.

Description

Dilution series where at each dilution of a suspension of potato flour a number of samples were examined for the presence of rope spores. These data are in data frame form.

Usage

data("ropespores.case")

Format

A data frame with 10 observations on the following 5 variables.

vdilution

a numeric vector

fdilution

a factor with levels 0.25 0.5 1 2 4 8 16 32 64 128

logdilution

a numeric vector

number.spores

a numeric vector

number.tested

a numeric vector

Source

Finney, D.J. (1971). Statistical Methods in Biological Assay. Griffin, London, 2nd edition.

Examples

data("ropespores.case")

Dilution series for the presence of rope spores.

Description

Dilution series where at each dilution of a suspension of potato flour a number of samples were examined for the presence of rope spores. These data are in list form.

Usage

data("ropespores.grouped")

Format

The format is: List of 4 $ vdilution : num [1:10] 0.25 0.5 1 2 4 8 16 32 64 128 $ fdilution : Factor w/ 10 levels "0.25","0.5","1",..: 1 2 3 4 5 6 7 8 9 10 $ offset.p : num [1:10] 1.386 0.693 0 -0.693 -1.386 ... $ number.spores:List of 10 ..$ : num [1:6] 0 0 0 0 0 1 ..$ : num [1:6] 0 0 0 0 0 1 ..$ : num [1:6] 0 0 0 0 0 1 ..$ : num [1:6] 0 0 0 0 0 1 ..$ : num [1:6] 0 0 0 0 1 0 ..$ : num [1:6] 0 0 0 1 0 0 ..$ : num [1:6] 0 0 1 0 0 0 ..$ : num [1:6] 0 0 1 0 0 0 ..$ : num [1:6] 1 0 0 0 0 0 ..$ : num [1:6] 1 0 0 0 0 0

Source

Finney, D.J. (1971). Statistical Methods in Biological Assay. Griffin, London, 2nd edition.

Examples

data("ropespores.grouped")

Summary of BinaryEPPM Objects

Description

This function is generic. Summary of objects of class "BinaryEPPM".

Usage

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

Arguments

object

Fitted model object of class "BinaryEPPM".

...

some methods for this generic function require additional arguments.

Details

Similar output to that of summary.glm "summary.glm" and summary.betareg Cribari-Neto and Zeileis (2010).

Value

An object of class "summaryBinaryEPPM" is constructed. This object has the following attributes.

data.type

Indicator of the type of data either 0 "data.frame" or 1 "list".

call

The "call" to the function "BinaryEPPM".

formula

The model formula in "call".

model.type

The model type in "call".

model.name

The model name in "call".

link

The link function in "call".

offset.p

The vector of offsets for the model for p.

offset.scalef

The vector of offsets for the model for scale-factor.

coeff.table.p

The coefficients of the fitted model for p.

coeff.table.scalef

The coefficients of the fitted model for scale-factor.

loglik

The log-likelihood of the fitted model.

n

The number of observations. Relabelled duplication of "nobs" needed when calling function "lrtest".

nobs

The number of observations.

df.null

The degrees of freedom of the null model.

df.residual

The degrees of freedom of the residual model.

vnmax

Vector of number of "trials" in each observation.

weights

Vector of weights for observation.

converged

Indicator of convergence.

method

Method used to calculate pseudo.r.squared.

pseudo.r.squared

The value of the coefficient of determination r squared.

optim

Final model fit.

control

Control parameters for optimization function "optim".

fitted.values

The fitted values.

y

The dependent variable in the model.

terms

The terms in the model.

npar

The number of parameters in the model.

Author(s)

David M. Smith <[email protected]>

References

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

See Also

summary.betareg print.summaryBinaryEPPM

Variance/Covariance Matrix for Coefficients

Description

Variance/covariance matrix for coefficients of fitted model.

Usage

## S3 method for class 'BinaryEPPM'
vcov(object, model = c("full", "p", "scale.factor"), ...)

Arguments

object

fitted model object of class "BinaryEPPM".

model

character indicating variance/covariance matrix for all coefficients to be output: all coefficients ("full"), variance/covariance matrix for coefficients of probability of success ("p"), variance/covariance matrix for coefficients of scale-factor ("scale.factor")

...

other parameters to be passed through to plotting functions.

Value

The variance/covariance matrix of the parameters of the fitted model object.

Author(s)

David M. Smith <[email protected]>

References

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

See Also

betareg

Examples

data("ropespores.case") 
output.fn <- BinaryEPPM(data = ropespores.case,
                  number.spores / number.tested ~ 1 + offset(logdilution),
                  model.type = 'p only', model.name = 'binomial')   
vcov(output.fn)

Wald Test of Nested Models for BinaryEPPM Objects

Description

waldtest is a generic function for comparisons of nested (generalized) linear models via Wald tests.

Usage

## S3 method for class 'BinaryEPPM'
waldtest(object, ..., vcov = NULL,
   test = c("Chisq", "F"))

Arguments

object

an object of class "BinaryEPPM".

...

further object specifications passed to methods. See below for details.

vcov

a function for estimating the covariance matrix of the regression coefficients. If only two models are compared it can also be the covariance matrix of the more general model.

test

character specifying whether to compute the large sample Chi-squared statistic (with asymptotic Chi-squared distribution) or the finite sample F statistic (with approximate F distribution).

Details

waldtest is a generic function for comparisons of nested (generalized)linear models via Wald tests. It does not have the same functionality as the versions of betareg and lmtest with a reduced list of arguments. With these caveats, more details can be obtained from the Details pages of those packages.

Value

An object of class "anova" which contains the residual degrees of freedom, the difference in degrees of freedom, Wald statistic (either "Chisq" or "F") and corresponding p value.

Author(s)

David M. Smith <[email protected]>

References

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

Zeileis A, Hothorn T. (2002). Diagnostic Checking in Regression Relationships. R News, 2(3), 7-10. https://CRAN.R-project.org/doc/Rnews/.

See Also

waldtest betareg

Examples

data("ropespores.case") 
output.fn <- BinaryEPPM(data = ropespores.case,
  number.spores / number.tested ~ 1 + offset(logdilution),
  model.type = 'p only', model.name = 'binomial')  
output.fn.one <- BinaryEPPM(data = ropespores.case,
  number.spores / number.tested ~ 1 + offset(logdilution),
  model.type = 'p only', model.name = 'beta binomial')   
waldtest.BinaryEPPM(output.fn, output.fn.one, test = c("Chisq", "F"),
  vcov =  vcov)

Number of occurences of an article in five-word and ten-word samples from two authors.

Description

The data are the number of occurences of an article in five-word and ten-word samples from Macaulay's 'Essay on Milton' and G.K. Chesterton's essay 'About the workers'.

Usage

data("wordcount.case")

Format

A data frame with 340 observations on the following 5 variables.

author

a factor with levels Macaulay Chesterton

fsize

a factor with levels 5 10

vsize

a numeric vector

number.words

a numeric vector

number.tested

a numeric vector

Source

Bailey, B.J.R. (1990). A model for Function Word Counts. Appl. Statist. 39(1), 107-114.

References

Sellers, K.F., Swift, A.W., Weems, K.S. (2017). A flexible distribution class for count data. Journal of Statistical Distributions and Applications 41(12), 2616-2626.

Examples

data(wordcount.case)

Number of occurences of an article in five-word and ten-word samples from two authors.

Description

The data are the number of occurences of an article in five-word and ten-word samples from Macaulay's 'Essay on Milton' and G.K. Chesterton's essay 'About the workers'.

Usage

data("wordcount.grouped")

Format

The format is: List of 4 $ author : Factor w/ 2 levels " Macaulay"," Chesterton": 1 1 2 2 $ fsize : Factor w/ 2 levels "5","10": 1 2 1 2 $ vsize : num [1:4] 5 10 5 10 $ number.words:List of 4 ..$ : num [1:6] 45 49 6 0 0 0 ..$ : num [1:11] 27 44 26 3 0 0 0 0 0 0 ... ..$ : num [1:6] 32 35 3 0 0 0 ..$ : num [1:11] 14 38 16 2 0 0 0 0 0 0 ...

Source

Bailey, B.J.R. (1990). A model for Function Word Counts. Appl. Statist. 39(1), 107-114.

References

Sellers, K.F., Swift, A.W., Weems, K.S. (2017). A flexible distribution class for count data. Journal of Statistical Distributions and Applications 41(12), 2616-2626.

Examples

data(wordcount.grouped)

The data are of the number of male piglets born in litters of varying sizes for the Yorkshire breed of pigs.

Description

The data are arranged as a list of binomial frequency distributions where the listing is by litter size which is included both as a variate (vsize) and as a factor (fsize)

Usage

data("Yorkshires.litters")

Format

The format is: List of 3 $ fsize : Factor w/ 9 levels " size 5"," size 6",..: 1 2 3 4 5 6 7 8 9 $ vsize : int [1:9] 5 6 7 8 9 10 11 12 13 $ number.success:List of 9 ..$ : num [1:6] 3 22 30 37 13 5 ..$ : num [1:7] 7 18 44 62 27 17 4 ..$ : num [1:8] 2 14 25 63 69 41 12 5 ..$ : num [1:9] 2 15 32 70 127 90 45 18 1 ..$ : num [1:10] 0 8 33 63 106 115 62 30 11 1 ..$ : num [1:11] 0 3 20 49 79 119 91 59 23 4 ... ..$ : num [1:12] 0 0 7 20 60 94 100 47 31 9 ... ..$ : num [1:13] 0 1 6 16 29 52 66 43 34 22 ... ..$ : num [1:14] 0 2 2 2 14 19 44 45 22 13 ...

Source

Brooks, R.J., James, W.H., Gray, E. (1993). Modelling Sub-Binomial Variation in the Frequency of Sex Combinations in Litters of Pigs. Biometrics 47, 403-417.

Examples

data("Yorkshires.litters")