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.
Author(s)
David M. Smith [aut, cre], Malcolm J. Faddy [aut]
Maintainer: David M. Smith <dmccsmith@verizon.net>
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
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 <dmccsmith@verizon.net>
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 <dmccsmith@verizon.net>
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
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 <dmccsmith@verizon.net>
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)
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 <dmccsmith@verizon.net>
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.
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 <dmccsmith@verizon.net>
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)
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.
Groupa factor with levels
ControlTreatedNumber.Deathsa numeric vector
Number.Implantsa 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 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 <dmccsmith@verizon.net>
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))))
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 <dmccsmith@verizon.net>
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")
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 <dmccsmith@verizon.net>
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 <dmccsmith@verizon.net>
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 <dmccsmith@verizon.net>
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 <dmccsmith@verizon.net>
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))
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")
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")
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 <dmccsmith@verizon.net>
See Also
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 <dmccsmith@verizon.net>
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
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 <dmccsmith@verizon.net>
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 <dmccsmith@verizon.net>
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
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 <dmccsmith@verizon.net>
See Also
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 <dmccsmith@verizon.net>
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
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)
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 <dmccsmith@verizon.net>
See Also
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 <dmccsmith@verizon.net>
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.
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 <dmccsmith@verizon.net>
References
Tibshirani RJ, Ciampi A (1983). "A Family of Proportional- and Additive-Hazards Models for Survival Data". Biometrics 39(1), 141-147.
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 <dmccsmith@verizon.net>
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
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 <dmccsmith@verizon.net>
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 <dmccsmith@verizon.net>
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
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 <dmccsmith@verizon.net>
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
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 <dmccsmith@verizon.net>
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
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 <dmccsmith@verizon.net>
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
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.
vdilutiona numeric vector
fdilutiona factor with levels
0.250.51248163264128logdilutiona numeric vector
number.sporesa numeric vector
number.testeda 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 <dmccsmith@verizon.net>
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 <dmccsmith@verizon.net>
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
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 <dmccsmith@verizon.net>
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
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.
authora factor with levels
MacaulayChestertonfsizea factor with levels
510vsizea numeric vector
number.wordsa numeric vector
number.testeda 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)