BinaryEPPM-package {BinaryEPPM}

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 <[e-mail]>

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)