# Negative binomial (NB2): generic synthetic negative binomial data and model nb2_syn is a generic function for developing synthetic NB2 data and a model given user defined specifications. ```r nb2_syn(nobs = 50000, off = 0, alpha = 1, xv = c(1, 0.75, -1.5)) ``` ## Arguments - `nobs`: number of observations in model, Default is 50000 - `alpha`: NB2 heterogeneity or ancillary parameter - `off`: optional: log of offset variable - `xv`: predictor coefficient values. First argument is intercept. Use as xv = c(intercept , x1_coef, x2_coef, ...) ## Details Create a synthetic negative binomial (NB2) regression model using the appropriate arguments. Model data with predictors indicated as a group with a period (.). Offset optional. If no offset is desired, drop "off= loff" from nb2_syn function call and "+ loff" from glm.nb function call. See examples. Data can be estimated using the glm.nb() function, or the ml.nb2() function in the COUNT package, or by using the gamlss function in the gamlss package, with "family=NBI" option. ## Returns - **nby**: Negative binomial response; number of counts - **sim.data**: synthetic data set ## References Hilbe, J.M. (2011), Negative Binomial Regression, second edition, Cambridge University Press. ## Author(s) Andrew Robinson, Universty of Melbourne, Australia, and Joseph M. Hilbe, Arizona State University, Jet Propulsion Laboratory, California Institute of Technology ## See Also `poisson_syn, nb1_syn`, `nbc_syn` ## Examples ```r library(MASS) sim.data <- nb2_syn(nobs = 500, alpha = .5, xv = c(2, .75, -1.25)) mynb2 <- glm.nb(nby ~ . , data = sim.data) summary(mynb2) confint(mynb2) # with offset oset <- rep(1:5, each=100, times=1)*100 loff <- log(oset) sim.data <- nb2_syn(nobs = 500, off = loff, alpha = .5, xv = c(1.2, -.75, .25, -1.3)) mypof <- glm.nb(nby ~ . + loff, data = sim.data) summary(mypof) confint(mypof) # without offset, exponentiated coefficients, CI's sim.data <- nb2_syn(nobs = 500, alpha = .75, xv = c(1, .5, -1.4)) mynbf <- glm.nb(nby ~ . , data = sim.data) exp(coef(mynbf)) exp(confint(mynbf)) ## Not run: # default, without offset sim.data <- nb2_syn() dnb2 <- glm.nb(nby ~ . , data = sim.data) summary(dnb2) ## End(Not run) # use ml.nb2.r function sim.data <- nb2_syn(nobs = 500, alpha = .5, xv = c(2, .75, -1.25)) mynb2x <- ml.nb2(nby ~ . , data = sim.data) mynb2x ## Not run: # use gamlss function for modeling data after sim.data created library(gamlss) sim.data <- nb2_syn(nobs = 500, alpha = .5, xv = c(2, .75, -1.25)) gamnb <- gamlss(nby ~ ., family=NBI, data = sim.data) gamnb ## End(Not run) ```