# Randomized quantile residual randomized quantile residual is available to assess possible departures from the multivariate negative binomial model for fitting correlated data with overdispersion. ```r qMNB(par, formula, dataSet) ``` ## Arguments - `par`: the maximum likelihood estimates. - `formula`: The structure matrix of covariates of dimension n x p (in models that include an intercept x should contain a column of ones). - `dataSet`: data ## Returns Randomized quantile Residuals ## Details The randomized quantile residual (Dunn and Smyth, 1996), which follow a standard normal distribution is used to assess departures from the multivariate negative binomial model. ## Examples ```r data(seizures) head(seizures) star <-list(phi=1, beta0=1, beta1=1, beta2=1, beta3=1) mod <- fit.MNB(formula=Y ~ trt + period + trt:period + offset(log(weeks)),star=star,dataSet=seizures,tab=FALSE) par <- mod$par names(par)<-c() res.q <- qMNB(par=par,formula=Y ~ trt + period + trt:period + offset(log(weeks)),dataSet=seizures) plot(res.q,ylim=c(-3,4.5),ylab="Randomized quantile residual", xlab="Index",pch=15,cex.lab = 1.5, cex = 0.6, bg = 5) abline(h=c(-2,0,2),lty=3) #identify(res.q) data(alzheimer) head(alzheimer) star <- list(phi=10,beta1=2, beta2=0.2) mod <- fit.MNB(formula = Y ~ trat, star = star, dataSet = alzheimer,tab=FALSE) par<- mod$par names(par) <- c() re.q <- qMNB(par=par,formula = Y ~ trat, dataSet = alzheimer) head(re.q) ``` ## References * Dunn, P. K. and Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics, 5, 236-244. * Fabio, L. C., Villegas, C., Carrasco, J. M. F., and de Castro, M. (2023). Diagnostic tools for a multivariate negative binomial model for fitting correlated data with overdispersion. Communications in Statistics - Theory and Methods, 52, 1833–1853. * Fabio, L. C., Villegas, C., Mamun, A. S., and Carrasco, J. M. F. (2025). Residual analysis for discrete correlated data in the multivariate approach. Brazilian Journal of Biometrics, 43, e43728. ## Author(s) Jalmar M F Carrasco , Cristian M Villegas Lobos and Lizandra C Fabio

qMNB function