qMNB function

Randomized quantile residual

randomized quantile residual is available to assess possible departures from the multivariate negative binomial model for fitting correlated data with overdispersion.

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

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 carrascojalmar@gmail.com, Cristian M Villegas Lobos master.villegas@gmail.com and Lizandra C Fabio lizandrafabio@gmail.com