MNB (version 1.2.0)

qMNB: Randomized quantile residual

Description

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

Usage

qMNB(par, formula, dataSet)

Value

Randomized quantile Residuals

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

Author

Jalmar M F Carrasco <[e-mail]>, Cristian M Villegas Lobos <[e-mail]> and Lizandra C Fabio <[e-mail]>

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.

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.

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)