MNB (version 1.2.0)

re.MNB: Residual analysis

Description

Weighted, standardized weighted, Pearson, standardized Pearson and standardized deviance component residuals are available to assess possible departures from the multivariate negative binomial model for fitting correlated data with overdispersion.

Usage

re.MNB(star, formula, dataSet)

Value

Residuals

Arguments

star

Initial values for the parameters to be optimized over.

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

Similarly to GLMs theory (Agresti, 2015; Faraway, 2016), weighted and the standardized weighted residuals are deduced trough Fisher scoring iterative process. Based in the Pearson residual, Fabio (2017) suggest the standardized Pearson residuals for the multivariate model from the random intercept Poisson-GLG model. In addition, it is available the standardized deviance component residual for the ith subject (Fabio et al., 2012).

References

• Agresti, A. (2015). Foundations of Linear and Generalized Linear Models. Wiley.

• Faraway, F. (2016). Extending the Linear Model with R: Generalized Linear, Mixed Effects and nonparametric regression models. Taylor & Francis, New York.

• Fabio, L., Paula, G. A., and de Castro, M. (2012). A Poisson mixed model with nonormal random effect distribution. Computational Statistics and Data Analysis, 56, 1499-1510.

• 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)

r <- re.MNB(formula=Y ~ trt + period + trt:period +
offset(weeks),star=star,dataSet=seizures)

plot(r$ij.Sweighted.residual,cex.axis = 1.2, cex.lab = 1.2,
pch = 15,cex = 0.6, bg = 5,ylab="weighted.residual")

abline(h=c(-3,0,3),lwd = 2, lty = 2)

data(alzheimer)
head(alzheimer)

star <- list(phi=10,beta1=2, beta2=0.2)
r <- re.MNB(formula = Y ~ trat,star=star,dataSet=alzheimer)
names(r)