Diagnostics for a Cumulative Multinomial Generalized Linear Model, with Applications to Grouped Toxicological Mortality Data

Overdispersion

“…Otherwise, the apparent overdispersion could reflect missing covariates, for example, interaction terms, implying systematic lack-of-fit, or the functional form of the mean may be inappropriate. Pregibon [10] develops a test for checking the form of the mean in GLMs; for multinomial models, O'Hara Hines et al [11] develop diagnostic tools for this purpose. Smith and Heitjan [12] develop a test for overdispersion, which results when the vector of coefficients in the mean is considered to be random.…”

Influence diagnostics for polyhazard models in the presence of covariates

“…2.4) that has been largely applied in generalized linear models (GLMs). Various authors have investigated the use of deviance residuals in GLMs (see, for instance, Williams 1984;O'Hara Hines et al 1992;Paula 1995) as well as in other regression models (see, for example, Fahrmeir and Tutz 1994;Klein and Moeschberger 1997). In polyhazard models the residual deviance component is expressed here as…”

Improved Added Variable and Partial Residual Plots for the Detection of Influential Observations in Generalized Linear Models

“…It should be noted that the above proposed model for the KSCN data only approximates the underlying biological processes and that there still remains some lack of fit in the model which cannot be taken into account by the use of simple linear functions of the covariates. An analysis of the complete set of data obtained in the experiment in which mortality counts were taken at five different time points, along with some proposed diagnostics, can be found in O'Hara Hines et al (1992). The effect on the estimated coefficients of removing observations 38, 39 and 26 can be seen in Table 3.…”