Williams (1982) [385] OD in binomial models. Quasi-likelihood estimation (GLIM).
Cox (1983) [92] Estimation of a a simple model in the presence of models amounts of overdispersion. ML estimates ignoring the OD are asymptotically efficient, provided that the target parameter is correctly chosen. Extensions and a model for overdispersed data.
Breslow (1984) [60] Modification of the method of [385] for overdispersed Poisson data. Nice examples.
Firth (1987) [135] Efficiency (relative to ML) of quasi-likelihood estimates under different types of models, including models with overdispersion. Efficiency is fairly high when OD is moderate.
Barron (1992) [26] Overdispersion and autocorrelation in count data. Discussion of causes (heterogeneity, contagion etc.). Negative binomial model, quasi-likelihood estimation.
Morgan and Smith (1992) [275] OD for Poisson regression. Emphasises that OD parameters should be estimated from a maximal (here saturated) model in order to separate OD from lack of fit.
Hamerle and Ronning (1995) [174] Review of the analysis of qualitative panel data for social scientists, fairly technical. Discussion of overdispersion, both random-effects and quasilikelihood modelling.
Fitzmaurice (1997) [136]
Impact of OD model selection criteria ($L^{2}$, AIC, BIC):
generally too complex models selected. OD represented as a model with
double-exponential family density. Estimation of OD parameters, simplest
when only one of them. Simple adjustment of model selection criteria
using OD parameter estimated from a `maximal' model. Application to data
on class and voting.
Fitzmaurice and Goldthorpe (1997) [137] Fitzmaurice (1997) [136] for sociological audience. Application to CASMIN data on social mobility.
Fitzmaurice et al. (1997) [138]
Discussion of causes and effects of OD. A simple method for detecting
and adjusting for OD: partition data into small number of strata of
roughly equal size, so that parameter of interest $\theta$ is
constant or varies randomly between strata; compute estimate
$\hat{\theta}_{j}$ in each stratum; estimate standard error of
est. of $\theta$ as standard deviation of
$\hat{\theta}_{j}$. If this is clearly greater than the standard
variance estimate of $\hat{\theta}$, this is evidence of OD, and
the between-statum s.d. is preferred as estimate of
$\var(\hat{\theta})$. Applied to model for education and social
class, with data from a 2 % sample from 1991 census.
Lindsey and Altham (1998) [246] Models for the human sex ratio using 19th-century data on 3.7 million births. Dispersion modelled as a linear function of family size. Three parametric OD models (including beta-binomial and double-binomial) compared using AIC. All preferred to saturated model, binomial model without OD does not fit at all.