General function for estimating a variance inflation factor (\(\hat c\)) from observed counts.
Fletcher.chat (observed, expected, np, verbose = TRUE,
type = c('Fletcher', 'Wedderburn', 'both'), multinomial = FALSE)
Output depends on `verbose', `observed' and `type':
-- if `observed' is a list of nk vectors (usually generated by simulation) then the output is a vector of (Fletcher or Wedderburn) \(\hat c\) values, one element for each component of `observed', unless type = "both" when the output is a list of two such vectors. Argument `verbose' is ignored.
-- if `observed' is a simple vector then `verbose' output is a list comprising input values, various summary statistics, and the computed Fletcher overdispersion (`chat'). The statistic `cX2' is the conventional variance inflation factor of Wedderburn (1974) -- \(X^2/df\). For verbose = FALSE, a single estimate of \(\hat c\) is returned when type = "Fletcher" or type = "Wedderburn", otherwise a vector of the two estimates.
integer vector of observed counts, or a list of such vectors
numeric vector of expected counts
integer number of parameters estimated
logical; if TRUE returns extended output
character
logical; if TRUE, one df is subtracted for the constraint
Fletcher.chat applies the overdispersion formula of Fletcher (2012) or computes the conventional (Wedderburn 1974) variance inflation factor \(X^2/df\). It is used by chat.nk and adjustVarD. The inputs `observed' and `expected' are vectors of counts (e.g., number of distinct individuals per detector); `observed' may also be a list of such vectors, possibly simulated.
Fletcher, D. (2012) Estimating overdispersion when fitting a generalized linear model to sparse data. Biometrika 99, 230--237.
Wedderburn, R. W. M. (1974) Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61, 439--47.
chat.nk,
adjustVarD