binomialff {VGAM} | R Documentation |
Family function for fitting generalized linear models to binomial responses, where the dispersion parameter may be known or unknown.
binomialff(link = "logit", dispersion = 1, multiple.responses = FALSE, onedpar = !multiple.responses, parallel = FALSE, zero = NULL, bred = FALSE, earg.link = FALSE)
link |
Link function;
see |
dispersion |
Dispersion parameter. By default, maximum likelihood is used to
estimate the model because it is known. However, the user can specify
|
multiple.responses |
Multivariate response? If If |
onedpar |
One dispersion parameter? If |
parallel |
A logical or formula. Used only if |
zero |
An integer-valued vector specifying which linear/additive predictors
are modelled as intercepts only. The values must be from the set
{1,2,...,M}, where M is the number of columns of the
matrix response.
See |
earg.link |
Details at |
bred |
Details at |
This function is largely to
mimic binomial
,
however there are some differences.
If the dispersion parameter is unknown, then the resulting estimate is not fully a maximum likelihood estimate (see pp.124–8 of McCullagh and Nelder, 1989).
A dispersion parameter that is less/greater than unity corresponds to under-/over-dispersion relative to the binomial model. Over-dispersion is more common in practice.
Setting multiple.responses = TRUE
is necessary
when fitting a Quadratic RR-VGLM
(see cqo
) because the response is a matrix of M
columns (e.g., one column per species). Then there will be M
dispersion parameters (one per column of the response matrix).
When used with cqo
and cao
, it may be
preferable to use the cloglog
link.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as
vglm
,
vgam
,
rrvglm
,
cqo
,
and cao
.
With a multivariate response, assigning a known dispersion parameter for each response is not handled well yet. Currently, only a single known dispersion parameter is handled well.
See the above note regarding bred
.
The maximum likelihood estimate will not exist if the data is
completely separable or quasi-completely separable.
See Chapter 10 of Altman et al. (2004) for more details,
and safeBinaryRegression.
Yet to do: add a sepcheck = TRUE
, say, argument to detect this
problem and give an appropriate warning.
If multiple.responses
is FALSE
(default) then
the response can be of one
of two formats:
a factor (first level taken as failure),
or a 2-column matrix (first column = successes) of counts.
The argument weights
in the modelling function can
also be specified as any vector of positive values.
In general, 1 means success and 0 means failure
(to check, see the y
slot of the fitted object).
Note that a general vector of proportions of success is no
longer accepted.
The notation M is used to denote the number of linear/additive predictors.
If multiple.responses
is TRUE
, then the matrix response
can only be of one format: a matrix of 1's and 0's (1 = success).
The call binomialff(dispersion = 0, ...)
is equivalent to
quasibinomialff(...)
. The latter was written so that R users
of quasibinomial()
would only need to add a “ff
”
to the end of the family function name.
Regardless of whether the dispersion parameter is to be estimated or
not, its value can be seen from the output from the summary()
of the object.
Fisher scoring is used. This can sometimes fail to converge by oscillating between successive iterations (Ridout, 1990). See the example below.
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
Altman, M. and Gill, J. and McDonald, M. P. (2004) Numerical Issues in Statistical Computing for the Social Scientist, Hoboken, NJ, USA: Wiley-Interscience.
Ridout, M. S. (1990) Non-convergence of Fisher's method of scoring—a simple example. GLIM Newsletter, 20(6).
hdeff.vglm
,
quasibinomialff
,
Links
,
rrvglm
,
cqo
,
cao
,
betabinomial
,
posbinomial
,
zibinomial
,
double.expbinomial
,
seq2binomial
,
amlbinomial
,
simplex
,
binomial
,
simulate.vlm
,
safeBinaryRegression.
quasibinomialff() quasibinomialff(link = "probit") shunua <- hunua[sort.list(with(hunua, altitude)), ] # Sort by altitude fit <- vglm(agaaus ~ poly(altitude, 2), binomialff(link = cloglog), data = shunua) ## Not run: plot(agaaus ~ jitter(altitude), shunua, ylab = "Pr(Agaaus = 1)", main = "Presence/absence of Agathis australis", col = 4, las = 1) with(shunua, lines(altitude, fitted(fit), col = "orange", lwd = 2)) ## End(Not run) # Fit two species simultaneously fit2 <- vgam(cbind(agaaus, kniexc) ~ s(altitude), binomialff(multiple.responses = TRUE), data = shunua) ## Not run: with(shunua, matplot(altitude, fitted(fit2), type = "l", main = "Two species response curves", las = 1)) ## End(Not run) # Shows that Fisher scoring can sometime fail. See Ridout (1990). ridout <- data.frame(v = c(1000, 100, 10), r = c(4, 3, 3), n = rep(5, 3)) (ridout <- transform(ridout, logv = log(v))) # The iterations oscillates between two local solutions: glm.fail <- glm(r / n ~ offset(logv) + 1, weight = n, binomial(link = 'cloglog'), ridout, trace = TRUE) coef(glm.fail) # vglm()'s half-stepping ensures the MLE of -5.4007 is obtained: vglm.ok <- vglm(cbind(r, n-r) ~ offset(logv) + 1, binomialff(link = cloglog), ridout, trace = TRUE) coef(vglm.ok) # Separable data set.seed(123) threshold <- 0 bdata <- data.frame(x2 = sort(rnorm(nn <- 100))) bdata <- transform(bdata, y1 = ifelse(x2 < threshold, 0, 1)) fit <- vglm(y1 ~ x2, binomialff(bred = TRUE), data = bdata, criter = "coef", trace = TRUE) coef(fit, matrix = TRUE) # Finite!! summary(fit) ## Not run: plot(depvar(fit) ~ x2, data = bdata, col = "blue", las = 1) lines(fitted(fit) ~ x2, data = bdata, col = "orange") abline(v = threshold, col = "gray", lty = "dashed") ## End(Not run)