amlbinomial {VGAM} | R Documentation |
Binomial quantile regression estimated by maximizing an asymmetric likelihood function.
amlbinomial(w.aml=1, parallel=FALSE, digw=4, link="logit", earg=list())
w.aml |
Numeric, a vector of positive constants controlling the percentiles.
The larger the value the larger the fitted percentile value
(the proportion of points below the ``w-regression plane'').
The default value of unity results in the ordinary maximum likelihood
(MLE) solution.
|
parallel |
If w.aml has more than one value then
this argument allows the quantile curves to differ by the same amount
as a function of the covariates.
Setting this to be TRUE should force the quantile curves to
not cross (although they may not cross anyway).
See CommonVGAMffArguments for more information.
|
digw |
Passed into Round as the digits argument
for the w.aml values;
used cosmetically for labelling.
|
link, earg |
See binomialff .
|
The general methodology behind this VGAM family function
is given in Efron (1992) and full details can be obtained there.
This model is essentially a logistic regression model
(see binomialff
) but the usual deviance is replaced by an
asymmetric squared error loss function; it is multiplied by
w.aml for positive residuals.
The solution is the set of regression coefficients that minimize the
sum of these deviance-type values over the data set, weighted by
the weights
argument (so that it can contain frequencies).
Newton-Raphson estimation is used here.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
and vgam
.
If w.aml
has more than one value then the value returned by
deviance
is the sum of all the (weighted) deviances taken over
all the w.aml
values.
See Equation (1.6) of Efron (1992).
On fitting, the extra
slot has list components "w.aml"
and
"percentile"
. The latter is the percent of observations below
the ``w-regression plane'', which is the fitted values.
Also, the individual deviance values corresponding to each element of
the argument w.aml
is stored in the extra
slot.
For amlbinomial
objects, methods functions for the generic functions
qtplot
and cdf
have not been written yet.
See amlpoisson
about comments on the jargon, e.g.,
expectiles etc.
Thomas W. Yee
Efron, B. (1992) Poisson overdispersion estimates based on the method of asymmetric maximum likelihood. Journal of the American Statistical Association, 87, 98–107.
amlpoisson
,
amlexponential
,
alsqreg
,
alaplace1
.
# Example: binomial data with lots of trials per observation set.seed(1234) sizevec = rep(100, length=(n <- 200)) mydat = data.frame(x = sort(runif(n))) mydat = transform(mydat, prob=logit(-0+2.5*x+x^2, inverse=TRUE)) mydat = transform(mydat, y = rbinom(n, size=sizevec, prob=prob)) mydat = transform(mydat, y = y / sizevec) # Convert to proportions (fit = vgam(y ~ s(x, df=3), fam=amlbinomial(w=c(0.01,0.2,1,5,60)), data=mydat, weight=sizevec, trace=TRUE)) fit@extra ## Not run: par(mfrow=c(1,2)) # Quantile plot with(mydat, plot(x, jitter(y), col="blue", las=1, main= paste(paste(round(fit@extra$percentile, dig=1), collapse=", "), "percentile-expectile curves"))) with(mydat, matlines(x, fitted(fit), lwd=2, col="blue", lty=1)) # Compare the fitted expectiles with the quantiles with(mydat, plot(x, jitter(y), col="blue", las=1, main= paste(paste(round(fit@extra$percentile, dig=1), collapse=", "), "percentile curves are red"))) with(mydat, matlines(x, fitted(fit), lwd=2, col="blue", lty=1)) for(ii in fit@extra$percentile) with(mydat, matlines(x, qbinom(p=ii/100, size=sizevec, prob=prob)/sizevec, col="red", lwd=2, lty=1)) ## End(Not run)