A simple, yet exceedingly useful, approach to estimate the variance of a function using the numerical delta method. A number of packages provide functions that analytically calculate the gradients; we use numerical derivatives, which generalises to models that do not offer analytical derivatives (e.g. ordinary differential equations, integration), or to examples that are tedious or error-prone to calculate (e.g. sums of predictions from GLMs).
# S3 method for default
predictnl(object, fun, newdata=NULL, gd=NULL, ...)
# S3 method for lm
predictnl(object, fun, newdata=NULL, ...)
# S3 method for predictnl
print(x, ...)
# S3 method for formula
predict(object,data,newdata,na.action,type="model.matrix",...)
# S3 method for predictnl
confint(object, parm, level=0.95, ...)Returns an object of class
an object with class c("predictnl","data.frame") elements
c("fit","se.fit","Estimate","SE") and with methods print
and confint. Note that the Estimate and SE fields are deprecated
and their use is discouraged, as we would like to remove them from future releases.
An object with coef, vcov and `coef<-`
methods (required).
A function that takes object as the first argument, possibly with
newdata and other arguments (required). See notes for why it is
often useful to include newdata as an argument to the function.
An optional argument that defines newdata to be passed to fun.
An optional matrix of gradients. If this is not specified, then the gradients are calculated using finite differences.
currently ignored
significance level for 2-sided confidence intervals
a predictnl object to be printed.
object used to define the model frame
passed to model.frame
currently restricted to "model.matrix"
Other arguments that are passed to fun.
Mark Clements
The signature for fun
is either fun(object, ...) or fun(object, newdata=NULL,
...).
The different predictnl methods call the utility function
numDeltaMethod, which in turn calls the grad function for
numerical differentiation. The numDeltaMethod function calls the
standard coef and vcov methods, and the non-standard
`coef<-` method for changing the coefficients in a regression
object. This non-standard method has been provided for several
regression objects and essentially mirrors the coef method.
One potential issue is that some predict methods do not
re-calculate their predictions for the fitted dataset (i.e. when
newdata=NULL). As the predictnl function changes the
fitted coefficients, it is required that the predictions are
re-calculated. One solution is to pass newdata as an argument to
both predictnl and fun; alternatively, newdata can
be specified in fun. These approaches are described in the examples
below. The numDeltaMethod method called by predictnl
provides a warning when the variance estimates are zero, which may be
due to this cause.
For completeness, it is worth discussing why the example
predictnl(fit,predict) does not work for when fit is a
glm object. First, predict.glm does not update the
predictions for the fitted data. Second, the default predict
method has a signature predict(object, ...), which does not
include a newdata argument. We could then either (i) require that
a newdata argument be passed to the fun function for all
examples, which would make this corner case work, or (ii) only pass the
newdata argument if it is non-null or in the formals for the
fun function, which would fail for this corner case. The current
API defaults to the latter case (ii). To support this approach, the
predictnl.lm method replaces a null newdata with
object$data. We also provide a revised
numdelta:::predict.lm method that performs the same operation,
although its use is not encouraged due to its clumsiness.
df <- data.frame(x=0:1, y=c(10, 20))
fit <- glm(y ~ x, df, family=poisson)
predictnl(fit,
function(obj,newdata)
diff(predict(obj,newdata,type="response")))
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