`delta.method`

is a generic function that uses the delta method to get a
first-order approximate
standard error for a nonlinear function of a vector of random variables
with known or estimated covariance matrix.```
delta.method(object, ...)
## S3 method for class 'default':
delta.method(object,g,var,...)
## S3 method for class 'lm':
delta.method(object, g, var=vcov,parameterPrefix="b",...)
## S3 method for class 'nls':
delta.method(object, g, var=vcov,...)
## S3 method for class 'lmList':
delta.method(object, g, var=vcov,parameterPrefix="b",...)
## S3 method for class 'nlsList':
delta.method(object, g, var=vcov,...)
## S3 method for class 'lme':
delta.method(object, g, var=vcov,parameterPrefix="b",...)
## S3 method for class 'nlme':
delta.method(object, g, var=vcov,...)
## S3 method for class 'multinom':
delta.method(object, g, var=vcov,parameterPrefix="b",...)
## S3 method for class 'polr':
delta.method(object, g, var=vcov,parameterPrefix="b",...)
```

object

For the default method,

`object`

is a named vector of `p`

elements. This means that the call `names(object)`

would return a list
of `p`

character strings that are the names of the elements of
`ob`

g

A quoted string that is the function of the parameter estimates to be
evaluated; see the details below.

var

The (estimated) covariance matrix of the coefficient
estimates. For the default method, this argument is required. For all
other methods, this argument must either provide the estimated covariance
matrix or a function that when applied
to

parameterPrefix

Typically a single letter with default

`"b"`

giving the prefix of the
names of the parameter names used in the argument `g`

; see details....

Additional arguments; not currently used.

- A data.frame with two components
named
`Estimate`

for the estimate,`SE`

for its standard error. The value of`g`

is given as a row label.

`object`

, $C$ in the argument `var`

, and a text expression
in argument `g`

that when evaluated gives the function $g$.
Since
the delta method is often applied to functions of regression parameter
estimates, the argument `object`

may be the name of a regression
object from which the vector $x$ will be taken from `coef(object)`

,
and $C$ will be taken from `vcov(object)`

unless you provide
some other estimate of variance, for example, using a sandwich estimator. Methods
have been provided for many common regression models.
For regression models for which methods are not provided, you must extract
the named vector of coefficient estimates and and estimate of its covariance
matrix and then apply the default delta.method function.
In the argument `g`

you must provide a quoted character string
that gives the function of interest, for example `g="b1/b2"`

, where
`b1`

and `b2`

are names of two of the coefficient estimates.
For nonlinear regression objects of type nls, the call `coef(object)`

returns the estimated
coefficient vectors with names corresponding to parameter names.
For example,
`m2 <- nls(y~theta/(1+gamma*x), start = list(theta=2,gamma=3))`

will
have parameters named `c("theta", "gamma")`

.
In many other familiar regression methods, such as lm and glm, the names of
the coefficient estimates are the corresponding variable names, not
parameter names. For example, in
`m2 <- lm(Y~X1+X2)`

, `names(coef(m2))`

returns
`c("(Intercept)","X1","X2")`

. For models where the
coefficient names are variable
names, `delta.method`

will
provide names for the parameter estimates, given by
`parameterPrefix`

is
left at its default value of `D`

function used to compute derivatives may
get confused. However, embedded spaces or `g`

are computed using symbolic differentiation
by the function `D`

.# cakes is a data frame with response Y, predictors X1 X2 data(cakes,package="alr3") m1 <- lm(Y~ X2 + I(X2^2), data = cakes) # quadratic polynomial delta.method(m1, "-b1/(2*b2)") # X2 that maximizes the quadratic # second order polynomial in two predictors: m2 <- lm(Y ~ X1 + X2 + I(X1^2) + I(X2^2) + X1:X2, data=cakes) # Find X1 to maximize Y when X2=350: delta.method(m2,"(b1+b5*350)/(-2*b3)")