deltamethod {symSEM}

Compute the Variance-Covariance Matrix of Functions using the first-order Delta Method

Description

It computes the variance-covariance matrix of functions using the first-order delta method.

Usage

deltamethod(fn, Covvars, vars, Var.name = "V", Cov.name = "C", simplify = TRUE)

Arguments

fn

A function in character strings or a vector of functions.

Covvars

Variance-covariance matrix of the variables. Users must ensure the order of variables is the same as that in vars; Otherwise, the results are likely incorrect. If it is not specified, they are automatically generated.

vars

A vector of characters of the random variables. If the random variables are not listed in 'vars', they are treated as constants. If 'vars' is missing, all names in 'RAM' are treated as random variables.

Var.name

Name of the variances.

Cov.name

Name of the covariances.

simplify

Attempt to simplify the output.

Value

Variance-covariance matrix of the functions.

Author(s)

Mike W.-L. Cheung <[e-mail]>

Examples

## Not run: 

#### Fisher-z-transformation
fn  <- "0.5*log((1+r)/(1-r))"

## Sampling variance of r
Covvars <- "(1-r^2)^2/n"

deltamethod(fn=fn, Covvars=Covvars, vars="r")
## $fn
##     [,1]
## fn1 "0.5*log((r+1)/(1-r))"

## $Covfn
##     fn1
## fn1 "1/n"

## $vars
## [1] "r"

## $Covvars
##   r
## r "(1-r^2)^2/n"

## $Jmatrix
##     r
## fn1 "(0.5*(1-r+r+1)*(1-r))/((1-r)^2*(r+1))"

#### Raw mean difference: y_treatment - y_control
fn <- "yt - yc"

## Sampling covariance matrix
## S2p: pooled variance
## nt: n_treatment
## nc: n_control
Covvars <- matrix(c("S2p/nt", 0,
                    0, "S2p/nc"),
                  ncol=2, nrow=2)

deltamethod(fn=fn, Covvars=Covvars, vars=c("yt", "yc"))
## $fn
##     [,1]
## fn1 "yt-yc"

## $Covfn
##     fn1
## fn1 "(S2p*nt+S2p*nc)/(nt*nc)"

## $vars
## [1] "yt" "yc"

## $Covvars
##    yt       yc
## yt "S2p/nt" "0"
## yc "0"      "S2p/nc"

## $Jmatrix
##     yt  yc
## fn1 "1" "-1"

#### log(odds)
fn <- "log(p/(1-p))"

## Sampling variance of p
Covvars <- "p*(1-p)/n"

## Though it is correct, the simplification does not work well.
deltamethod(fn=fn, Covvars=Covvars, vars="p")
## $fn
##     [,1]
## fn1 "log(p/(1-p))"

## $Covfn
##     fn1
## fn1 "(3*p^2-p^3-3*p+1)/((p^4-4*p^3+6*p^2-4*p+1)*p*n)"

## $vars
## [1] "p"

## $Covvars
##   p
## p "(p*(1-p))/n"

## $Jmatrix
##     p
## fn1 "((1-p+p)*(1-p))/((1-p)^2*p)"

## End(Not run)