# DeltaMethod: Numeric Delta Method approximation for the... In mrds: Mark-Recapture Distance Sampling

 DeltaMethod R Documentation

## Numeric Delta Method approximation for the variance-covariance matrix

### Description

Computes delta method variance-covariance matrix of results of any generic function `fct` that computes a vector of estimates as a function of a set of estimated parameters `par`.

### Usage

```DeltaMethod(par, fct, vcov, delta, ...)
```

### Arguments

 `par` vector of parameter values at which estimates should be constructed `fct` function that constructs estimates from parameters `par` `vcov` variance-covariance matrix of the parameters `delta` proportional change in parameters used to numerically estimate first derivative with central-difference formula `...` any additional arguments needed by `fct`

### Details

The delta method (aka propagation of errors is based on Taylor series approximation - see Seber's book on Estimation of Animal Abundance). It uses the first derivative of `fct` with respect to `par` which is computed in this function numerically using the central-difference formula. It also uses the variance-covariance matrix of the estimated parameters which is derived in estimating the parameters and is an input argument.

The first argument of `fct` should be `par` which is a vector of parameter estimates. It should return a single value (or vector) of estimate(s). The remaining arguments of `fct` if any can be passed to `fct` by including them at the end of the call to `DeltaMethod` as `name=value` pairs.

### Value

a list with values

 `variance` estimated variance-covariance matrix of estimates derived by `fct` `partial` matrix (or vector) of partial derivatives of `fct` with respect to the parameters `par`

### Note

This is a generic function that can be used in any setting beyond the `mrds` package. However this is an internal function for `mrds` and the user does not need to call it explicitly.

### Author(s)

Jeff Laake

mrds documentation built on March 18, 2022, 5:26 p.m.