# deltaMethod: Variance Matrix of a Nonlinear Estimator Using the Delta... In CDM: Cognitive Diagnosis Modeling

## Description

Computes the variance of a nonlinear parameter using the delta method.

## Usage

 `1` ```deltaMethod(derived.pars, est, Sigma, h=1e-05) ```

## Arguments

 `derived.pars` Vector of derived parameters written in R formula framework (see Examples). `est` Vector of parameter estimates `Sigma` Covariance matrix of parameters `h` Numerical differentiation parameter

## Value

 `coef` Vector of nonlinear parameters `vcov` Covariance matrix of nonlinear parameters `se` Vector of standard errors `A` First derivative of nonlinear transformation `univarTest` Data frame containing univariate summary of nonlinear parameters `WaldTest` Multivariate parameter test for nonlinear parameter

See `car::deltaMethod` or `msm::deltamethod`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```############################################################################# # EXAMPLE 1: Nonlinear parameter ############################################################################# #-- parameter estimate est <- c( 510.67, 102.57) names(est) <- c("mu", "sigma") #-- covariance matrix Sigma <- matrix( c(5.83, 0.45, 0.45, 3.21 ), nrow=2, ncol=2 ) colnames(Sigma) <- rownames(Sigma) <- names(est) #-- define derived nonlinear parameters derived.pars <- list( "d"=~ I( ( mu - 508 ) / sigma ), "dsig"=~ I( sigma / 100 - 1) ) #*** apply delta method res <- CDM::deltaMethod( derived.pars, est, Sigma ) res ```