aldvmm.cv {aldvmm}

Numerical Approximation of Covariance Matrix

Description

aldvmm.cv performs a numerical approximation of the covariance matrix of parameter estimates.

Usage

aldvmm.cv(ll, par, X, y, dist, psi, ncmp, lcoef, lcpar, lcmp, optim.method)

Arguments

ll

a function returning the negative log-likelihood of the adjusted limited dependent variable mixture model as a scalar result (aldvmm.ll).

par

a named numeric vector of parameter values.

X

a list of design matrices returned by aldvmm.mm. 'X' is of length 2 and includes a design matrix for the model of component distributions and a design matrix for the model of probabilities of group membership.

y

a numeric vector of observed outcomes from complete observations in 'data' supplied to aldvmm.

dist

an optional character value of the distribution used in the components. In this release, only the normal distribution is available, and the default value is set to "normal".

psi

a numeric vector of minimum and maximum possible utility values smaller than or equal to 1 (e.g. c(-0.594, 0.883)). The potential gap between the maximum value and 1 represents an area with zero density in the value set from which utilities were obtained. The order of the minimum and maximum limits in 'psi' does not matter.

ncmp

a numeric value of the number of components that are mixed. The default value is 2. A value of 1 represents a tobit model with a gap between 1 and the maximum value in 'psi'.

lcoef

a character vector of length 2 with labels of objects including regression coefficients of component distributions (default "beta") and coefficients of probabilities of component membership (default "delta").

lcpar

a character vector with the labels of objects including constant parameters of component distributions (e.g. the standard deviation of the normal distribution). The length of 'lcpar' depends on the distribution supplied to 'dist'.

lcmp

a character value representing a stub (default "Comp") for labeling objects including regression coefficients in different components (e.g. "Comp1", "Comp2", ...). This label is also used in summary tables returned by summary.aldvmm.

optim.method

an optional character value of one of the following optimr methods: "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "nlminb", "Rcgmin", "Rvmmin" and "hjn". The default method is "BFGS". The method "L-BFGS-B" is used when lower and/or upper constraints are set using 'init.lo' and 'init.hi'. The method "nlm" cannot be used in the 'aldvmm' package.

Details

aldvmm.cv uses hessian to calculate the hessian matrix of the log-likelihood function supplied to 'll' at parameter values supplied to 'par'.

Value

aldvmm.cv returns a list with the following objects.

hessian

a numeric matrix with second-order partial derivatives of the likelihood function 'll'.

cv

a numeric matrix with covariances/variances of parameters in 'par'.

se

a numeric vector of standard errors of parameters in 'par'.

z

a numeric vector of z-values of parameters in 'par'.

p

a numeric vector of p-values of parameter estimates.

upper

a numeric vector of upper 95% confidence limits of parameter estimates in 'par'.

lower

a numeric vector of lower 95% confidence limits of parameter estimates in 'par'.