aldvmm.sc {aldvmm}

Calculating analytical Gradients of the Negative Log-Likelihood for each observation

Description

aldvmm.sc calculates analytical gradients of the negative log-likelihood with respect to parameter values in 'par' for each observation in the estimation data.

Usage

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

Arguments

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.

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.

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".

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").

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.

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'.

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.sc calculates gradients of the negative log-likelihood.

Value

a named numeric matrix of first derivatives of the negative log-likelihood of the data with respect to parameters in 'par'.