aldvmm.ll {aldvmm}

Calculating the Negative Log-Likelihood of the Adjusted Limited Dependent Variable Mixture Model

Description

aldvmm.ll calculates the negative log-likelihood of 'data' supplied to aldvmm at the parameter values in 'par'.

Usage

aldvmm.ll(par, X, y, psi, ncmp, dist, lcoef, lcpar, lcmp, 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.

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'.

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".

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.ll calculates the negative log-likelihood of the adjusted limited dependent variable mixture model using the likelihood function published in Hernandez Alava and Wailoo (2015). Constant distribution parameters that need to be non-negative (i.e. the standard deviations of normal distributions) enter the likelihood function as log-transformed values.

As the "L-BFGS-B" and "Rcgmin" methods in optimr fail if they encounter infinite values, the log-likelihood function takes the value -1e+20 if it is infinite during these algorithms.

The names of the parameter vector supplied to 'par' must be generated using aldvmm.getnames because they will be inherited by return values of other functions in the package 'aldvmm'. The names will also be used in the extraction of parameters from parameter vectors into nested lists using aldvmm.getpar.

Value

a scalar of the negative log-likelihood of the data at parameter values in 'par'.

References

Alava, M. H. and Wailoo, A. (2015) Fitting adjusted limited dependent variable mixture models to EQ-5D. The Stata Journal, 15(3), 737–750. doi:10.1177/1536867X1501500307