aldvmm.init: Creating Initial Values

Description

aldvmm.init creates initial values for the minimization of the negative log-likelihood returned by aldvmm.ll using optimr.

Usage

aldvmm.init(
  X,
  y,
  psi,
  ncmp,
  dist,
  init.method,
  init.est,
  init.lo,
  init.hi,
  optim.method,
  optim.control = list(),
  optim.grad,
  lcoef,
  lcpar,
  lcmp
)

Value

aldvmm.init

returns a list with the following objects.

est: a numeric vector of initial values of parameters.
lo: a numeric vector of lower limits of parameters.
hi: a numeric vector of upper limits of parameters.

Arguments

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".
init.method: an optional character value indicating the method for obtaining initial values. The following values are available: "zero", "random", "constant" and "sann". The default value is "zero".
init.est: an optional numeric vector of user-defined initial values. User-defined initial values override the 'init.method' argument. Initial values have to follow the same order as parameter estimates in the return value 'coef'.
init.lo: an optional numeric vector of user-defined lower limits for constrained optimization. When 'init.lo' is not NULL, the optimization method "L-BFGS-B" is used. Lower limits of parameters have to follow the same order as parameter estimates in the return value 'coef'.
init.hi: an optional numeric vector of user-defined upper limits for constrained optimization. When 'init.hi' is not NULL, the optimization method "L-BFGS-B" is used. Upper limits of parameters have to follow the same order as parameter estimates in the return value 'coef'.
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.
optim.control: an optional list of optimr control parameters.
optim.grad: an optional logical value indicating if an analytical gradient should be used in optimr methods that can use this information. The default value is TRUE. If 'optim.grad' is set to FALSE, a finite difference approximation is used.
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.

Details

'init.method' accepts four methods for generating initial values: "zero", "random", "constant", "sann". The method "zero" sets initial values of all parameters to 0. The method "random" draws random starting values from a standard normal distribution. The method "constant" estimates a constant-only model and uses estimates as initial values for intercepts and constant distribution parameters and 0 for all other parameters. The method "sann" estimates the full model using the simulated annealing optimization method and uses all parameter estimates as initial values. When user-specified initial values are supplied in 'init.est', the argument 'init.method' is ignored.

By default, aldvmm performs unconstrained optimization with upper and lower limits at -Inf and Inf. When user-defined lower and upper limits are supplied to 'init.lo' and/or 'init-hi', these default limits are replaced with the user-specified values, and the method "L-BFGS-B" is used for box-constrained optimization instead of the user defined 'optim.method'. It is possible to only set either maximum or minimum limits. When initial values supplied to 'init.est' or from default methods lie outside the limits, the in-feasible values will be set to the limits using the function bmchk.