Parameter estimation for Lagrangian correlation functions for an mcgf object.

Parameter estimation for Lagrangian correlation functions for an mcgf object.

Usage

# S3 method for mcgf
fit_lagr(
  x,
  model = c("lagr_tri", "lagr_askey", "lagr_exp", "none"),
  method = c("wls", "mle"),
  optim_fn = c("nlminb", "optim", "other"),
  par_fixed = NULL,
  par_init,
  lower = NULL,
  upper = NULL,
  other_optim_fn = NULL,
  dists_base = FALSE,
  dists_lagr = NULL,
  ...
)

Arguments

x

An mcgf object containing attributes dists, acfs, ccfs, and sds. x must have been passed to add_base() or base<-

model

Base model, one of lagr_tri, lagr_askey, lagr_exp, or none. If none, NULLs are returned.

method

Parameter estimation methods, weighted least square (wls) or maximum likelihood estimation (mle).

optim_fn

Optimization functions, one of nlminb, optim, other. When optim_fn = other, supply other_optim_fn.

par_fixed

Fixed parameters.

par_init

Initial values for parameters to be optimized.

lower

Optional; lower bounds of parameters lambda, v1, v2, and k.

upper

Optional: upper bounds of parameters lambda, v1, v2, and k.

other_optim_fn

Optional, other optimization functions. The first two arguments must be initial values for the parameters and a function to be minimized respectively (same as that of optim and nlminb).

dists_base

Logical; if TRUE dists_base from the base model is used as the distance.

dists_lagr

List of distance matrices/arrays. Used when dists_base is FALSE. If NULL, dists(x) is used.

...

Additional arguments passed to optim_fn.

Value

A list containing outputs from optimization functions of optim_fn.

Details

This function fits the Lagrangian models using weighted least squares and maximum likelihood estimation. The base model must be fitted first using add_base() or base<-. Optimization functions such as nlminb and optim are supported. Other functions are also supported by setting optim_fn = "other" and supplying other_optim_fn. lower and upper are lower and upper bounds of parameters in par_init and default bounds are used if they are not specified.

Note that both wls and mle are heuristic approaches when x contains observations from a subset of the discrete spatial domain, though estimation results are close to that using the full spatial domain for large sample sizes.

Since parameters for the base model and the Lagrangian model are estimated sequentially, more accurate estimation may be obtained if the full model is fitted all at once.

See also

Other functions on fitting an mcgf: add_base.mcgf(), add_lagr.mcgf(), fit_base.mcgf(), krige.mcgf(), krige_new.mcgf()

Examples

data(sim1)
sim1_mcgf <- mcgf(sim1$data, dists = sim1$dists)
#> `time` is not provided, assuming rows are equally spaced temporally.
sim1_mcgf <- add_acfs(sim1_mcgf, lag_max = 5)
sim1_mcgf <- add_ccfs(sim1_mcgf, lag_max = 5)

# Fit a separable model and store it to 'sim1_mcgf'
fit_sep <- fit_base(
    sim1_mcgf,
    model = "sep",
    lag = 5,
    par_init = c(
        c = 0.001,
        gamma = 0.5,
        a = 0.3,
        alpha = 0.5
    ),
    par_fixed = c(nugget = 0)
)
sim1_mcgf <- add_base(sim1_mcgf, fit_base = fit_sep)

# Fit a Lagrangian model
fit_lagr <- fit_lagr(
    sim1_mcgf,
    model = "lagr_tri",
    par_init = c(v1 = 300, v2 = 300, lambda = 0.15),
    par_fixed = c(k = 2)
)
fit_lagr$fit
#> $par
#>      lambda          v1          v2 
#>   0.1625903 224.5776224 188.5158088 
#> 
#> $objective
#> [1] 1.533448
#> 
#> $convergence
#> [1] 0
#> 
#> $iterations
#> [1] 34
#> 
#> $evaluations
#> function gradient 
#>       37      118 
#> 
#> $message
#> [1] "relative convergence (4)"
#>