Parameter estimation for Lagrangian correlation functions for an mcgf_rs object.

Parameter estimation for Lagrangian correlation functions for an mcgf_rs object.

Usage

# S3 method for mcgf_rs
fit_lagr(
  x,
  model_ls,
  method_ls = "wls",
  optim_fn_ls = "nlminb",
  par_fixed_ls = list(NULL),
  par_init_ls,
  lower_ls = list(NULL),
  upper_ls = list(NULL),
  other_optim_fn_ls = list(NULL),
  dists_base_ls,
  dists_lagr_ls = list(NULL),
  rs = TRUE,
  ...
)

Arguments

x

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

model_ls

List of base models, each element must be one of lagr_tri, lagr_askey, lagr_exp, or none. If none, NULLs are returned.

method_ls

List of parameter estimation methods, weighted least square (wls) or maximum likelihood estimation (mle).

optim_fn_ls

List of optimization functions, each element must be one of nlminb, optim, other. When use other, supply other_optim_fn_ls

par_fixed_ls

List of fixed parameters.

par_init_ls

List of initial values for parameters to be optimized.

lower_ls

Optional; list of lower bounds of parameters.

upper_ls

Optional: list of upper bounds of parameters.

other_optim_fn_ls

Optional, list of 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_ls

List of lists of distance matrices. If NULL, dists(x) is used. Each element must be a matrix or an array of distance matrices.

dists_lagr_ls

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

rs

Logical; if TRUE x is treated as a regime-switching, FALSE if the parameters need to be estimated in a non-regime-switching setting.

...

Additional arguments passed to optim_fn.

Value

A list containing outputs from optimization functions of optim_fn.

Details

This functions is the regime-switching variant of fit_lagr.mcgf(). Arguments are in lists. The length of arguments that end in _ls must be 1 or the same as the number of regimes in x. If the length of an argument is 1, then it is set the same for all regimes. Refer to fit_lagr.mcgf() for more details of the arguments.

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_rs: add_base.mcgf_rs(), add_lagr.mcgf_rs(), fit_base.mcgf_rs(), krige.mcgf_rs(), krige_new.mcgf_rs()

Examples

data(sim3)
sim3_mcgf <- mcgf_rs(sim3$data, dists = sim3$dists, label = sim3$label)
#> `time` is not provided, assuming rows are equally spaced temporally.
sim3_mcgf <- add_acfs(sim3_mcgf, lag_max = 5)
sim3_mcgf <- add_ccfs(sim3_mcgf, lag_max = 5)

# Fit a fully symmetric model with known variables
fit_fs <- fit_base(
    sim3_mcgf,
    lag_ls = 5,
    model_ls = "fs",
    rs = FALSE,
    par_init_ls = list(list(beta = 0)),
    par_fixed_ls = list(list(
        nugget = 0,
        c = 0.05,
        gamma = 0.5,
        a = 0.5,
        alpha = 0.2
    ))
)

# Set beta to 0 to fit a separable model with known variables
fit_fs[[1]]$fit$par <- 0

# Store the fitted separable model to 'sim3_mcgf'
sim3_mcgf <- add_base(sim3_mcgf, fit_base_ls = fit_fs)

# Fit a regime-switching Lagrangian model.
fit_lagr_rs <- fit_lagr(
    sim3_mcgf,
    model_ls = list("lagr_tri"),
    par_init_ls = list(
        list(v1 = -50, v2 = 50),
        list(v1 = 100, v2 = 100)
    ),
    par_fixed_ls = list(list(lambda = 0.2, k = 2))
)
lapply(fit_lagr_rs[1:2], function(x) x$fit)
#> $`Regime 1`
#> $`Regime 1`$par
#>        v1        v2 
#> -106.5181  119.4434 
#> 
#> $`Regime 1`$objective
#> [1] 5.137749
#> 
#> $`Regime 1`$convergence
#> [1] 0
#> 
#> $`Regime 1`$iterations
#> [1] 26
#> 
#> $`Regime 1`$evaluations
#> function gradient 
#>       29       61 
#> 
#> $`Regime 1`$message
#> [1] "relative convergence (4)"
#> 
#> 
#> $`Regime 2`
#> $`Regime 2`$par
#>       v1       v2 
#> 210.1156 242.3082 
#> 
#> $`Regime 2`$objective
#> [1] 5.902847
#> 
#> $`Regime 2`$convergence
#> [1] 0
#> 
#> $`Regime 2`$iterations
#> [1] 29
#> 
#> $`Regime 2`$evaluations
#> function gradient 
#>       31       77 
#> 
#> $`Regime 2`$message
#> [1] "relative convergence (4)"
#> 
#>