EstPSTR: Estimate a PSTR model by nonlinear least squares

Description

EstPSTR estimates either a nonlinear PSTR model (when iq is provided) or a linear fixed-effects panel regression (when iq = NULL).

Usage

EstPSTR(
  use,
  im = 1,
  iq = NULL,
  par = NULL,
  useDelta = FALSE,
  vLower = 2,
  vUpper = 2,
  method = "L-BFGS-B"
)

Value

Invisibly returns use with estimation results added. In particular, for a nonlinear PSTR model (iq not NULL), the object contains (among others):

delta: Estimate of $\delta$.
gamma: Estimate of $\gamma = \exp(\delta)$.
c: Estimates of $c_1,\ldots,c_m$.
vg: Estimated transition-function values $g_{it}$.
beta: Estimated coefficients (named as var_0 for linear-part coefficients and var_1 for nonlinear-part coefficients).
vU: Residuals.
vM: Estimated individual effects.
s2: Estimated residual variance.
cov: Cluster-robust and heteroskedasticity-consistent covariance matrix of all estimates.
se: Standard errors corresponding to est.
est: Vector of all estimates (coefficients followed by nonlinear parameters).
mbeta: Estimates of coefficients in the second extreme regime (when available).
mse: Standard errors for mbeta (when available).

For a linear fixed-effects model (iq = NULL), the object contains beta, vU, vM, s2, cov, se, and est.

Arguments

use: An object of class "PSTR" created by NewPSTR.
im: Integer. Number of switches $m$ in the transition function. Default is 1.
iq: Either an integer index (column number in the transition-variable matrix) or a character string (transition-variable name) specifying which transition variable to use. If NULL, a linear fixed-effects panel regression is estimated.
par: Numeric vector of length im + 1 giving initial values for the nonlinear parameters. The expected order is c(delta, c_1, ..., c_m) if useDelta = TRUE, or c(gamma, c_1, ..., c_m) if useDelta = FALSE. If NULL, defaults are constructed automatically and useDelta is ignored.
useDelta: Logical. If TRUE, the first element of par is interpreted as $\delta$. If FALSE, it is interpreted as $\gamma$ and internally converted to $\delta = \log(\gamma)$ before optimisation.
vLower: Numeric scalar or vector. Lower offsets defining the lower bounds in the optimiser. Bounds are applied to the internal parameter vector used in optimisation (with the first element being $\delta$).
vUpper: Numeric scalar or vector. Upper offsets defining the upper bounds in the optimiser. Bounds are applied to the internal parameter vector used in optimisation (with the first element being $\delta$).
method: Character. Optimisation method passed to stats::optim. Default is "L-BFGS-B" (bounded optimisation).

Details

Two equivalent interfaces are available:

Wrapper function: EstPSTR(use = obj, ...).
R6 method: obj$EstPSTR(...).

The wrapper calls the corresponding R6 method and returns use invisibly.

The transition function is logistic and depends on a transition variable $q_{it}$ and nonlinear parameters $\gamma > 0$ and switching locations $c_1 < \cdots < c_m$: $$g(q_{it}; \gamma, c_1,\ldots,c_m) = \left(1 + \exp\left[-\gamma \prod_{j=1}^{m}(q_{it}-c_j)\right]\right)^{-1}.$$ The smoothness parameter is internally reparametrised as $\gamma = \exp(\delta)$, where $\delta \in \mathbb{R}$. The optimisation is always carried out in $\delta$ and $c$.

If par = NULL, the function constructs default initial values from quantiles of the selected transition variable and treats the first element as $\delta$.

Examples

Run this code

# \donttest{
pstr <- NewPSTR(Hansen99, dep = "inva", indep = 4:20,
               indep_k = c("vala","debta","cfa","sales"),
               tvars = c("vala"), iT = 14)

# 1) Linear fixed-effects model
pstr <- EstPSTR(use = pstr)
print(pstr, mode = "estimates", digits = 6)

# 2) Nonlinear PSTR model
pstr <- EstPSTR(use = pstr, im = 1, iq = 1, useDelta = TRUE,
               par = c(.63, 0), vLower = 4, vUpper = 4)
print(pstr, mode = "estimates", digits = 6)

# R6 method interface (equivalent)
pstr$EstPSTR(im = 1, iq = 1, useDelta = TRUE, par = c(.63, 0), method = "CG")
# }