EstPSTR: Estimate a PSTR model by nonlinear least squares
In PSTR: Panel Smooth Transition Regression Modelling

EstPSTR

R Documentation

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"
)

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.

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.

Examples


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")

PSTR documentation built on Feb. 28, 2026, 1:06 a.m.