nlsur: Fitting Iterative Feasible Non-Linear Seemingly Unrelated...

In JanMarvin/nlsur: Estimating Nonlinear Least Squares for Equation Systems

Fitting Iterative Feasible Non-Linear Seemingly Unrelated Regression Model

Description

nlsur() is used to fit nonlinear regression models. It can handle the feasible and iterative feasible variants.

Usage

nlsur(
  eqns,
  data,
  startvalues,
  type = NULL,
  S = NULL,
  trace = FALSE,
  robust = FALSE,
  stata = TRUE,
  qrsolve = FALSE,
  weights,
  MASS = FALSE,
  maxiter = 1000,
  val = 0,
  tol = 1e-07,
  eps = 1e-05,
  ifgnlseps = 1e-10,
  tau = 0.001,
  initial = FALSE
)

Arguments

eqns	is a list object containing the model as formula. This list can handle contain only a single equations (although in this case nls() might be a better choice) or a system of equations.
data	an (optional) data frame containing the variables that will be evaluated in the formula.
startvalues	initial values for the parameters to be estimated.
type	can be 1 Nonlinear Least Squares (NLS), 2 Feasible Generalized NLS (FGNLS) or 3 Iterative FGNLS (IFGNLS) or the respective abbreviations in character form.
S	is a weight matrix used for evaluation. If no weight matrix is provided the identity matrix I will be used.
trace	logical whether or not SSR information should be printed. Default is FALSE.
robust	logical if true robust standard errors are estimated.
stata	is a logical. If TRUE for nls a second evaluation will be run. Stata does this by default. For this second run Stata replaces the diagonal of the I matrix with the coefficients.
qrsolve	logical
weights	Additional weight vector.
MASS	is a logical whether an R function similar to the MASS::lm.gls() function should be used for weighted Regression. This can cause sever RAM usage as the weight matrix tend to be huge (n-equations * n-rows).
maxiter	Maximum number of iterations.
val	If no start values supplied, create them with this start value. Default is 0.
tol	qr.solves tolerance for detecting linear dependencies.
eps	the epsilon used for convergence in nlsur(). Default is 1e-5.
ifgnlseps	is epsilon for ifgnls(). Default is 1e-10.
tau	is another convergence variable. Default is 1e-3.
initial	logical value to define if rankMatrix is calculated every iteration of nlsur.

Details

nlsur() is a wrapper around .nlsur(). The function was initially inspired by the Stata Corp Function nlsur. Nlsur estimates a nonlinear least squares demand system. With nls, fgnls or ifgnls which is equivalent to Maximum Likelihood estimation. Nonlinear least squares requires start values and nlsur requires a weighting matrix for the demand system. If no weight matrix is provided, nlsur will use the identity matrix I. If type = 1 or type = "nls" is added, nlsur will use the matrix for an initial estimation, once the estimation is done, it will swap the diagonal with the estimated results.

Most robust regression estimates shall be returned with both qrsolve and MASS TRUE, but memory consumption is largest this way. If MASS is FALSE a memory efficient RcppArmadillo solution is used for fgnls and ifgnls. If qrsolve is FALSE as well, only the Armadillo function is used.

If robust is selected Whites HC0 is used to calculate Heteroscedasticity Robust Standard Errors.

If initial is TRUE rankMatrix will be calculated every iteration of nlsur. Meaning for nls at least once, for fgnls at least twice and for ifgnls at least three times. This adds a lot of overhead, since rankMatrix is used to calculate k. To assure that k does not change this can be set to TRUE.

Nlsur has methods for the generic functions coef, confint, deviance, df.residual, fitted, predict, print, residuals, summary and vcov.

Value

The function returns a list object of class nlsur. The list includes:

coefficients:

estimated coefficients

residuals:

residuals

xi:

residuals of each equation in a single list

eqnames:

list of equation names

sigma:

the weight matrix

ssr:

Residual sum of squares

lhs:

Left hand side of the evaluated model

rhs:

Right hand side of the evaluated model

nlsur:

model type. "NLS", "FGNLS" or "IFGNLS"

se:

standard errors

t:

t values

covb:

asymptotic covariance matrix

zi:

equation wise estimation results of SSR, MSE, RMSE, MAE, R2 and Adj-R2. As well as n, k and df.

model:

equation or system of equations as list containing formulas

References

Gallant, A. Ronald (1987): Nonlinear Statistical Models. Wiley: New York

See Also

nls

Examples

## Not run: 
# Greene Example 10.3
library(nlsur)

url <- "http://www.stern.nyu.edu/~wgreene/Text/Edition7/TableF10-2.txt"
dd <- read.table(url, header = T)

names(dd) <-
 c("Year", "Cost", "Sk", "Sl", "Se", "Sm", "Pk", "Pl", "Pe", "Pm")


eqns <-
 list( Sk ~ bk + dkk * log(Pk/Pm) + dkl * log(Pl/Pm) + dke * log(Pe/Pm),
       Sl ~ bl + dkl * log(Pk/Pm) + dll * log(Pl/Pm) + dle * log(Pe/Pm),
       Se ~ be + dke * log(Pk/Pm) + dle * log(Pl/Pm) + dee * log(Pe/Pm))

strtvls <- c(be = 0, bk = 0, bl = 0,
             dkk = 0, dkl = 0, dke = 0,
             dll = 0, dle = 0, dee = 0)


erg <- nlsur(eqns = eqns, data = dd, startvalues = strtvls, type = 2,
             trace = TRUE, eps = 1e-10)

erg

## End(Not run)

JanMarvin/nlsur documentation built on June 24, 2024, 2:58 a.m.