getRestrict-methods: Methods for Function `getRestrict` in Package momentfit

Description

It computes the matrices related to linear and nonlinear contraints. Those matrices are used to perform hypothesis tests.

Usage

# S4 method for rlinearModel
getRestrict(object, theta)
# S4 method for rslinearModel
getRestrict(object, theta)
# S4 method for rsnonlinearModel
getRestrict(object, theta)
# S4 method for rnonlinearModel
getRestrict(object, theta)
# S4 method for rformulaModel
getRestrict(object, theta)
# S4 method for momentModel
getRestrict(object, theta, R, rhs=NULL)
# S4 method for sysModel
getRestrict(object, theta, R, rhs=NULL)
# S4 method for rfunctionModel
getRestrict(object, theta)

Arguments

object: Object of class included in momentModel, rmomentModel, and rsysModel.
theta: A vector of coefficients for the unrestricted model (see examples).
R: A matrix, character or list of formulas that specifies the contraints to impose on the coefficients. See restModel for more details.
rhs: The right hand side for the restriction on the coefficients. See restModel for more details. It is ignored for objects of class "nonlinearModel".

Methods

signature(object = "momentModel"): A restricted model is created from the constraints, and the restriction matrices are returned. The methods is applied to linear and nonlinear models in a regression form.
signature(object = "sysModel"): A restricted model is created from the constraints, and the restriction matrices are returned. The methods is applied to systems of linear and nonlinear models.
signature(object = "rlinearModel"): The restriction matrices are evaluated at the coefficient vector theta of the unrestricted representation.
signature(object = "rslinearModel"): The restriction matrices are evaluated at the coefficient vector theta of the unrestricted representation.
signature(object = "rsnonlinearModel"): The restriction matrices are evaluated at the coefficient vector theta of the unrestricted representation.
signature(object = "rnonlinearModel"): The restriction matrices are evaluated at the coefficient vector theta of the unrestricted representation.
signature(object = "rfunctionModel"): The restriction matrices are evaluated at the coefficient vector theta of the unrestricted representation.

Examples

Run this code

data(simData)
theta <- c(beta0=1,beta1=2)

## Unrestricted model
model1 <- momentModel(y~x1+x2+x3+z1, ~x1+x2+z1+z2+z3+z4, data=simData)

## The restricted model
R1 <- c("x1","2*x2+z1=2", "4+x3*5=3")
res <- gmmFit(model1)
rest <- getRestrict(model1, coef(res), R1)

## it allows to test the restriction
g <- rest$R-rest$q
v <- rest$dR%*%vcov(res)%*%t(rest$dR)
(test <- crossprod(g, solve(v, g)))
(pv <- 1-pchisq(test, length(rest$R)))


## Delta Method:
## To impose nonlinear restrictions, we need to convert
## the linear model into a nonlinear one
NLmodel <- as(model1, "nonlinearModel")
R1 <- c("theta2=2", "theta3=theta4^2")
res <- gmmFit(NLmodel)
rest <- getRestrict(NLmodel, coef(res), R1)

g <- rest$R-rest$q
v <- rest$dR%*%vcov(res)%*%t(rest$dR)
(test <- crossprod(g, solve(v, g)))
(pv <- 1-pchisq(test, length(rest$R)))

## See hypothesisTest method for an easier approach.

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