Version: 1.1.3
Date: 2016-03-22
Title: Wald Test of Nonlinear Restrictions and Nonlinear CI
Description: Wald Test for nonlinear restrictions on model parameters and confidence intervals for nonlinear functions of parameters using delta-method. Applicable after ANY model, provided parameters estimates and their covariance matrix are available.
Author: Oleh Komashko
Maintainer: Oleh Komashko <oleg_komashko@ukr.net>
Depends: R (≥ 3.0.2)
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
LazyData: yes
Repository: CRAN
NeedsCompilation: no
Packaged: 2016-03-24 09:42:58 UTC; oleh
Date/Publication: 2016-03-25 00:12:23

Data for testing CES production function

Description

Data for estimation and testing CES production function: q-output, l-labor, k-capital

Usage

CESdata

Format

A data frame with 25 observations on the following 3 variables.

k

capital

l

labor

q

output

Source

EViews, coef_test.wf1

Examples

attach(CESdata)

Confidence intervals for nonlinear functions of parameters

Description

Computes confidence intervals for nonlinear functions of a model parameters. Delta method is used to compute standard errors. Applicable after any model provided estimates of parameters and their covariance matrix are available.

Usage

nlConfint(obj = NULL, texts, level = 0.95, coeff = NULL,
          Vcov = NULL, df2 = NULL, x = NULL)
# Standard:
# nlConfint(obj, texts) # based on z-statistics
# nlWaldtest(obj, texts, df2 = T) # based on z-statistics

# If coef(obj) and vcov(obj) are not available
# nlWaldtest(texts = funcions, coeff = vector, Vcov = matrix)

Arguments

obj

model object of any class, for which vcov.class(obj) and coef.class(obj) methods are defined. Otherwise, both coeff and Vcov should be inputted directly.

texts

function(s) of parameters, b[i], as string or vector of strings. Several functions can be inputted as a string, separated by semicolon, or as a character vector, e.g. texts = "b[1]^b[2]-1; b[3]", or texts = c("b[1]^b[2]-1", "b[3]"); b's should be numbered as in coeff vector.

level

confidence level, a number in (0, 1). Default is 0.95.

coeff

vector of parameter estimates. If missing, it is set for coef(obj) when available. It allows, for example, to compute CI for functions of marginal effects and elasticities provided their covariance matrix is inputted.

Vcov

covariance matrix of parameters. If missing, it is set to coef(obj) when available. If coeff and/or Vcov are inputed, theirs counterparts from obj are superseded.

df2

defines whether CI will be computed based on z (the default method) or t statistics. To compute t-based intervals, one can use df2 = T, provided a method for df.residual is available. Otherwise, one could input df2 = n, where n is a natural number. df2 is the df in the t statistics. If df2 = T but df.residuals(obj) doesn't exist, z-based intervals are forced, followed by a message.

x

number, or numeric vector. Provides a way to supply cumbersome coefficients into functions, e.g. texts = "b[1]^x[1] + x[2]", x = c(0.1234, 5.6789) to compute CI for b[1]^0.1234 + 5.6789.

Details

The function should be applicable after (almost) any regression-type model, estimated using cross-section, time series, or panel data. If there are no methods for coef(obj) and/or vcov(obj), coeff and Vcov arguments should be inputted directly. To realize the delta-method, the function first tries to compute analytical derivatives using deriv. If failed, it computes numerical derivatives, calling numericDeriv.

Value

an r by 3 matrix, where r is the number of functions in texts argument. The first column is formed of values of the functions computed at parameters estimates. The two last columns are confidence bounds.

Author(s)

Oleh Komashko

References

Greene, W.H. (2011). Econometric Analysis, 7th edition. Upper Saddle River, NJ: Prentice Hall

See Also

nlWaldtest

Examples

set.seed(13)
x1<-rnorm(30);x2<-rnorm(30);x3<-rnorm(30);y<-rnorm(30)
set.seed(NULL)
lm1a<-lm(y~x1+x2+x3)
nlConfint(lm1a, c("b[2]^3+b[3]*b[1]","b[2]"))

Nonlinear restriction(s) Wald test

Description

Tests restriction(s) on model parameters of the form R(b)=q, where R is vector or scalar valued (non)linear function of b, the vector of model parameters, and q is numeric vector or scalar. Delta method is used for covariance matrix. Applicable after any model provided parameters estimates and their covariance matrix are available.

Usage

nlWaldtest(obj = NULL, texts, rhss = NULL, coeff = NULL, 
           Vcov = NULL, df2 = NULL, x = NULL)
# Standard:
# nlWaldtest(obj, texts) # Chi square test
# nlWaldtest(obj, texts, df2 = T) # F test

# Force different covariance matrix:
# nlWaldtest(obj, texts, Vcov =  vcovHC(obj))

# If coef(obj) and vcov(obj) are not available
# nlWaldtest(texts = restrictions, coeff = vector, Vcov = matrix)

# Backward compatibility:
# nlWaldtest(obj, texts, rhss)

Arguments

obj

model object of any class, for which vcov.class(obj) and coef.class(obj) methods are defined. If missing, both coeff and Vcov should be inputted.

texts

left-side(s) of normalized restriction(s), R(b), as string or vector of strings. Multiple restrictions can be inputted as a character vector or as a character, separated by semicolon. Right-hand sides can be included either separated by "=", or substracted, e.g. texts = "b[1]^b[2] = 1; b[3] = 2", or, the same, texts = c("a[1]^a[2] - 1", "a[3] = 2"); b's should be numbered as in coeff vector.

rhss

right-side(s) of normalized restriction(s) as number or vector. Retained mostly for backward compatibility. Set to zero(s), if missing.

coeff

vector of parameter estimates. If missing, it is set to coef(obj) when available. It allows, for example, to test hypotheses in terms of marginal effects and elasticities provided their covariance matrix is inputted.

Vcov

covariance matrix of parameters. If missing, it is set to coef(obj) when available. If coeff and/or Vcov are inputed, theirs counterparts from obj are superseded.

df2

defines the type of the test. By default, Chi square test is performed. To perfom F test one can use df2 = T, if a method for df.residual is available. Otherwise, one could input df2 = n, where n is a natural number. df2 is the denominator df in the F statistics. If df2 = T but df.residuals(obj) doesn't exist, Chi square test is forced, followed by a message.

x

number, or numeric vector. Provides a way to supply cumbersome coefficients into restrictions, e.g. texts = "b[1]^x[1] = x[2]", x = c(0.1234, 5.6789) to test b[1]^0.1234 = 5.6789. Instead of "b", one can use any valid variable name excluding "x". The "cumbersome" coefficients must be named only as x[i].

Details

The test should be applicable after (almost) any regression-type model, estimated using cross-section, time series, or panel data. If there are no methods for coef(obj) and/or vcov(obj), coeff and Vcov arguments should be inputted directly. To realize the delta-method, the function first tries to compute analytical derivatives using deriv. If failed, it computes numerical derivatives, calling numericDeriv.

Value

an object of "htest" class.

Author(s)

Oleh Komashko

References

Greene, W.H. (2011). Econometric Analysis, 7th edition. Upper Saddle River, NJ: Prentice Hall

See Also

nlConfint

Examples

set.seed(13)
x1<-rnorm(30);x2<-rnorm(30);x3<-rnorm(30);y<-rnorm(30)
set.seed(NULL)
lm1<-lm(y~x1+x2+x3)
nlConfint(lm1, "b[2]^3+b[3]*b[1];b[2]")
nlWaldtest(lm1,"a[2]^3+a[3]*a[1] = x[1]; a[2]", x = -0.07)
nlWaldtest(lm1,c("b[2]^3+b[3]*b[1]+0.07", "b[2]"))



# Reproduce example in EVievs 8 Users Guide II, pp. 149-151.

## Not run: 
require(nlme) 
nl1<-nls(log(q)~c1+c2*log(c3*(k^c4)+(1-c3)*(l^c4)),
data=CESdata,start=list(c1=-2.6,c2=1.8,c3=0.0001,c4=-6),
nls.control(maxiter = 100, tol = 1e-05,minFactor = 1/2^15))
nlWaldtest(nl1,"b[2]-1/b[4]",0)
nlWaldtest(nl1,"b[2]*b[4]",1)

## End(Not run)