nlWaldtest {nlWaldTest}

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 If coeff and/or Vcov are inputed, theirs counterparts from obj are superseded.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)