nlConfint {nlWaldTest}

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 If coeff and/or Vcov are inputed, theirs counterparts from obj are superseded.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