# nlConfint: Confidence intervals for nonlinear functions of parameters In nlWaldTest: Wald Test of Nonlinear Restrictions and Nonlinear CI

## 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

 ```1 2 3 4 5 6 7 8``` ```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 If `coeff` and/or `Vcov` are inputed, theirs counterparts from `obj` are superseded.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.

Oleh Komashko

## References

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

`nlWaldtest`

## Examples

 ```1 2 3 4 5``` ```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]")) ```

### Example output

```                       value       2.5 %     97.5 %
b[2]^3+b[3]*b[1] -0.01258957 -0.07624856 0.05106942
b[2]              0.02359922 -0.31708313 0.36428156
```

nlWaldTest documentation built on May 2, 2019, 2:06 a.m.