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Wald Test for Linear Restrictions

Source: R/mlmodel-tests.R
waldtest.Rd

Performs a Wald test of linear restrictions on the parameters of an mlmodel object.

Usage

waldtest(object, ...)

# S3 method for class 'mlmodel'
waldtest(
  object,
  indices = NULL,
  coef_names = NULL,
  rest_matrix = NULL,
  rhs = 0,
  vcov = NULL,
  vcov.type = "oim",
  cl_var = NULL,
  repetitions = 999,
  seed = NULL,
  progress = FALSE,
  ...
)

Arguments

object

An object of class "mlmodel".

...

Further arguments passed to methods.

indices

Integer vector. Positions of the coefficients to be tested.

coef_names

Character vector. Names of the coefficients to test.

rest_matrix

Numeric matrix. A q × k restriction matrix (advanced use).

rhs

Numeric vector. Value(s) the linear combination(s) should equal. Default is 0.

vcov

Optional user-supplied variance-covariance matrix.

vcov.type

Character string. Type of variance-covariance matrix to use. One of "oim" (default), "opg", "robust", "boot", or "jack". See vcov.mlmodel() for details.

cl_var

Character string or vector. Clustering variable when vcov.type = "robust" or "boot".

repetitions

Integer. Number of bootstrap replications when vcov.type = "boot". Default is 999.

seed

Integer. Random seed for bootstrap.

progress

Logical. Show progress bar during bootstrapping? Default FALSE.

Value

An object of class "waldtest.mlmodel".

Details

The Wald test evaluates linear restrictions of the form \(R\beta = r\).

Three convenient interfaces are provided:

  • indices or coef_names: Test individual coefficients (or groups of coefficients) against the value(s) in rhs (defaults to 0, which is useful for joint significance tests).

  • rest_matrix + rhs: Test general linear combinations of coefficients (advanced use).

The test statistic follows a \(\chi^2\) distribution with degrees of freedom equal to the number of restrictions under the null hypothesis.

See also

lrtest(), IMtest(), confint.mlmodel()

Author

Alfonso Sanchez-Penalver

Examples


data(mroz)
mroz$incthou <- mroz$faminc / 1000

fit <- ml_lm(incthou ~ age + I(age^2) + huswage + educ + unem, 
             data = mroz)

# 1. Test single coefficients using indices (default OIM)
waldtest(fit, indices = c(2, 5))
#> 
#> Wald Test of Linear Restrictions
#> 
#> Variance type: Original Information Matrix
#> ---------------------------------------
#> Restrictions:
#>   1: value::age = 0
#>   2: value::educ = 0
#> Chisq(2) = 59.026    Pr(>Chisq) = < 1e-8
#> --------------------------------------------
#> 

# 2. Test using coefficient names and robust standard errors
waldtest(fit, coef_names = c("value::educ", "value::unem"), 
         vcov.type = "robust")
#> 
#> Wald Test of Linear Restrictions
#> 
#> Variance type: Robust
#> ---------------------------------------
#> Restrictions:
#>   1: value::educ = 0
#>   2: value::unem = 0
#> Chisq(2) = 43.248    Pr(>Chisq) = < 1e-8
#> --------------------------------------------
#> 
         
# 3. Test explicit constraints
waldtest(fit, coef_names = "value::educ", rhs = 1, vcov.type = "robust")
#> 
#> Wald Test of Linear Restrictions
#> 
#> Variance type: Robust
#> ---------------------------------------
#> Restrictions:
#>   1: value::educ = 1
#> Chisq(1) = 0.049    Pr(>Chisq) = 0.8256
#> --------------------------------------------
#> 

# 4. Test a linear combination of two coefficients using a restriction matrix
# H0: educ + huswage = 3
R <- matrix(c(0, 0, 0, 1, 1, 0, 0), nrow = 1)
waldtest(fit, rest_matrix = R, rhs = 3, vcov.type = "boot", 
         repetitions = 100, seed = 123)
#> 
#> Wald Test of Linear Restrictions
#> 
#> Variance type: Bootstrap (100/100 reps. - 100.00% rate)
#> ---------------------------------------
#> Restrictions:
#>   1: value::huswage + value::educ = 3
#> Chisq(1) = 0.209    Pr(>Chisq) = 0.6473
#> --------------------------------------------
#>