Test parameter constraints in a fitted linear regression model

Wald_test reports Wald-type tests of linear contrasts from a fitted linear regression model, using a sandwich estimator for the variance-covariance matrix and a small sample correction for the p-value. Several different small-sample corrections are available.

Usage

Wald_test(
  obj,
  constraints,
  vcov,
  null_constant = 0,
  test = "HTZ",
  tidy = FALSE,
  ...
)

Arguments

obj: Fitted model for which to calculate Wald tests.
constraints: constraint or list of multiple constraints to test. See details and examples.
vcov: Variance covariance matrix estimated using vcovCR or a character string specifying which small-sample adjustment should be used to calculate the variance-covariance.
null_constant: vector of null values or list of such vectors for each set of constraints to test. For a single constraint, the null values must have length equal to the number of rows in the constraint. For lists of null values, each entry must have length equal to the number of rows in the corresponding entry of constraints. Default is 0, in which case the null values are taken to be zero (for every entry, if constraints is a list).
test: Character vector specifying which small-sample correction(s) to calculate. The following corrections are available: "chi-sq", "Naive-F", "Naive-Fp", "HTA", "HTB", "HTZ", "EDF", "EDT". Default is "HTZ".
tidy: Logical value controlling whether to tidy the test results. If constraints is a list with multiple constraints, the result will be coerced into a data frame when tidy = TRUE.
...: Further arguments passed to vcovCR, which are only needed if vcov is a character string.

Value

A list of test results.

Details

Constraints can be specified directly as q X p matrices or indirectly through constrain_equal, constrain_zero, or constrain_pairwise. By default, each constraint will be tested against the null hypothesis that it equal to a zero vector. Non-zero values for null-hypotheses can be specified using the null_constant argument.

Examples



if (requireNamespace("carData", quietly = TRUE)) withAutoprint({

data(Duncan, package = "carData")
Duncan$cluster <- sample(LETTERS[1:8], size = nrow(Duncan), replace = TRUE)

Duncan_fit <- lm(prestige ~ 0 + type + income + type:income + type:education, data=Duncan)
# Note that type:income terms are interactions because main effect of income is included
# but type:education terms are separate slopes for each unique level of type

# Test equality of intercepts
Wald_test(Duncan_fit,
          constraints = constrain_equal(1:3),
          vcov = "CR2", cluster = Duncan$cluster)

# Test equality of type-by-education slopes
Wald_test(Duncan_fit,
          constraints = constrain_equal(":education", reg_ex = TRUE),
          vcov = "CR2", cluster = Duncan$cluster)

# Pairwise comparisons of type-by-education slopes
Wald_test(Duncan_fit,
          constraints = constrain_pairwise(":education", reg_ex = TRUE),
          vcov = "CR2", cluster = Duncan$cluster)

# Test type-by-income interactions
Wald_test(Duncan_fit,
          constraints = constrain_zero(":income", reg_ex = TRUE),
          vcov = "CR2", cluster = Duncan$cluster)

# Pairwise comparisons of type-by-income interactions
Wald_test(Duncan_fit,
          constraints = constrain_pairwise(":income", reg_ex = TRUE, with_zero = TRUE),
          vcov = "CR2", cluster = Duncan$cluster)

})
#> > data(Duncan, package = "carData")
#> > Duncan$cluster <- sample(LETTERS[1:8], size = nrow(Duncan), replace = TRUE)
#> > Duncan_fit <- lm(prestige ~ 0 + type + income + type:income + type:education, 
#> +     data = Duncan)
#> > Wald_test(Duncan_fit, constraints = constrain_equal(1:3), vcov = "CR2", 
#> +     cluster = Duncan$cluster)
#>  test Fstat df_num df_denom p_val sig
#>   HTZ  1.47      2      1.7 0.426    
#> > Wald_test(Duncan_fit, constraints = constrain_equal(":education", reg_ex = TRUE), 
#> +     vcov = "CR2", cluster = Duncan$cluster)
#>  test  Fstat df_num df_denom p_val sig
#>   HTZ 0.0648      2     2.72 0.939    
#> > Wald_test(Duncan_fit, constraints = constrain_pairwise(":education", reg_ex = TRUE), 
#> +     vcov = "CR2", cluster = Duncan$cluster)
#> $`typeprof:education - typebc:education`
#>  test   Fstat df_num df_denom p_val sig
#>   HTZ 0.00289      1      4.3  0.96    
#> 
#> $`typewc:education - typebc:education`
#>  test Fstat df_num df_denom p_val sig
#>   HTZ 0.136      1      4.2 0.731    
#> 
#> $`typewc:education - typeprof:education`
#>  test  Fstat df_num df_denom p_val sig
#>   HTZ 0.0918      1     2.63 0.784    
#> 
#> > Wald_test(Duncan_fit, constraints = constrain_zero(":income", reg_ex = TRUE), 
#> +     vcov = "CR2", cluster = Duncan$cluster)
#>  test Fstat df_num df_denom p_val sig
#>   HTZ  1.07      2     1.93 0.486    
#> > Wald_test(Duncan_fit, constraints = constrain_pairwise(":income", reg_ex = TRUE, 
#> +     with_zero = TRUE), vcov = "CR2", cluster = Duncan$cluster)
#> $`typeprof:income`
#>  test Fstat df_num df_denom p_val sig
#>   HTZ   1.5      1     2.77 0.314    
#> 
#> $`typewc:income`
#>  test Fstat df_num df_denom p_val sig
#>   HTZ  2.15      1     2.28 0.265    
#> 
#> $`typewc:income - typeprof:income`
#>  test    Fstat df_num df_denom p_val sig
#>   HTZ 0.000588      1     2.41 0.983    
#>