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, test = "HTZ", tidy = FALSE, ...)

Arguments

obj: Fitted model for which to calculate Wald tests.
constraints: List of one or more 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.
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

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$cluster <- sample(LETTERS[1:8], size = nrow(Duncan), replace = TRUE)
#> > Duncan_fit <- lm(prestige ~ 0 + type + income + type:income + type:education, data=Duncan)
#> > # Note that type:income terms are interactions because main effect of income is included
#> > # but type:education terms are separate slopes for each unique level of type
#> > 
#> > # Test equality of intercepts
#> > Wald_test(Duncan_fit,
#> +           constraints = constrain_equal(1:3),
#> +           vcov = "CR2", cluster = Duncan$cluster)
#>  test Fstat df_num df_denom p_val sig
#>   HTZ  1.47      2      1.7 0.426    
#> > # Test equality of type-by-education slopes
#> > Wald_test(Duncan_fit,
#> +           constraints = constrain_equal(":education", reg_ex = TRUE),
#> +           vcov = "CR2", cluster = Duncan$cluster)
#>  test  Fstat df_num df_denom p_val sig
#>   HTZ 0.0648      2     2.72 0.939    
#> > # Pairwise comparisons of type-by-education slopes
#> > Wald_test(Duncan_fit,
#> +           constraints = constrain_pairwise(":education", reg_ex = TRUE),
#> +           vcov = "CR2", cluster = Duncan$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    
#> 
#> $`typewc:education - typeprof:education`
#>  test  Fstat df_num df_denom p_val sig
#>   HTZ 0.0918      1     2.63 0.784    
#> 
#> > # Test type-by-income interactions
#> > Wald_test(Duncan_fit,
#> +           constraints = constrain_zero(":income", reg_ex = TRUE),
#> +           vcov = "CR2", cluster = Duncan$cluster)
#>  test Fstat df_num df_denom p_val sig
#>   HTZ  1.07      2     1.93 0.486    
#> > # 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)
#> $`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    
#>