Variance-Covariance Matrix for mlmodel Objects

Returns the variance-covariance matrix of the estimated parameters using different methods.

Usage

# S3 method for class 'mlmodel'
vcov(
  object,
  type = "oim",
  cl_var = NULL,
  repetitions = 999,
  seed = NULL,
  progress = TRUE,
  ...
)

Arguments

object: An object of class "mlmodel" or a model inheriting from it (e.g. "ml_lm").
type: Character string specifying the type of variance-covariance matrix. One of "oim" (default), "robust", "opg", "cluster", "boot", and "jack" or "jackknife".
cl_var: Character string or vector. Name of the clustering variable in the data, or the vector itself.
repetitions: Integer. Number of bootstrap replications to use when type = "boot". Default is 999.
seed: Integer. Random seed for reproducibility when type = "boot". If NULL, a random seed is generated.
progress: Logical. Should a progress bar be displayed? Default is TRUE when type is "boot" or "jack"/"jackknife". Ignored for other types.
...: Further arguments passed to methods.

Value

A symmetric variance-covariance matrix with coefficient names on the rows and columns.

Details

The package provides several variance-covariance estimators through the type argument:

"oim" - Observed Information Matrix (default)
"opg" - Outer Product of Gradients (BHHH)
"robust" - Robust (sandwich) estimator
"cluster" - Alias for "robust" when clustering the variance but requires cl_var to be set.
"boot" - Bootstrap (with optional clustering)
"jack" - Jackknife (with optional clustering)
"jackknife" - alias for "jack"

Clustered standard errors are obtained by setting cl_var when using "robust"/"cluster", "boot", or "jack".

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)

# Different variance-covariance estimators
v_oim   <- vcov(fit, type = "oim")      # Observed Information Matrix (default)
v_opg   <- vcov(fit, type = "opg")      # Outer Product of Gradients (BHHH)
v_robust <- vcov(fit, type = "robust")   # Robust / Sandwich estimator

# Clustered robust standard errors
v_clust <- vcov(fit, type = "robust", cl_var = "age")

# Bootstrap variance-covariance matrix
v_boot  <- vcov(fit, type = "boot", repetitions = 100, seed = 123)
#> ℹ Bootstrap with 100 repetitions.
#>  0        10        20        30        40        50
#> ====================================================
#>  ..................................................
#>  ..................................................
#> ====================================================
#> 
#> Bootstrapping finished - 100% of replications converged.

# Jackknife variance-covariance matrix
v_jack  <- vcov(fit, type = "jack")
#> ℹ Jackknife variance.
#>  0        10        20        30        40        50
#> ====================================================
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ..................................................
#>  ...
#> ====================================================
#> 
#> Jackknife finished - 100% of replications converged.

# Compare standard errors across methods
sterrors <- data.frame(
  oim = sqrt(diag(v_oim)),
  opg = sqrt(diag(v_opg)),
  robust = sqrt(diag(v_robust)),
  cluster = sqrt(diag(v_clust)),
  bootstrap = sqrt(diag(v_boot)),
  jackknife = sqrt(diag(v_jack))
)

sterrors
#>                            oim         opg      robust    cluster   bootstrap
#> value::(Intercept) 8.636925227 9.281669188 8.411271366 7.23859394 7.413482653
#> value::age         0.399627579 0.431781719 0.382284787 0.32571570 0.341291878
#> value::I(age^2)    0.004609191 0.005002672 0.004391868 0.00383376 0.003966148
#> value::huswage     0.073304149 0.044304744 0.135952916 0.14449057 0.150892743
#> value::educ        0.135599149 0.116741374 0.165176906 0.14021038 0.151153737
#> value::unem        0.095744322 0.096801039 0.098676875 0.08041205 0.105188018
#> scale::lnsigma     0.025768404 0.014396434 0.055550631 0.05915267 0.052628926
#>                      jackknife
#> value::(Intercept) 8.507232115
#> value::age         0.386935880
#> value::I(age^2)    0.004446869
#> value::huswage     0.144060112
#> value::educ        0.167837527
#> value::unem        0.100966601
#> scale::lnsigma     0.057408605