Type of degree of freedom in fixest summary

Provides how the degrees of freedom should be calculated in vcov.fixest/summary.fixest.

dof(
  adj = TRUE,
  fixef.K = "nested",
  cluster.adj = TRUE,
  cluster.df = "min",
  t.df = "min",
  fixef.force_exact = FALSE
)

setFixest_dof(dof.type = dof())

getFixest_dof

Arguments

adj	Logical scalar, defaults to `TRUE`. Whether to apply a small sample adjustment of the form `(n - 1) / (n - K)`, with `K` the number of estimated parameters. If `FALSE`, then no adjustment is made.
fixef.K	Character scalar equal to `"nested"` (default), `"none"` or `"full"`. In the small sample adjustment, how to account for the fixed-effects parameters. If `"none"`, the fixed-effects parameters are discarded, meaning the number of parameters (`K`) is only equal to the number of variables. If `"full"`, then the number of parameters is equal to the number of variables plus the number of fixed-effects. Finally, if `"nested"`, then the number of parameters is equal to the number of variables plus the number of fixed-effects that are not nested in the clusters used to cluster the standard-errors.
cluster.adj	Logical scalar, default is `TRUE`. How to make the small sample correction when clustering the standard-errors? If `TRUE` a `G/(G-1)` correction is performed with `G` the number of cluster values.
cluster.df	Either "conventional" or "min" (default). Only relevant when the variance-covariance matrix is two-way clustered (or higher). It governs how the small sample adjustment for the clusters is to be performed. [Sorry for the jargon that follows.] By default a unique adjustment is made, of the form G_min/(G_min-1) with G_min the smallest G_i. If `cluster.df="conventional"` then the i-th "sandwich" matrix is adjusted with G_i/(G_i-1) with G_i the number of unique clusters.
t.df	Either "conventional" or "min" (default). Only relevant when the variance-covariance matrix is clustered. It governs how the p-values should be computed. By default, the degrees of freedom of the Student t distribution is equal to the minimum size of the clusters with which the VCOV has been clustered. If `t.df="conventional"`, then the degrees of freedom of the Student t distribution is equal to the number of observations minus the number of estimated variables.
fixef.force_exact	Logical, default is `FALSE`. If there are 2 or more fixed-effects, these fixed-effects they can be irregular, meaning they can provide the same information. If so, the "real" number of parameters should be lower than the total number of fixed-effects. If `fixef.force_exact = TRUE`, then `fixef.fixest` is first run to determine the exact number of parameters among the fixed-effects. Mostly, panels of the type individual-firm require `fixef.force_exact = TRUE` (but it adds computational costs).
dof.type	An object of class `dof.type` obtained with the function `dof`.

Format

An object of class function of length 1.

Value

It returns a dof.type object.

Details

The following vignette: On standard-errors, describes in details how the standard-errors are computed in fixest and how you can replicate standard-errors from other software.

Author

Laurent Berge

Examples


#
# Equivalence with lm/glm standard-errors
#

# LM
# In the absence of fixed-effects,
# by default, the standard-errors are computed in the same way

res = feols(Petal.Length ~ Petal.Width + Species, iris)
res_lm = lm(Petal.Length ~ Petal.Width + Species, iris)
vcov(res) / vcov(res_lm)
#>                   (Intercept) Petal.Width Speciesversicolor Speciesvirginica
#> (Intercept)                 1           1                 1                1
#> Petal.Width                 1           1                 1                1
#> Speciesversicolor           1           1                 1                1
#> Speciesvirginica            1           1                 1                1

# GLM
# By default, there is no small sample adjustment in glm, as opposed to feglm.
# To get the same SEs, we need to use dof(adj = FALSE)

res_pois = fepois(round(Petal.Length) ~ Petal.Width + Species, iris)
res_glm = glm(round(Petal.Length) ~ Petal.Width + Species, iris, family = poisson())
vcov(res_pois, dof = dof(adj = FALSE)) / vcov(res_glm)
#>                   (Intercept) Petal.Width Speciesversicolor Speciesvirginica
#> (Intercept)                 1           1                 1                1
#> Petal.Width                 1           1                 1                1
#> Speciesversicolor           1           1                 1                1
#> Speciesvirginica            1           1                 1                1

# Same example with the Gamma
res_gamma = feglm(round(Petal.Length) ~ Petal.Width + Species, iris, family = Gamma())
res_glm_gamma = glm(round(Petal.Length) ~ Petal.Width + Species, iris, family = Gamma())
vcov(res_gamma, dof = dof(adj = FALSE)) / vcov(res_glm_gamma)
#>                   (Intercept) Petal.Width Speciesversicolor Speciesvirginica
#> (Intercept)                 1           1                 1                1
#> Petal.Width                 1           1                 1                1
#> Speciesversicolor           1           1                 1                1
#> Speciesvirginica            1           1                 1                1

#
# Fixed-effects corrections
#

# We create "irregular" FEs
base = data.frame(x = rnorm(10))
base$y = base$x + rnorm(10)
base$fe1 = rep(1:3, c(4, 3, 3))
base$fe2 = rep(1:5, each = 2)

est = feols(y ~ x | fe1 + fe2, base)

# fe1: 3 FEs
# fe2: 5 FEs

#
# Clustered standard-errors: by fe1
#

# Default: fixef.K = "nested"
#  => adjustment K = 1 + 5 (i.e. x + fe2)
summary(est)
#> OLS estimation, Dep. Var.: y
#> Observations: 10 
#> Fixed-effects: fe1: 3,  fe2: 5
#> Standard-errors: Clustered (fe1) 
#>   Estimate Std. Error  t value Pr(>|t|)) 
#> x 0.079171   0.281686 0.281061  0.805072 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 0.873241     Adj. R2: -1.7512 
#>                  Within R2: 0.003658
attributes(vcov(est, attr = TRUE))[c("dof.type", "dof.K")]
#> $dof.type
#> [1] "dof(adj = TRUE, fixef.K = 'nested', cluster.adj = TRUE, cluster.df = 'min', t.df = 'min', fixef.force_exact = FALSE)"
#> 
#> $dof.K
#> [1] 6
#> 


# fixef.K = FALSE
#  => adjustment K = 1 (i.e. only x)
summary(est, dof = dof(fixef.K = "none"))
#> OLS estimation, Dep. Var.: y
#> Observations: 10 
#> Fixed-effects: fe1: 3,  fe2: 5
#> Standard-errors: Clustered (fe1) 
#>   Estimate Std. Error  t value Pr(>|t|)) 
#> x 0.079171   0.187791 0.421592  0.714314 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 0.873241     Adj. R2: -1.7512 
#>                  Within R2: 0.003658
attr(vcov(est, dof = dof(fixef.K = "none"), attr = TRUE), "dof.K")
#> [1] 1


# fixef.K = TRUE
#  => adjustment K = 1 + 3 + 5 - 1 (i.e. x + fe1 + fe2 - 1 restriction)
summary(est, dof = dof(fixef.K = "full"))
#> OLS estimation, Dep. Var.: y
#> Observations: 10 
#> Fixed-effects: fe1: 3,  fe2: 5
#> Standard-errors: Clustered (fe1) 
#>   Estimate Std. Error t value Pr(>|t|)) 
#> x 0.079171   0.398364 0.19874  0.860837 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 0.873241     Adj. R2: -1.7512 
#>                  Within R2: 0.003658
attr(vcov(est, dof = dof(fixef.K = "full"), attr = TRUE), "dof.K")
#> [1] 8


# fixef.K = TRUE & fixef.force_exact = TRUE
#  => adjustment K = 1 + 3 + 5 - 2 (i.e. x + fe1 + fe2 - 2 restrictions)
summary(est, dof = dof(fixef.K = "full", fixef.force_exact = TRUE))
#> OLS estimation, Dep. Var.: y
#> Observations: 10 
#> Fixed-effects: fe1: 3,  fe2: 5
#> Standard-errors: Clustered (fe1) 
#>   Estimate Std. Error  t value Pr(>|t|)) 
#> x 0.079171   0.325263 0.243406   0.83038 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 0.873241     Adj. R2: -1.7512 
#>                  Within R2: 0.003658
attr(vcov(est, dof = dof(fixef.K = "full", fixef.force_exact = TRUE), attr = TRUE), "dof.K")
#> [1] 7

# There are two restrictions:
attr(fixef(est), "references")
#> NOTE: The fixed-effects are not regular, they cannot be straightforwardly interpreted.
#> fe1 fe2 
#>   0   2 

#
# To permanently set the default dof:
#

# eg no small sample adjustment:
setFixest_dof(dof(adj = FALSE))

# Factory default
setFixest_dof()