| effClust.default {effClust} | R Documentation |
Compute Approximate Effective Number of Clusters for Regression Coefficients
Description
Specifically, for each coefficient the function returns the quantity
G^{*A}, the feasible version of G^*, introduced by
Carter, Schnepel, and Steigerwald (2017). G^{*A} does not
accommodate multi-way clustering.
Usage
## Default S3 method:
effClust(
object,
cluster,
tags = colnames(object),
rho = 0.999,
nominal = FALSE,
XpXinv = NULL,
...
)
## S3 method for class 'fixest'
effClust(
object,
cluster,
include.only = NULL,
exclude = NULL,
fixed = FALSE,
nominal = FALSE,
rho = 0.999,
...
)
## S3 method for class 'formula'
effClust(
object,
cluster,
data,
subset = NULL,
include.only = NULL,
exclude = NULL,
fixed = FALSE,
nominal = FALSE,
rho = 0.999,
...
)
## S3 method for class 'lm'
effClust(
object,
cluster,
include.only = NULL,
exclude = NULL,
fixed = FALSE,
nominal = FALSE,
rho = 0.999,
...
)
## S3 method for class 'plm'
effClust(
object,
cluster,
include.only = NULL,
exclude = NULL,
fixed = FALSE,
nominal = FALSE,
rho = 0.999,
...
)
effClust(object, cluster, ...)
Arguments
object |
a formula or an object of class "lm", "plm", "fixest" (with method "feols"), or (for the default method) a matrix of regressors |
cluster |
cluster identifier:
a variable, a formula (see details), or, a length one
character vector naming a variable in |
tags |
a character vector containing a subset of the column names of
|
rho |
numeric scalar that changes assumed variance matrix (see details) |
nominal |
logical indicating whether the number of clusters should be included as the first element of the return vector |
XpXinv |
the |
... |
arguments passed to methods |
include.only |
a vector of regular expressions for variables to be included in the return (implying others excluded) |
exclude |
a vector of regular expressions for variables to be excluded from the return |
fixed |
logical indicates how regular expressions in |
data |
a dataframe (see details) |
subset |
an optional vector used to select cases from |
Details
When object is a formula, it does not need a response variable
(left-hand side), but if the response variable might have different
missing cases than the right-hand side, it should be included.
Cluster fixed effects, if any, may be explicitly included in the main
formula, or be specified with the syntax used by fixest:
~ X1 + X2 + factor(id) (fixed effects id in main formula)
~ X1 + X2 | id (fixest way to specify fixed effects)
The first approach can be computationally demanding if there are too
many units. Alternatively, data can contain appropriately
transformed variables (see the example below).
For regression objects, when cluster is a formula or a one
element character vector, it is evaluated in the context of the data
used for the model, and the data and subset arguments
are ignored.
The data argument is required when object is a formula.
In this case, object is evaluated in the context of the data
argument. If cluster is a formula or length 1 character vector,
it is interpreted as the name of a column of data.
If cluster is a variable, its length must equal nobs(object)
for regression objects or the number of rows in data
when object is a formula. If cluster contains NA,
a warning is issued.
By default G^{*A} is returned for all coefficients.
The output may be limited by using include.only
or exclude. This does not affect the computation
for coefficients that are included, only the vector returned.
The regular expressions used by include.only or exclude
should refer to the contents of names(coef(object)), which might differ
from how the regression formula refers to the same things.
For example, groups of variables entered by using something
like factor(statefip) in the regression formula show up in the
coefficient vector names looking like factor(statefip)27.
They can be excluded en mass by the regular expression
exclude="^factor\(statefip\)" (parentheses need to be
escaped in a regular expression). Alternatively, you can
specify fixed=TRUE, which has the same meaning as for grep.
Carter et al. recommend assuming every element of the variance matrix of
errors in a cluster is 1, a conservative scenario. However, as explained
in "A Note on Computation," the default rho is 0.999, so that the
variance matrix has 1 on the diagonal and 0.999 off the diagonal. It is
possible to set rho=1, but that produces incorrect values in
when there are cluster fixed effects. In other cases the
computation is not very sensitive to the value of rho, so there
is no appreciable difference between rho=1 and rho=0.999.
MacKinnon, Nielsen, and Webb (2022) argue that cluster fixed effects
usually remove much of the intra-cluster correlation, justifying rho
close to zero. (However, this is inconsistent with the “worst case
scenario” approach that motivates Carter et al.'s recommendation.)
effClust will return a value for a glm object (or a formula
intended for a GLM). The result might or might not be a useful diagnostic.
On one hand, G^* is fundamentally about the characteristics of
the clusters. On the other hand, the derivation by Carter et. al.
is based on linear regression.
Default method.
The default method is a bare-bones function that does the actual
calculation of the effective number of clusters; it is mainly intended to
be a tool for adding methods. It provides none of the error checking that
is normally performed by the effClust methods.
The matrix object must have column names. It also must
include a column of ones if the hypothetical regression includes
an intercept.
If XpXinv is provided, it will
be indexed using tags, so its row and column names must be
identical to (or a superset of) tags.
If object cannot be coerced to numeric, the function will fail.
Logical columns of object will be coerced to numeric, but factors
will not be expanded to dummy variables as done by model.matrix.
Value
vector of effective number of clusters for coefficients.
References
Andrew V. Carter, Kevin T. Schnepel, and Douglas G. Steigerwald, "Asymptotic Behavior of a $t$-test Robust to Cluster Heterogeneity," The Review of Economics and Statistics, October 2017, 99(4). doi:10.1162/REST_a_00639.
James G. MacKinnon, Morten Ørregaard Nielsen, and Matthew D. Webb, "Leverage, Influence, and the Jackknife in Clustered Regression Models: Reliable Inference Using summclust," QED Working Paper 1483, Queen's University (2022). https://www.econ.queensu.ca/research/working-papers/1483.
Examples
# some data with correlated errors
set.seed(85914270)
G <- 50
cl.sizes <- sample(10:100, G, replace=TRUE)
n <- sum(cl.sizes)
id <- rep(1:G, cl.sizes)
X1 <- rchisq(n, 5)
X2 <- ifelse(id %% 4 == 0, 1, 0)
e <- rnorm(n)
eg <- rep(rnorm(G), cl.sizes)
Y <- 1 + 2*X1 + 3*X2 - 1*X1*X2 + e + eg
d <- data.frame(Y, X1, X2, id)
f1 <- Y ~ X1 + X1:X2 + factor(id)
f2 <- Y ~ X1 + X1:X2 | id # fixest syntax
r <- lm(f1, data=d)
effClust(r, ~d$id, exclude=c("factor\\(id\\)","Intercept"))
effClust(f2, ~id, data=d)
library(data.table)
setDT(d)
d[ , `:=`(X1dot = X1 - mean(X1),
X2dot = X2 - mean(X2),
X1X2dot = X1*X2 - mean(X1*X2)),
by = id]
effClust(~ -1+X1dot+X1X2dot, cluster=~id, data=d)