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vcovCR returns a sandwich estimate of the variance-covariance matrix of a set of regression coefficient estimates from a plm object.

Usage

# S3 method for plm
vcovCR(
  obj,
  cluster,
  type,
  target,
  inverse_var,
  form = "sandwich",
  ignore_FE = FALSE,
  ...
)

Arguments

obj

Fitted model for which to calculate the variance-covariance matrix

cluster

Optional character string, expression, or vector indicating which observations belong to the same cluster. For fixed-effect models that include individual effects or time effects (but not both), the cluster will be taken equal to the included fixed effects if not otherwise specified. Clustering on individuals can also be obtained by specifying the name of the individual index (e.g., cluster = "state") or cluster = "individual"; clustering on time periods can be obtained by specifying the name of the time index (e.g., cluster = "year") or cluster = "time"; if a group index is specified, clustering on groups (in which individuals are nested) can be obtained by specifying the name of the group index or cluster = "group". For random-effects models, the cluster will be taken equal to the included random effect identifier if not otherwise specified.

type

Character string specifying which small-sample adjustment should be used, with available options "CR0", "CR1", "CR1p", "CR1S", "CR2", or "CR3". See "Details" section of vcovCR for further information.

target

Optional matrix or vector describing the working variance-covariance model used to calculate the CR2 and CR4 adjustment matrices. By default, the target is taken to be an identity matrix for fixed effect models or the estimated compound-symmetric covariance matrix for random effects models.

inverse_var

Optional logical indicating whether the weights used in fitting the model are inverse-variance. If not specified, vcovCR will attempt to infer a value.

form

Controls the form of the returned matrix. The default "sandwich" will return the sandwich variance-covariance matrix. Alternately, setting form = "meat" will return only the meat of the sandwich and setting form = B, where B is a matrix of appropriate dimension, will return the sandwich variance-covariance matrix calculated using B as the bread. form = "estfun" will return the (appropriately scaled) estimating function, the transposed crossproduct of which is equal to the sandwich variance-covariance matrix.

ignore_FE

Optional logical controlling whether fixed effects are ignored when calculating small-sample adjustments in models where fixed effects are estimated through absorption.

...

Additional arguments available for some classes of objects.

Value

An object of class c("vcovCR","clubSandwich"), which consists of a matrix of the estimated variance of and covariances between the regression coefficient estimates.

See also

Examples


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

  library(plm)
  # fixed effects
  data("Produc", package = "plm")
  plm_FE <- plm(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp,
                data = Produc, index = c("state","year","region"),
                effect = "individual", model = "within")
  vcovCR(plm_FE, type="CR2")
  vcovCR(plm_FE, type = "CR2", cluster = Produc$region) # clustering on region
  
  # random effects
  plm_RE <- update(plm_FE, model = "random")
  vcovCR(plm_RE, type = "CR2")
  vcovCR(plm_RE, type = "CR2", cluster = Produc$region) # clustering on region
  
  # nested random effects
  plm_nested <- update(plm_FE, effect = "nested", model = "random")
  vcovCR(plm_nested, type = "CR2") # clustering on region
})
#> > library(plm)
#> > data("Produc", package = "plm")
#> > plm_FE <- plm(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp, data = Produc, 
#> +     index = c("state", "year", "region"), effect = "individual", model = "within")
#> > vcovCR(plm_FE, type = "CR2")
#>               log(pcap)       log(pc)      log(emp)         unemp
#> log(pcap)  3.900840e-03 -7.382313e-04 -0.0024837779 -7.825846e-05
#> log(pc)   -7.382313e-04  4.177767e-03 -0.0040101610 -9.960967e-05
#> log(emp)  -2.483778e-03 -4.010161e-03  0.0073152051  1.736024e-04
#> unemp     -7.825846e-05 -9.960967e-05  0.0001736024  6.745842e-06
#> > vcovCR(plm_FE, type = "CR2", cluster = Produc$region)
#>               log(pcap)       log(pc)      log(emp)         unemp
#> log(pcap)  6.973505e-03 -0.0022279395 -0.0044833594 -6.786254e-05
#> log(pc)   -2.227940e-03  0.0054359010 -0.0043767642 -1.297104e-04
#> log(emp)  -4.483359e-03 -0.0043767642  0.0108260634  2.011267e-04
#> unemp     -6.786254e-05 -0.0001297104  0.0002011267  1.170089e-05
#> > plm_RE <- update(plm_FE, model = "random")
#> > vcovCR(plm_RE, type = "CR2")
#>               (Intercept)     log(pcap)       log(pc)      log(emp)
#> (Intercept)  0.0608153880 -8.772256e-03 -7.015754e-03  0.0136354448
#> log(pcap)   -0.0087722560  3.221991e-03  3.731861e-05 -0.0031502393
#> log(pc)     -0.0070157539  3.731861e-05  2.060851e-03 -0.0020993882
#> log(emp)     0.0136354448 -3.150239e-03 -2.099388e-03  0.0054047466
#> unemp        0.0004200323 -7.947309e-05 -6.416279e-05  0.0001390737
#>                     unemp
#> (Intercept)  4.200323e-04
#> log(pcap)   -7.947309e-05
#> log(pc)     -6.416279e-05
#> log(emp)     1.390737e-04
#> unemp        5.848168e-06
#> > vcovCR(plm_RE, type = "CR2", cluster = Produc$region)
#>               (Intercept)     log(pcap)       log(pc)      log(emp)
#> (Intercept)  0.0565942863 -0.0138696773 -0.0056768267  0.0190768009
#> log(pcap)   -0.0138696773  0.0065345184 -0.0003786724 -0.0063601303
#> log(pc)     -0.0056768267 -0.0003786724  0.0024373929 -0.0022193705
#> log(emp)     0.0190768009 -0.0063601303 -0.0022193705  0.0091711531
#> unemp        0.0004716871 -0.0000926249 -0.0000839537  0.0001715663
#>                     unemp
#> (Intercept)  4.716871e-04
#> log(pcap)   -9.262490e-05
#> log(pc)     -8.395370e-05
#> log(emp)     1.715663e-04
#> unemp        1.057574e-05
#> > plm_nested <- update(plm_FE, effect = "nested", model = "random")
#> > vcovCR(plm_nested, type = "CR2")
#>               (Intercept)     log(pcap)       log(pc)      log(emp)
#> (Intercept)  0.0537315947 -1.210951e-02 -0.0073309652  0.0193853190
#> log(pcap)   -0.0121095110  6.078432e-03 -0.0003141431 -0.0060636185
#> log(pc)     -0.0073309652 -3.141431e-04  0.0027593587 -0.0025387198
#> log(emp)     0.0193853190 -6.063618e-03 -0.0025387198  0.0091748282
#> unemp        0.0005354663 -9.267671e-05 -0.0001000830  0.0001852566
#>                     unemp
#> (Intercept)  5.354663e-04
#> log(pcap)   -9.267671e-05
#> log(pc)     -1.000830e-04
#> log(emp)     1.852566e-04
#> unemp        1.135799e-05

pkgs_available <- requireNamespace("plm", quietly = TRUE) & requireNamespace("AER", quietly = TRUE)

if (pkgs_available) withAutoprint({
  # first differencing
  data(Fatalities, package = "AER")
  Fatalities <- within(Fatalities, {
    frate <- 10000 * fatal / pop
    drinkagec <- cut(drinkage, breaks = 18:22, include.lowest = TRUE, right = FALSE)
    drinkagec <- relevel(drinkagec, ref = 4)
  })

  plm_FD <- plm(frate ~ beertax + drinkagec + miles + unemp + log(income),
                data = Fatalities, index = c("state", "year"),
                model = "fd")
  vcovHC(plm_FD, method="arellano", type = "sss", cluster = "group")
  vcovCR(plm_FD, type = "CR1S")
  vcovCR(plm_FD, type = "CR2")
  
})
#> > data(Fatalities, package = "AER")
#> > Fatalities <- within(Fatalities, {
#> +     frate <- 10000 * fatal/pop
#> +     drinkagec <- cut(drinkage, breaks = 18:22, include.lowest = TRUE, right = FALSE)
#> +     drinkagec <- relevel(drinkagec, ref = 4)
#> + })
#> > plm_FD <- plm(frate ~ beertax + drinkagec + miles + unemp + log(income), 
#> +     data = Fatalities, index = c("state", "year"), model = "fd")
#> > vcovHC(plm_FD, method = "arellano", type = "sss", cluster = "group")
#>                    (Intercept)       beertax drinkagec[18,19) drinkagec[19,20)
#> (Intercept)       4.491252e-04  1.312107e-03     3.177175e-05    -3.224139e-05
#> beertax           1.312107e-03  6.112682e-02    -1.374164e-03    -2.155192e-03
#> drinkagec[18,19)  3.177175e-05 -1.374164e-03     5.978249e-03     2.531421e-03
#> drinkagec[19,20) -3.224139e-05 -2.155192e-03     2.531421e-03     2.130959e-03
#> drinkagec[20,21) -2.531288e-04 -9.279081e-04     1.738413e-03     1.185214e-03
#> miles             4.688676e-09 -1.642830e-07    -8.440044e-08    -5.492005e-08
#> unemp            -7.197958e-05 -3.079273e-04    -4.794408e-05    -3.200981e-05
#> log(income)      -1.853129e-02 -2.489411e-02     3.443431e-03     4.787025e-03
#>                  drinkagec[20,21)         miles         unemp   log(income)
#> (Intercept)         -2.531288e-04  4.688676e-09 -7.197958e-05 -1.853129e-02
#> beertax             -9.279081e-04 -1.642830e-07 -3.079273e-04 -2.489411e-02
#> drinkagec[18,19)     1.738413e-03 -8.440044e-08 -4.794408e-05  3.443431e-03
#> drinkagec[19,20)     1.185214e-03 -5.492005e-08 -3.200981e-05  4.787025e-03
#> drinkagec[20,21)     2.529571e-03 -9.131630e-08  1.900456e-04  1.890722e-02
#> miles               -9.131630e-08  1.570809e-11  1.928974e-09 -6.148657e-07
#> unemp                1.900456e-04  1.928974e-09  1.970444e-04  8.234312e-03
#> log(income)          1.890722e-02 -6.148657e-07  8.234312e-03  1.034150e+00
#> attr(,"cluster")
#> [1] "group"
#> > vcovCR(plm_FD, type = "CR1S")
#>                    (Intercept)       beertax drinkagec[18,19) drinkagec[19,20)
#> (Intercept)       4.491252e-04  1.312107e-03     3.177175e-05    -3.224139e-05
#> beertax           1.312107e-03  6.112682e-02    -1.374164e-03    -2.155192e-03
#> drinkagec[18,19)  3.177175e-05 -1.374164e-03     5.978249e-03     2.531421e-03
#> drinkagec[19,20) -3.224139e-05 -2.155192e-03     2.531421e-03     2.130959e-03
#> drinkagec[20,21) -2.531288e-04 -9.279081e-04     1.738413e-03     1.185214e-03
#> miles             4.688676e-09 -1.642830e-07    -8.440044e-08    -5.492005e-08
#> unemp            -7.197958e-05 -3.079273e-04    -4.794408e-05    -3.200981e-05
#> log(income)      -1.853129e-02 -2.489411e-02     3.443431e-03     4.787025e-03
#>                  drinkagec[20,21)         miles         unemp   log(income)
#> (Intercept)         -2.531288e-04  4.688676e-09 -7.197958e-05 -1.853129e-02
#> beertax             -9.279081e-04 -1.642830e-07 -3.079273e-04 -2.489411e-02
#> drinkagec[18,19)     1.738413e-03 -8.440044e-08 -4.794408e-05  3.443431e-03
#> drinkagec[19,20)     1.185214e-03 -5.492005e-08 -3.200981e-05  4.787025e-03
#> drinkagec[20,21)     2.529571e-03 -9.131630e-08  1.900456e-04  1.890722e-02
#> miles               -9.131630e-08  1.570809e-11  1.928974e-09 -6.148657e-07
#> unemp                1.900456e-04  1.928974e-09  1.970444e-04  8.234312e-03
#> log(income)          1.890722e-02 -6.148657e-07  8.234312e-03  1.034150e+00
#> > vcovCR(plm_FD, type = "CR2")
#>                    (Intercept)       beertax drinkagec[18,19) drinkagec[19,20)
#> (Intercept)       4.926777e-04  0.0014903060     5.194011e-05    -1.917433e-05
#> beertax           1.490306e-03  0.0639227452    -1.545309e-03    -2.356755e-03
#> drinkagec[18,19)  5.194011e-05 -0.0015453092     6.783986e-03     2.627033e-03
#> drinkagec[19,20) -1.917433e-05 -0.0023567549     2.627033e-03     2.182684e-03
#> drinkagec[20,21) -2.585076e-04 -0.0011673142     1.811511e-03     1.193471e-03
#> miles            -1.036421e-07 -0.0000011056    -1.901583e-07    -1.298187e-07
#> unemp            -7.270549e-05 -0.0002748930    -3.606990e-05    -3.739358e-05
#> log(income)      -1.903417e-02 -0.0209995682     3.953875e-03     4.817831e-03
#>                  drinkagec[20,21)         miles         unemp   log(income)
#> (Intercept)         -2.585076e-04 -1.036421e-07 -7.270549e-05 -1.903417e-02
#> beertax             -1.167314e-03 -1.105600e-06 -2.748930e-04 -2.099957e-02
#> drinkagec[18,19)     1.811511e-03 -1.901583e-07 -3.606990e-05  3.953875e-03
#> drinkagec[19,20)     1.193471e-03 -1.298187e-07 -3.739358e-05  4.817831e-03
#> drinkagec[20,21)     2.626823e-03 -1.514746e-07  1.955850e-04  1.969001e-02
#> miles               -1.514746e-07  4.431806e-10 -5.460872e-10 -1.329604e-06
#> unemp                1.955850e-04 -5.460872e-10  2.005515e-04  8.377011e-03
#> log(income)          1.969001e-02 -1.329604e-06  8.377011e-03  1.065829e+00