vcovHC               package:sandwich               R Documentation

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_D_e_s_c_r_i_p_t_i_o_n:

     Heteroskedasticity-consistent estimation of the covariance matrix
     of the coefficient estimates in a linear regression model.

_U_s_a_g_e:

     vcovHC(x, order.by = NULL, data = list(),
       type = c("HC3", "const", "HC", "HC0", "HC1", "HC2", "HC4"),
       omega = NULL)

_A_r_g_u_m_e_n_t_s:

       x: a fitted model object of class '"lm"'.

order.by: formula. A formula with a single explanatory variable like '~
          x'. The observations in the model are ordered by the size of
          'x'. If set to 'NULL' (the default) the observations are
          assumed to be ordered (e.g. a time series).

    data: an optional data frame containing the variables in the
          'order.by'  model. By default the variables are taken from
          the environment which 'vcovHC' is called from.

    type: a character string specifying the estimation type. For
          details see below.

   omega: a function depending on the arguments 'residuals' (the
          residuals of the linear model), 'diaghat' (the diagonal  of
          the corresponding hat matrix) and 'df' (the residual degrees
          of freedom). For details see below.

_D_e_t_a_i_l_s:

     When 'type = "const"' constant variances are assumed and and
     'covHC' gives the usual estimate of the covariance matrix of the
     coefficient estimates:


                          sigma^2 (X'X)^{-1}


     All other methods do not assume constant variances and are
     suitable in case of heteroskedasticity. '"HC"' (or equivalently
     '"HC0"') gives White's estimator, the other estimators are
     refinements of this. They are all of form


                   (X'X)^{-1} X' Omega X (X'X)^{-1}


     and differ in the choice of Omega. This is in all cases a diagonal
     matrix whose  elements are function of the residuals, the diagonal
     elements of the hat matrix and the residual degrees of freedom.
     For White's estimator

     'omega <- function(residuals, diaghat, df) residuals^2'

     Instead of specifying a 'type' the argument 'omega' can also be
     specified directly. For details see the references.

_V_a_l_u_e:

     A matrix containing the covariance matrix estimate.

_R_e_f_e_r_e_n_c_e_s:

     Cribari-Neto F. (2004), Asymptotic inference under
     heteroskedasticity of unknown form. _Computational Statistics &
     Data Analysis_ *45*, 215-233.

     MacKinnon J. G., White H. (1985), Some
     heteroskedasticity-consistent covariance matrix estimators with
     improved finite sample properties. _Journal of Econometrics_ *29*,
     305-325.

     White H. (1980), A heteroskedasticity-consistent covariance matrix
     and a direct test for heteroskedasticity. _Econometrica_ *48*,
     817-838.

_S_e_e _A_l_s_o:

     'lm', 'hccm', 'bptest', 'ncv.test'

_E_x_a_m_p_l_e_s:

     ## generate linear regression relationship
     ## with homoskedastic variances
     x <- sin(1:100)
     y <- 1 + x + rnorm(100)
     ## compute usual covariance matrix of coefficient estimates
     fm <- lm(y ~ x)
     vcovHC(fm, type="const")
     vcov(fm)

     sigma2 <- sum(residuals(lm(y~x))^2)/98
     sigma2 * solve(crossprod(cbind(1,x)))

