vcovHC               package:sandwich               R Documentation

_H_e_t_e_r_o_s_k_e_d_a_s_t_i_c_i_t_y-_C_o_n_s_i_s_t_e_n_t _C_o_v_a_r_i_a_n_c_e _M_a_t_r_i_x _E_s_t_i_m_a_t_i_o_n

_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,
       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"'.

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

   omega: a vector or 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.

     ...: currently not used.

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

     When 'type = "const"' constant variances are assumed and and
     'vcovHC' 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 can be either supplied as a vector 'omega'
     or as a a function 'omega' 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 of providing the diagonal 'omega' or a
     function for estimating it, the 'type' argument can be used to
     specify the  HC0 to HC4 estimators. If 'omega' is used, 'type' is
     ignored.

     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)))

