aple                  package:spdep                  R Documentation

_A_p_p_r_o_x_i_m_a_t_e _p_r_o_f_i_l_e-_l_i_k_e_l_i_h_o_o_d _e_s_t_i_m_a_t_o_r (_A_P_L_E)

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

     The Approximate profile-likelihood estimator (APLE) of the
     simultaneous autoregressive model's spatial dependence parameter
     was introduced in Li et al. (2007). It employs a correction term
     using the eigenvalues of the spatial weights matrix, and
     consequently should not be used for large numbers of observations.
     It also requires that the variable has a mean of zero, and it is
     assumed that it has been detrended. The spatial weights object is
     assumed to be row-standardised, that is using default 'style="W"'
     in 'nb2listw'.

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

     aple(x, listw, override_similarity_check=FALSE)

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

       x: a zero-mean detrended continuous variable

   listw: a 'listw' object from for example 'nb2listw'

override\_similarity\_check: default FALSE, if TRUE - typically for
          row-standardised weights with asymmetric underlying general
          weights - similarity is not checked

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

     This implementation has been checked with Hongfei Li's own
     implementation using her data; her help was very valuable.

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

     A scalar APLE value.

_A_u_t_h_o_r(_s):

     Roger Bivand Roger.Bivand@nhh.no

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

     Li, H, Calder, C. A. and Cressie N. A. C. (2007) Beyond Moran's I:
     testing for spatial dependence based on the spatial autoregressive
     model. Geographical Analysis 39, 357-375.

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

     'nb2listw', 'aple.mc', 'aple.plot'

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

     example(wheat)
     nbr1 <- poly2nb(wheat, queen=FALSE)
     nbrl <- nblag(nbr1, 2)
     nbr12 <- nblag_cumul(nbrl)
     cms0 <- with(as(wheat, "data.frame"), tapply(yield, c, median))
     cms1 <- c(model.matrix(~ factor(c) -1, data=wheat) %*% cms0)
     wheat$yield_detrend <- wheat$yield - cms1
     isTRUE(all.equal(c(with(as(wheat, "data.frame"),
      tapply(yield_detrend, c, median))), rep(0.0, 25),
      check.attributes=FALSE))
     moran.test(wheat$yield_detrend, nb2listw(nbr12, style="W"))
     aple(scale(wheat$yield_detrend, scale=FALSE), nb2listw(nbr12, style="W"))
     errorsarlm(yield_detrend ~ 1, wheat, nb2listw(nbr12, style="W"))

