errorsarlm               package:spdep               R Documentation

_S_p_a_t_i_a_l _s_i_m_u_l_t_a_n_e_o_u_s _a_u_t_o_r_e_g_r_e_s_s_i_v_e _e_r_r_o_r _m_o_d_e_l _e_s_t_i_m_a_t_i_o_n

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

     Maximum likelihood estimation of spatial simultaneous
     autoregressive error models of the form:


                  y = X beta + u, u = lambda W u + e


     where $lambda$ is found by 'optimize()', or by 'optim()' using
     method "L-BFGS-B" if argument optim=TRUE, first, and $beta$ and
     other parameters by generalized least squares subsequently.

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

     errorsarlm(formula, data=list(), listw, na.action=na.fail, method="eigen",
       quiet=TRUE, zero.policy=FALSE, interval = c(-1, 0.999), tol.solve=1.0e-10, 
       tol.opt=.Machine$double.eps^0.5, control, optim=FALSE)

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

 formula: a symbolic description of the model to be fit. The details 
          of model specification are given for 'lm()'

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

   listw: a 'listw' object created for example by 'nb2listw'

na.action: a function (default 'na.fail'), can also be 'na.omit' or
          'na.exclude' with consequences for residuals and fitted
          values - in these cases the weights list will be subsetted to
          remove NAs in the data. It may be necessary to set
          zero.policy to TRUE because this subsetting may create
          no-neighbour observations. Note that only weights lists
          created without using the glist argument to 'nb2listw' may be
          subsetted.

  method: "eigen" (default) - the Jacobian is computed as the product 
          of (1 - rho*eigenvalue) using 'eigenw', and "SparseM" for
          strictly symmetric weights lists of styles "B", "C" and "U",
          or made symmetric by similarity (Ord, 1975, Appendix C) if
          possible for styles "W" and "S", using code from the SparseM
          package to calculate the determinant. 

   quiet: default=TRUE; if FALSE, reports function values during
          optimization.

zero.policy: if TRUE assign zero to the lagged value of zones without 
          neighbours, if FALSE (default) assign NA - causing
          'errorsarlm()' to terminate with an error

interval: search interval for autoregressive parameter when not using
          method="eigen"; default is c(-1,1)

tol.solve: the tolerance for detecting linear dependencies in the
          columns of matrices to be inverted - passed to 'solve()'
          (default=1.0e-10). This may be used if necessary to extract
          coefficient standard errors (for instance lowering to 1e-12),
          but errors in 'solve()' may constitute indications of poorly
          scaled variables: if the variables have scales differing much
          from the autoregressive coefficient, the values in this
          matrix may be very different in scale, and inverting such a
          matrix is analytically possible by definition, but
          numerically unstable; rescaling the RHS variables alleviates
          this better than setting tol.solve to a very small value

 tol.opt: the desired accuracy of the optimization - passed to
          'optim()' (default=square root of double precision machine
          tolerance, a larger root may be used if the warning: ERROR:
          ABNORMAL_TERMINATION_IN_LNSRCH is seen, see help(boston) for
          an example)

 control: A list of control parameters passed to 'optim', se details in
          'optim'

   optim: If TRUE use experimental 'optim' branch and control argument

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

     The asymptotic standard error of $lambda$ is only computed when
     method=eigen, because the full matrix operations involved would be
     costly for large n typically associated with the choice of
     method="SparseM". The same applies to the coefficient covariance
     matrix. Taken as the asymptotic matrix from the literature, it is
     typically badly scaled, being block-diagonal, and with the
     elements involving lambda being very small, while other parts of
     the matrix can be very large (often many orders of magnitude in
     difference). It often happens that the 'tol.solve' argument needs
     to be set to a smaller value than the default, or the RHS
     variables can be centred or reduced in range.

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

     A list object of class 'sarlm' 

    type: "error"

  lambda: simultaneous autoregressive error coefficient

coefficients: GLS coefficient estimates

 rest.se: GLS coefficient standard errors (are equal to asymptotic
          standard errors)

      LL: log likelihood value at computed optimum

      s2: GLS residual variance

     SSE: sum of squared GLS errors

parameters: number of parameters estimated

lm.model: the 'lm' object returned when estimating for $lambda=0$

  method: the method used to calculate the Jacobian

    call: the call used to create this object

residuals: GLS residuals

lm.target: the 'lm' object returned for the GLS fit

fitted.values: Difference between residuals and response variable

     ase: TRUE if method=eigen

 formula: model formula

  se.fit: Not used yet

lambda.se: if ase=TRUE, the asymptotic standard error of $lambda$

  LMtest: NULL for this model

zero.policy: zero.policy for this model

na.action: (possibly) named vector of excluded or omitted observations
          if non-default na.action argument used


     The internal sar.error.* functions return the value of the log
     likelihood function at $lambda$.

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

     Roger Bivand Roger.Bivand@nhh.no

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

     Cliff, A. D., Ord, J. K. 1981 _Spatial processes_, Pion; Ord, J.
     K. 1975 Estimation methods for models of spatial interaction,
     _Journal of the American Statistical Association_, 70, 120-126;
     Anselin, L. 1988 _Spatial econometrics: methods and models._
     (Dordrecht: Kluwer); Anselin, L. 1995 SpaceStat, a software
     program for the analysis of spatial data, version 1.80. Regional
     Research Institute, West Virginia University, Morgantown, WV
     (<URL: www.spacestat.com>); Anselin L, Bera AK (1998) Spatial
     dependence in linear regression models with an introduction to
     spatial econometrics. In: Ullah A, Giles DEA (eds) Handbook of
     applied economic statistics. Marcel Dekker, New York, pp. 237-289.

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

     'lm', 'lagsarlm',  'eigenw', 'asMatrixCsrListw', 'similar.listw',
     'predict.sarlm', 'residuals.sarlm'

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

     data(oldcol)
     COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
      nb2listw(COL.nb, style="W"), method="eigen", quiet=FALSE)
     COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
      nb2listw(COL.nb, style="W"), method="eigen", quiet=FALSE)
     COL.errB.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
      nb2listw(COL.nb, style="B"), method="eigen", quiet=FALSE)
     COL.errW.SM <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
      nb2listw(COL.nb, style="W"), method="SparseM", quiet=FALSE)
     summary(COL.errW.eig, correlation=TRUE)
     summary(COL.errB.eig, correlation=TRUE)
     summary(COL.errW.SM, correlation=TRUE)
     NA.COL.OLD <- COL.OLD
     NA.COL.OLD$CRIME[20:25] <- NA
     COL.err.NA <- errorsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,
      nb2listw(COL.nb), na.action=na.exclude)
     COL.err.NA$na.action
     COL.err.NA
     resid(COL.err.NA)

