Maximum likelihood estimation of spatial simultaneous autoregressive
error models of the form:$$y = X \beta + u, u = \lambda W u + \varepsilon$$
where $$ is found by optimize() first and $$ and other
parameters by generalized least squares subsequently.
errorsarlm(formula, data=list(), listw, method="eigen", quiet=TRUE,
zero.policy=FALSE, tol.solve=1.0e-7, tol.opt=.Machine$double.eps^0.5)
sar.error.f(lambda, eig, y, wy, x, WX, n, quiet)
sar.error.f.s(lambda, sn, y, wy, x, WX, n, quiet)- 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}
- method
{"eigen" (default) - the Jacobian is computed as the product
of (1 - rho*eigenvalue) using eigenw
, and "sparse" - computes the
determinant of the sparse matrix (I - rho*W) directly using log.spwdet.
}
- 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}
- tol.solve
{the tolerance for detecting linear dependencies in the columns of matrices to be inverted - passed to solve() (default=1.0e-7)}
- tol.opt
{the desired accuracy of the optimization - passed to optimize() (default=square root of double precision machine tolerance)}
- lambda
{value of the spatial parameter}
- eig
{eigenvalues of the full spatial weights matrix from eigenw}
- y
{dependent variable}
- wy
{spatially lagged dependent variable}
- x
{independent variables}
- WX
{spatially lagged independent variables}
- n
{length of y (and eig)}
- sn
{sparse spatial neighbour object from listw2sn}
The asymptotic standard error of $$ is only computed when
method=eigen, because the full matrix operations involved would be costly
for large n typically associated with the choice of method=sparse.
A list object of class sarlm
- type
{"error"}
- lambda
{simultaneous autoregressive error coefficient}
- coefficients
{GLS coefficient estimates}
- rest.se
{GLS coefficient standard errors (are equal to asymptotic
standard errors)}
- LL
{log likelihood value at computed optimum}
- s2
{GLS residual variance}
- SSE
{sum of squared GLS errors}
- parameters
{number of parameters estimated}
- lm.model
{the lm object returned when estimating for $=0$
- method
{the method used to calculate the Jacobian}
- call
{the call used to create this object}
- residuals
{GLS residuals}
- lm.target
{the lm object returned for the GLS fit}
- fitted.values
{GLS fitted values}
- ase
{TRUE if method=eigen}
- se.fit
{The GLS standard errors of the fitted values (not taking into
account the standard error of $$)
- lambda.se
{if ase=TRUE, the asymptotic standard error of $$
- LMtest
{NULL for this model}
- zero.policy
{zero.policy for this model}
The sar.error.* functions return the value of the log likelihood function
at $$.
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 (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.
[object Object],[object Object],[object Object]
lm, lagsarlm,
eigenw, log.spwdet
data(oldcol)
COL.err.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
nb2listw(COL.nb), method="eigen", quiet=FALSE)
COL.err.sp <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
nb2listw(COL.nb), method="sparse", quiet=FALSE)
summary(COL.err.eig)
summary(COL.err.sp)
spatial