Maximum likelihood estimation of spatial simultaneous autoregressive
lag and mixed models of the form:$$y = \rho W y + X \beta + \varepsilon$$
where $$ is found by optimize() first and $$ and other
parameters by generalized least squares subsequently. In the mixed model,
the spatially lagged independent variables are added to X.
lagsarlm(formula, data=list(), listw, type="lag", method="eigen", quiet=TRUE,
zero.policy=FALSE, tol.solve=1.0e-7, tol.opt=.Machine$double.eps^0.5)
sar.lag.mixed.f.s(rho, sn, e.a, e.b, e.c, n, quiet)
sar.lag.mixed.f(rho, eig, e.a, e.b, e.c, n, quiet)
dosparse(listw, y, x, wy, K, quiet, tol.opt)- 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}
- type
{default "lag", may be set to "mixed"}
- 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 lagsarlm() 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). This may be used if necessary to extract coefficient standard errors, but errors in solve() do constitute indicatations of model misspecification}
- tol.opt
{the desired accuracy of the optimization - passed to optimize() (default=square root of double precision machine tolerance)}
- rho
{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}
- n
{length of y (and eig)}
- e.a
{term used in computing likelihood}
- e.b
{term used in computing likelihood}
- e.c
{term used in computing likelihood}
- K
{1 if no intercept, 2 if intercept present in x}
- sn
{sparse spatial neighbour object from listw2sn}
sarlm
- type
{"lag" or "mixed"}
- rho
{simultaneous autoregressive lag coefficient}
- coefficients
{GLS coefficient estimates}
- rest.se
{asymptotic standard errors if ase=TRUE}
- 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}
- se.fit
{The GLS standard errors of the fitted values (not taking into
account the standard error of $$)
- ase
{TRUE if method=eigen}
- LLs
{if ase=FALSE (for method="sparse"), the log likelihood values of
models estimated dropping each of the independent variables in turn, used
in the summary function as a substitute for variable coefficient
significance tests}
- rho.se
{if ase=TRUE, the asymptotic standard error of $$
- LMtest
{if ase=TRUE, the Lagrange Multiplier test for the absence
of spatial autocorrelation in the lag model residuals}
- zero.policy
{zero.policy for this model}
The sar.lag.mixed.* 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]
lm, errorsarlm,
eigenw, log.spwdet
data(oldcol)
COL.lag.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
nb2listw(COL.nb), method="eigen", quiet=FALSE)
COL.lag.sp <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
nb2listw(COL.nb), method="sparse", quiet=FALSE)
summary(COL.lag.eig)
summary(COL.lag.sp)
spatial