errorsarlm {spdep}R Documentation

Spatial simultaneous autoregressive error model estimation

Description

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

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

where $λ$ is found by optimize() first and $β$ and other parameters by generalized least squares subsequently.

Usage

errorsarlm(formula, data=list(), listw, method="eigen", quiet=TRUE,
  zero.policy=FALSE, tol.solve=1.0e-7, tol.opt=.Machine$double.eps^0.5,
  sparsedebug=FALSE)

Arguments

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)
sparsedebug if TRUE, writes a log file on sparse matrix operations (name sparsestats) in the current directory. To be used if sparse estimation fails!

Details

The asymptotic standard error of $λ$ 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.

When using the sparse method, the user takes (unfortunately) full responsibility for possible failures, including R terminating with a core dump! Safeguards have been put in place to try to trap errant behaviour in the sparse functions' memory allocation, but they may not always help. When sparsedebug is TRUE, a log file (sparsestats) is written in the working directory - the figure of interest is the number of allocated blocks. At present, spwdet will fail when this increases over the number initially allocated, but will not release memory allocated by the sparse functions. In the event of problems, save your workspace and quit R. Problems seem to be related to larger n, and to an unknown trigger precipitating incontrolled fillin, in the course of which the sparse routines lose track of their memory pointers, and then provoke a segmentation fault trying to free unallocated memory.

Value

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 $λ=0$
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 $λ$
LMtest NULL for this model
zero.policy zero.policy for this model


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

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

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.

See Also

lm, lagsarlm, eigenw, log.spwdet, predict.sarlm, residuals.sarlm

Examples

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)

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