spdep (version 0.2-9)

lagsarlm: Spatial simultaneous autoregressive lag model estimation

Description

Maximum likelihood estimation of spatial simultaneous autoregressive lag and mixed models of the form:

$$y = \rho W y + X \beta + \varepsilon$$

where $\rho$ is found by optimize() first and $\beta$ and other parameters by generalized least squares subsequently. In the mixed model, the spatially lagged independent variables are added to X.

Usage

lagsarlm(formula, data=list(), listw, na.action=na.fail,
  type="lag", 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

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

type

default "lag", may be set to "mixed"; when "mixed", the lagged intercept is dropped for spatial weights style "W", that is row-standardised weights, but otherwise included

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 logSpwdet.

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 (for instance lowering to 1e-10), but errors

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!

Value

• A list object of class 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 $\rho=0$
• 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
• se.fit
  Not used yet
• formula
  model formula
• 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 $\rho$
• 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
• na.action
  (possibly) named vector of excluded or omitted observations if non-default na.action argument used
• The internal sar.lag.mixed.* functions return the value of the log likelihood function at $\rho$.

Details

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.

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, errorsarlm, eigenw, logSpwdet, predict.sarlm, residuals.sarlm

Examples

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)
COL.lag.B <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
 nb2listw(COL.nb, style="B"))
summary(COL.lag.B)
COL.mixed.B <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
 nb2listw(COL.nb, style="B"), type="mixed", tol.solve=1e-9)
summary(COL.mixed.B)
COL.mixed.W <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
 nb2listw(COL.nb, style="W"), type="mixed")
summary(COL.mixed.W)
NA.COL.OLD <- COL.OLD
NA.COL.OLD$CRIME[20:25] <- NA
COL.lag.NA <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,
 nb2listw(COL.nb), na.action=na.exclude)
COL.lag.NA$na.action
COL.lag.NA
resid(COL.lag.NA)