spdep (version 0.6-15)

stsls: Generalized spatial two stage least squares

Description

The function fits a spatial lag model by two stage least squares, with the option of adjusting the results for heteroskedasticity.

Usage

stsls(formula, data = list(), listw, zero.policy = NULL,
 na.action = na.fail, robust = FALSE, HC=NULL, legacy=FALSE, W2X = TRUE)

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

zero.policy

default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE (default) assign NA - causing lagsarlm() to terminate with an error

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.

robust

default FALSE, if TRUE, apply a heteroskedasticity correction to the coefficients covariances

HC

default NULL, if robust is TRUE, assigned “HC0”, may take values “HC0” or “HC1” for White estimates or MacKinnon-White estimates respectively

legacy

the argument chooses between two implementations of the robustness correction: default FALSE - use the estimate of Omega only in the White consistent estimator of the variance-covariance matrix, if TRUE, use the original implementation which runs a GLS using the estimate of Omega, and yields different coefficient estimates as well - see example below

W2X

default TRUE, if FALSE only WX are used as instruments in the spatial two stage least squares; until release 0.4-60, only WX were used - see example below

Value

an object of class "stsls" containing:

coefficients

coefficient estimates

var

coefficient covariance matrix

sse

sum of squared errors

residuals

model residuals

df

degrees of freedom

Details

The fitting implementation fits a spatial lag model:

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

by using spatially lagged X variables as instruments for the spatially lagged dependent variable.

References

Kelejian, H.H. and I.R. Prucha (1998). A generalized spatial two stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. Journal of Real Estate Finance and Economics 17, 99-121.

Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 1-36. http://www.jstatsoft.org/v63/i18/.

See Also

lagsarlm

Examples

# NOT RUN {
data(oldcol)
COL.lag.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb))
summary(COL.lag.eig, correlation=TRUE)
COL.lag.stsls <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb))
summary(COL.lag.stsls, correlation=TRUE)
COL.lag.stslsW <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb), W2X=FALSE)
summary(COL.lag.stslsW, correlation=TRUE)
COL.lag.stslsR <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb),
robust=TRUE, W2X=FALSE)
summary(COL.lag.stslsR, correlation=TRUE)
COL.lag.stslsRl <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb),
robust=TRUE, legacy=TRUE, W2X=FALSE)
summary(COL.lag.stslsRl, correlation=TRUE)
data(boston)
gp2a <- stsls(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + I(RM^2) +
  AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),
 data=boston.c, nb2listw(boston.soi))
summary(gp2a)
# }