a symbolic description of the model to be estimated
data
an object of class data.frame or pdata.frame. A data frame containing the variables
in the model. When the object is a data.frame, the first two columns shall contain the indexes, unless otherwise specified. See index
index
if not NULL (default), a character vector to identify the indexes among the columns of the data.frame
w
an object of class listw or a matrix. It represents the spatial weights to be used in estimation.
w2
an object of class listw or a
matrix. Second set of spatial weights for estimation, if
different from the first (e.g., in a 'sarar' model).
lag
default=FALSE. If TRUE, a spatial lag of the dependent variable is added.
errors
Specifies the error covariance structure. See details.
pvar
legacy parameter here only for compatibility.
hess
default=FALSE. If TRUE estimate the
covariance for beta_hat by numerical Hessian instead of GLS at optimal
values.
quiet
default=TRUE. If FALSE, report function and
parameters values during optimization.
initval
one of c("zeros", "estimate"), the initial values for
the parameters. If "zeros" a vector of zeros is used. if
"estimate" the initial values are retreived from the estimation
of the nested specifications. Alternatively, a numeric vector can be
specified.
x.tol
control parameter for tolerance. See nlminb for details.
rel.tol
control parameter for relative tolerance. See nlminb for details.
...
additional arguments to pass over to other functions, e.g. method.
Details
Second-level wrapper for estimation of random effects models
with serial and spatial correlation. The specifications without serial
correlation (no "sr" in errors) can be called through
spml, the extended ones only through spreml.
The models are estimated by two-step Maximum Likelihood.
Abbreviations in errors correspond to: "sem"
Anselin-Baltagi type spatial autoregressive error: if
present, random effects are not spatially correlated; "sem2"
Kapoor, Kelejian and Prucha-type spatial autoregressive error model
with spatially correlated random effects; "sr" serially
correlated remainder errors; "re" random effects; "ols"
spherical errors (usually combined with lag=T).
The optimization method can be passed on as optional
parameter. Default is "nlminb"; all constrained optimization
methods from maxLik are allowed ("BFGS", "NM", "SANN")
but the latter two are still experimental.
Value
An object of class "splm".
coefficients
coefficients estimate of the model parameters
arcoef
the coefficient for the spatial lag on y
errcomp
the estimates of the error variance components
vcov
the asymptotic variance covariance matrix of the estimated coefficients
vcov.arcoef
the asymptotic variance of the
estimated spatial lag parameter
vcov.errcomp
the asymptotic variance covariance matrix of the
estimated error covariance parameters
type
'random effects ML'
residuals
the model residuals
fitted.values
the fitted values, calculated as hat{y}=X hat{β}
sigma2
GLS residuals variance
model
the matrix of the data used
call
the call used to create the object
logLik
the value of the log likelihood function at the optimum
errors
the value of the errors argument
Author(s)
Giovanni Millo
References
Millo, G. (2014)
Maximum likelihood estimation of spatially and serially correlated
panels with random effects. Computational Statistics and Data
Analysis, 71, 914–933.
See Also
spml
Examples
data(Produc, package = "plm")
data(usaww)
fm <- log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp
## random effects panel with spatial lag and serial error correlation
## optimization method set to "BFGS"
sarsrmod <- spreml(fm, data = Produc, w = usaww, errors="sr", lag=TRUE,
method="BFGS")
summary(sarsrmod)