formula: 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.
Returns
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 y^=Xβ^
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
References
Millo, G. (2014) Maximum likelihood estimation of spatially and serially correlated panels with random effects. Computational Statistics and Data Analysis, 71 , 914--933.
Author(s)
Giovanni Millo
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)