spreml function

Spatial Panel Model with Random Effects by Maximum Likelihood

Spatial Panel Model with Random Effects by Maximum Likelihood

Maximum likelihood (ML) estimation of spatial panel models with random effects and serial error correlation.

spreml(formula, data, index = NULL, w, w2=w, lag = FALSE, errors = c("semsrre", "semsr", "srre", "semre", "re", "sr", "sem","ols", "sem2srre", "sem2re", "semgre"), pvar = FALSE, hess = FALSE, quiet = TRUE, initval = c("zeros", "estimate"), x.tol = 1.5e-18, rel.tol = 1e-15, ...)

Arguments

  • 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^\hat{y}=X \hat{\beta}

  • 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)
  • Maintainer: Giovanni Millo
  • License: GPL-2
  • Last published: 2023-12-20

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