blmpSDPD function

Bayesian log-marginal posterior probabilities for spatial panel models

Calculates log-marginal posterior probabilities for model comparison purposes.

blmpSDPD(
  formula,
  data,
  W,
  index,
  model = list("ols", "slx", "sar", "sdm", "sem", "sdem"),
  effect = "individual",
  ldet = NULL,
  lndetspec = list(m = NULL, p = NULL, sd = NULL),
  dynamic = FALSE,
  tlaginfo = list(ind = NULL),
  LYtrans = FALSE,
  incr = NULL,
  rintrv = TRUE,
  prior = "uniform",
  bprarg = 1.01
)

Arguments

• formula: a symbolic description for the model to be estimated
• data: a data.frame
• W: spatial weights matrix (row-normalized)
• index: the indexes (names of the variables for the spatial and time component)
• model: a list of models for which the Bayesian log-marginal posterior probabilities need to be calculated, list("ols","slx","sar","sdm","sem","sdem")
• effect: type of fixed effects, c("none","individual","time","twoways"), default ="individual"
• ldet: Type of computation of log-determinant, c("full","mc"). Default "full" for smaller problems, "mc" for large problems.
• lndetspec: specifications for the calculation of the log-determinant
• dynamic: logical, if TRUE time lag of the dependent variable is included. Default = FALSE
• tlaginfo: specification for the time lag, default = list(ind=NULL), ind - i-th column in the data frame which represents the time lag
• LYtrans: logical, default FALSE. If Lee-Yu transformation should be used for demeaning of the variables
• incr: increment for vector of values for rho
• rintrv: logical, default TRUE, calculates eigenvalues of W. If FALSE, the interval for rho is (-1,1).
• prior: type of prior to be used c("uniform","beta"). Default "uniform"
• bprarg: argument for the beta prior. Default = 1.01

Returns

A list - lmarginal: log-marginal posterior

• probs: model probability

Details

For the Spatial Durbin Error Model (SDEM) the marginal distribution is:

For the Spatial Durbin Model (SDM) the marginal distribution is:

where $p(\lambda)$ is prior on $\lambda$ and $p(\rho)$ is prior on $\rho$, either uniform $\frac{1}{D}$, $D = 1/\omega_{max}-1/\omega_{min}$ or beta prior; No priors on beta and sige; $\omega_{max}$ and $\omega_{min}$ are the maximum and minimum eigenvalues of W - spatial weights matrix; $Z = X$ for lag or error model and $Z = [X WX]$ for Durbin model; X - matrix of $k$ covariates.

For more details, see LeSage (2014).

Based on MatLab function log_marginal_panelprob.m.

In tlaginfo = list(ind = NULL):

ind i-th column in data which represents the time lag, if not specified then the lag from the dependent variable is created and the panel is reduced from nt to n(t-1)

Examples

## US States Production data
data(Produc, package = "plm")
## Spatial weights row-normalized matrix of 48 US states
data(usaww, package = "splm")
isrownor(usaww)
form1 <- log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp
res1  <- blmpSDPD(formula = form1, data=Produc, W = usaww,
                 index = c("state","year"),
                 model = list("sar","sdm","sem","sdem"),
                 effect = "twoways")
res1
res2  <- blmpSDPD(formula = form1, data = Produc, W = usaww,
                 index = c("state","year"),
                 model = list("sar","sdm","sem","sdem"),
                 effect = "twoways", dynamic = TRUE)
res2

References

LeSage, J. P., & Parent, O. (2007). Bayesian model averaging for spatial econometric models. Geographical Analysis, 39(3), 241-267.

LeSage, J. P. (2014). Spatial econometric panel data model specification: A Bayesian approach. Spatial Statistics, 9, 122-145.

Author(s)

Rozeta Simonovska