Double-Power Distance Weights Matrix

Description

This function calculates the double-power distance matrix, for a given distance cutoff and a positive exponent.

Usage

DDistMat(distMat, distCutOff = NULL, powr = 2, mevn = FALSE)

Arguments

Details

W is an nxn matrix with elements w_{ij}, i, j = 1, ... n, where w_{ij} = (1-(\frac{d_{ij}}{D})^p)^p, if 0 <= d_{ij} < D and w_{ij} = 0, if d_{ij} > D or i = j. D is the cut-off distance point (maximum radius of influence), d_{ij} is the distance between spatial units i and j, and p is the power value (e.g. p = 2, 3, 4,...).

Value

Author(s)

Rozeta Simonovska

Examples

data(gN3dist) ##distance in meters
W1    <- DDistMat(distMat = gN3dist,
                  distCutOff = 300000,
                  powr = 3) ##distance cutoff in meters
dist2 <- gN3dist/1000 ##in km
W2    <- DDistMat(distMat = dist2, 300, 3)  ##distance cutoff in kilometers

Distance weights matrix (Inverse distance, Exponential distance or Double-Distance matrix)

Description

This function calculates the spatial distance weights matrix (inverse, exponential or double-distance), with a given cutoff distance and a positive exponent (alpha).

Usage

DistWMat(
  distMat,
  distCutOff = NULL,
  type = "inverse",
  alpha = NULL,
  mevn = FALSE
)

Arguments

Value

Author(s)

Rozeta Simonovska

See Also

InvDistMat ExpDistMat DDistMat vignette("spatial_matrices", package = "SDPDmod")

Examples

## distance between centroids of NUTS3 regions in Germany (in meters)
data(gN3dist, package = "SDPDmod")
##inverse distance matrix with cutoff 100000 meters
W1    <- DistWMat(distMat = gN3dist, distCutOff = 100000)
dist2 <- gN3dist/1000 ##distance in km
## normalized exponential distance matrix
W2    <- DistWMat(distMat=dist2, distCutOff = 100, type = "expo",
                  alpha = 2, mevn = TRUE)

Exponential distance matrix

Description

This function calculates the (negative) exponential distance matrix, with a given cutoff distance and a positive exponent value.

Usage

ExpDistMat(distMat, distCutOff = NULL, expn = 0.01, mevn = FALSE)

Arguments

Details

W is an nxn matrix with elements w_{ij}, i, j = 1,..n, where w_{ij}=e^{-\alpha d_{ij}}, if 0 <= d_{ij} < D and w_{ij}=0, if d_{ij} > D or i = j. D is the distance cutoff point (maximum radius of influence), d_{ij} is the distance between spatial units i and j, and \alpha is the positive exponent (e.g. \alpha= 0.01, 0.02,...).

Value

Author(s)

Rozeta Simonovska

Examples

data(gN3dist) ##distance in meters
W1    <- ExpDistMat(distMat = gN3dist, distCutOff = 100000)
dist2 <- gN3dist/1000 ##in km
W2    <- ExpDistMat(distMat = dist2, distCutOff = 100, expn = 0.02)
W2nor <- ExpDistMat(distMat = dist2, 100000, 0.001, mevn = TRUE)

Inverse distance matrix

Description

This function calculates the inverse distances, with a given cutoff distance and a positive exponent.

Usage

InvDistMat(distMat, distCutOff = NULL, powr = 1, mevn = FALSE)

Arguments

Details

W is an nxn matrix with elements w_{ij}, i,j=1,..n, where w_{ij}=1/d_{ij}^\gamma, if 0 <= d_{ij} < D and w_{ij}=0, if d_{ij} > D or i = j. D is the distance cutoff point (maximum radius of influence), d_{ij} is the distance between spatial units i and j, and \gamma is the value for the exponent (e.g. \gamma = 1, 2, 3, 4,...).

Value

Author(s)

Rozeta Simonovska

Examples

## distance between centroids of NUTS3 regions in Germany (in meters)
data(gN3dist, package = "SDPDmod")
## inverse distance matrix with cutoff 100000 meters
W1    <- InvDistMat(distMat = gN3dist, distCutOff = 100000)
dist2 <- gN3dist/1000 ##distance in km
## normalized distance matrix with cutoff 100km
W2    <- InvDistMat(distMat = dist2, distCutOff=100, powr = 2, mevn = TRUE)

Spatial dynamic panel data lag model with fixed effects maximum likelihood estimation.

Description

This function estimates spatial panel model with fixed effects for static or dynamic model. It includes the transformation approach suggested by Yu et al (2008) and Lee and Yu (2010).

Usage

SDPDm(
  formula,
  data,
  W,
  index,
  model = "sar",
  effect = "individual",
  ldet = NULL,
  lndetspec = list(p = NULL, m = NULL, sd = NULL),
  dynamic = FALSE,
  tlaginfo = list(ind = NULL, tl = TRUE, stl = TRUE),
  LYtrans = TRUE,
  incr = NULL,
  rintrv = TRUE,
  demn = FALSE,
  DIRtrans = FALSE
)

Arguments

Details

Based on MatLab functions sar_jihai.m, sar_jihai_time.m and sar_panel_FE.m

In tlaginfo = list(ind = NULL, tl = TRUE, stl = TRUE):

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)

tl logical, default TRUE. If TRUE y_{t-1} (the lagged dependent variable in time is included)

stl logical, default TRUE. If TRUE Wy_{t-1} (the lagged dependent variable in space and time is included)

Value

An object of class "SDPDm"

Author(s)

Rozeta Simonovska

References

Yu, J., De Jong, R., & Lee, L. F. (2008). Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large. Journal of Econometrics, 146(1), 118-134.

Lee, L. F., & Yu, J. (2010). Estimation of spatial autoregressive panel data models with fixed effects. Journal of Econometrics, 154(2), 165-185.

Lee, L. F., & Yu, J. (2010). A spatial dynamic panel data model with both time and individual fixed effects. Econometric Theory, 564-597.

See Also

vignette("spatial_model", package = "SDPDmod")

Examples

library("SDPDmod")
data(Produc, package = "plm")
data(usaww, package = "splm")
form1 <- log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp
mod1  <- SDPDm(formula = form1, data = Produc, W = usaww, index = c("state","year"),
               model = "sar", effect = "individual", LYtrans = TRUE)
summary(mod1)
imp1  <- impactsSDPDm(mod1)
summary(imp1)
mod2  <- SDPDm(formula = form1, data = Produc, W = usaww, index = c("state","year"),
               model = "sdm", effect = "twoways", LYtrans = TRUE,
               dynamic = TRUE, tlaginfo=list(ind = NULL, tl = TRUE, stl = TRUE))
summary(mod2)

Shared boundary matrix

Description

This function calculates the shared boundary matrix

Usage

SharedBMat(sf_pol, rn = FALSE)

Arguments

Value

Author(s)

Rozeta Simonovska

Examples

library("sf")

ger   <- st_read(system.file("shape/GermanyNUTS3.shp",
                             package = "SDPDmod"),
                 quiet = TRUE)
bav <- ger[which(substr(ger$NUTS_CODE,1,3)=="DE2"),] ## Bavarian districts
W     <- SharedBMat(bav)

Bayesian log-marginal posterior probabilities for spatial panel models

Description

Calculates log-marginal posterior probabilities for model comparison purposes.

Usage

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

Details

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

p(\lambda|y) = \frac{1}{p(y)} p(\lambda) \Gamma(a) (2\pi)^{-a} \frac{|P|^{T-1}}{|Z'Z|^{1/2}} (e'e)^{-a}

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

p(\rho|y) = \frac{1}{p(y)} p(\rho) \Gamma(a) (2\pi)^{-a} \frac{|P|}{|Z'Z|^{1/2}} (e'e)^{-a}

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)

Value

A list

Author(s)

Rozeta Simonovska

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.

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

Extract coefficients from model of class SDPDm

Description

Method for extracting coefficients of objects of class "SDPDm"

Usage

## S3 method for class 'SDPDm'
coef(object, ...)

Arguments

Value

Coefficients extracted from the model object of class "SDPDm".

Author(s)

Rozeta Simonovska

See Also

SDPDm

Maximum eigenvalue normalization

Description

Maximum eigenvalue row normalization of a spatial weights matrix.

Usage

eignor(W)

Arguments

Value

Author(s)

Rozeta Simonovska

See Also

rownor

Examples

data(gN3dist)
dist2 <- gN3dist/1000 ##distance in km
W     <- InvDistMat(distMat = dist2, distCutOff = 100, powr = 2)
Wnor  <- eignor(W)

Distance between the centroids of NUTS3 regions in Germany

Description

Distance between the centroids of NUTS3 regions in Germany

Usage

gN3dist

Format

matrix of distances

Impacts for 'SDPDm' objects

Description

Direct and indirect effects estimates

Usage

impactsSDPDm(res, NSIM = 200, sd = 12345)

Arguments

Details

For spatial dynamic panel data model:

y_{t} = \tau y_{t-1} + \rho W y_{t} + \eta W y_{t-1} + X_{t} \beta + W X_{t} \theta + \alpha + \mu + u_{t}

Short term effects for kth explanatory variable:

(I - \rho W)^{-1}(\beta_{k} I_{n} + \theta_{k} W)

Long term effects for kth explanatory variable:

((1-\tau)I_{n} - (\rho+\eta)W)^{-1}(\beta_{k} I_{n} + \theta_{k} W)

The direct effect is the average of the diagonal elements, and the indirect effect is the average of the row sums of the non-diagonal elements of the matrix.

Value

An object of class 'impactsSDPDm'

Author(s)

Rozeta Simonovska

See Also

SDPDm

Is the matrix row-normalized

Description

Checks if a spatial weights matrix is row-normalized.

Usage

isrownor(W)

Arguments

Value

Logical value. If the weights matrix is row-normalized such that all rows sum up to 1, the value is TRUE.

Author(s)

Rozeta Simonovska

See Also

rownor

Examples

data("usa46", package="SDPDmod")
isrownor(usa46)

m nearest neighbors based on a distance matrix

Description

This function finds the m nearest neighbors, given a matrix of distances.

Usage

mNearestN(distMat, m = 5, listv = FALSE, rn = FALSE)

Arguments

Value

Author(s)

Rozeta Simonovska

Examples

data(gN3dist, package = "SDPDmod")
fournn <- mNearestN(gN3dist, m = 4)
mat1   <- rownor(fournn)
tennn  <- mNearestN(gN3dist, 10, listv = TRUE, rn = TRUE)
mat2   <- tennn$W

1st to m-th order neighbors matrix

Description

Finds the 1th to m-th order neighbors matrix.

Usage

mOrdNbr(sf_pol = NULL, m = 1, neigbs = NULL, listv = FALSE, rn = FALSE)

Arguments

Value

Author(s)

Rozeta Simonovska

Examples

library("sf")
ger   <- st_read(system.file("shape/GermanyNUTS3.shp",
                             package = "SDPDmod"),
                 quiet = TRUE)
m1thn <- mOrdNbr(ger)

m4thn <- mOrdNbr(ger, 4)
mat1  <- rownor(m4thn)
m4thn2<- mOrdNbr(ger, 4, listv = TRUE, rn = TRUE)
mat2  <- m4thn2$W

print for class SDPDm

Description

Method for sprinting the results of objects of class "SDPDm"

Usage

## S3 method for class 'SDPDm'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Value

No return value

Author(s)

Rozeta Simonovska

See Also

SDPDm

Print for class blmpSDPD

Description

Method for printing the results of objects of class "blmpSDPD"

Usage

## S3 method for class 'blmpSDPD'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Value

No return value

Author(s)

Rozeta Simonovska

Print of summary for class SDPDm

Description

Method for printing the summary the results of objects of class "SDPDm"

Usage

## S3 method for class 'summary.SDPDm'
print(x, ...)

Arguments

Value

No return value

Author(s)

Rozeta Simonovska

See Also

SDPDm

Print summary for class impactsSDPDm

Description

Method for printing the summary the results of objects of class "impactsSDPDm"

Usage

## S3 method for class 'summary.impactsSDPDm'
print(x, ...)

Arguments

Author(s)

Rozeta Simonovska

Row-normalization

Description

Row-normalization of a spatial weights matrix.

Usage

rownor(W)

Arguments

Value

Author(s)

Rozeta Simonovska

See Also

eignor

Examples

library("sf")
ger   <- st_read(system.file("shape/GermanyNUTS3.shp",
                             package = "SDPDmod"),
                 quiet = TRUE)
W     <- mOrdNbr(ger, 3)
Wnor  <- rownor(W)

Summary for class SDPDm

Description

Method for summarizing the results of objects of class "SDPDm"

Usage

## S3 method for class 'SDPDm'
summary(object, ...)

Arguments

Value

Summary of SDPDm

Author(s)

Rozeta Simonovska

See Also

SDPDm

Summary for class impactsSDPDm

Description

Method for summarizing the results of objects of class "impactsSDPDm"

Usage

## S3 method for class 'impactsSDPDm'
summary(object, ...)

Arguments

Value

Summary of impacts

Author(s)

Rozeta Simonovska

See Also

SDPDm

Spatial weights matrix of 46 USA states

Description

Spatial weights matrix of 46 USA states

Usage

usa46

Format

binary coded matrix