spsur (version 1.0.1.4)

wald_deltas: Wald tests for spatial parameters coefficients.

Description

Function wald_deltas obtains Wald tests for linear restrictions on the spatial coefficients of a SUR model that has been estimated previously through the function spsurml. The restrictions can affect to coefficients of the same equation (i.e., \(\lambda_{g}=\rho_{g} forall g\)) or can involve coefficients from different equations (i.e., \(\lambda_{g}=\lambda_{h}\)). The function has great flexibility in this respect. Note that wald_deltas only works in a maximum-likelihood framework.

In order to work with wald_betas, the model on which the linear restrictions are to be tested needs to exists as an spsur object. Using the information contained in the object, wald_deltas obtains the corresponding Wald estatistic for the null hypotheses specified by the user through the R row vector and b column vector discussed, used also in spsurml. The function shows the resulting Wald test statistics and their corresponding p-values.

Usage

wald_deltas (obj , R , b)

Arguments

obj

An spsur object created by spsurml, spsur3sls or spsurtime.

R

A row vector of order (1xGr) or (1x2Gr) showing the set of r linear constraints on the spatial parameters. The last case is reserved to "sarar" models where there appear G parameters \(\lambda_{g}\) and G parameters \(\rho_{g}\), 2G spatial in total. The first restriction appears in the first G terms in R (2G for the "sarar" case), the second restriction in the next G terms (2G for the "sarar" case) and so on.

b

A column vector of order (rx1) with the values of the linear restrictions on the \(\beta\) parameters.

Value

Object of htest including the Wald statistic, the corresponding p-value, the degrees of freedom and the values of the sample estimates.

See Also

spsurml, spsur3sls

Examples

# NOT RUN {
#################################################
######## CROSS SECTION DATA (G>1; Tm=1) ########
#################################################
rm(list = ls()) # Clean memory
data(spc, package = "spsur")
lwspc <- spdep::mat2listw(Wspc, style = "W")
Tformula <- WAGE83 | WAGE81 ~ UN83 + NMR83 + SMSA | UN80 + NMR80 + SMSA

#################################
## Estimate SUR-SLM model
spcsur.slm <-spsurml(formula = Tformula, data = spc, 
                       type = "slm", listw = lwspc)
summary(spcsur.slm)
## H_0: equality of the lambda parameters of both equations.
R1 <- matrix(c(1,-1), nrow=1)
b1 <- matrix(0, ncol=1)
wald_deltas(spcsur.slm, R = R1, b = b1)


## VIP: The output of the whole set of the examples can be examined 
## by executing demo(demo_wald_deltas, package="spsur")

# }
# NOT RUN {
#################################
### Estimate SUR-SEM model
spcsur.sem <-spsurml(form = Tformula, data = spc, 
                     type = "sem", listw = lwspc)
summary(spcsur.sem)
### H_0: equality of the rho parameters of both equations.
R2 <- matrix(c(1,-1), nrow=1)
b2 <- matrix(0, ncol=1)
wald_deltas(spcsur.sem, R = R2, b = b2)

##################################
### Estimate SUR-SARAR model
### It usually requires 2-3 minutes maximum
spcsur.sarar <-spsurml(formula = Tformula, data = spc,
                       type = "sarar", listw = lwspc,
                       control = list(tol=0.1))
summary(spcsur.sarar)
### H_0: equality of the lambda and rho parameters of both equations.
R3 <- matrix(c(1,-1,0,0,0,0,1,-1), nrow=2, ncol=4, byrow=TRUE)
b3 <- matrix(c(0,0), ncol=1)
wald_deltas(spcsur.sarar, R = R3, b = b3)

#####################################
#########  G=1; Tm>1         ########
#####################################

##' ##### Example 2: Homicides + Socio-Economics (1960-90)
rm(list = ls()) # Clean memory
### Read NCOVR.sf object
data(NCOVR, package = "spsur")
nbncovr <- spdep::poly2nb(NCOVR.sf, queen = TRUE)
### Some regions with no links...
lwncovr <- spdep::nb2listw(nbncovr, style = "W", zero.policy = TRUE)
Tformula <- HR80  | HR90 ~ PS80 + UE80 | PS90 + UE90

##################################
### A SUR-SLM model
NCOVRSUR.slm <-spsurml(formula = Tformula, data = NCOVR.sf, 
                       type = "slm", listw = lwncovr,
                       method = "Matrix", zero.policy = TRUE, 
                       control = list(fdHess = TRUE))
summary(NCOVRSUR.slm)
### H_0: equality of the lambda parameters of both equations.
R1 <- matrix(c(1,-1), nrow=1)
b1 <- matrix(0, ncol=1)
wald_deltas( NCOVRSUR.slm, R = R1, b = b1)

##################################
### Estimate SUR-SEM model
NCOVRSUR.sem <-spsurml(formula = Tformula, data = NCOVR.sf, 
                       type = "sem", listw = lwncovr,
                       method = "Matrix", zero.policy = TRUE, 
                       control = list(fdHess = TRUE))
summary(NCOVRSUR.sem)
### H_0: equality of the rho parameters of both equations.
R2 <- matrix(c(1,-1), nrow=1)
b2 <- matrix(0, ncol=1)
wald_deltas(NCOVRSUR.sem, R = R2, b = b2)
# }