wald_deltas | R Documentation |
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., λ_{g}=ρ_{g} forall g) or can involve coefficients
from different equations (i.e., λ_{g}=λ_{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 statistic 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.
wald_deltas (obj , R , b)
obj |
An |
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 λ_{g} and G parameters ρ_{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 β parameters. |
Object of htest
including the Wald
statistic, the corresponding p-value, the degrees of
freedom and the values of the sample estimates.
Fernando Lopez | fernando.lopez@upct.es |
Roman Minguez | roman.minguez@uclm.es |
Jesus Mur | jmur@unizar.es |
spsurml
, spsur3sls
################################################# ######## 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") ################################# ### 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)
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