spsur (version 1.0.0.2)

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(results, R, b)

Arguments

results

: An object created with spsurml or spsur3sls. This argument serves the user to indicate the spatial SUR model, previously estimated by maximum-likelihood or 3sls, where the set of linear restrictions are to be tested.

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 parameters 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. Default = NULL.

b

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

Value

The output of the function is very simple and consists of two pieces of information, the value of the Wald statistic and the corresponding p-value, plus the degrees of freedom of the test.

Wald stat	The value of Wald test.
p_val	The p-value of Wald test.
q	Degrees of freedom of the corresponding \(\chi^{2}\) distribution.

See Also

spsurml, spsur3sls

Examples

# NOT RUN {
#################################################
######## CROSS SECTION DATA (G>1; Tm=1) ########
#################################################
rm(list = ls()) # Clean memory
data(spc)
Tformula <- WAGE83 | WAGE81 ~ UN83 + NMR83 + SMSA | UN80 + NMR80 + SMSA
#################################
## Estimate SUR-SLM model
spcsur.slm <-spsur3sls(Form = Tformula, data = spc, type = "slm", W= Wspc)
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(results = spcsur.slm, R = R1, b = b1)

# }