wald_betas | R Documentation |
The function wald_betas
can be seen as a complement
to the restricted estimation procedures included in the functions
spsurml
and spsur3sls
.
wald_betas
obtains Wald tests for sets of linear
restrictions on the coefficients β of the SUR model.
The restrictions may involve coefficients of the same equation or
coefficients from different equations. The function has great flexibility
in this respect. Note that wald_betas
is more general than
lr_betas
in the sense that the last function
only allows to test for restrictions of homogeneity of subsets of
β coefficients among the different equations in the SUR model,
and 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_betas
obtains the corresponding Wald estatistic
for the null hypotheses specified by the user through the R row
vector and b column vector, used also in spsurml
and spsur3sls
. The function shows the value of the Wald test
statistics and its associated p-values.
wald_betas (obj , R , b)
obj |
An |
R |
A row vector of order (1xPr) showing the set of r linear constraints on the β parameters. The first restriction appears in the first K terms in R, the second restriction in the next K terms and so on. |
b |
A column vector of order (rx1) with the values of the linear restrictions on the β parameters. |
Object of htest
class 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 |
Lopez, F.A., Mur, J., and Angulo, A. (2014). Spatial model selection strategies in a SUR framework. The case of regional productivity in EU. Annals of Regional Science, 53(1), 197-220. <doi:10.1007/s00168-014-0624-2>
Mur, J., Lopez, F., and Herrera, M. (2010). Testing for spatial effects in seemingly unrelated regressions. Spatial Economic Analysis, 5(4), 399-440. <doi:10.1080/17421772.2010.516443>
Anselin, L. (2016) Estimation and Testing in the Spatial Seemingly Unrelated Regression (SUR). Geoda Center for Geospatial Analysis and Computation, Arizona State University. Working Paper 2016-01. <doi:10.13140/RG.2.2.15925.40163>
Minguez, R., Lopez, F.A. and Mur, J. (2022). spsur: An R Package for Dealing with Spatial Seemingly Unrelated Regression Models. Journal of Statistical Software, 104(11), 1–43. <doi:10.18637/jss.v104.i11>
spsurml
, spsur3sls
, lr_betas
## VIP: The output of the whole set of the examples can be examined ## by executing demo(demo_wald_betas, package="spsur") ################################################# ######## CROSS SECTION DATA (G=1; Tm>1) ######## ################################################# ##### Example 1: Spatial Phillips-Curve. Anselin (1988, p. 203) rm(list = ls()) # Clean memory data(spc) 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 between SMSA coefficients in both equations. R1 <- matrix(c(0,0,0,1,0,0,0,-1), nrow=1) b1 <- matrix(0, ncol=1) wald_betas(spcsur.slm, R = R1, b = b1)
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