SD.RStests {spdep}

Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models

Description

Rao's score and adjusted Rao's score tests of linear hypotheses applied to a fitted linear model to examine whether either the spatially lagged dependent variable lag or the spatially lagged independent variable(s) WX should be included in the model, or both (SDM). Adjusted tests are provided for lag and WX adapting to the presence of the other, and a joint test for both. The joint test is equal to the unadjusted of one plus the adjusted of the other. In addition, draft tests are added from Koley (2024, section 6) for spatial Durbin error models to examine whether either the spatially lagged error err or the spatially lagged independent variable(s) WX should be included in the model, or both (SDEM); because of orthogonality, no adjusted tests are required.

Usage

SD.RStests(model, listw, zero.policy = attr(listw, "zero.policy"), test = "SDM",
 Durbin = TRUE)

Arguments

model

an object of class lm returned by lm

listw

a listw object created for example by nb2listw, expected to be row-standardised (W-style)

zero.policy

default attr(listw, "zero.policy") as set when listw was created, if attribute not set, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA

test

test=“SDM” computes the SDM tests, a character vector of tests requested chosen from SDM_RSlag, SDM_adjRSlag, SDM_RSWX, SDM_adjRSWX, SDM_Joint, test=“SDEM” computes the SDEM tests, a character vector of tests requested chosen from SDEM_RSerr, SDEM_RSWX, SDEM_Joint; test=“all” computes all the tests

Durbin

default TRUE for Durbin models including WX; if TRUE, full spatial Durbin model; if a formula object, the subset of explanatory variables to lag

Value

A list of class LMtestlist of htest objects, each with:

statistic

the value of the Lagrange Multiplier test.

parameter

number of degrees of freedom

p.value

the p-value of the test.

method

a character string giving the method used.

data.name

a character string giving the name(s) of the data.

Note

The results in the example below agree with those in Table 3, p. 22 in Koley and Bera (2024).

Author(s)

Roger Bivand [e-mail], Malabika Koley and Anil K. Bera

References

Malabika Koley and Anil K. Bera (2024) To use, or not to use the spatial Durbin model? – that is the question, Spatial Economic Analysis, 19:1, 30-56, doi:10.1080/17421772.2023.2256810; Malabika Koley (2024) Specification Testing under General Nesting Spatial Model (Appendix C), https://sites.google.com/view/malabikakoley/research.

See Also

lm, lm.RStests

Examples

columbus <- sf::st_read(system.file("shapes/columbus.gpkg", package="spData")[1])
col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
col.listw <- nb2listw(col.gal.nb, style="W")
lm_obj <- lm(CRIME ~ INC + HOVAL, data=columbus)
summary(lm.RStests(lm_obj, col.listw, test="all"))
res <- SD.RStests(lm_obj, col.listw, test="SDM")
summary(res)
all.equal(unname(res$SDM_Joint$statistic),
 unname(res$SDM_RSlag$statistic + res$SDM_adjRSWX$statistic))
all.equal(unname(res$SDM_Joint$statistic),
 unname(res$SDM_adjRSlag$statistic + res$SDM_RSWX$statistic))
res <- SD.RStests(lm_obj, col.listw, test="SDEM")
summary(res)
all.equal(unname(res$SDEM_Joint$statistic),
 unname(res$SDEM_RSerr$statistic + res$SDEM_RSWX$statistic))
summary(SD.RStests(lm_obj, nb2listw(col.gal.nb, style="C"), test="all"))
summary(SD.RStests(lm_obj, col.listw, test="all", Durbin= ~ INC))
lm_obj0 <- lm(I(scale(CRIME)) ~ 0 + I(scale(INC)) + I(scale(HOVAL)),
 data=columbus)
summary(SD.RStests(lm_obj0, col.listw, test="all"))
columbusNA <- columbus
columbusNA$HOVAL[15] <- NA
lm_objNA <- lm(CRIME ~ INC + HOVAL, data=columbusNA)
summary(SD.RStests(lm_objNA, col.listw, test="all"))