Likelihood ratio test

The LR.Sarlm() function provides a likelihood ratio test for objects for which a logLik() function exists for their class, or for objects of class logLik. LR1.Sarlm() and Wald1.Sarlm() are used internally in summary.Sarlm(), but may be accessed directly; they report the values respectively of LR and Wald tests for the absence of spatial dependence in spatial lag or error models. The spatial Hausman test is available for models fitted with errorSarlm and GMerrorsar.

Usage

LR.Sarlm(x, y)
# S3 method for class 'Sarlm'
logLik(object, ...)
LR1.Sarlm(object)
Wald1.Sarlm(object)
# S3 method for class 'Sarlm'
Hausman.test(object, ..., tol=NULL)
# S3 method for class 'Sarlm'
anova(object, ...)
bptest.Sarlm(object, varformula=NULL, studentize = TRUE, data=list())
# S3 method for class 'Sarlm'
impacts(obj, ..., tr, R = NULL, listw = NULL, evalues=NULL,
 useHESS = NULL, tol = 1e-06, empirical = FALSE, Q=NULL)

Arguments

x: a logLik object or an object for which a logLik() function exists
y: a logLik object or an object for which a logLik() function exists
object, obj: a Sarlm object
...: further arguments passed to or from other methods

varformula: a formula describing only the potential explanatory variables for the variance (no dependent variable needed). By default the same explanatory variables are taken as in the main regression model
studentize: logical. If set to TRUE Koenker's studentized version of the test statistic will be used.
data: an optional data frame containing the variables in the varformula
tr: A vector of traces of powers of the spatial weights matrix created using trW, for approximate impact measures; if not given, listw must be given for exact measures (for small to moderate spatial weights matrices); the traces must be for the same spatial weights as were used in fitting the spatial regression, and must be row-standardised
listw: If tr is not given, a spatial weights object as created by nb2listw; they must be the same spatial weights as were used in fitting the spatial regression, but do not have to be row-standardised
evalues: vector of eigenvalues of spatial weights matrix for impacts calculations
R: If given, simulations are used to compute distributions for the impact measures, returned as mcmc objects; the objects are used for convenience but are not output by an MCMC process
useHESS: Use the Hessian approximation (if available) even if the asymptotic coefficient covariance matrix is available; used for comparing methods
tol: Argument passed to mvrnorm and solve: tolerance (relative to largest variance) for numerical lack of positive-definiteness in the coefficient covariance matrix
empirical: Argument passed to mvrnorm (default FALSE): if true, the coefficients and their covariance matrix specify the empirical not population mean and covariance matrix
Q: default NULL, else an integer number of cumulative power series impacts to calculate if tr is given

Value

The tests return objects of class htest with:

statistic: value of statistic
parameter: degrees of freedom
p.value: Probability value
estimate: varies with test
method: description of test method

logLik.Sarlm() returns an object of class logLik LR1.Sarlm, Hausman.Sarlm and Wald1.Sarlm returm objects of class htest

Note

The numbers of degrees of freedom returned by logLik.Sarlm() include nuisance parameters, that is the number of regression coefficients, plus sigma, plus spatial parameter esitmate(s).

References

LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 61–63; Pace RK and LeSage J (2008) A spatial Hausman test. Economics Letters 101, 282–284. T.S. Breusch & A.R. Pagan (1979), A Simple Test for Heteroscedasticity and Random Coefficient Variation. Econometrica 47, 1287–1294

W. Krämer & H. Sonnberger (1986), The Linear Regression Model under Test. Heidelberg: Physica.

L. Anselin (1988) Spatial econometrics: methods and models. Dordrecht: Kluwer, pp. 121–122.

Author

Roger Bivand Roger.Bivand@nhh.no, bptest: Torsten Hothorn and Achim Zeileis, modified by Roger Bivand

Examples

require("sf", quietly=TRUE)
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
#require("spdep", quietly=TRUE)
col.gal.nb <- spdep::read.gal(system.file("weights/columbus.gal", package="spData")[1])
lm.mod <- lm(CRIME ~ HOVAL + INC, data=columbus)
lag <- lagsarlm(CRIME ~ HOVAL + INC, data=columbus, spdep::nb2listw(col.gal.nb))
mixed <- lagsarlm(CRIME ~ HOVAL + INC, data=columbus, spdep::nb2listw(col.gal.nb), type="mixed")
error <- errorsarlm(CRIME ~ HOVAL + INC, data=columbus, spdep::nb2listw(col.gal.nb))
Hausman.test(error)
#> 
#> 	Spatial Hausman test (asymptotic)
#> 
#> data:  NULL
#> Hausman test = 6.4729, df = 3, p-value = 0.09074
#> 
LR.Sarlm(mixed, error)
#> 
#> 	Likelihood ratio for spatial linear models
#> 
#> data:  
#> Likelihood ratio = 4.2782, df = 2, p-value = 0.1178
#> sample estimates:
#> Log likelihood of mixed Log likelihood of error 
#>               -182.0161               -184.1552 
#> 
anova(lag, lm.mod)
#>        Model df    AIC  logLik Test L.Ratio   p-value
#> lag        1  5 376.34 -183.17    1                  
#> lm.mod     2  4 382.75 -187.38    2  8.4179 0.0037154
anova(lag, error, mixed)
#>       Model df    AIC  logLik Test L.Ratio p-value
#> lag       1  5 376.34 -183.17    1                
#> error     2  5 378.31 -184.16    1                
#> mixed     3  7 378.03 -182.02    2  4.2782 0.11776
AIC(lag, error, mixed)
#>       df      AIC
#> lag    5 376.3366
#> error  5 378.3104
#> mixed  7 378.0322
bptest.Sarlm(error)
#> 
#> 	studentized Breusch-Pagan test
#> 
#> data:  
#> BP = 9.3694, df = 2, p-value = 0.009235
#> 
bptest.Sarlm(error, studentize=FALSE)
#> 
#> 	Breusch-Pagan test
#> 
#> data:  
#> BP = 16.285, df = 2, p-value = 0.0002908
#>