lm.LMtests: Lagrange Multiplier diagnostics for spatial dependence in...

In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models

Description

The function reports the estimates of tests chosen among five statistics for testing for spatial dependence in linear models. The statistics are the simple LM test for error dependence (LMerr), the simple LM test for a missing spatially lagged dependent variable (LMlag), variants of these robust to the presence of the other (RLMerr, RLMlag - RLMerr tests for error dependence in the possible presence of a missing lagged dependent variable, RLMlag the other way round), and a portmanteau test (SARMA, in fact LMerr + RLMlag). Note: from spdep 0.3-32, the value of the weights matrix trace term is returned correctly for both underlying symmetric and asymmetric neighbour lists, before 0.3-32, the value was wrong for listw objects based on asymmetric neighbour lists, such as k-nearest neighbours (thanks to Luc Anselin for finding the bug).

Usage

lm.LMtests(model, listw, zero.policy=NULL, test="LMerr", spChk=NULL, naSubset=TRUE)
## S3 method for class 'LMtestlist'
print(x, ...)
## S3 method for class 'LMtestlist'
summary(object, p.adjust.method="none", ...)
## S3 method for class 'LMtestlist.summary'
print(x, digits=max(3, getOption("digits") - 2), ...)

Arguments

model	an object of class lm returned by lm, or optionally a vector of externally calculated residuals (run though na.omit if any NAs present) for use when only "LMerr" is chosen; weights and offsets should not be used in the lm object
listw	a listw object created for example by nb2listw, expected to be row-standardised (W-style)
zero.policy	default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA
test	a character vector of tests requested chosen from LMerr, LMlag, RLMerr, RLMlag, SARMA; test="all" computes all the tests.
spChk	should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()
naSubset	default TRUE to subset listw object for omitted observations in model object (this is a change from earlier behaviour, when the model$na.action component was ignored, and the listw object had to be subsetted by hand)
x, object	object to be printed
p.adjust.method	a character string specifying the probability value adjustment (see p.adjust) for multiple tests, default "none"
digits	minimum number of significant digits to be used for most numbers
...	printing arguments to be passed through

Details

The two types of dependence are for spatial lag rho and spatial error lambda:

y = X beta + rho W1 y + u

u = lambda W2 u + e

where e is a well-behaved, uncorrelated error term. Tests for a missing spatially lagged dependent variable test that rho = 0, tests for spatial autocorrelation of the error u test whether lambda = 0. W is a spatial weights matrix; for the tests used here they are identical.

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.

Author(s)

Roger Bivand [e-mail] and Andrew Bernat

References

Anselin, L. 1988 Spatial econometrics: methods and models. (Dordrecht: Kluwer); Anselin, L., Bera, A. K., Florax, R. and Yoon, M. J. 1996 Simple diagnostic tests for spatial dependence. Regional Science and Urban Economics, 26, 77–104.

See Also

lm

Examples

data(oldcol)
oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD)
summary(oldcrime.lm)
res <- lm.LMtests(oldcrime.lm, nb2listw(COL.nb), test=c("LMerr", "LMlag",
  "RLMerr", "RLMlag", "SARMA"))
summary(res)
lm.LMtests(oldcrime.lm, nb2listw(COL.nb))
lm.LMtests(residuals(oldcrime.lm), nb2listw(COL.nb))

Example output

Loading required package: sp
Loading required package: Matrix

Call:
lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)

Residuals:
    Min      1Q  Median      3Q     Max 
-34.418  -6.388  -1.580   9.052  28.649 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  68.6190     4.7355  14.490  < 2e-16 ***
HOVAL        -0.2739     0.1032  -2.654   0.0109 *  
INC          -1.5973     0.3341  -4.780 1.83e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 11.43 on 46 degrees of freedom
Multiple R-squared:  0.5524,	Adjusted R-squared:  0.5329 
F-statistic: 28.39 on 2 and 46 DF,  p-value: 9.341e-09

	Lagrange multiplier diagnostics for spatial dependence
data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb)
 
       statistic parameter  p.value   
LMerr   5.723131         1 0.016743 * 
LMlag   9.363684         1 0.002213 **
RLMerr  0.079495         1 0.777983   
RLMlag  3.720048         1 0.053763 . 
SARMA   9.443178         2 0.008901 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

	Lagrange multiplier diagnostics for spatial dependence

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb)

LMErr = 5.7231, df = 1, p-value = 0.01674


	Lagrange multiplier diagnostics for spatial dependence

data:  
residuals: residuals(oldcrime.lm)
weights: nb2listw(COL.nb)

LMErr = 5.7231, df = 1, p-value = 0.01674

spdep documentation built on Aug. 19, 2017, 3:01 a.m.