lm.LMtests | R Documentation |

The function reports the estimates of tests chosen among five statistics for
testing for spatial dependence in linear models. The statistics are
the simple RS test for error dependence (“RSerr”), the simple RS test
for a missing spatially lagged dependent variable (“RSlag”), variants
of these adjusted for the presence of the other (“adjRSerr”
tests for error dependence in the possible presence of a missing lagged
dependent variable, “adjRSlag” the other way round), and a portmanteau test
(“SARMA”, in fact “RSerr” + “adjRSlag”). Note: from spdep 1.3-2, the tests are re-named “RS” - Rao's score tests, rather than “LM” - Lagrange multiplier tests to match the naming of tests from the same family in `SDM.RStests`

.

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

`model` |
an object of class |

`listw` |
a |

`zero.policy` |
default |

`test` |
a character vector of tests requested chosen from RSerr, RSlag, adjRSerr, adjRSlag, 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 |

`naSubset` |
default TRUE to subset listw object for omitted observations in model object (this is a change from earlier behaviour, when the |

`x` , `object` |
object to be printed |

`p.adjust.method` |
a character string specifying the probability value adjustment (see |

`digits` |
minimum number of significant digits to be used for most numbers |

`...` |
printing arguments to be passed through |

The two types of dependence are for spatial lag `\rho`

and spatial error `\lambda`

:

```
\mathbf{y} = \mathbf{X \beta} + \rho \mathbf{W_{(1)} y} + \mathbf{u},
```

```
\mathbf{u} = \lambda \mathbf{W_{(2)} u} + \mathbf{e}
```

where `\mathbf{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 `\mathbf{u}`

test whether `\lambda = 0`

. `\mathbf{W}`

is a spatial weights matrix; for the tests used
here they are identical.

A list of class `RStestlist`

of `htest`

objects, each with:

`statistic` |
the value of the Rao's score (a.k.a 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. |

Roger Bivand Roger.Bivand@nhh.no and Andrew Bernat

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 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/0166-0462(95)02111-6")}; Malabika Koley (2024) Specification Testing under General Nesting Spatial Model, https://sites.google.com/view/malabikakoley/research.

`lm`

, `SD.RStests`

```
data(oldcol)
oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD)
summary(oldcrime.lm)
lw <- nb2listw(COL.nb)
res <- lm.RStests(oldcrime.lm, listw=lw, test="all")
summary(res)
if (require("spatialreg", quietly=TRUE)) {
oldcrime.slx <- lm(CRIME ~ HOVAL + INC, data = COL.OLD, listw=lw)
summary(lm.RStests(oldcrime.slx, listw=lw, test=c("adjRSerr", "adjRSlag")))
}
```

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