Description Usage Arguments Details Value References See Also Examples

This function implements the eigenvector-based semiparametric spatial filtering approach in a linear regression framework using ordinary least squares (OLS). Eigenvectors are selected by an unsupervised stepwise regression technique. Supported selection criteria are the minimization of residual autocorrelation, maximization of model fit, significance of residual autocorrelation, and the statistical significance of eigenvectors. Alternatively, all eigenvectors in the candidate set can be included as well.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 |

`y` |
response variable |

`x` |
vector/ matrix of regressors (default = NULL) |

`W` |
spatial connectivity matrix |

`objfn` |
the objective function to be used for eigenvector selection. Possible criteria are: the maximization of the adjusted R-squared ('R2'), minimization of residual autocorrelation ('MI'), significance level of candidate eigenvectors ('p'), significance of residual spatial autocorrelation ('pMI') or all eigenvectors in the candidate set ('all') |

`MX` |
covariates used to construct the projection matrix (default = NULL) - see Details |

`sig` |
significance level to be used for eigenvector selection
if |

`bonferroni` |
Bonferroni adjustment for the significance level
(TRUE/ FALSE) if |

`positive` |
restrict search to eigenvectors associated with positive levels of spatial autocorrelation (TRUE/ FALSE) |

`ideal.setsize` |
if |

`alpha` |
a value in (0,1] indicating the range of candidate eigenvectors according to their associated level of spatial autocorrelation, see e.g., Griffith (2003) |

`tol` |
if |

`boot.MI` |
number of iterations used to estimate the variance of Moran's I.
If |

`na.rm` |
remove observations with missing values (TRUE/ FALSE) |

`object` |
an object of class |

`EV` |
display summary statistics for selected eigenvectors (TRUE/ FALSE) |

`...` |
additional arguments |

If * W* is not symmetric, it gets symmetrized by
1/2 * (

If covariates are supplied to `MX`

, the function uses these regressors
to construct the following projection matrix:

**M** = **I** - **X** (**X**'**X**)^-1**X**'

Eigenvectors from * MWM* using this specification of

`MX`

. Alternatively, if `MX = NULL`

, the
projection matrix becomes The Bonferroni correction is only possible if eigenvector selection is based on
the significance level of the eigenvectors (`objfn = 'p'`

). It is set to
FALSE if eigenvectors are added to the model until the residuals exhibit no
significant level of spatial autocorrelation (`objfn = 'pMI'`

).

An object of class `spfilter`

containing the following
information:

`estimates`

summary statistics of the parameter estimates

`varcovar`

estimated variance-covariance matrix

`EV`

a matrix containing the summary statistics of selected eigenvectors

`selvecs`

vector/ matrix of selected eigenvectors

`evMI`

Moran coefficient of all eigenvectors

`moran`

residual autocorrelation in the initial and the filtered model

`fit`

adjusted R-squared of the initial and the filtered model

`residuals`

initial and filtered model residuals

`other`

a list providing supplementary information:

`ncandidates`

number of candidate eigenvectors considered

`nev`

number of selected eigenvectors

`sel_id`

ID of selected eigenvectors

`sf`

vector representing the spatial filter

`sfMI`

Moran coefficient of the spatial filter

`model`

type of the fitted regression model

`dependence`

filtered for positive or negative spatial dependence

`objfn`

selection criterion specified in the objective function of the stepwise regression procedure

`bonferroni`

TRUE/ FALSE: Bonferroni-adjusted significance level (if

`objfn = 'p'`

)`siglevel`

if

`objfn = 'p'`

or`objfn = 'pMI'`

: actual (unadjusted/ adjusted) significance level

Tiefelsdorf, Michael and Daniel A. Griffith (2007): Semiparametric filtering of spatial autocorrelation: the eigenvector approach. Environment and Planning A: Economy and Space, 39 (5): pp. 1193 - 1221.

Griffith, Daniel A. (2003): Spatial Autocorrelation and Spatial Filtering: Gaining Understanding Through Theory and Scientific Visualization. Berlin/ Heidelberg, Springer.

Chun, Yongwan, Daniel A. Griffith, Monghyeon Lee, Parmanand Sinha (2016): Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters. Journal of Geographical Systems, 18, pp. 67 – 85.

Le Gallo, Julie and Antonio Páez (2013): Using synthetic variables in instrumental variable estimation of spatial series models. Environment and Planning A: Economy and Space, 45 (9): pp. 2227 - 2242.

Tiefelsdorf, Michael and Barry Boots (1995): The Exact Distribution of Moran's I. Environment and Planning A: Economy and Space, 27 (6): pp. 985 - 999.

1 2 3 4 5 6 7 8 9 10 11 | ```
data(fakedata)
y <- fakedataset$x1
X <- cbind(fakedataset$x2, fakedataset$x3, fakedataset$x4)
res <- lmFilter(y = y, x = X, W = W, objfn = 'MI', positive = FALSE)
print(res)
summary(res, EV = TRUE)
E <- res$selvecs
(ols <- coef(lm(y ~ X + E)))
coef(res)
``` |

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