a symbolic description of the model to be fit, assuming a spatial error representation; when lagformula is given, it should include only the response and the intercept term

An extra one-sided formula to be used when a spatial lag representation is desired; the intercept is excluded within the function if present because it is part of the formula argument, but excluding it explicitly in the lagformula argument in the presence of factors generates a collinear model matrix

an optional data frame containing the variables in the model

an object of class nb

list of general weights corresponding to neighbours

style can take values W, B, C, U, and S

a function (default options("na.action")), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the spatial weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.

default NULL, use global option value; if FALSE stop with error for any empty neighbour sets, if TRUE permit the weights list to be formed with zero-length weights vectors

tolerance value for convergence of spatial filtering

eigenvectors with eigenvalues of an absolute value smaller than zerovalue will be excluded in eigenvector search

Set ExactEV=TRUE to use exact expectations and variances rather than the expectation and variance of Moran's I from the previous iteration, default FALSE

Should the spatial weights matrix be forced to symmetry, default TRUE

if not NULL, used instead of the tol= argument as a stopping rule to choose all eigenvectors up to and including the one with a probability value exceeding alpha.

a character string specifying the alternative hypothesis, must be one of greater, less or two.sided (default).

default NULL, use global option value; if TRUE report eigenvectors selected

a matrix summarising the selection of eigenvectors for inclusion, with columns:

Step

Step counter of the selection procedure

SelEvec

number of selected eigenvector (sorted descending)

Eval

its associated eigenvalue

MinMi

value Moran's I for residual autocorrelation

ZMinMi

standardized value of Moran's I assuming a normal approximation

pr(ZI)

probability value of the permutation-based standardized deviate for the given value of the alternative argument

R2

R\^2 of the model including exogenous variables and eigenvectors

gamma

regression coefficient of selected eigenvector in fit

The first row is the value at the start of the search

a matrix of the selected eigenvectors in order of selection