Spatial heteroscedasticity test¶

Source: R/modern_diagnostics.R · Help: ?performSpatialHeteroTest

Evaluates spatial clustering in squared residuals using Moran's I with a permutation reference distribution. Significant positive autocorrelation in the squared residuals is evidence of spatially varying variance.

Usage¶

performSpatialHeteroTest(
  model,
  data = NULL,
  listw,
  permutations = 999,
  zero.policy = NULL
)

Arguments¶

model: A fitted stats::lm object describing the mean structure whose residual variance is to be assessed.
data: The data frame model was fitted to, or NULL, the default. The residuals and weights are read from the fit itself, so a model that transforms its variables, has an offset() term, or takes its weights or offset from a column of the data needs no data, and the model frame of model is accepted as data (since 0.16.0; before, such models needed data). The test reads no column of data, and listw is matched to the observations of the fit, not to the rows of data. Data that are given are matched to the observations of the fit: rows with row names of their own by name, in any order; rows that only number themselves (a tibble, a data.table, a data frame whose row names were reset) by the row numbers of the fit, or in the order of the fit when they hold one row per observation. The rows the fit dropped may be there or not. Data whose rows cannot be shown to hold the observations of the fit are refused; see test_results.
listw: Spatial weights in spdep listw format or a numeric matrix coercible via spdep::mat2listw(). They list the observations of the fit, one per residual, in the order of the rows model was fitted to after subset and after na.omit dropped incomplete rows, whatever the order of data, as before 0.16.0.
permutations: Number of Monte Carlo permutations used to compute the reference distribution. Defaults to 999, the default of every resampling test in the package since 0.15.0; it was 499 before.
zero.policy: Logical flag forwarded to the spatial diagnostic to permit islands with no neighbours.

Value¶

An htest result with Moran's I statistic applied to squared residuals.

Supported models¶

It accepts an lm and a glm with the Gaussian family and the identity link, unweighted or with positive weights, a fitWLS() fit and, since 0.16.0, a rank-deficient fit, which it tests on the estimable part of its design: it gives the value of the same model fitted without the aliased columns. It refuses a glm of another family or link, a survey::svyglm() fit, a fit with a zero weight, a coefficient that is not finite for another reason, and data that lack rows or variables of the fit. It refuses a multivariate lm ("needs a model with one response"), since 0.16.0; before, it stopped with a coercion error. An mgcv::gam() fit is tested as before 0.16.0, with penalised smooth terms too: the test reads its residuals and does not fit it again, so it does not take them for least-squares residuals (decision 37 of the design of the model context). Which model each test accepts, and why, is set out in test_results, under Supported models.

References¶

Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer.

Bivand, R. S., Pebesma, E., & Gómez-Rubio, V. (2013). Applied Spatial Data Analysis with R (2nd ed.). Springer.

Examples¶

if (requireNamespace("spdep", quietly = TRUE)) {
  data(mtcars)
  coords <- cbind(runif(nrow(mtcars)), runif(nrow(mtcars)))
  nb <- spdep::knn2nb(spdep::knearneigh(coords, k = 4))
  lw <- spdep::nb2listw(nb)
  model <- lm(mpg ~ wt + hp, data = mtcars)
  performSpatialHeteroTest(model, mtcars, listw = lw, permutations = 199)
}