Type: Package
Title: Spatial-X (SLX) Models for Applied Researchers
Version: 0.1.1
Description: Tools for estimating, interpreting, and visualizing Spatial-X (SLX) regression models. Provides a formula-based interface with first-class support for variable-specific weights matrices, higher-order spatial lags, temporally-lagged spatial variables (TSLS), and tidy effects decomposition (direct, indirect, total). Designed to lower the barrier to SLX modeling for applied researchers who already work with 'sf' and 'lm'-style formulas. Methods follow Wimpy, Whitten, and Williams (2021) <doi:10.1086/710089>.
License: MIT + file LICENSE
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.3.3
Depends: R (≥ 4.1.0)
Imports: spdep, sf, Matrix, tibble, stats, generics, rlang
Suggests: ggplot2, modelsummary, broom, knitr, rmarkdown, testthat (≥ 3.0.0), dplyr, tidyr, haven
Config/testthat/edition: 3
VignetteBuilder: knitr
URL: https://github.com/cwimpy/slxr
BugReports: https://github.com/cwimpy/slxr/issues
NeedsCompilation: no
Packaged: 2026-04-20 21:41:04 UTC; cwimpy
Author: Cameron Wimpy ORCID iD [aut, cre]
Maintainer: Cameron Wimpy <cwimpy@astate.edu>
Repository: CRAN
Date/Publication: 2026-04-22 13:10:02 UTC

slxr: Spatial-X (SLX) Models for Applied Researchers

Description

Tools for estimating, interpreting, and visualizing Spatial-X regression models, with first-class support for variable-specific weights matrices, higher-order spatial lags, and temporally-lagged spatial variables.

Author(s)

Maintainer: Cameron Wimpy cwimpy@astate.edu (ORCID)

See Also

Useful links:

Defense burden data, 1995 cross-section

Description

A 179-country cross-section of defense spending and conflict indicators for 1995, drawn from the replication archive of Wimpy, Whitten, and Williams (2021). Three row-standardized spatial weights matrices connect the units through different channels: contiguity, alliance, and defense pact.

Usage

defense_burden

Format

A named list with four elements:

data

A tibble with 179 rows and 12 variables, arranged by Correlates of War country code (ccode). Variables:

  • ccode - Correlates of War country code.

  • year - Calendar year (1995).

  • ch_milex - Change in military expenditures (outcome).

  • milex_tm1 - Lagged military expenditures.

  • log_pop_tm1 - Lagged log population.

  • civilwar_tm1 - Lagged civil war indicator.

  • total_wars_tm1 - Lagged count of interstate wars.

  • alliance_us - Alliance with the United States.

  • ch_milex_us - Change in U.S. military expenditures.

  • ch_milex_ussr - Change in Soviet/Russian military expenditures.

  • region - Integer region code (1-5).

  • region_name - Factor: Europe, N Africa/Middle East, Africa, Asia/Oceania, Americas.

W_contig

A 179 x 179 row-standardized sparse dgCMatrix encoding geographic contiguity.

W_alliance

A 179 x 179 row-standardized sparse dgCMatrix encoding alliance ties.

W_defense

A 179 x 179 row-standardized sparse dgCMatrix encoding mutual defense pacts.

Details

This cross-section is intended for pedagogical demonstration of variable-specific SLX specifications. The original paper estimates a pooled panel SLX across 1950-2008 with year-specific weights matrices; that full-panel replication requires block-diagonal W support, which is planned for slxr v0.2.

Source

Wimpy, Whitten, and Williams (2021) replication archive, Journal of Politics Dataverse. doi:10.1086/710089

References

Wimpy, C., Whitten, G. D., & Williams, L. K. (2021). X Marks the Spot: Unlocking the Treasure of Spatial-X Models. Journal of Politics, 83(2), 722-739.

Examples

data(defense_burden)
dim(defense_burden$data)
dim(defense_burden$W_contig)

Defense burden panel, 1951-2008

Description

The full country-year panel underlying Wimpy, Whitten, and Williams (2021) Table 3, Model 3. Includes a tibble of 7,661 country-year observations and three named lists of row-standardized sparse weights matrices, one matrix per year, encoding contiguity, alliance, and defense-pact connections.

Usage

defense_burden_panel

Format

A named list:

data

A tibble with 7,661 rows and the same 12 columns as defense_burden⁠$data⁠, but spanning 1951-2008.

W_contig

Named list of 58 sparse matrices, one per year, keyed by year as a string. Each matrix is row-standardized and contains the countries observed in that year.

W_alliance

As above, for alliance ties.

W_defense

As above, for mutual defense pacts.

Details

Sample excludes observations with missing covariates. Panel is unbalanced: between 63 and 187 countries per year.

Source

Wimpy, Whitten, and Williams (2021) replication archive, Journal of Politics Dataverse. doi:10.1086/710089

See Also

defense_burden for the 1995 cross-section.

Examples

data(defense_burden_panel)
names(defense_burden_panel$W_contig)[1:5]
dim(defense_burden_panel$W_contig[["1990"]])

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

generics

glance, tidy

Fit a Spatial-X (SLX) model

Description

Estimates a Spatial-X regression of the form

y = X\beta + WX\theta + \varepsilon,

where W is a spatial weights matrix and X includes both the directly-entering regressors and a user-specified subset that is spatially lagged. SLX estimation is OLS on the augmented design matrix, which makes estimation, interpretation, and effects decomposition much simpler than for SAR-family models (Wimpy, Whitten, and Williams 2021).

Usage

slx(
  formula,
  data,
  W = NULL,
  lag = NULL,
  order = 1L,
  spatial = NULL,
  time_lag = 0L,
  id = NULL,
  time = NULL,
  na.action = stats::na.omit
)

Arguments

formula

A standard model formula, e.g. y ~ x1 + x2 + x3.

data

A data frame (or sf object) whose rows correspond, in order, to the rows/columns of W (cross-sectional mode) or contain id and time columns (panel mode).

W

An slx_W object produced by slx_weights(), a numeric or sparse matrix, or - in panel mode - a named list of such objects keyed by time value. Required when spatial is not supplied.

lag

Character vector of variable names from formula that should be spatially lagged. If NULL (default) and W is supplied, all right-hand-side variables are lagged.

order

Integer vector giving the orders of W to include for each lagged variable (e.g. 1:2 adds both Wx and ⁠W^2 x⁠). Default 1.

spatial

Optional named list for variable-specific weights matrices. Names must match variables in formula. Each element is either an slx_W, a list of slx_Ws (multiple channels for one variable), a time-keyed list of slx_Ws (single channel, time- varying), or a named list of channels whose values are themselves single or time-keyed slx_Ws.

time_lag

Integer, number of time periods to lag the spatial terms (TSLS). Requires id and time. Default 0.

id, time

Column names identifying the panel unit and period. Required for panel mode or TSLS. time must be numeric.

na.action

How to handle missing values. Defaults to stats::na.omit in cross-sectional mode. In panel mode missing values on formula variables are dropped; id and time must never be missing.

Value

An object of class slx with elements:

fit

The underlying lm object.

formula

The expanded model formula.

call

The original call.

W

The weights matrix (or list thereof) used.

lag_terms

A data frame mapping spatial-lag terms to their source variable, W matrix, order, and time lag.

data

The (possibly augmented) model frame.

panel

Logical flag.

Cross-sectional and panel modes

When id and time are NULL, slx() treats the data as a single cross-section: rows of data must correspond, in order, to the rows and columns of W. When both id and time are supplied, slx() enters panel mode and performs block-wise spatial lagging period by period. In panel mode the weights matrices must have dimnames matching the unit identifiers in data[[id]]; the same units need not appear in every period (unbalanced panels are supported).

Time-varying weights

In panel mode, a W argument can be either (a) a single slx_W object applied to every period or (b) a named list of slx_W objects keyed by the stringified time value (e.g. list("1990" = W_90, "1991" = W_91)). The same options apply to any entry inside spatial.

Temporally-lagged spatial lag (TSLS)

The time_lag argument implements equation 7 of Wimpy, Whitten, and Williams (2021): it lags every constructed spatial term ⁠W_t x⁠ by time_lag periods within each unit so that the regressor becomes ⁠W_t x_{t - time_lag}⁠. The first time_lag periods per unit drop out, mirroring any temporally-lagged variable.

References

Wimpy, C., Whitten, G. D., & Williams, L. K. (2021). X Marks the Spot: Unlocking the Treasure of Spatial-X Models. Journal of Politics, 83(2), 722-739.

Vega, S. H., & Elhorst, J. P. (2015). The SLX Model. Journal of Regional Science, 55(3), 339-363.

Examples

data(defense_burden)
W_c <- slx_weights(style = "custom", matrix = defense_burden$W_contig,
                   row_standardize = FALSE)
fit <- slx(ch_milex ~ milex_tm1 + log_pop_tm1 + civilwar_tm1,
           data = defense_burden$data, W = W_c, lag = "civilwar_tm1")
slx_effects(fit)

Tidy and glance methods for SLX models

Description

These methods make slx objects compatible with the broom and modelsummary ecosystems.

Usage

## S3 method for class 'slx'
tidy(x, conf.int = FALSE, conf.level = 0.95, ...)

## S3 method for class 'slx'
glance(x, ...)

Arguments

x

An slx object.

conf.int

Logical; include confidence intervals?

conf.level

Confidence level.

...

Unused.

Value

tidy.slx() returns a tibble::tibble() with one row per model coefficient (both direct and spatial-lag terms) and columns term, estimate, std.error, statistic, and p.value. When conf.int = TRUE, conf.low and conf.high columns are added.

glance.slx() returns a one-row tibble::tibble() summarizing the overall fit, with columns r.squared, adj.r.squared, sigma, statistic (F statistic), df, df.residual, nobs, and n_lag_terms (the number of spatial-lag regressors in the model).

Examples

data(defense_burden)
W <- slx_weights(style = "custom", matrix = defense_burden$W_contig,
                 row_standardize = FALSE)
fit <- slx(ch_milex ~ milex_tm1 + civilwar_tm1,
           data = defense_burden$data, W = W, lag = "civilwar_tm1")
tidy(fit)
glance(fit)

Compare OLS, SLX, and other lm-like models side by side

Description

Builds a tidy tibble of fit statistics (observations, coefficient count, R-squared, adjusted R-squared, residual standard error, AIC, BIC) for any combination of lm and slx objects. If a weights matrix is supplied, also reports Moran's I on each model's residuals - the standard diagnostic for spatial autocorrelation left unexplained by the fitted model.

Usage

slx_compare(..., W = NULL)

Arguments

...

Named lm or slx models. Names are used as the model labels in the output.

W

Optional weights matrix to use for Moran's I on residuals. Accepts an slx_W, a listw object from spdep, or NULL to skip the test. In panel mode, supply a list keyed by time value.

Value

A tibble with one row per model.

Examples

data(defense_burden)
W <- slx_weights(style = "custom", matrix = defense_burden$W_contig,
                 row_standardize = FALSE)
ols <- lm(ch_milex ~ milex_tm1 + civilwar_tm1,
          data = defense_burden$data)
slx_fit <- slx(ch_milex ~ milex_tm1 + civilwar_tm1,
               data = defense_burden$data, W = W,
               lag = "civilwar_tm1")
slx_compare(OLS = ols, SLX = slx_fit, W = W)

Direct, indirect, and total effects from an SLX model

Description

For an SLX model the effects decomposition is trivial — no matrix inversion, no simulation. For each variable x that enters both directly and as a spatial lag, the direct effect is its OLS coefficient \hat\beta and the indirect effect at order k is \hat\theta_k. Standard errors come straight from vcov().

Usage

slx_effects(object, by_order = FALSE, conf.level = 0.95)

Arguments

object

An slx object returned by slx().

by_order

Logical; if TRUE, report indirect effects separately by order of W. Default FALSE sums across orders for a single indirect effect per variable–W combination.

conf.level

Confidence level for reported intervals. Default 0.95.

Value

A tibble with columns variable, w_name, order (when by_order = TRUE), type (direct/indirect/total), estimate, std.error, conf.low, conf.high, p.value.

Examples

data(defense_burden)
W <- slx_weights(style = "custom", matrix = defense_burden$W_contig,
                 row_standardize = FALSE)
fit <- slx(ch_milex ~ milex_tm1 + civilwar_tm1,
           data = defense_burden$data, W = W, lag = "civilwar_tm1")
slx_effects(fit)

Heatmap of a spatial weights matrix

Description

A quick visual check on the structure of a weights matrix. For large n the heatmap becomes noisy; use the max_n argument to subsample.

Usage

slx_plot_W(W, max_n = NULL, labels = NULL)

Arguments

W

An slx_W object.

max_n

Optional integer; if nrow(W) > max_n, a random sample of rows/columns is plotted. Default NULL (plot everything).

labels

Optional character vector of row/column labels.

Value

A ggplot object.

Plot how indirect effects decay across orders of W

Description

For SLX models fit with higher-order lags (order = 1:k), shows the size of the indirect effect at each order, with confidence intervals.

Usage

slx_plot_decay(fit, variables = NULL, conf.level = 0.95)

Arguments

fit

An slx model fit with higher-order W terms.

variables

Optional character vector restricting to specific lagged variables. Default plots all.

conf.level

Confidence level.

Value

A ggplot object.

Coefficient plot of direct, indirect, and total effects

Description

Produces a ggplot of the direct, indirect, and total effects from an SLX model, with 95% confidence intervals. For models with variable-specific weights matrices, effects are faceted by w_name so spillover patterns from each matrix are visible side-by-side.

Usage

slx_plot_effects(
  fit,
  types = c("direct", "indirect", "total"),
  conf.level = 0.95,
  by_order = FALSE,
  ...
)

Arguments

fit

An slx object returned by slx().

types

Character vector of effect types to include. Any subset of c("direct", "indirect", "total"). Default shows all three.

conf.level

Confidence level for the intervals. Default 0.95.

by_order

Logical; if TRUE, break indirect effects out by order of W. Default FALSE.

...

Passed to slx_effects().

Value

A ggplot object.

Examples

data(defense_burden)
W <- slx_weights(style = "custom", matrix = defense_burden$W_contig,
                 row_standardize = FALSE)
fit <- slx(ch_milex ~ milex_tm1 + civilwar_tm1,
           data = defense_burden$data, W = W, lag = "civilwar_tm1")
slx_plot_effects(fit)

Counterfactual shock plot

Description

Given a fitted SLX model, a choice of variable, and a target unit, returns a plot of the predicted change in the outcome across every unit in the sample under a unit shock to that variable in the target unit.

Usage

slx_plot_shock(fit, variable, unit, magnitude = 1, geom = NULL, top_n = 15)

Arguments

fit

A cross-sectional slx model. Panel shocks are planned for a future release.

variable

Character, the name of a spatially-lagged regressor in fit to shock.

unit

Integer row index (or character id, if the weights matrix has dimnames matching something in fit$data) of the unit receiving the shock.

magnitude

Numeric, shock size. Default 1.

geom

Optional sf object with nrow(geom) == fit$n aligned to fit$data. If supplied, the function returns a map.

top_n

For the non-map plot, how many non-zero indirect effects to show. Default 15.

Details

For an SLX model at first order with channels indexed by c, the predicted change at unit j from a shock of size magnitude to variable x in unit i is

\text{magnitude}\ \left(\beta\ \mathbb{1}\{j=i\} + \sum_c \theta_c\ W_c[j, i]\right).

Higher-order lags add additional ⁠theta_{c,k} (W_c^k)[j, i]⁠ terms. No simulation is required: the shock effect is a single column of the spatial multiplier.

If an sf object with matching row count is supplied via geom, the result is drawn as a choropleth. Otherwise a horizontal bar of the largest effects is returned.

Value

A ggplot object.

Examples

data(defense_burden)
W_c <- slx_weights(style = "custom", matrix = defense_burden$W_contig,
                   row_standardize = FALSE)
fit <- slx(ch_milex ~ milex_tm1 + civilwar_tm1,
           data = defense_burden$data, W = W_c,
           lag = "civilwar_tm1")
slx_plot_shock(fit, variable = "civilwar_tm1", unit = 1)

Sensitivity across alternative weights matrices

Description

Stub - v0.2. Planned: refit an SLX model across a list of alternative W specifications and return a tidy comparison of key effects.

Usage

slx_sensitivity(fit, W_list)

Arguments

fit

An slx model.

W_list

A named list of slx_W objects.

Value

Not yet implemented; currently called only for its side effect of signalling an error. A future release will return a tibble::tibble() comparing key effect estimates across alternative weights matrices.

Construct a spatial weights matrix

Description

A thin, opinionated wrapper around common spdep weights constructors. Returns a standardized slx_W object that carries both the sparse matrix and the listw form used by downstream routines.

Usage

slx_weights(
  x = NULL,
  style = c("contiguity", "rook", "knn", "distance", "custom"),
  k = 5,
  threshold = NULL,
  row_standardize = TRUE,
  matrix = NULL,
  ...
)

Arguments

x

An sf object (for "contiguity", "knn", "distance"), a matrix of coordinates, or a raw numeric/sparse matrix (for "custom").

style

Weights style. One of "contiguity" (queen), "rook", "knn", "distance", or "custom".

k

Number of neighbors for style = "knn".

threshold

Distance threshold for style = "distance" (units of the coordinate system).

row_standardize

Logical; row-standardize the matrix? Default TRUE. The paper notes row-standardization is a theoretical choice; set to FALSE when connection count should itself carry weight.

matrix

A numeric or sparse Matrix for style = "custom".

...

Passed to the underlying spdep constructor.

Value

An object of class slx_W with elements W (sparse matrix), listw (spdep listw object), style, and row_standardized.

Examples

# Custom weights matrix from bundled data
data(defense_burden)
W <- slx_weights(style = "custom", matrix = defense_burden$W_contig,
                 row_standardize = FALSE)
W


# Contiguity weights from an sf polygon layer
if (requireNamespace("sf", quietly = TRUE) &&
    requireNamespace("spdep", quietly = TRUE)) {
  nc <- sf::st_read(system.file("shape/nc.shp", package = "sf"),
                    quiet = TRUE)
  W_nc <- slx_weights(nc, style = "contiguity")
  W_nc
}