Calculate a spatial filter

This function builds a spatial filter by iteratively adding eigenvectors to a linear model. Only eigenvectors with a p-value below a threshold are retained and cumulatively added to the filter (default <= 0.05). The function can optionally divide the data by one or more categorical variables (e.g., mode, education level) and calculate separate filters for each subset. The result is a single data frame containing the identifier, the response variable, the computed filter, and the grouping columns (if any).

Usage

calculate_spatial_filter(
  spatial_data_frame,
  matrix_eigv,
  by = "ID",
  group_vars = NULL,
  response = "access",
  ev_prefix = "EV",
  threshold = 0.05
)

Arguments

spatial_data_frame

A data frame containing the spatial variable (response) and the identifier (join key). Must contain a column named by response and a column matching by (or the left side of by if it is named).

matrix_eigv

A data frame containing the eigenvectors (columns starting with ev_prefix) and an identifier (join key) matching the right side of by.

by

A character string or a named character vector of length 1 specifying the join key(s). If a single string, it is used as the column name in both tables. If named (e.g. c("ID" = "CTUID")), the name is the column in spatial_data_frame and the value is the column in matrix_eigv. Default: "ID".

group_vars

Optional character vector naming columns in spatial_data_frame by which to divide the data before computing the filter. For each unique combination of these variables, a separate filter is built. If NULL (default), a single filter is computed for all rows.

response

Character string naming the response (e.g., y, dependent) variable in spatial_data_frame. Default: "access".

ev_prefix

Character string giving the prefix of the eigenvector columns in matrix_eigv. Default: "EV".

threshold

Numeric p-value threshold for including an eigenvector in the filter (two-sided test). Default: 0.05.

Value

A data frame with the following columns:

• the identifier column (named as in by or its left side)

• the response variable (named response)

• the spatial filter, named Sf_<response>

• any grouping columns specified in group_vars (if provided)

The rows are in the same order as the original spatial_data_frame.

Details

The function performs a forward selection procedure:

1. Join spatial_data_frame with matrix_eigv on the specified key.

2. Initialize Sf = 0 and x = 1.

3. For each eigenvector (in the order they appear in the joined data), fit the model response ~ x + Sf + EV_i.

4. If the coefficient of EV_i has a p-value < threshold, add coef(EV_i) * EV_i to Sf.

5. Return a data frame with only the ID, response, filter, and groups.

The same procedure is applied independently to each group defined by group_vars, and the results are row-bound into a single data frame.

Note

The eigenvectors are assumed to have been pre-computed (e.g., from a spatial weights matrix).

References

This function is based on the study of Le Gallo, J., & Paez, A. (2013).

Le Gallo, J., & Paez, A. (2013). Using synthetic variables in instrumental variable estimation of spatial series models.. Environment and Planning A, 45(9), 2227-2242. doi:10.1068/a45443

Examples

if (FALSE) { # \dontrun{
# Single group (no splitting)
result_df <- calculate_spatial_filter(spatial_data_frame = my_access,
  matrix_eigv = eigen_matrix)

# Split by transportation mode (column "PwMode")
result_by_mode <- calculate_spatial_filter(spatial_data_frame = SA_mode,
  matrix_eigv = matrix_eigv,
  by = "PRCDDA",
  group_vars = "PwMode",
  response = "SA_im")

# Split by combination of education and mode
result_by_edu_mode <- calculate_spatial_filter(spatial_data_frame = my_data,
  matrix_eigv = eigen_matrix,
  by = c("CTUID" = "ID"),
  group_vars = c("Education", "Mode"),
  response = "SA_i",
  ev_prefix = "EIG",
  threshold = 0.10)
} # }