conleyreg {conleyreg}

Conley standard error estimations

Description

This function estimates ols, logit, probit, and poisson models with Conley standard errors.

Usage

conleyreg(
  formula,
  data,
  dist_cutoff,
  model = c("ols", "logit", "probit", "poisson"),
  unit = NULL,
  time = NULL,
  lat = NULL,
  lon = NULL,
  kernel = c("bartlett", "uniform"),
  lag_cutoff = 0,
  intercept = TRUE,
  verbose = TRUE,
  ncores = NULL,
  par_dim = c("cross-section", "time", "r", "cpp"),
  dist_comp = NULL,
  crs = NULL,
  st_distance = FALSE,
  dist_which = NULL,
  sparse = FALSE,
  batch = TRUE,
  batch_ram_opt = NULL,
  float = FALSE,
  rowwise = FALSE,
  reg_ram_opt = FALSE,
  dist_mat = NULL,
  dist_mat_conv = TRUE,
  vcov = FALSE,
  gof = FALSE
)

Arguments

formula

regression equation as formula or character string. Avoid interactions and transformations inside the equation. I.e. use y ~ x1 + x1_2, data = dplyr::mutate(data, x1_2 = x1^2) instead of y ~ x1 + x1^2, data = data).

data

input data. Either (i) in non-spatial data frame format (includes tibbles and data tables) with columns denoting coordinates or (ii) in sf format. In case of an sf object, all non-point geometry types are converted to spatial points, based on the feature's centroid. When using a non-spatial data frame format with projected, i.e. non-longlat, coordinates, crs must be specified. Note that the projection can influence the computed distances, which is a general phenomenon in GIS software and not specific to conleyreg. The computationally fastest option is to use a data table with coordinates in the crs in which the distances are to be derived (longlat for spherical and projected for planar), and with time and unit set as keys in the panel case. An sf object as input is the slowest option.

dist_cutoff

the distance cutoff in km

model

the applied model. Either "ols" (default), "logit", "probit" or "poisson". "logit", "probit", and "poisson" are currently restricted to cross-sectional applications.

unit

the variable identifying the cross-sectional dimension. Only needs to be specified, if data is not cross-sectional. Assumes that units do not change their location over time.

time

the variable identifying the time dimension. Only needs to be specified, if data is not cross-sectional.

lat

the variable specifying the latitude

lon

the variable specifying the longitude

kernel

the kernel applied within the radius. Either "bartlett" (default) or "uniform".

lag_cutoff

the cutoff along the time dimension. Defaults to 0, meaning that standard errors are only adjusted cross-sectionally.

intercept

logical specifying whether to include an intercept. Defaults to TRUE. Fixed effects models omit the intercept automatically.

verbose

logical specifying whether to print messages on intermediate estimation steps. Defaults to TRUE.

ncores

the number of CPU cores to use in the estimations. Defaults to the machine's number of CPUs.

par_dim

the dimension along which the function parallelizes in panel applications. Can be set to "cross-section" (default) or "time". With the former option, the function parallelizes the spatial correlation code in C++ using OpenMP and the serial correlation part in R using the parallel package. With the latter option, it is the other way around. Use "r" and "cpp" to define parallelization based on the language rather than the dimension. Some MAC users do not have access to OpenMP by default. par_dim is then always set to "r". Thus, depending on the application, the function can be notably faster on Windows and Linux than on MACs.

dist_comp

choice between "spherical" and "planar" distance computations. When unspecified, the input data determines the method: longlat uses spherical (Haversine) distances, alternatives (projected data) use planar (Euclidean) distances. When inserting projected data but specifying dist_comp = "spherical", the data is transformed to longlat. Combining unprojected data with dist_comp = "planar" transforms the data to an azimuthal equidistant format centered at the data's centroid.

crs

the coordinate reference system, if the data is projected. Object of class crs or input string to sf::st_crs. This parameter can be omitted, if the data is in longlat format (EPSG: 4326), i.e. not projected. If the projection does not use meters as units, this function converts to units to meters.

st_distance

logical specifying whether distances should be computed via sf::st_distance (TRUE) or via conleyreg's internal, computationally optimized distance functions (FALSE). The default (FALSE) produces the same distances as sf::st_distance does with S2 enabled. I.e. it uses Haversine (great circle) distances for longlat data and Euclidean distances otherwise. Cases in which you might want to set this argument to TRUE are e.g. when you want enforce the GEOS approach to computing distances or when you are using an peculiar projection, for which the sf package might include further procedures. Cross-sectional parallelization is not available when st_distance = TRUE and the function automatically switches to parallelization along the time dimension, if the data is a panel and ncores != 1. Third and fourth dimensions, termed Z and M in sf, are not accounted for in any case. Note that sf::st_distance is considerably slower than conleyreg's internal distance functions.

dist_which

the type of distance to use when st_distance = TRUE. If unspecified, the function defaults to great circle distances for longlat data and to Euclidean distances otherwise. See sf::st_distance for options.

sparse

logical specifying whether to use sparse rather than dense (regular) matrices in distance computations. Defaults to FALSE. Only has an effect when st_distance = FALSE. Sparse matrices are more efficient than dense matrices, when the distance matrix has a lot of zeros arising from points located outside the respective dist_cutoff. It is recommended to keep the default unless the machine is unable to allocate enough memory.

batch

logical specifying whether distances are inserted into a sparse matrix element by element (FALSE) or all at once as a batch (TRUE). Defaults to TRUE. This argument only has an effect when st_distance = FALSE and sparse = TRUE. Batch insertion is faster than element-wise insertion, but requires more memory.

batch_ram_opt

the degree to which batch insertion should be optimized for RAM usage. Can be set to one out of the three levels: "none", "moderate" (default), and "heavy". Higher levels imply lower RAM usage, but also lower speeds.

float

logical specifying whether distance matrices should use the float (TRUE) rather than the double (FALSE) data type. Floats are less precise and than doubles and thereby occupy less space than doubles do. They should only be used when the machine's RAM is insufficient for both the dense and the sparse matrix cases, as they affect the precision of distance values. The float option only has an effect in Bartlett kernel cases because uniform kernel applications store the data in a smaller integer data type.

rowwise

logical specifying whether to store individual rows of the distance matrix only, instead of the full matrix. If TRUE, the function uses these rows directly in the standard error correction. This option's advantage is that it induces the function to store only N x ncores cells, instead of the full N x N matrix, lowering RAM requirements. The disadvantage is that the function needs to compute twice as many distance values as in the default case (FALSE), since the symmetry of the matrix is not utilized. It hence sacrifices speed for lower RAM utilization. This parameter only has an effect in cross-sectional and unbalanced panel applications with st_distance = FALSE and sparse = FALSE.

reg_ram_opt

logical specifying whether the regression should be optimized for RAM usage. Defaults to FALSE. Changing it to TRUE slows down the function. This argument only affects the baseline estimation, not the standard error correction.

dist_mat

a distance matrix. Pre-computing a distance matrix and passing it to this argument is only more efficient than having conleyreg derive it, if you execute conleyreg multiple times with the same input data. In that case, it is recommended to compute the distance matrix via dist_mat, which is optimized for this purpose and also evaluates various other steps that are identical across regressions on the same input data. Generally, you must not modify the input data between deriving the distance matrix and running conleyreg. That includes dropping observations or changing values of the unit, time, or coordinate variables. In cross-sectional settings, you must not re-order rows either. If you compute distances through a function other than dist_mat, there are a few additional issues to account for. (i) In the panel scenario, you must order observations by time and unit in ascending order. I.e. cells [1, 2] and [2, 1] of the distance matrix must refer to the distance between unit 1 and unit 2, cells [2, 3] and [3, 2] to the distance between unit 2 and unit 3 etc. The unit numbers in this example refer to their rank when they are sorted. (ii) dist_cutoff does not refer to kilometers, but to the units of the matrix. (iii) While in a balanced panel you only enter one matrix that is applied to all periods, you supply distances as a list of matrices in the unbalanced case. The matrices must be sorted, with the first list element containing the first period's distance matrix etc. (iv) Zeros in sparse matrices are interpreted as values above the distance cutoff and NaN values are interpreted as zeros. (v) The matrices in the list must all be of the same type - all dense or all sparse. (vi) Distance matrices must only contain non-missing, finite numbers (and NaN in the case of sparse matrices).

dist_mat_conv

logical specifying whether to convert the distance matrix to a list, if the panel turns out to be unbalanced because of missing values. This setting is only relevant, if you enter a balanced panel's distance matrix not derived via dist_mat. If TRUE (the default), the function only drops rows with missing values. If FALSE, the function maintains the panel's balanced character by dropping units with missing values in at least one period from the entire data set.

vcov

logical specifying whether to return variance-covariance matrix (TRUE) rather than the default lmtest::coeftest matrix of coefficient estimates and standard errors (FALSE).

gof

logical specifying whether to return goodness of fit measures. Defaults to FALSE. If TRUE, the function produces a list.

Details

This code is an extension and modification of earlier Conley standard error implementations by (i) Richard Bluhm, (ii) Luis Calderon and Leander Heldring, (iii) Darin Christensen and Thiemo Fetzer, and (iv) Timothy Conley. Results vary across implementations because of different distance functions and buffer shapes.

This function has reasonable defaults. If your machine has insufficent RAM to allocate the default dense matrices, try sparse matrices. If the RAM error persists, try setting a lower dist_cutoff, use floats, select a uniform kernel, experiment with batch_ram_opt, reg_ram_opt, or batch.

Consult the vignette, vignette("conleyreg_introduction", "conleyreg"), for a more extensive discussion.

Value

Returns a lmtest::coeftest matrix of coefficient estimates and standard errors by default. Can be changed to the variance-covariance matrix by specifying vcov = TRUE. ⁠ ⁠

References

Calderon L, Heldring L (2020). “Spatial standard errors for several commonly used M-estimators.” Mimeo.

Conley TG (1999). “GMM estimation with cross sectional dependence.” Journal of Econometrics, 92(1), 1-45.

Conley TG (2008). “Spatial Econometrics.” In Durlauf SN, Blume LE (eds.), Microeconometrics, 303-313. London: Palgrave Macmillan.

Examples

## Not run: 
# Generate cross-sectional example data
data <- rnd_locations(100, output_type = "data.frame")
data$y <- sample(c(0, 1), 100, replace = TRUE)
data$x1 <- stats::runif(100, -50, 50)

# Estimate ols model with Conley standard errors using a 1000 km radius
conleyreg(y ~ x1, data, 1000, lat = "lat", lon = "lon")

# Estimate logit model
conleyreg(y ~ x1, data, 1000, "logit", lat = "lat", lon = "lon")

# Estimate ols model with fixed effects
data$x2 <- sample(1:5, 100, replace = TRUE)
conleyreg(y ~ x1 | x2, data, 1000, lat = "lat", lon = "lon")

# Estimate ols model using panel data
data$time <- rep(1:10, each = 10)
data$unit <- rep(1:10, times = 10)
conleyreg(y ~ x1, data, 1000, unit = "unit", time = "time", lat = "lat", lon = "lon")

# Estimate same model with an sf object of another projection as input
data <- sf::st_as_sf(data, coords = c("lon", "lat"), crs = 4326) |>
  sf::st_transform(crs = "+proj=aeqd")
conleyreg(y ~ x1, data, 1000)

## End(Not run)