Type: Package
Title: Bayesian Spatial Regression Models
Version: 0.0.2
Date: 2022-02-25
Author: Nikolas Kuschnig ORCID iD [aut, cre]
Maintainer: Nikolas Kuschnig <nikolas.kuschnig@wu.ac.at>
Description: Fit Bayesian models with a focus on the spatial econometric models.
Depends: R (≥ 3.5.0)
Imports: R6, Matrix, stats, graphics, utils, grDevices
Suggests: stochvol, coda
License: GPL-3 | file LICENSE
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.1.2
NeedsCompilation: no
Packaged: 2022-02-25 14:19:17 UTC; nikolas
Repository: CRAN
Date/Publication: 2022-02-25 14:40:02 UTC

Bayesian Spatial Regression Models

Description

Fit Bayesian models with a focus on the spatial econometric models.

Fit a Bayesian model

Description

Fit a Bayesian model

Usage

bm(x, ...)

## S3 method for class 'formula'
bm(
  x,
  data = NULL,
  n_save = 1000L,
  n_burn = 500L,
  options = set_options(),
  mh = set_mh(),
  verbose = TRUE,
  W,
  X_SLX,
  type = c("lm", "slx", "sar", "sem", "sdm", "sdem", "sv"),
  ...
)

## S3 method for class 'bm'
bm(x, n_save = 1000L, n_burn = 0L, verbose = TRUE, ...)

blm(...)

bslx(...)

bsar(...)

bsem(...)

bsdm(...)

bsdem(...)

bsv(...)

Arguments

x

Formula or bm object to sample with.

...

Not used.

data

A data.frame containing the variables in the model.

n_save, n_burn

Integer scalar. Number of draws for the burn-in period and to store for inference.

options

Settings for the prior setup. See set_options.

mh

Settings to tune the Metropolis-Hastings step. See set_mh.

verbose

Logical scalar. Whether to print status updates.

W

Numeric matrix (or function to construct one) with the spatial connectivities.

X_SLX

Numeric matrix with explanatory variables that should be lagged spatially.

type

Character scalar used to specify the desired model.

Value

Returns a list with draws from the specified Bayesian model and an object to obtain further samples.

Examples

N <- 100L
beta <- 1:5
X <- matrix(rnorm(N * 5), N, 5)
y <- X %*% beta + rnorm(N)

bm(y ~ X, n_burn = 100, n_draw = 100)


# Reproduce the linear model in Kuschnig (2022)
blm(log(sales) ~ log(price / cpi) + log(ndi / cpi) +
  factor(name) + factor(year), data = cigarettes)

Cigarette demand

Description

Panel dataset on cigarette demand in 46 US states from 1963 until 1992, see Baltagi and Levin (1992) and Baltagi and Li (2004). Extended with longitude and latitude from the us_states dataset.

Usage

cigarettes

Format

A data.frame object.

References

Baltagi, B. H. and Levin, D. (1992). Cigarette taxation: raising revenues and reducing consumption, Structural Change and Economic Dynamics, 3(2), 321-335. doi: 10.1016/0954-349X(92)90010-4. Baltagi, B. H. and Li, D. (2004). Prediction in the panel data model with spatial correlation. Advances in Spatial Econometrics, 283-295. Springer, Berlin. doi: 10.1007/978-3-662-05617-2_13.

Methods for coda Markov chain Monte Carlo objects

Description

Methods to convert parameter and/or coefficient draws to coda's mcmc format for further processing.

Usage

as.mcmc.bm(x, ...)

Arguments

x

A bm object, obtained from bm.

...

Other parameters for as.mcmc.

Value

Returns a coda mcmc object.

Obtain draws from a Bayesian model sampler

Description

Obtain draws from a Bayesian model sampler

Usage

sample(x, n_save = 1000L, n_burn = 0L, mh = set_mh(), verbose = TRUE)

Arguments

x

Bayesian model

n_save, n_burn

Integer scalar with number of draws to save / burn.

mh

Settings to tune the Metropolis-Hastings step. See set_mh.

verbose

Logical scalar. Whether to print status updates.

Value

Returns a numeric matrix with stored draws. The Bayesian model is modified in place.

Set up a Normal-Gamma prior

Description

Set up a Normal-Gamma prior

Usage

set_NG(
  mu = 0,
  precision = 1e-08,
  shape = 0.01,
  rate = 0.01,
  beta = NULL,
  sigma = NULL
)

set_SNG(
  lambda_a = 0.01,
  lambda_b = 0.01,
  theta_scale = 0,
  theta_a = 1,
  lambda = 1,
  tau = 10,
  theta = 0.1
)

set_HS(lambda = 1, tau = 1, zeta = 1, nu = 1)

Arguments

mu

Numeric scalar or vector with the prior mean of 'beta'.

precision

Numeric scalar or matrix with the prior precision of 'beta'. Not used for shrinkage priors.

shape, rate

Numeric scalars with the prior shape and rate of 'sigma'.

lambda_a, lambda_b

Numeric scalars with the prior shape and rate of 'lambda'.

theta_scale

Numeric scalar with the proposal scale of 'theta'. Defaults to zero for a fixed value.

theta_a

Numeric scalar with the prior rate of 'theta'.

lambda, tau, theta, zeta, nu, beta, sigma

Numerics with starting values for the respective parameter.

Value

Returns a list with priors and settings.

Set up a spatial prior

Description

Set up a spatial prior

Usage

set_SAR(
  lambda_a = 1.01,
  lambda_b = 1.01,
  lambda = 0,
  lambda_scale = 0.1,
  lambda_min = -1,
  lambda_max = 1 - 1e-12,
  delta_a = 1.01,
  delta_b = 1.01,
  delta = 1,
  delta_scale = 0,
  delta_min = 1e-12,
  delta_max = Inf
)

set_SLX(
  lambda_a = 1.01,
  lambda_b = 1.01,
  lambda = 0,
  lambda_scale = 0.1,
  lambda_min = -1,
  lambda_max = 1 - 1e-12,
  delta_a = 1.01,
  delta_b = 1.01,
  delta = 1,
  delta_scale = 0,
  delta_min = 1e-12,
  delta_max = Inf
)

set_SEM(
  lambda_a = 1.01,
  lambda_b = 1.01,
  lambda = 0,
  lambda_scale = 0.1,
  lambda_min = -1,
  lambda_max = 1 - 1e-12,
  delta_a = 1.01,
  delta_b = 1.01,
  delta = 1,
  delta_scale = 0,
  delta_min = 1e-12,
  delta_max = Inf
)

Arguments

lambda_a, lambda_b

Numeric scalars with the prior shapes of the connectivity strength 'lambda'.

lambda, delta

Numerics with starting values for the respective parameter.

lambda_scale

Numeric scalar with the proposal scale of 'lambda'.

lambda_min, lambda_max

Numeric scalars with upper and lower bounds for 'lambda'.

delta_a, delta_b

Numeric scalars with the prior shapes of the connectivity parameter 'delta'.

delta_scale

Numeric scalar with the proposal scale of 'delta'. Defaults to zero for a fixed value.

delta_min, delta_max

Numeric scalars with upper and lower bounds for 'delta'.

Value

Returns a list with priors and settings.

Set up a volatility prior

Description

Set up a volatility prior

Usage

set_SV(
  priors,
  mu = 0,
  phi = 0.5,
  sigma = 1,
  nu = Inf,
  rho = 0,
  beta = 0,
  latent0 = 0
)

Arguments

priors

Prior settings from specify_priors.

mu, phi, sigma, nu, rho, beta, latent0

Numerics with starting values for the respective parameter.

Value

Returns a list with priors and settings.

Settings to tune a Metropolis-Hastings step

Description

Settings to tune a Metropolis-Hastings step

Usage

set_mh(adjust_burn = 0.8, acc_target = c(0.2, 0.45), acc_change = 0.01)

Arguments

adjust_burn

Numeric scalar with the percentage of burn-in that should be used to tune the MH step.

acc_target

Numeric vector with the lower and upper bound of the target acceptance rate for the MH step.

acc_change

Numeric scalar with the percentage adjustment to the proposal scale for tuning.

Value

Returns a list with settings to tune the Metropolis-Hastings step of a Bayesian model.

Examples

set_mh(0.5, c(0.1, 0.5), .05)

Set up Bayesian model priors and settings

Description

Set up Bayesian model priors and settings

Usage

set_options(
  type = c("Independent", "Conjugate", "Shrinkage", "Horseshoe"),
  NG = set_NG(),
  SNG = set_SNG(),
  HS = set_HS(),
  SAR = set_SAR(),
  SLX = set_SLX(),
  SEM = set_SEM(),
  SV = set_SV(),
  ...
)

Arguments

type

Character scalar with the prior type for the nested linear model.

NG

Settings for the Normal-Gamma prior (independent or conjugate). See set_NG.

SNG

Settings for the Normal-Gamma shrinkage prior (Polson and Scott, 2010). See set_NG.

HS

Settings for the Horseshoe shrinkage prior (Makalic and Schmidt, 2015). See set_NG.

SAR

Settings for the spatial autoregressive setup. See set_SAR.

SLX

Settings for the spatially lagged explanatory setup. See set_SAR. Note that settings for the spatial term 'theta' are provided to NG instead.

SEM

Settings for the spatial error setup. See set_SAR.

SV

Settings for the stochastic volatility setup. See set_SV.

...

Used to provide custom prior elements.

Value

Returns a list with priors and settings for a Bayesian model.

Examples

set_options("Shrinkage", SNG = set_SNG(lambda_a = 1, lambda_b = 1))

Burn-in and tune a Bayesian model sampler

Description

Burn-in and tune a Bayesian model sampler

Usage

tune(x, n_burn = 1000L, mh = set_mh(), verbose = TRUE)

burn(x, n_burn = 1000L, verbose = TRUE)

Arguments

x

Bayesian model

n_burn

Integer scalar with number of draws to save / burn.

mh

Settings to tune the Metropolis-Hastings step. See set_mh.

verbose

Logical scalar. Whether to print status updates.

Value

Modifies the Bayesian model in place and returns it invisibly.

United States Historical States

Description

Polygons of US state boundaries for the period 1960–2000. Subset from Siczewicz (2011). Licensed under CC BY-NC-SA 2.5 by the Atlas of Historical County Boundaries.

Usage

us_states

Format

A data.frame object.

Source

https://publications.newberry.org/ahcbp/

References

Siczewicz, P. (2011) U.S. Historical States and Territories (Generalized 0.01 deg). Dataset. Atlas of Historical County Boundaries, edited by Long, J. H. . Chicago: The Newberry Library, 2011. Available online from https://publications.newberry.org/ahcbp/.

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