Help for package hgwrr

Type:

Package

Title:

Hierarchical and Geographically Weighted Regression

Version:

0.6-1

Date:

2024-11-15

Maintainer:

Yigong Hu <yigong.hu@bristol.ac.uk>

Description:

This model divides coefficients into three types, i.e., local fixed effects, global fixed effects, and random effects (Hu et al., 2022)<doi:10.1177/23998083211063885>. If data have spatial hierarchical structures (especially are overlapping on some locations), it is worth trying this model to reach better fitness.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

URL:

https://github.com/HPDell/hgwrr/, https://hpdell.github.io/hgwrr/

Imports:

Rcpp (≥ 1.0.8)

LinkingTo:

Rcpp, RcppArmadillo

Depends:

R (≥ 3.5.0), sf, stats, utils, MASS

NeedsCompilation:

yes

Suggests:

knitr, rmarkdown, testthat (≥ 3.0.0), furrr, progressr,

SystemRequirements:

GNU make

RoxygenNote:

7.2.3

VignetteBuilder:

knitr

Config/Needs/website:

tidyverse, ggplot2, tmap, lme4, spdep, GWmodel

Packaged:

2024-11-15 16:39:59 UTC; yigong

Author:

Yigong Hu [aut, cre], Richard Harris [aut], Richard Timmerman [aut]

Repository:

CRAN

Date/Publication:

2024-11-16 11:50:02 UTC

HGWR: Hierarchical and Geographically Weighted Regression

Description

An R and C++ implementation of Hierarchical and Geographically Weighted Regression (HGWR) model is provided in this package. This model divides coefficients into three types: local fixed effects, global fixed effects, and random effects. If data have spatial hierarchical structures (especially are overlapping on some locations), it is worth trying this model to reach better fitness.

Details

Package:	hgwrr
Type:	Package
Title:	Hierarchical and Geographically Weighted Regression
Version:	0.6-1
Date:	2024-11-15
Authors@R:	c(person(given = "Yigong", family = "Hu", role = c("aut", "cre"), email = "yigong.hu@bristol.ac.uk"), person(given = "Richard", family = "Harris", role = "aut"), person(given = "Richard", family = "Timmerman", role = "aut"))
Maintainer:	Yigong Hu <yigong.hu@bristol.ac.uk>
Description:	This model divides coefficients into three types, i.e., local fixed effects, global fixed effects, and random effects (Hu et al., 2022)<doi:10.1177/23998083211063885>. If data have spatial hierarchical structures (especially are overlapping on some locations), it is worth trying this model to reach better fitness.
License:	GPL (>= 2)
URL:	https://github.com/HPDell/hgwrr/, https://hpdell.github.io/hgwrr/
Imports:	Rcpp (>= 1.0.8)
LinkingTo:	Rcpp, RcppArmadillo
Depends:	R (>= 3.5.0), sf, stats, utils, MASS
NeedsCompilation:	yes
Suggests:	knitr, rmarkdown, testthat (>= 3.0.0), furrr, progressr,
SystemRequirements:	GNU make
Roxygen:	list(markdown = TRUE)
RoxygenNote:	7.2.3
VignetteBuilder:	knitr
Config/Needs/website:	tidyverse, ggplot2, tmap, lme4, spdep, GWmodel
Author:	Yigong Hu [aut, cre], Richard Harris [aut], Richard Timmerman [aut]

Note

Acknowledgement: We gratefully acknowledge support from China Scholarship Council.

Author(s)

Yigong Hu, Richard Harris, Richard Timmerman

References

Hu, Y., Lu, B., Ge, Y., Dong, G., 2022. Uncovering spatial heterogeneity in real estate prices via combined hierarchical linear model and geographically weighted regression. Environment and Planning B: Urban Analytics and City Science. doi:10.1177/23998083211063885

Get estimated coefficients.

Description

Get estimated coefficients.

Usage

## S3 method for class 'hgwrm'
coef(object, ...)

Arguments

object

An hgwrm object returned by hgwr().

...

Parameter received from other functions.

Value

A DataFrame object consists of all estimated coefficients.

Get fitted response.

Description

Get fitted response.

Usage

## S3 method for class 'hgwrm'
fitted(object, ...)

Arguments

object

An hgwrm object returned by hgwr().

...

Parameter received from other functions.

Value

A vector consists of fitted response values.

Log likelihood function

Description

Log likelihood function

Usage

## S3 method for class 'hgwrm'
logLik(object, ...)

Arguments

object

An hgwrm object.

...

Additional arguments.

Value

An logLik instance used for S3 method logLik().

Make Dummy Variables

Description

Function make_dummy converts categorical variables in a data frame to dummy variables.

Function make_dummy_extract converts a column to dummy variables if necessary and assign appropriate names. See the "detail" section for further information. Users can define their own functions to allow the model deal with some types of variables properly.

Usage

make_dummy(data)

make_dummy_extract(col, name)

## S3 method for class 'character'
make_dummy_extract(col, name)

## S3 method for class 'factor'
make_dummy_extract(col, name)

## S3 method for class 'logical'
make_dummy_extract(col, name)

## Default S3 method:
make_dummy_extract(col, name)

Arguments

data

The data frame from which dummy variables need to be extracted.

col

A vector to extract dummy variables.

name

The vector's name.

Details

If col is a character vector, the function will get unique values of its elements and leave out the last one. Then, all the unique values are combined with the name argument as names of new columns.

If col is a factor vector, the function will get its levels and leave out the last one. Then, all level labels are combined with the name argument as names of new columns.

If col is a logical vector, the function will convert it to a numeric vector with value TRUE mapped to 1 and FALSE to 0.

If col is of other types, the default behaviour for extracting dummy variables is just to copy the original value and try to convert it to numeric values.

Value

The data frame with extracted dummy variables.

Examples

make_dummy(iris["Species"])

make_dummy_extract(iris$Species, "Species")

make_dummy_extract(c("top", "mid", "low", "mid", "top"), "level")

make_dummy_extract(factor(c("far", "near", "near")), "distance")

make_dummy_extract(c(TRUE, TRUE, FALSE), "sold")

Simulated Spatial Multisampling Data For Test (DataFrame)

Description

A simulation data set for testing use of spatial hierarchical structure and samples overlapping on certain locations.

Usage

data(mulsam.test)

Format

A list of three items called "data", "coords" and "beta". Item "data" is a data frame with 873 observations at 25 locations and the following 6 variables.

y: a numeric vector, dependent variable y
g1: a numeric vector, group level independent variable g_1
g2: a numeric vector, group level independent variable g_2
z1: a numeric vector, sample level independent variable z_1
x1: a numeric vector, sample level independent variable x_1
group: a numeric vector, group id of each sample

where g1 and g2 are used to estimate local fixed effects; x1 is used to estimate global fixed effects and z1 is used to estimate random effects.

Author(s)

Yigong Hu yigong.hu@bristol.ac.uk

Examples

data(mulsam.test)
hgwr(formula = y ~ L(g1 + g2) + x1 + (z1 | group),
     data = mulsam.test$data,
     coords = mulsam.test$coords,
     bw = 10, kernel = "bisquared")

Large Scale Simulated Spatial Multisampling Data (DataFrame)

Description

A simulation data of spatial hierarchical structure and samples overlapping on certain locations.

Usage

data(multisampling)

Format

A list of three items called "data", "coords" and "beta". Item "data" is a data frame with 21434 observations at 625 locations and the following 6 variables.

y: a numeric vector, dependent variable y
g1: a numeric vector, group level independent variable g_1
g2: a numeric vector, group level independent variable g_2
z1: a numeric vector, sample level independent variable z_1
x1: a numeric vector, sample level independent variable x_1
group: a numeric vector, group id of each sample

where g1 and g2 are used to estimate local fixed effects; x1 is used to estimate global fixed effects and z1 is used to estimate random effects.

Author(s)

Yigong Hu yigong.hu@bristol.ac.uk

Examples

## Not run: 
data(multisampling)
hgwr(formula = y ~ L(g1 + g2) + x1 + (z1 | group),
     data = multisampling$data,
     coords = multisampling$coords,
     bw = 32)

## End(Not run)

Print description of a `hgwrm` object.

Description

Print description of a hgwrm object.

Usage

## S3 method for class 'hgwrm'
print(x, decimal.fmt = "%.6f", ...)

Arguments

x

An hgwrm object returned by hgwr().

decimal.fmt

The format string passing to base::sprintf().

...

Arguments passed on to print_table_md

col_sep: Column separator. Default to "".
header_sep: Header separator. Default to "-". If header_sep only contains one character, it will be repeated for each column. If it contains more than one character, it will be printed below the first row.
row_begin: Character at the beginning of each row. Default to col_sep.
row_end: Character at the ending of each row. Default to col_sep.
table_before: Characters to be printed before the table.
table_after: Characters to be printed after the table.
table_style: Name of pre-defined style. Possible values are "plain", "md", "latex", or "booktabs". Default to "plain".

Value

No return.

Examples

data(mulsam.test)
model <- hgwr(
  formula = y ~ L(g1 + g2) + x1 + (z1 | group),
  data = mulsam.test$data,
  coords = mulsam.test$coords,
  bw = 10
)
print(model)
print(model, table.style = "md")

Print the result of spatial heterogeneity test

Description

Print the result of spatial heterogeneity test

Usage

## S3 method for class 'spahetbootres'
print(x, ...)

Arguments

x

A spahetbootres object.

...

Other unused arguments.

Print summary of an `hgwrm` object.

Description

Print summary of an hgwrm object.

Usage

## S3 method for class 'summary.hgwrm'
print(x, decimal.fmt = "%.6f", ...)

Arguments

x

An object returned from summary.hgwrm().

decimal.fmt

The format string passing to base::sprintf().

...

Arguments passed on to print_table_md

col_sep: Column separator. Default to "".
header_sep: Header separator. Default to "-". If header_sep only contains one character, it will be repeated for each column. If it contains more than one character, it will be printed below the first row.
row_begin: Character at the beginning of each row. Default to col_sep.
row_end: Character at the ending of each row. Default to col_sep.
table_before: Characters to be printed before the table.
table_after: Characters to be printed after the table.
table_style: Name of pre-defined style. Possible values are "plain", "md", "latex", or "booktabs". Default to "plain".

Value

No return.

Examples

data(mulsam.test)
model <- hgwr(
  formula = y ~ L(g1 + g2) + x1 + (z1 | group),
  data = mulsam.test$data,
  coords = mulsam.test$coords,
  bw = 10
)
summary(model)

Print a character matrix as a table.

Description

Print a character matrix as a table.

Usage

print_table_md(
  x,
  col_sep = "",
  header_sep = "",
  row_begin = "",
  row_end = "",
  table_before = NA_character_,
  table_after = NA_character_,
  table_style = c("plain", "md", "latex", "booktabs"),
  ...
)

Arguments

x

A character matrix.

col_sep

Column separator. Default to "".

header_sep

Header separator. Default to "-". If header_sep only contains one character, it will be repeated for each column. If it contains more than one character, it will be printed below the first row.

row_begin

Character at the beginning of each row. Default to col_sep.

row_end

Character at the ending of each row. Default to col_sep.

table_before

Characters to be printed before the table.

table_after

Characters to be printed after the table.

table_style

Name of pre-defined style. Possible values are "plain", "md", "latex", or "booktabs". Default to "plain".

...

Additional style control arguments.

Details

When table_style is specified, col_sep, header_sep, row_begin and row_end would not take effects. Because this function will automatically set their values. For each possible value of table_style, its corresponding style settings are shown in the following table.

	`plain`	`md`	`latex`
`col_sep`	`""`	`"\|"`	`"&"`
`header_sep`	`""`	`"-"`	`""`
`row_begin`	`""`	`"\|"`	`""`
`row_end`	`""`	`"\|"`	`"\\"`

In this function, characters are right padded by spaces.

Value

No return.

Get residuals.

Description

Get residuals.

Usage

## S3 method for class 'hgwrm'
residuals(object, ...)

Arguments

object

An hgwrm object returned by hgwr().

...

Parameter received from other functions.

Value

A vector consists of residuals.

Generic method to test spatial heterogeneity

Description

Generic method to test spatial heterogeneity

Usage

spatial_hetero_test(x, ...)

## Default S3 method:
spatial_hetero_test(x, ...)

## S3 method for class 'matrix'
spatial_hetero_test(x, coords, ...)

## S3 method for class 'numeric'
spatial_hetero_test(x, coords, ...)

## S3 method for class 'vector'
spatial_hetero_test(x, coords, ...)

## S3 method for class 'data.frame'
spatial_hetero_test(x, coords, ...)

## S3 method for class 'sf'
spatial_hetero_test(x, ...)

Arguments

x

The data to be tested.

...

Arguments passed on to spatial_hetero_test_data, spatial_hetero_test_data

resample: The total times of resampling with replacement. Default to 5000.
poly: The number of polynomial terms used by the polynomial estimator. Default to 2.
bw: The adaptive bandwidth used by the polynomial estimator. Default to 10.
kernel: The kernel function used by the polynomial estimator.
verbose: The verbosity level. Default to 0.

coords

The coordinates used for testing. Accepts a matrix or vector. For matrix, it needs to have the same number of rows as x. For vector, it indicates the columns in x and the actual coordinates will be taken from x.

Methods (by class)

spatial_hetero_test(default): Default behavior.
spatial_hetero_test(matrix): For the matrix, coords is necessary.
spatial_hetero_test(numeric): Takes x as values of a series variables stored by column, and coords as coordinates for each row in x.
spatial_hetero_test(vector): Takes x as values of the variable, and coords as coordinates for each element in x.
spatial_hetero_test(data.frame): Takes x as variable values (each column is a variable), and coords as coordinates for each row in x.
spatial_hetero_test(sf): For the sf object, coordinates of centroids are used. Only the numerical columns are tested.

Hierarchical and Geographically Weighted Regression

Description

A Hierarchical Linear Model (HLM) with group-level geographically weighted effects.

Usage

## S3 method for class 'hgwrm'
spatial_hetero_test(
  x,
  round = 99,
  statistic = stat_glsw,
  parallel = FALSE,
  verbose = 0,
  ...
)

hgwr(
  formula,
  data,
  ...,
  bw = "CV",
  kernel = c("gaussian", "bisquared"),
  alpha = 0.01,
  eps_iter = 1e-06,
  eps_gradient = 1e-06,
  max_iters = 1e+06,
  max_retries = 1e+06,
  ml_type = c("D_Only", "D_Beta"),
  f_test = FALSE,
  verbose = 0
)

## S3 method for class 'sf'
hgwr(
  formula,
  data,
  ...,
  bw = "CV",
  kernel = c("gaussian", "bisquared"),
  alpha = 0.01,
  eps_iter = 1e-06,
  eps_gradient = 1e-06,
  max_iters = 1e+06,
  max_retries = 1e+06,
  ml_type = c("D_Only", "D_Beta"),
  f_test = FALSE,
  verbose = 0
)

## S3 method for class 'data.frame'
hgwr(
  formula,
  data,
  ...,
  coords,
  bw = "CV",
  kernel = c("gaussian", "bisquared"),
  alpha = 0.01,
  eps_iter = 1e-06,
  eps_gradient = 1e-06,
  max_iters = 1e+06,
  max_retries = 1e+06,
  ml_type = c("D_Only", "D_Beta"),
  f_test = FALSE,
  verbose = 0
)

hgwr_fit(
  formula,
  data,
  coords,
  bw = c("CV", "AIC"),
  kernel = c("gaussian", "bisquared"),
  alpha = 0.01,
  eps_iter = 1e-06,
  eps_gradient = 1e-06,
  max_iters = 1e+06,
  max_retries = 1e+06,
  ml_type = c("D_Only", "D_Beta"),
  f_test = FALSE,
  verbose = 0
)

Arguments

x

An hgwrm object

round

The number of times to sampling from model.

statistic

A function used to calculate the statistics on the original data and bootstrapped data. Default to the variance of standardlised GLSW estimates.

parallel

If TRUE, use furrr package to parallel.

verbose

An integer value. Determine the log level. Possible values are:

0: no log is printed.
1: only logs in back-fitting are printed.
2: all logs are printed.

...

Further arguments for the specified type of data.

formula

A formula. Its structure is similar to lmer function in lme4 package. Models can be specified with the following form:

response ~ L(glsw) + fixed + (random | group)

For more information, please see the formula subsection in details.

data

The data.

bw

A numeric value. It is the value of bandwidth or "CV". In this stage this function only support adaptive bandwidth. And its unit must be the number of nearest neighbours. If "CV" is specified, the algorithm will automatically select an optimized bandwidth value.

kernel

A character value. It specify which kernel function is used in GWR part. Possible values are

gaussian: Gaussian kernel function k(d)=\exp\left(-\frac{d^2}{b^2}\right)
bisquared: Bi-squared kernel function. If d<b then k(d)=\left(1-\frac{d^2}{b^2}\right)^2 else k(d)=0

alpha

A numeric value. It is the size of the first trial step in maximum likelihood algorithm.

eps_iter

A numeric value. Terminate threshold of back-fitting.

eps_gradient

A numeric value. Terminate threshold of maximum likelihood algorithm.

max_iters

An integer value. The maximum of iteration.

max_retries

An integer value. If the algorithm tends to be diverge, it stops automatically after trying max_retires times.

ml_type

An integer value. Represent which maximum likelihood algorithm is used. Possible values are:

D_Only: Only D is specified by maximum likelihood.
D_Beta: Both D and beta is specified by maximum likelihood.

f_test

A logical value. Determine whether to do F test on GLSW effects. If f_test=TURE, there will be a f_test item in the returned object showing the F test for each GLSW effect.

coords

A 2-column matrix. It consists of coordinates for each group.

Details

Effect Specification in Formula

In the HGWR model, there are three types of effects specified by the formula argument:

Group-level spatially weighted (GLSW, aka. local fixed) effects: Effects wrapped by functional symbol L.
Sample-level random (SLR) effects: Effects specified outside the functional symbol L but to the left of symbol |.
Fixed effects: Other effects

For example, the following formula in the example of this function below is written as

y ~ L(g1 + g2) + x1 + (z1 | group)

where g1 and g2 are GLSW effects, x1 is the fixed effects, and z1 is the SLR effects grouped by the group indicator group. Note that SLR effects can only be specified once!

Value

A list describing the model with following fields.

gamma: Coefficients of group-level spatially weighted effects.
beta: Coefficients of fixed effects.
mu: Coefficients of sample-level random effects.
D: Variance-covariance matrix of sample-level random effects.
sigma: Variance of errors.
effects: A list including names of all effects.
call: Calling of this function.
frame: The DataFrame object sent to this call.
frame.parsed: Variables extracted from the data.
groups: Unique group labels extracted from the data.
f_test: A list of F test for GLSW effects. Only exists when f_test=TRUE. Each item contains the F value, degrees of freedom in the numerator, degrees of freedom in the denominator, and p value of F>F_\alpha.

Functions

spatial_hetero_test(hgwrm): Test the spatial heterogeneity with bootstrapping.
hgwr_fit(): Fit a HGWR model

Examples

data(mulsam.test)
hgwr(
  formula = y ~ L(g1 + g2) + x1 + (z1 | group),
  data = mulsam.test$data,
  coords = mulsam.test$coords,
  bw = 10
)

mod_Ftest <- hgwr(
  formula = y ~ L(g1 + g2) + x1 + (z1 | group),
  data = mulsam.test$data,
  coords = mulsam.test$coords,
  bw = 10
)
summary(mod_Ftest)

Test the spatial heterogeneity in data based on permutation.

Description

Test the spatial heterogeneity in data based on permutation.

Usage

spatial_hetero_test_data(
  x,
  coords,
  ...,
  resample = 5000,
  poly = 2,
  bw = 10,
  kernel = c("bisquared", "gaussian"),
  verbose = 0
)

Arguments

x

A matrix of data to be tested. Each column is a variable.

coords

A matrix of coordinates.

...

Additional arguments.

resample

The total times of resampling with replacement. Default to 5000.

poly

The number of polynomial terms used by the polynomial estimator. Default to 2.

bw

The adaptive bandwidth used by the polynomial estimator. Default to 10.

kernel

The kernel function used by the polynomial estimator.

verbose

The verbosity level. Default to 0.

Value

A spahetbootres object of permutation-test results with the following items:

vars: The names of variables.
t0: The value of the statistics on original values.
t: The value of the same statistics on permuted values.
p: The p-value for each variable.

Currently, variance is used as the statistics.

Summary an `hgwrm` object.

Description

Summary an hgwrm object.

Usage

## S3 method for class 'hgwrm'
summary(object, ..., test_hetero = FALSE, verbose = 0)

Arguments

object

An hgwrm object returned from hgwr().

...

Other arguments passed from other functions.

test_hetero

Logical/list value. Whether to test the spatial heterogeneity of GLSW effects. If it is set to FALSE, the test will not be executed. If it is set to TRUE, the test will be executed with default parameters (see details below). It accepts a list to enable the test with specified parameters.

verbose

An Integer value to control whether additional messages during testing spatial heterogeneity should be reported.

Details

The parameters used to perform test of spatial heterogeneity are

bw: Bandwidth (unit: number of nearest neighbours) used to make spatial kernel density estimation. Default: 10.
poly: The number of polynomial terms used in the local polynomial estimation. Default: 2.
resample: Total resampling times. Default: 5000.
kernel: The kernel function used in the local polynomial estimation. Options are "gaussian" and "bisquared". Default: "bisquared".

Value

A list containing summary informations of this hgwrm object with the following fields.

diagnostic: A list of diagnostic information.
random.stddev: The standard deviation of random effects.
random.corr: The correlation matrix of random effects.
residuals: The residual vector.

Examples

data(mulsam.test)
m <- hgwr(
  formula = y ~ L(g1 + g2) + x1 + (z1 | group),
  data = mulsam.test$data,
  coords = mulsam.test$coords,
  bw = 10
)
summary(m)
summary(m, test_hetero = TRUE)
summary(m, test_hetero = list(kernel = "gaussian"))

Wuhan Second-hand House Price and POI Data (DataFrame)

Description

A data set of second-hand house price in Wuhan, China collected in 2018.

Usage

data(multisampling)

Format

A list of two items called "data" and "coords". Item "data" is a data frame with 13862 second-hand properties at 779 neighbourhoods and the following 22 variables.

Price: House price per square metre.
Floor.High: 1 if a property is on a high floor, otherwise 0.
Floor.Low: 1 if a property is on a low floor, otherwise 0.
Decoration.Fine: 1 if a property is well decorated, otherwise 0.
PlateTower: 1 if a property is of the plate-tower type, otherwise 0.
Steel: 1 if a property is of 'steel' structure, otherwise 0.
BuildingArea: Building area in square metres.
Fee: Management fee per square meter per month.
d.Commercial: Distance to the nearest commercial area.
d.Greenland: Distance to the nearest green land.
d.Water: Distance to the nearest river or lake.
d.University: Distance to the nearest university.
d.HighSchool: Distance to the nearest high school.
d.MiddleSchool: Distance to the nearest middle school.
d.PrimarySchool: Distance to the nearest primary school.
d.Kindergarten: Distance to the nearest kindergarten.
d.SubwayStation: Distance to the nearest subway station.
d.Supermarket: Distance to the nearest supermarket.
d.ShoppingMall: Distance to the nearest shopping mall.
lon: Longitude coordinates (Projected CRS: EPSG 3857).
lat: Latitude coordinates (Projected CRS: EPSE 3857).
group: Group id of each sample.

The following variables are group level:

- Fee - d.Commercial - d.Greenland - d.Water - d.University - d.HighSchool - d.MiddleSchool - d.PrimarySchool - d.Kindergarten - d.SubwayStation - d.Supermarket - d.ShoppingMall

The following variables are sample level:

- Price - Floor.High - Floor.Low - Decoration.Fine - PlateTower - Steel - BuildingArea

Item "coords" is a 779-by-2 matrix of coordinates of all neighbourhoods.

Author(s)

Yigong Hu yigong.hu@bristol.ac.uk

Examples

## Not run: 
data(wuhan.hp)
hgwr(
  formula = Price ~ L(d.Water + d.Commercial + d.PrimarySchool +
            d.Kindergarten + Fee) + BuildingArea + (Floor.High | group),
  data = wuhan.hp$data,
  coords = wuhan.hp$coords, bw = 50, kernel = "bisquared")

## End(Not run)

HGWR: Hierarchical and Geographically Weighted Regression

Description

Details

Note

Author(s)

References

Get estimated coefficients.

Description

Usage

Arguments

Value

See Also

Get fitted response.

Description

Usage

Arguments

Value

See Also

Log likelihood function

Description

Usage

Arguments

Value

Make Dummy Variables

Description

Usage

Arguments

Details

Value

Examples

Simulated Spatial Multisampling Data For Test (DataFrame)

Description

Usage

Format

Author(s)

Examples

Large Scale Simulated Spatial Multisampling Data (DataFrame)

Description

Usage

Format

Author(s)

Examples

Print description of a hgwrm object.

Description

Usage

Arguments

Value

See Also

Examples

Print the result of spatial heterogeneity test

Description

Usage

Arguments

Print summary of an hgwrm object.

Description

Usage

Arguments

Value

See Also

Examples

Print a character matrix as a table.

Description

Usage

Arguments

Details

Value

See Also

Get residuals.

Description

Usage

Arguments

Value

See Also

Generic method to test spatial heterogeneity

Description

Usage

Arguments

Methods (by class)

Hierarchical and Geographically Weighted Regression

Description

Print description of a `hgwrm` object.

Print summary of an `hgwrm` object.

Summary an `hgwrm` object.