Package 'hgwrr'

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

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

Description

Get estimated coefficients.

Usage

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

Arguments

Value

A DataFrame object consists of all estimated coefficients.

See Also

hgwr(), summary.hgwrm(), fitted.hgwrm() and residuals.hgwrm().

Description

Get fitted response.

Usage

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

Arguments

Value

A vector consists of fitted response values.

See Also

hgwr(), summary.hgwrm(), coef.hgwrm() and residuals.hgwrm().

Description

Log likelihood function

Usage

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

Arguments

Value

An logLik instance used for S3 method logLik().

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

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")

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 [email protected]

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")

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 [email protected]

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)

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

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.

In this function, characters are right padded by spaces.

Value

No return.

See Also

print.hgwrm(), summary.hgwrm().

Description

Print description of a hgwrm object.

Usage

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

Arguments

Value

No return.

See Also

summary.hgwrm(), print_table_md().

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")

Description

Print the result of spatial heterogeneity test

Usage

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

Arguments

Description

Print summary of an hgwrm object.

Usage

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

Arguments

Value

No return.

See Also

summary.hgwrm(), print_table_md().

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)

Description

Get residuals.

Usage

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

Arguments

Value

A vector consists of residuals.

See Also

hgwr(), summary.hgwrm(), coef.hgwrm() and fitted.hgwrm().

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

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.

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

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.

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

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

Description

Summary an hgwrm object.

Usage

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

Arguments

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.

See Also

hgwr().

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"))

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 [email protected]

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)