hgwr {hgwrr}

Hierarchical and Geographically Weighted Regression

Description

A Hierarchical Linear Model (HLM) with local fixed effects.

Usage

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"),
  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"),
  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"),
  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"),
  verbose = 0
)

Arguments

formula

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

response ~ L(local.fixed) + global.fixed + (random | group)

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

data

The data.

...

Further arguments for the specified type of 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.

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.

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:

Local fixed effects

Effects wrapped by functional symbol L.

Random effects

Effects specified outside the functional symbol L but to the left of symbol |.

Global 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 local fixed effects, x1 is the global fixed effects, and z1 is the random effects grouped by the group indicator group. Note that random effects can only be specified once!

Value

A list describing the model with following fields.

gamma

Coefficients of local fixed effects.

beta

Coefficients of global fixed effects.

mu

Coefficients of random effects.

D

Variance-covariance matrix of 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.

Functions

• hgwr_fit(): Fit a HGWR model

Examples

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