mgwrhw {mgwrhw}

mgwrhw

Description

displays the GWR and mixed GWR models automatically along with the tests and significance maps that are formed.

Usage

mgwrhw(dpk, pers.reg, coor_lat, coor_long, vardep, GWRonly, kp, alp)

Arguments

dpk

dataframe all variables that come from the shp data format and have geometric attributes that are usually imported with the st_read function from library(sf)

pers.reg

The form of the regression equation that will be used as a GWR model is in the general form y~x1+x2+x3

coor_lat

the name of the variable that is in the dpk dataframe that contains latitude coordinates and is written with quotation marks such as "Latitude" which indicates a column named Latitude

coor_long

the name of the variable that is in the dpk dataframe that contains latitude coordinates and is written with quotation marks such as "Longitude" which indicates a column named Longitude

vardep

the name of a variable that is in a dpk dataframe that contains one dependent variable and is written with quotation marks such as "y" which indicates a column named y

GWRonly

user option to choose to display GWR results only or to form an MGWR model. Option 1 displays GWR output only while option 0 displays GWR and MGWR output.

kp

user option to select kernel functions. Option 1 for Fixed Bisquare, option 2 for Fixed Gaussian, option 3 for Adaptive Bisquare, and option 4 for Adaptive Bisquare

alp

alpha value (type 1 error) used in spatial regression model

Value

no return value, called for side effects

This function returns a list with the following objects:

for Mixed GWR model (GWRonly = 0)

the general equation form of the Mixed GWR model is

y_{i} = \beta_{0}(u_{i},v_{i}) + \sum\beta_{k}(u_{i},v_{i})x_{ik} + \sum\beta_{k}x_{ik} + \epsilon_{i}

output

A character vector containing the captured output of GWR model and Mixed GWR model.

gwr

The result of the GWR model include CV, bandwith, Quasi R square, etc.

Variability.Test

Results of the variability test for global and local variables.

H_{0} : \beta_{k}(u_{1},v_{1}) = \beta_{k}(u_{2},v_{2}) = ... = \beta_{k}(u_{n},v_{n})

H_{1} : not all \beta_{k}(u_{i},v_{i}) (i = 1, 2, ..., n) are equal

F_{Variability.Test_{k}} = \frac{V^{2}_{k}{/}\gamma_{1}}{\widehat{\sigma}}

Conclusion : Reject H_{0} if F_{Variability.Test_{k}} \geq F_{\alpha}(\frac{\gamma_{1}^{2}}{\gamma_{2}},\frac{\delta_{1}^{2}}{\delta_{2}}) or p-value < \alpha.

If H_{0} is rejected, it means that the k-th variable has a local influence, while if H_{0} fails to be rejected, it means that the k-th variable has a global influence.

Reference : Leung, Y., Mei, C.L., & Zhang, W.X., (2000). "Statistic Tests for Spatial Non-Stationarity Based on the Geographically Weighted Regression Model", Environment and Planning A, 32 pp. 9-32. doi:10.1068/a3162.

F1.F2.F3.mgwr.Test

Results of the F1(GoF Mixed GWR), F2(Global Simultaneous), F3(Local Simultaneous) tests.

F1(GoF Mixed GWR) :

H_{0} : \beta_{k}(u_{i},v_{i}) = \beta_{k}

H_{1} : at least there is one \beta_{k}(u_{i},v_{i}) \neq \beta_{k}

F(1) = \frac{y^{T}((I-H)-(I-S)^{T}(I-S))y {/} v_{1}} {y^{T}(I-S)^{T}(I-S)y {/} u_{1}}

if H_{0} is rejected, it shows that the Mixed GWR model is different from the OLS model]

F2(Global Simultaneous) :

H_{0} : \beta_{q+1} = \beta_{q+2} = ... = \beta_{p} = 0

H_{1} : at least one of \beta_{k} \neq 0

F(2) = \frac{y^{T}((I-S_{l})^{T}(I-S_{l})-(I-S)^{T}(I-S))y {/} r_{1}} {y^{T}(I-S)^{T}(I-S)y {/} u_{1}}

If H_{0} is rejected, it indicates that there is at least one global variable that has a significant effect in the model

F3(Local Simultaneous)

H_{0} : \beta_{1}(u_{i},v_{i}) = \beta_{2}(u_{i},v_{i}) = ... = \beta_{q}(u_{i},v_{i}) = 0

H_{1} : at least one of \beta_{k}(u_{i},v_{i}) \neq 0

F(2) = \frac{y^{T}((I-S_{g})^{T}(I-S_{g})-(I-S)^{T}(I-S))y {/} r_{1}} {y^{T}(I-S)^{T}(I-S)y {/} u_{1}}

If H_{0} is rejected, it indicates that there is at least one local variable that has a significant effect in the model

Reference : Yasin, & Purhadi. (2012). "Mixed Geographically Weighted Regression Model (Case Study the Percentage of Poor Households in Mojokerto 2008)". European Journal of Scientific Research, 188-196. https://www.researchgate.net/profile/Hasbi-Yasin-2/publication/289689583_Mixed_geographically_weighted_regression_model_case_study_The_percentage_of_poor_households_in_Mojokerto_2008/links/58e46aa40f7e9bbe9c94d641/Mixed-geographically-weighted-regression-model-case-study-The-percentage-of-poor-households-in-Mojokerto-2008.pdf.

Global.Partial.Test

Results of the global partial test.

H_{0} : \beta_{k} = 0 (k-th global variables are not significant)

H_{1} : \beta_{k} \neq 0 (k-th global variables are significant)

T_{g} = \frac{\widehat{\beta_{k}}}{\widehat{\sigma}\sqrt{g_{kk}}}

If H_{0} is rejected, it indicates that the k-th global variable has a significant effect

Reference : Yasin, & Purhadi. (2012). "Mixed Geographically Weighted Regression Model (Case Study the Percentage of Poor Households in Mojokerto 2008)". European Journal of Scientific Research, 188-196. https://www.researchgate.net/profile/Hasbi-Yasin-2/publication/289689583_Mixed_geographically_weighted_regression_model_case_study_The_percentage_of_poor_households_in_Mojokerto_2008/links/58e46aa40f7e9bbe9c94d641/Mixed-geographically-weighted-regression-model-case-study-The-percentage-of-poor-households-in-Mojokerto-2008.pdf.

map.mgwr

Visualization of Mixed GWR results in the form of a regional map with variables that are significant globally and locally.

Global_variable

A list of global variables used in the analysis.

Local_variable

A list of local variables used in the analysis.

AICc

The corrected Akaike Information Criterion.

AIC

The Akaike Information Criterion.

R_square

The coefficient of determination.

adj_R_square

The adjusted coefficient of determination.

table.mgwr

A data frame about output table of MGWR model (include estimator, standar error, t-statistics, p-value).

for GWR model (GWRonly = 1)

the general equation form of the GWR model is

y_{i} = \beta_{0}(u_{i},v_{i}) + \sum\beta_{k}(u_{i},v_{i})x_{ik} + \epsilon_{i}

output

A character vector containing the captured output of GWR model.

gwr

A character vector containing the result of the GWR model include CV, bandwith, Quasi R square, etc.

GoF.test

A character vector containing the results of the Godness of Fit Test.

anova_gwr

Results of the anova table.

map.gwr

Visualization of the GWR results.

table.gwr

A data frame about output table of GWR model (include estimator, standar error, t-statistics, p-value).

Examples

mod1 = mgwrhw(dpk=redsb, pers.reg = Y ~ X2 + X4 + X5 + X6,
coor_lat = "Latitude", coor_long = "Longitude",
vardep = "Y", GWRonly = 0, kp = 3, alp = 0.05)
mod1$gwr
mod1$Variability.Test
mod1$Global_variable
mod1$Local_variable
mod1$F1.F2.F3.mgwr.Test
mod1$Global.Partial.Test
mod1$map.mgwr