Package 'SCDA'

Title: Spatially-Clustered Data Analysis
Description: Contains functions for statistical data analysis based on spatially-clustered techniques. The package allows estimating the spatially-clustered spatial regression models presented in Cerqueti, Maranzano \& Mattera (2024), "Spatially-clustered spatial autoregressive models with application to agricultural market concentration in Europe", arXiv preprint 2407.15874 <doi:10.48550/arXiv.2407.15874>. Specifically, the current release allows the estimation of the spatially-clustered linear regression model (SCLM), the spatially-clustered spatial autoregressive model (SCSAR), the spatially-clustered spatial Durbin model (SCSEM), and the spatially-clustered linear regression model with spatially-lagged exogenous covariates (SCSLX). From release 0.0.2, the library contains functions to estimate spatial clustering based on Adiajacent Matrix K-Means (AMKM) as described in Zhou, Liu \& Zhu (2019), "Weighted adjacent matrix for K-means clustering", Multimedia Tools and Applications, 78 (23) <doi:10.1007/s11042-019-08009-x>.
Authors: Paolo Maranzano [aut, cre, cph] , Raffaele Mattera [aut, cph] , Camilla Lionetti [aut, cph], Francesco Caccia [aut, cph]
Maintainer: Paolo Maranzano <[email protected]>
License: GPL (>= 2)
Version: 0.0.2
Built: 2025-02-20 03:30:30 UTC
Source: https://github.com/cran/SCDA

Help Index

Spatial dataset to replicate the results for 2010 from Cerqueti, R., Maranzano, P. & Mattera, R. "Spatially-clustered spatial autoregressive models with application to agricultural market concentration in Europe". arXiv preprints (<https://doi.org/10.48550/arXiv.2407.15874>

Description

The 'Data_RC_PM_RM_JABES2024' dataset was created merging information from the Eurostat regional database (<https://ec.europa.eu/eurostat/web/regions/database>). it is a spatial dataset to replicate the results for 2010 from Cerqueti, R., Maranzano, P. & Mattera, R. "Spatially-clustered spatial autoregressive models with application to agricultural market concentration in Europe". arXiv preprints (<https://doi.org/10.48550/arXiv.2407.15874>). Data contained in this file refer to the agricultural sector industry for 222 European regions (NUTS-2 classification) for 2010. For more information see the database 'Economic accounts for agriculture by NUTS 2 region' (agr_r_accts, DOI:10.2908/agr_r_accts). The file includes 6 mixed-type objects:

Usage

data(Data_RC_PM_RM_JABES2024)

Format

Data2010 is a spatial data frame (sf/data.frame) with 222 rows, 13 variables and a geometry representing the regions' polygons:

Year

Reference year for the data, that is, 2010

geo_lab

Extended name (English-translated) of the regions

geo

Eurostat NUTS-2 code of the regions

Gini_SO

Gini index for the standard output of farms and agricultural holdings in each region

GDPPC_PPS2020

Regional per capita GDP measured as Euros PPS 2020

Share_AgroEmp

Share of employment in agriculture: relevance of agricultural industry on the regional labor market

HoursWorked_AgroEmp

Hours worked per agro-employed: agricultural labor market intensity

GVA_AgroEmp

Gross value added per agro-employed: agricultural productivity intensity

GFCF_AgroEmp

Investment per agro-employed: propensity to invest according to the economic size

Share_AgroGVA

Share of agricultural GVA on total GVA: relevance of agricultural industry on the regional economy

Share_AgroLand

Share of agricultural land: relevance of agricultural industry on the regional activities

Alt_mean

Average altitude: geography and landscape

HDD

Heating degree days (HDD): proxy of temperature and weather conditions

Note

All source data files prepared by Paolo Maranzano (Department of Economics, Management and Statistics, University of Milano-Bicocca, Italy).

Source

Eurostat – Economic accounts for agriculture by NUTS 2 region' (agr_r_accts, DOI:10.2908/agr_r_accts)

Spatial dataset to replicate the results for 2020 from Cerqueti, R., Maranzano, P. & Mattera, R. "Spatially-clustered spatial autoregressive models with application to agricultural market concentration in Europe". arXiv preprints (<https://doi.org/10.48550/arXiv.2407.15874>)

Description

The 'Data_RC_PM_RM_JABES2024' dataset was created merging information from the Eurostat regional database (<https://ec.europa.eu/eurostat/web/regions/database>). it is a spatial dataset to replicate the results for 2020 from Cerqueti, R., Maranzano, P. & Mattera, R. "Spatially-clustered spatial autoregressive models with application to agricultural market concentration in Europe". arXiv preprints (<https://doi.org/10.48550/arXiv.2407.15874>). Data contained in this file refer to the agricultural sector industry for 222 European regions (NUTS-2 classification) for 2020. For more information see the database 'Economic accounts for agriculture by NUTS 2 region' (agr_r_accts, DOI:10.2908/agr_r_accts). The file includes 6 mixed-type objects:

Usage

data(Data_RC_PM_RM_JABES2024)

Format

Data2020 is a data frame with 222 rows, 13 variables and a geometry representing the regions' polygons:

Year

Reference year for the data, that is, 2020

geo_lab

Extended name (English-translated) of the regions

geo

Eurostat NUTS-2 code of the regions

Gini_SO

Gini index for the standard output of farms and agricultural holdings in each region

GDPPC_PPS2020

Regional per capita GDP measured as Euros PPS 2020

Share_AgroEmp

Share of employment in agriculture: relevance of agricultural industry on the regional labor market

HoursWorked_AgroEmp

Hours worked per agro-employed: agricultural labor market intensity

GVA_AgroEmp

Gross value added per agro-employed: agricultural productivity intensity

GFCF_AgroEmp

Investment per agro-employed: propensity to invest according to the economic size

Share_AgroGVA

Share of agricultural GVA on total GVA: relevance of agricultural industry on the regional economy

Share_AgroLand

Share of agricultural land: relevance of agricultural industry on the regional activities

Alt_mean

Average altitude: geography and landscape

HDD

Heating degree days (HDD): proxy of temperature and weather conditions

Note

All source data files prepared by Paolo Maranzano (Department of Economics, Management and Statistics, University of Milano-Bicocca, Italy).

Source

Eurostat – Economic accounts for agriculture by NUTS 2 region' (agr_r_accts, DOI:10.2908/agr_r_accts)

Automatically selects the optimal number of clusters based on elbow criterion.

Description

Automatically selects the optimal number of clusters (X-axis) based on elbow criterion computed on a metric (Y-axis). Potential metrics are the AIC and the BIC. The function can be applied to any other context in which the objective is to find the optimal X producing an elbow in Y.

Usage

Elbow_finder(x, y, Plot = TRUE)

Arguments

x

Numeric (m x 1) vector of integer values (usually, the number of clusters from 1 to G)
y

Numeric (m x 1) vector of values (usually, the criterion values) associated with the number of groups.
Plot

Logical value (TRUE or FALSE). If Plot = TRUE a plot of the relationship between x and y is produced. The plot is a scatterplot with connecting lines. A vertical line is depicted in correspondence of the optimal value of x.

Value

Returns the following outputs:

  • x_max_dist: optimal value of x (i.e., the x satisfying the elbow rule)

  • y_max_dist: optimal value of y (i.e., the y satisfying the elbow rule)

  • Scatterplot (non-compulsory) of x and y with connecting lines and vertical line in correspondence of the optimal value of x.

Examples

## Compute the Elbow criterion on two generic vectors x and y
x <- 1:10
y <- c(10,9,6,5,4,3,2,1,1,1)
Elbow_finder(x,y,Plot = TRUE)

List of 222 spatial weights (style = "W", zero.policy=TRUE) used in Cerqueti, R., Maranzano, P. & Mattera, R. "Spatially-clustered spatial autoregressive models with application to agricultural market concentration in Europe". arXiv preprints (<https://doi.org/10.48550/arXiv.2407.15874>)

Description

The 'Data_RC_PM_RM_JABES2024' dataset was created merging information from the Eurostat regional database (<https://ec.europa.eu/eurostat/web/regions/database>). it is a spatial dataset to replicate the results for 2020 from Cerqueti, R., Maranzano, P. & Mattera, R. "Spatially-clustered spatial autoregressive models with application to agricultural market concentration in Europe". arXiv preprints (<https://doi.org/10.48550/arXiv.2407.15874>). Data contained in this file refer to the agricultural sector industry for 222 European regions (NUTS-2 classification) for 2020. For more information see the database 'Economic accounts for agriculture by NUTS 2 region' (agr_r_accts, DOI:10.2908/agr_r_accts). The file includes 6 mixed-type objects:

Usage

data(Data_RC_PM_RM_JABES2024)

Format

listW is a list of 222 spatial weights (style = "W", zero.policy=TRUE) for the European NUTS-2 regions

Note

All source data files prepared by Paolo Maranzano (Department of Economics, Management and Statistics, University of Milano-Bicocca, Italy).

Source

Eurostat – GISCO Territorial units for statistics (NUTS) (https://ec.europa.eu/eurostat/web/gisco/geodata/statistical-units/territorial-units-statistics)

Spatial Clustering for sf data

Description

Perform spatial clustering using K-means and AMKM (Adjacent Matrix K-Means) algorithms on sf data.

Usage

SC_AMKM(
  Data_sf,
  IndexCol,
  Method,
  Distance = "euclidean",
  MinNc = 2,
  MaxNc = 10,
  Metric = "silhouette",
  RidDim = "pca",
  CenterVars = T,
  ScaleVars = T,
  MakePlot = T,
  ExplainedVariance = 0.9,
  KeepCoord = T,
  Seed = 123456789,
  Verbose = T,
  CRS = 4326
)

Arguments

Data_sf

A data.frame object of class sf with n rows (each one corresponding to a location) and a user-defined number of columns. It must include the geometry feature for spatial modelling and representation. Typically, sf data.frame are built using the st_as_sf(...) command from the sf package (see its documentation for details).
IndexCol

Integer value. Number of the dataset ID column. If there isn't an ID column IndexCol=0.
Method

Character. Must be one of: 'AMKM' or 'K-means'. If method='AMKM', the Adjacent Matrix K-Means clustering is performed. If method='K-means', K-means clustering is performed.
Distance

Character. The distance measure to be used to compute the dissimilarity matrix. This must be one of: "euclidean", "maximum", "manhattan", "canberra", "binary", "minkowski". By default, distance='euclidean'.
MinNc

Integer value. Minimal number of clusters, between 1 and (number of objects - 1). Default is MinNc=2.
MaxNc

Integer value. Maximal number of clusters, between 2 and (number of objects - 1), greater or equal to MinNc. Default is MaxNc=10.
Metric

Character. The validation index to be calculated for the selection of the optimal clustering partition. This should be one of : "kl", "ch", "hartigan", "ccc", "scott", "marriot", "trcovw", "tracew", "friedman", "rubin", "cindex", "db", "silhouette", "duda", "pseudot2", "beale", "ratkowsky", "ball", "ptbiserial", "gap", "frey", "mcclain", "gamma", "gplus", "tau", "dunn", "hubert", "sdindex", "dindex", "sdbw", "all" (all indices except GAP, Gamma, Gplus and Tau), "alllong" (all indices with Gap, Gamma, Gplus and Tau included). Default is Metric='silhouette'.
RidDim

Character.The dimensionality reduction method. This should be one of : 'pca' or 'laplacian'. if 'RidDim='pca”, a principal component analysis is performed. if 'RidDim='laplacian” the laplacian matrix dimensionality reduction method is performed . Default is RidDim='pca'.
CenterVars

Logical value (TRUE or FALSE) stating whether the features have to be centered around the mean. Default is TRUE.
ScaleVars

Logical value (TRUE or FALSE) stating whether the features have to be scaled with respect to their standard deviation. Default is TRUE.
MakePlot

Logical value (TRUE or FALSE) stating whether the plot must be displayed. Default is TRUE.
ExplainedVariance

numeric. cumulate percentage of the variance explained by the eigenvalues of the dimesionality reduction method. Must be between 0 and 1. Default is ExplainedVariance=0.9.
KeepCoord

Logical value (TRUE or FALSE) stating whether the coordinate must be taken into account in K-means algorithm. Available only when 'method='K-means”. Default is TRUE.
Seed

Integer value. Define the random number generator (RNG) state for random number generation in R. Deafult is seed = 123456789.
Verbose

Logical value (TRUE or FALSE). Toggle warnings and messages. If verbose = TRUE (default) the function prints on the screen some messages describing the progress of the tasks. If verbose = FALSE any message about the progression is suppressed. Default is TRUE.
CRS

Integer value. Coordinate reference system. something suitable as input to st_crs.command from the sf package (see its documentation for details). Default is CRS=4326

Details

AMKM calculations is done decomposing the input dataset in two subset. The first one contains the features while the second one contains the coordinates (longitude and latitude). A dissimilarity matrix is calculated on both subset using the parameter distance for the feature and the Great Circle distance for coordinates. Then an adjacent matrix (n x n) is computed on every dissimilarity matrix using gaussian kernel. To reduce the dimensionality of the adjacent matrix a dimentionality reduction method is necessary (see RidDim param. for more) K-means is applied with no modification at its original algorithm.

Value

A list object containing the following outputs:

  • df: n row dataframe with the following columns : ID, Longitude, Latitude and Cluster (the optimal partition)

  • plot: Display cluster partition in a map.

Author(s)

Camilla Lionetti <[email protected]>, Francesco Caccia <[email protected]>

Examples

library(sp)
library(sf)
data("meuse")
dati<-meuse
dati<-subset(dati,select=sapply(dati,is.numeric))
dati<-st_as_sf(dati, coords = c("x", "y"),crs =28992)
SC <- SC_AMKM(Data_sf=dati,IndexCol=0, Method="AMKM",MinNc = 5,MaxNc = 5 ,CRS=28992)

Estimate spatially-clustered spatial regression models

Description

Estimates spatially-clustered spatial regression (SCSR) models, such as the spatially-clustered linear regression model (SCLM), the spatially-clustered spatial autoregressive model (SCSAR), the spatially-clustered spatial durbin model (SCSEM), and the spatially-clustered linear regression model with spatially-lagged exogenous covariates and response variable (SCSLX). Estimation is performed via cluster-wise maximum likelihood as presented in <https://arxiv.org/abs/2407.15874>.

Usage

SCSR_Estim(
  Formula,
  Data_sf,
  listW,
  G = 2,
  Phi = 1,
  Type = c("SCLM", "SCSAR", "SCSEM", "SCSLX"),
  CenterVars = FALSE,
  ScaleVars = FALSE,
  Maxitr = 100,
  RelTol = 10^-6,
  AbsTol = 10^-5,
  Verbose = TRUE,
  Seed = 123456789
)

Arguments

Formula

a symbolic description of the regression model to be fit. The details of model specification are given for lm(...)
Data_sf

A data.frame object of class sf with n rows (each one corresponding to a location/polygon) and a user-defined number of columns. The data frame must contain the response variable and all the covariates to be used in the model. Also, it must include the geometry feature for spatial modelling and representation. Typically, sf data.frame are built using the st_as_sf(...) command from the sf package (see its documentation for details).
listW

listw object. It contains the spatial weights for the spatial autoregressive component. Typically, listW is built using the nb2listw(...) command from the spdep package (see its documentation for details). We suggest to adopt one of matrix styles suggested in the spdep package, such as W (row-standardized) or B (binary). We also suggest to adopt a zero.policy = TRUE option to allow the computation of groups/clusters with isolated units. In this regard, we recall that if zero.policy = FALSE and Type = "SCSAR" causes SCSR_Estim(...) to terminate with an error. See package spatialreg for details on the zero.policy input.
G

Integer value. Number of clusters to be considered. When 'G=1', the pooled regression (no clusterwise) is estimated. Default is 'G = 2'.
Phi

Non-negative (>=0) real value. Spatial penalty parameter. Default is 'Phi = 1'.
Type

Character. Declares which model specification has to be estimated. Admitted strings are:

  • "SCLM" for linear regression model without spatial effects (LM);

  • "SCSAR" for spatial autoregressive (SAR) model;

  • "SCSEM" for linear regression model with spatial autoregressive error term or spatial Durbin model (SEM);

  • "SCSLX" for linear regression model with spatially-lagged response variable and covariates (SLX);

CenterVars

Logical value (TRUE or FALSE) stating whether the response variable and the covariates have to be centered around the mean in the iterative algorithm to update memberships and group-wise parameters. Centering is only use in the iterative procedure, while final estimates provided to the user are computed original (i.e., non-centered) variables.
ScaleVars

Logical value (TRUE or FALSE) stating whether the response variable and the covariates have to be scaled with respect to their standard deviation in the iterative algorithm to update memberships and group-wise parameters. Scaling is only used in the iterative procedure, while final estimates provided to the user are computed original (i.e., non-scaled) variables.
Maxitr

Integer value. Maximum number of iterations for the iterative algorithm. Convergence criterion is fixed to ε\varepsilon = 10^(-5).
RelTol

Tolerance for the relative improvement in the log-likelihood (exit criterion) from iteration k to k+1. Default is εRel\varepsilon_{Rel} = 10^-6
AbsTol

Tolerance for the absolute improvement in the log-likelihood (exit criterion) from iteration k to k+1. Default is εAbs\varepsilon_{Abs} = 10^-5
Verbose

Logical value (TRUE or FALSE). Toggle warnings and messages. If verbose = TRUE (default) the function prints on the screen some messages describing the progress of the tasks. If verbose = FALSE any message about the progression is suppressed.
Seed

Integer value. Define the random number generator (RNG) state for random number generation in R. Deafult is seed = 123456789.

Details

The package SCSR computes the spatially-clustered spatial regression models based on the spatialreg package (see <https://cran.r-project.org/web/packages/spatialreg/index.html>). SCSAR model is estimated using the function lagsarlm; SCSEM model is estimated using the function errorsarlm; SCSLX model is estimated using the function lmSLX. SCLM model is estimated using the lm function from package stats. Thus, estimated SCSAR, SCSEM and SCSLX models belong to class Sarlm, while estimated SCLM belongs to class lm. We kindly refer to the package spatialreg for any detail regarding computational aspects (e.g., optimization). Also, we refer to the package spdep for computational details on the spatial weighting matrix via listw2mat(...), nb2listw(...) and nb2mat(...) from the spdep package. For computional details on the spatially-clustered models, we kindly refer to Cerqueti, R., Maranzano, P. & Mattera, R. "Spatially-clustered spatial autoregressive models with application to agricultural market concentration in Europe". arXiv preprints (<doi:10.48550/arXiv.2407.15874>)

Value

A list object containing the following outputs:

  • ClusterFitModels: G-dimensional list containing the estimated clustered regression models of class lm or Sarlm

  • Beta: (G x p) matrix of cluster-wise or pooled regression coefficients

  • Sig: G-dimensional vector of cluster-wise standard deviations

  • VCov: (p x p x G) array of cluster-wise variance-covariance matrices of coefficients

  • W_g: G-dimensional list containing for the g-th cluster with cardinality n_g a (n_g x n_g) spatial weighting matrix

  • listW_g: G-dimensional list containing for the g-th cluster the weights list

  • Group: (n x 1) vector of group assignment

  • sBeta: (n x p) matrix of location-wise regression coefficients

  • sSig: (n x 1) vector of location-wise standard deviations

  • MLE: Estimated maximum log-likelihood

  • Iter: The number of iteration needed to satisfy the convergence criterion and end up the clustering iterative loop

Examples

data(Data_RC_PM_RM_JABES2024, package="SCDA")
SCSAR <- SCSR_Estim(Formula = "Gini_SO ~ GDPPC_PPS2020 + Share_AgroEmp",
                    Data_sf = Data2020, G=3, listW=listW, Type="SCSAR", Phi = 0.50)
SCLM <- SCSR_Estim(Formula = "Gini_SO ~ GDPPC_PPS2020 + Share_AgroEmp",
                   Data_sf = Data2020, G=3, listW=listW, Type="SCLM", Phi = 0.50)

Automatically select the optimal number of clusters based on likelihood information criteria (i.e., AIC, BIC and HQC) for a given SCSR model.

Description

Computes the likelihood-based information criteria (i.e, Akaike's IC, Bayesian IC, and Hannan–Quinn IC) for every SCSR model given by the combination of the G and Phi contained in the G.set and Phi.set inputs and provides the associated likelihood-based information criteria. Given the minimization rule, SCSR_InfoCrit automatically identifies the optimal number of clusters for every criterion.

Usage

SCSR_InfoCrit(
  Formula,
  Data_sf,
  listW,
  Phi.set = c(0.5, 1),
  G.set = c(2, 3, 4),
  Type = c("SCLM", "SCSAR", "SCSEM", "SCSLX"),
  CenterVars = TRUE,
  ScaleVars = TRUE,
  Maxitr = 200,
  RelTol = 10^-6,
  AbsTol = 10^-5,
  Verbose = TRUE,
  Seed = 123456789
)

Arguments

Formula

a symbolic description of the regression model to be fit. The details of model specification are given for lm(...)
Data_sf

A data.frame object of class sf with n rows (each one corresponding to a location/polygon) and a user-defined number of columns. The data frame must contain the response variable and all the covariates to be used in the model. Also, it must include the geometry feature for spatial modelling and representation. Typically, sf data.frame are built using the st_as_sf(...) command from the sf package (see its documentation for details).
listW

listw object. It contains the spatial weights for the spatial autoregressive component. Typically, listW is built using the nb2listw(...) command from the spdep package (see its documentation for details). We suggest to adopt one of matrix styles suggested in the spdep package, such as W (row-standardized) or B (binary). We also suggest to adopt a zero.policy = TRUE option to allow the computation of groups/clusters with isolated units. In this regard, we recall that if zero.policy = FALSE and Type = "SCSAR" causes SCSR_Estim(...) to terminate with an error. See package spatialreg for details on the zero.policy input.
Phi.set

Non-negative (>=0) real-valued vector. Sequence of spatial penalty parameter. Default is Phi = c(0.50,1).
G.set

Integer vector. Sequence of clusters to be considered. Default is G = c(2,3,4).
Type

Character. Declares which model specification has to be estimated. Admitted strings are:

  • "SCLM" for linear regression model without spatial effects (LM);

  • "SCSAR" for spatial autoregressive (SAR) model;

  • "SCSEM" for linear regression model with spatial autoregressive error term or spatial Durbin model (SEM);

  • "SCSLX" for linear regression model with spatially-lagged response variable and covariates (SLX);

CenterVars

Logical value (TRUE or FALSE) stating whether the response variable and the covariates have to be centered around the mean in the iterative algorithm to update memberships and group-wise parameters. Centering is only use in the iterative procedure, while final estimates provided to the user are computed original (i.e., non-centered) variables.
ScaleVars

Logical value (TRUE or FALSE) stating whether the response variable and the covariates have to be scaled with respect to their standard deviation in the iterative algorithm to update memberships and group-wise parameters. Scaling is only used in the iterative procedure, while final estimates provided to the user are computed original (i.e., non-scaled) variables.
Maxitr

Integer value. Maximum number of iterations for the iterative algorithm. Convergence criterion is fixed to ε\varepsilon = 10^(-5).
RelTol

Tolerance for the relative improvement in the log-likelihood (exit criterion) from iteration k to k+1. Default is εRel\varepsilon_{Rel} = 10^-6
AbsTol

Tolerance for the absolute improvement in the log-likelihood (exit criterion) from iteration k to k+1. Default is εAbs\varepsilon_{Abs} = 10^-5
Verbose

Logical value (TRUE or FALSE). Toggle warnings and messages. If verbose = TRUE (default) the function prints on the screen some messages describing the progress of the tasks. If verbose = FALSE any message about the progression is suppressed.
Seed

Integer value. Define the random number generator (RNG) state for random number generation in R. Deafult is seed = 123456789.

Details

Given the vectors G.set = c(2,3,4) and Phi.set = c(0.50,1), the function 'SCSR_InfoCrit' will compute 3x2=6 models, each at a given combination of G and Phi. For computional details on the spatially-clustered models, we kindly refer to Cerqueti, R., Maranzano, P. & Mattera, R. "Spatially-clustered spatial autoregressive models with application to agricultural market concentration in Europe". arXiv preprints (<doi:10.48550/arXiv.2407.15874>)

Value

A list object containing the following outputs:

  • IC: a data.frame object containing one row for each combination of the supplied vectors G.set and Phi.set and 5 columns (G,Phi,AIC,BIC,HQC).

  • OptimPars: a data.frame object with 3 rows (criteria) and 2 columns (Parameters) with the optimal combination of G and Phi for every criterion.

Author(s)

Paolo Maranzano <>

Raffaele Mattera <>

Examples

data(Data_RC_PM_RM_JABES2024, package="SCDA")
SCSAR_IC <- SCSR_InfoCrit(Formula = "Gini_SO ~ GDPPC_PPS2020 + Share_AgroEmp",
                          Data_sf = Data2020, listW=listW, Type="SCSAR",
                          Maxitr = 100, Phi.set = c(0.50,1), G.set=c(2,3))

Extracts numerical values for the estimated regression parameters (i.e., spatial coefficients, regression coefficients, and residuals variance) for a given spatial regression model of class lm or Sarlm.

Description

Extracts the numerical values for the regression parameters (i.e., estimated spatial parameters, regression coefficients, and residuals variance) for a given spatial regression model of class lm or Sarlm as defined in package spatialreg. The function can be applied to the output of any SCSR model and contained in the ClusterFitModels output of SCSR_Estim function.

Usage

SpatReg_Extract(SRModel)

Arguments

SRModel

Estimated spatial or non-spatial regression model of class lm or Sarlm (see package spatialreg for details.)

Value

A named vector containing numerical values for the estimated spatial parameters (e.g., ρ\rho in SAR or λ\lambda in SEM), regression coefficients, and residuals variance for the input model in SRModel.

Examples

data(Data_RC_PM_RM_JABES2024, package="SCDA")
SCSAR <- SCSR_Estim(Formula = "Gini_SO ~ GDPPC_PPS2020 + Share_AgroEmp",
                    Data_sf = Data2020, G=3, listW=listW, Type="SCSAR", Phi = 0.50)
SpatReg_Extract(SRModel = SCSAR$ClusterFitModels[[1]])
SpatReg_Extract(SRModel = SCSAR$ClusterFitModels[[2]])
SpatReg_Extract(SRModel = SCSAR$ClusterFitModels[[3]])

Computes a set of goodness-of-fit indices (e.g., likelihood-based information criteria, Wald and LR test, Moran's I statistic) for a given spatial regression model of class lm or Sarlm.

Description

Computes a set of goodness-of-fit indices (e.g., likelihood-based information criteria, Wald and LR test, Moran's I statistic) for a given spatial regression model of class lm or Sarlm as defined in package spatialreg. The function can be applied to the output of any SCSR model and contained in the ClusterFitModels output of SCSR_Estim function.

Usage

SpatReg_GoF(SRModel_list, SRModel_W_list)

Arguments

SRModel_list

List of estimated spatial or non-spatial regression model of class lm or Sarlm (see package spatialreg for details.)
SRModel_W_list

List of listw objects (see package spdep for details) containing the spatial weights for the spatial autoregressive component for the G groups.

Value

A matrix containing 15 goodness-of-fit indices (e.g., likelihood-based information criteria, Wald and LR test, Moran's I statistic) for the list of models given as a input in SRModel_list.

Examples

data(Data_RC_PM_RM_JABES2024, package="SCDA")
SCSAR <- SCSR_Estim(Formula = "Gini_SO ~ GDPPC_PPS2020 + Share_AgroEmp",
                    Data_sf = Data2020, G=3, listW=listW, Type="SCSAR", Phi = 0.50)
reglist <- c(SCSAR$ClusterFitModels[1],SCSAR$ClusterFitModels[2],SCSAR$ClusterFitModels[3])
Wlist <- c(SCSAR$listW_g[1],SCSAR$listW_g[2],SCSAR$listW_g[3])
SpatReg_GoF(SRModel_list = reglist,SRModel_W_list = Wlist)

Computes a set of in-sample performance metrics (i.e., AIC, BIC, RMSE, Sigma, and Pseudo R2^2) for a given spatial regression model of class lm or Sarlm.

Description

Computes a set of in-sample performance metrics (i.e., AIC, BIC, RMSE, Sigma, and Pseudo R$^2$) for a given spatial regression model of class lm or Sarlm as defined in package spatialreg. The function can be applied to the output of any SCSR model and contained in the ClusterFitModels output of SCSR_Estim function.

Usage

SpatReg_Perf(SRModel)

Arguments

SRModel

Estimated spatial or non-spatial regression model of class lm or Sarlm (see package spatialreg for details.)

Value

A named vector containing numerical values for the estimated performance metrics (i.e., AIC, BIC, RMSE, Sigma, and Pseudo R2^2) for the input model in SRModel.

Examples

data(Data_RC_PM_RM_JABES2024, package="SCDA")
SCSAR <- SCSR_Estim(Formula = "Gini_SO ~ GDPPC_PPS2020 + Share_AgroEmp",
                    Data_sf = Data2020, G=3, listW=listW, Type="SCSAR", Phi = 0.50)
SpatReg_Perf(SRModel = SCSAR$ClusterFitModels[[1]])
SpatReg_Perf(SRModel = SCSAR$ClusterFitModels[[2]])
SpatReg_Perf(SRModel = SCSAR$ClusterFitModels[[3]])

Computes the Pseudo R2^2 metric for a given spatial regression model of class lm or Sarlm.

Description

Computes the Pseudo R2^2 metric for a given spatial regression model of class lm or Sarlm as defined in package spatialreg. The function can be applied to the output of any SCSR model and contained in the ClusterFitModels output of SCSR_Estim function.

Usage

SpatReg_PseudoR2(SRModel)

Arguments

SRModel

Estimated spatial or non-spatial regression model of class lm or Sarlm (see package spatialreg for details.)

Value

A numeric value reporting the Pseudo R2^2 for the input model in SRModel.

Examples

data(Data_RC_PM_RM_JABES2024, package="SCDA")
SCSAR <- SCSR_Estim(Formula = "Gini_SO ~ GDPPC_PPS2020 + Share_AgroEmp",
                    Data_sf = Data2020, G=3, listW=listW, Type="SCSAR", Phi = 0.50)
SpatReg_PseudoR2(SRModel = SCSAR$ClusterFitModels[[1]])
SpatReg_PseudoR2(SRModel = SCSAR$ClusterFitModels[[2]])
SpatReg_PseudoR2(SRModel = SCSAR$ClusterFitModels[[3]])