---
title: "REAT: A Regional Economic Analysis Toolbox for R"
author: "Thomas Wieland"
output: 
  html_document:
    number_sections: true
    toc: true
highlight: pygments
theme: spacelab
fig_retina: 2
header-includes:
- \usepackage{amsmath}
- \usepackage{amssymb}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(prompt =  TRUE)
```

# Introduction 

This Rmd file provides all the R-code from the paper **REAT: A Regional Economic Analysis Toolbox for R** by _Thomas Wieland_ published
in REGION ([DOI](\textcolor{blue}{https://doi.org/10.18335/region.v6i3.267})). This Rmd file contains the structure of the paper, but not all its text. Please,
consult the PDF- or HTML-version of the paper for the text.


# Concentration, dispersion and regional disparities

## Indicators of concentration and dispersion

## Application in REAT

### REAT functions for concentration and dispersion indicators

### Application example: Small-scale regional disparities in health care provision

```{r loadRchoice, message = FALSE}
library("REAT")
```
```{r}
data(GoettingenHealth2)
```
```{r}
gini (GoettingenHealth2$phys_gen)
```
```{r}
gini (GoettingenHealth2$phys_gen, coefnorm = TRUE)
```
```{r}
herf (GoettingenHealth2$phys_gen)
```
```{r}
herf (GoettingenHealth2$phys_gen, coefnorm = TRUE)
```
```{r}
gini(GoettingenHealth2$pop, lc = TRUE, lsize = 1, le.col = "black",
 lc.col = "orange", lcx = "Shares of districts", lcy = "Shares of
 providers", lctitle = "Spatial concentration of health care
 providers", lcg = TRUE, lcgn = TRUE, lcg.caption =
 "Population 2016:", lcg.lab.x = 0, lcg.lab.y = 1)

gini(GoettingenHealth2$phys_gen, lc = TRUE, lsize = 1, add.lc = TRUE,
 lc.col = "red", lcg = TRUE, lcgn = TRUE, lcg.caption =
 "Physicians 2016:", lcg.lab.x = 0, lcg.lab.y = 0.85)

gini(GoettingenHealth2$psych, lsize = 1, lc = TRUE, add.lc = TRUE,
 lc.col = "blue", lcg = TRUE, lcgn = TRUE, lcg.caption =
 "Psychotherapists 2016:", lcg.lab.x = 0, lcg.lab.y = 0.7)
```
```{r}
disp(GoettingenHealth2[c(5,6,7)], weighting = GoettingenHealth2$pop)
```
```{r}
gini_phys <- gini (GoettingenHealth2$phys_gen)
# save as gini_phys (numeric vector of length = 1)
gini_phys
```
```{r}
disp_Goettingen <- disp(GoettingenHealth2[c(5,6,7)],
 weighting = GoettingenHealth2$pop)

disp_Goettingen
```

# Regional convergence

## The concept of beta and sigma convergence

## Application in REAT

### REAT functions for beta and sigma convergence

### Application example: Beta and sigma convergence in Germany on the county level



```{r}
data (G.counties.gdp)
```
```{r}
options(scipen = 100, digits = 4)
```

**PLEASE CHECK**
        
```{r}
betaconv.ols (G.counties.gdp$gdppc2010, 2010, G.counties.gdp$gdppc2014,
 2014, print.results = TRUE)
```
```{r}
sigmaconv (G.counties.gdp$gdppc2010, 2010, G.counties.gdp$gdppc2014,
 2014, sigma.measure = "cv", print.results = TRUE)
```
```{r}
rca (G.counties.gdp$gdppc2000, 2000, G.counties.gdp[55:68], 2014,
 conditions = NULL, sigma.type = "trend", sigma.measure = "cv",
 beta.plot = TRUE, beta.plotLine = TRUE, beta.plotX =
 "Ln (initial GDP p.c.)", beta.plotY = "Ln (av. growth GDP p.c.)",
 beta.plotTitle = "Beta convergence of German counties 2000-2014",
 sigma.plot = TRUE, sigma.plotY = "cv of ln (GDP p.c.)",
 sigma.plotTitle = "Sigma convergence of German counties 2000-2014")
```
```{r}
regionaldummies <- to.dummy(G.counties.gdp$regional)
# Creating dummy variables for West/East
# regionaldummies[,1] = East (1/0), regionaldummies[,2] = West (1/0)
G.counties.gdp$West <- regionaldummies[,2]
# Adding the dummy variable for West

converg_results <- rca (G.counties.gdp$gdppc2000, 2000,
 G.counties.gdp[55:68], 2014, conditions = G.counties.gdp[c(70)],
 sigma.type = "trend")
```
```{r}
converg_results$betaconv$regdata
# All results in list converg_results
# converg_results contains list betaconv (beta convergence results)
# betaconv contains data frame regdata (regression data)

```
```{r}
converg_results$sigmaconv$sigma.trend

# All results in list converg_results
# converg_results contains list sigmaconv (sigma convergence results)
# sigmaconv contains data frame sigma.trend (sigma values)

```

# Specialization of regions and spatial concentration of industries

## Indicators of regional specialization and industry concentration

## Application in REAT

### REAT functions for regional specialization and industry concentration

### Application example 1: Regional specialization of Göttingen


```{r}
data(Goettingen)
```
```{r}
locq (Goettingen$Goettingen2017[4], Goettingen$Goettingen2017[1],
 Goettingen$BRD2017[4], Goettingen$BRD2017[1])
```
```{r}
# Industry: manufacturing (letter C) in row 4
# row 1 = all-over employment
 
locq (Goettingen$Goettingen2017[2:16], Goettingen$Goettingen2017[1],
 Goettingen$BRD2017[2:16], Goettingen$BRD2017[1],
 industry.names = Goettingen$WZ2008_Code[2:16], plot.results = TRUE,
 plot.title = "Location quotients for Gottingen 2017")
# all industries (rows 2-16 in the dataset)
```
```{r}
herf(Goettingen$Goettingen2017[2:16])
```
```{r}
herf(Goettingen$BRD2017[2:16])
```
```{r}
hoover(Goettingen$Goettingen2017[2:16], ref = Goettingen$BRD2017[2:16])
```
```{r}
gini.spec(Goettingen$Goettingen2017[2:16], Goettingen$BRD2017[2:16])
```
```{r}
krugman.spec(Goettingen$Goettingen2017[2:16], Goettingen$BRD2017[2:16])
```
 
### Application example 2: Identifying clusters in Germany using aggregate data


```{r}
data(G.regions.industries)
```
```{r}
conc_i <- conc (e_ij = G.regions.industries$emp_all,
 industry.id = G.regions.industries$ind_code,
 region.id = G.regions.industries$region_code)
```
```{r}
cor(conc_i[,1:3])
```
```{r}
spec_j <- spec (e_ij = G.regions.industries$emp_all,
 industry.id = G.regions.industries$ind_code,
 region.id = G.regions.industries$region_code)
```
```{r}
cor(spec_j[,1:3])
```
```{r}
locq2(e_ij = G.regions.industries$emp_all,
 G.regions.industries$ind_code, G.regions.industries$region_code)
```
```{r}
lqs <- locq2(e_ij = G.regions.industries$emp_all,
 G.regions.industries$ind_code, G.regions.industries$region_code,
 LQ.output = "df")
```

```{r}
lqs_sort <- lqs[order(lqs$LQ, decreasing = TRUE),]
# Sort decreasing by size of LQ
lqs_sort[1:5,]
```

```{r}
litzenberger2(G.regions.industries$emp_all,
 G.regions.industries$ind_code, G.regions.industries$region_code,
 G.regions.industries$area_sqkm, G.regions.industries$pop,
 G.regions.industries$firms)
```

```{r}
lss <- litzenberger2(G.regions.industries$emp_all,
 G.regions.industries$ind_code, G.regions.industries$region_code,
 G.regions.industries$area_sqkm, G.regions.industries$pop,
 G.regions.industries$firms, CI.output = "df")
```
```{r}
lss_sort <- lss[order(lss$CI, decreasing = TRUE),]
lss_sort[1:5,]
```

### Application example 3: Identifying clusters using micro-data

```{r}
region <- c("Wien", "Wien", "Wien", "Wien", "Wien", "Linz",
 "Linz", "Linz", "Linz", "Graz")
# regions (Austrian cities)
emp_firm <- c(200,650,12000,100,50,16000,13000,1500,1500,25000)
# employment of the ten firms
emp_region <- c(500000,400000,100000)
# employment of the three regions
ellison.a (emp_firm, emp_region, region)
```


```{r}
data(FK2014_EGC)
ega <- ellison.a2 (FK2014_EGC$emp_firm, FK2014_EGC$industry,
 FK2014_EGC$region)
```

```{r}
ellison.c (FK2014_EGC$emp_firm, FK2014_EGC$industry,
 FK2014_EGC$region, FK2014_EGC$emp_region)
```
```{r}
ellison.c2 (FK2014_EGC$emp_firm, FK2014_EGC$industry,
 FK2014_EGC$region, FK2014_EGC$emp_region)
```
```{r}
howard.xcl2 (FK2014_EGC$firm, FK2014_EGC$industry,
 FK2014_EGC$region)
```

**PLEASE NOTE**

The computation of this index implies sampling. Therefore, the numbers differ with each run.        



# Proximity and accessibility

## Distance-based measures of accessibility and proximity using individual point-level data

## Application in REAT

### REAT functions for accessibility and proximity on the point level

### Application example 1: Location analysis of medical practices

```{r}
data(GoettingenHealth1)
data(GoettingenHealth2)
physgen <- GoettingenHealth1[GoettingenHealth1$type == "phys_gen",]
# general practitioners: column "type" is equal to "phys_gen"
physgen_sample <- physgen[sample(nrow(physgen),10),]
# random sampling of ten general practitioners
physgen_pot <- dist.buf (physgen_sample, "location", "lat", "lon",
 GoettingenHealth2, "district", "lat", "lon", bufdist = 1000,
 ep_sum = "pop")
# counting all districts within a radius of 1000 meters
# and summing the corresponding population
```
**PLEASE NOTE**

The data used in this section are randomly sampled from the available dataset. Therefore, the
results differ with each run.

```{r}
mean2(physgen_pot$count_table$sum_pop)
#[1] 4967
```
```{r}
physgen_od <- dist.mat(GoettingenHealth2, "district", "lat", "lon",
 physgen_sample, "location", "lat", "lon")
# creating OD matrix from all districts to the
# sampled general practitioners
physgen_od <- merge (physgen_od, GoettingenHealth2,
 by.x = "from", by.y = "district")
# merging with GoettingenHealth2 to include the
# population values of the districts
physgen_hansen <- hansen (physgen_od, "to", "from", "pop",
 "distance", dtype = "exp", lambda = -0.28)
```
```{r}
# calculating Hansen accessibility for the ten
# sampled general practitioners
mean2(physgen_hansen$accessibility)
# [1] 30207
```
```{r}
psychgen <- GoettingenHealth1[GoettingenHealth1$type == "psych",]
psych_sample <- psychgen[sample(nrow(psychgen),10),]
psych_pot <- dist.buf (psych_sample, "location", "lat", "lon",
 GoettingenHealth2, "district", "lat", "lon", bufdist = 1000,
 ep_sum = "pop")
mean2(psych_pot$count_table$sum_pop)
# [1] 14221
```
```{r}
psych_od <- dist.mat(GoettingenHealth2, "district", "lat", "lon",
 psych_sample, "location", "lat", "lon")
psych_od <- merge (psych_od, GoettingenHealth2,
 by.x = "from", by.y = "district")
psych_hansen <- hansen (psych_od, "to", "from", "pop",
 "distance", dtype = "exp", lambda = -0.11)
```
```{r}
mean2(psych_hansen$accessibility)
# [1] 116846
```
```{r}
data (GoettingenHealth1)
```
```{r}
area_goe <- 1753000000
# area of Landkreis Goettingen (sqm)
area_nom <- 1267000000
# area of Landkreis Northeim (sqm)
area_gn <- area_goe+area_nom
ripley(GoettingenHealth1[GoettingenHealth1$type == "pharm",],
 "location", "lat", "lon", area = area_gn, t.max = 30000, t.sep = 300,
 K.local = TRUE, ci.boot = TRUE, ci.alpha = 0.05, ciboot.samples = 100,
 plot.title = "Ripley's K: Clustering of pharmacies")
```
```{r}
ripley(GoettingenHealth1[GoettingenHealth1$type == "psych",],
 "location", "lat", "lon", area = area_gn, t.max = 30000, t.sep = 300,
 K.local = TRUE, ci.boot = TRUE, ci.alpha = 0.05, ciboot.samples = 100,
 plot.title = "Ripley's K: Clustering of psychotherapists")
```

# Analysis and prognosis of regional growth
 
## Tools and models concerning regional growth

### Analyzing regional growth: shift-share analysis and portfolio matrix

### Commercial area prognosis

## Commercial area prognosis

### REAT functions for analyzing and forecasting regional growth

### Application example 1: Analysis of regional growth in Göttingen

```{r}
data(Goettingen)
```
```{r}
portfolio (Goettingen$Goettingen2008[2:16],
 Goettingen$Goettingen2017[2:16],
 Goettingen$BRD2008[2:16], Goettingen$BRD2017[2:16],
 psize = Goettingen$Goettingen2017[2:16], psize.factor = 15,
 pmtitle = "Growth of 15 industries in Göttingen",
 industry.names = Goettingen$WZ2008_Code[2:16],
 pmx = "Growth Göttingen 2008-2017 [%]",
 pmy = "Growth Germany 2008-2017 [%]",
 pcol.border = "grey",
 pcol = c("darkgreen", "powderblue", "chocolate", "darkred",
 "orange", "cadetblue1", "chartreuse1", "red", "coral",
 "coral4", "cyan", "darkcyan", "yellow", "green", "deeppink"),
 leg = TRUE, leg.x = -90)

locq.growth (Goettingen$Goettingen2008[2:16],
 Goettingen$Goettingen2017[2:16],
 Goettingen$BRD2008[2:16], Goettingen$BRD2017[2:16],
 psize = Goettingen$Goettingen2017[2:16], psize.factor = 15,
 y.axis = "r", industry.names = Goettingen$WZ2008_Code[2:16],
 pmtitle = "Growth and specialization in Göttingen",
 pmx = "Regional specialization Göttingen",
 pmy = "Growth Götingen 2008-2017 [%]", pcol.border = "grey",
 pcol = c("darkgreen", "powderblue", "chocolate", "darkred",
 "orange", "cadetblue1", "chartreuse1", "red", "coral",
 "coral4", "cyan", "darkcyan", "yellow", "green", "deeppink"),
 leg = TRUE, leg.x = 0.1)
 
shift(Goettingen$Goettingen2008[2:16], Goettingen$Goettingen2017[2:16],
 Goettingen$BRD2008[2:16], Goettingen$BRD2017[2:16])
```

```{r}
shift(Goettingen$Goettingen2008[2:16], Goettingen$Goettingen2017[2:16],
 Goettingen$BRD2008[2:16], Goettingen$BRD2017[2:16],
 shift.method = "Gerfin")
```

```{r}
shiftid(Goettingen$Goettingen2008[2:16], Goettingen[2:16,3:12],
 Goettingen$BRD2008[2:16], Goettingen[2:16,13:22],
 time1 = 2008, time2 = 2017,
 industry.names = Goettingen$WZ2008_Code[2:16])
# columns 3-12: employment in Göttingen 2009-2017
# columns 13-22: employment in Germany 2009-2017
```

### Application example 2: Commercial area prognosis for Göttingen


```{r}
data(Goettingen)
```
```{r}
ca_share <- c(0, 0, 100, 90, 70, 100, 10, 20, 20, 20, 20, 0, 0, 0, 0)
# industry-specific shares of employees in commercial areas
sq_quote <- c(0.77, 0.77, 0.15, 0.15, 0.77, 0.15, 0.77, 0.77,
 0.77, 0.77, 0.77, 0.77, 0.77, 0.77, 0.77)
# industry-specific resettlement quote
rq_quote <- rep(0.7, 15)
# industry-specific relocation quote (0.7 for each of the 15 industries)
area_index <- c(0, 0, 200, 75, 250, 250, 50, 100, 100, 100, 100,
 50, 50, 50, 50)
# industry-specific area index (sqm commercial area per employee)
gifpro_goettingen <- gifpro (e_ij = Goettingen$Goettingen2017[2:16],
 a_i = ca_share, sq_ij = sq_quote, rq_ij = rq_quote, tinterval = 5,
 ai_ij = area_index, time.base = 2017,
 industry.names = Goettingen$WZ2008_Code[2:16], output = "full")
```

```{r}
gifpro_goettingen$components
```
```{r}
gifpro.tbs (e_ij = Goettingen[2:16,3:12],
 a_i = ca_share, sq_ij = sq_quote, rq_ij = rq_quote, tinterval = 5,
 prog.func = rep("exp", nrow(Goettingen[2:16,3:12])),
 ai_ij = area_index, time.base = 2008,
 industry.names = Goettingen$WZ2008_Code[2:16],
 prog.plot = TRUE, plot.single = FALSE, output = "full")
```

# Final remarks