Efficient and reliable geocoding of Twitter data

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.title[
# Efficient and reliable geocoding of Twitter data
]
.subtitle[
## for spatial linkage with official statistics
]
.author[
### Long Nguyen, Dorian Tsolak, Anna Karmann, Stefan Knauff, Simon Kühne
]
.date[
### AAPOR 2022 · Chicago, IL
]

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## Agenda

- Potentials of Twitter data for regional analyses of public opinion 
- Data 
- Geocoding 
- Evaluation 
- Example use cases 
- Discussion

.footnote[Link to slides: https://lo-ng.netlify.app/slides/2022-05-13-aapor-twitter-geocoding]

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# Potentials of Twitter data for regional analyses of public opinion

---
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- Twitter: one of the most common sources of digital data on public attitudes and behaviour
  
  Data on tweets and profiles comparatively easy to collect thanks to publicly accessible API

- Use of geographic information about tweets or profiles (typically geolocation provided by Twitter in the form of geocoordinates) for regional analyses:

Political polling (Beauchamp 2017), conspiracy theories (Stephens 2020), anti-immigrant attitudes (Menshikova & van Tubergen 2022), health behaviour (Martinez et al. 2018, Wiedener & Li 2014), happiness (Mitchell et al. 2013)

- Mostly in combination with data from other sources (survey data, official statistics, etc.)

--
  
  → Geographic indicators needed to aggregate data at a specific (e.g. administrative) level and combine it with data from other sources

---
background-color: white

#### Problem:

Ready-to-use geoinformation – i.e., GPS geotags by Twitter – is only available for a tiny part of the tweets.

- Sloan & Morgan (2015): 0.85% of tweets worldwide have Twitter geotags

#### But:

- Alternative source of geoinformation: location given by user as free text in profile

.center[
<img src="./img/twitter-long.png" width="640px" style="display: block; margin: auto;" />
]

---
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### Research question

How can we use user profile locations to increase the amount of geolocated Twitter data?

---
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# Data

---

### Data collection

- Real-time collection of tweets since October 2018 via the Twitter [Filter-API](https://developer.twitter.com/en/docs/twitter-api/v1/tweets/filter-realtime/overview)

- so-called 1% API: ≤ 1% of the global rate (≈ 6000 tweets per second, Tromble et al. 2017) can be collected at any given time

- Our filter:

- Tweets that were marked as German by Twitter's speech recognition and...

- ... contained one of the [100 most frequent words in the German language](https://www.ids-mannheim.de/digspra/kl/projekte/methoden/derewo) (IDS Mannheim).

- Over 1.1 billion tweets; on average 15.7 tweets per second

- For the analysis in this presentation:

Subset 10/15/2018 to 10/14/2021, excluding retweets, excluding professional ("verified") accounts: 866 million tweets

---

### Ready-to-use geoinformation

- Only **1.52 million** (**0.18%**) of the collected tweets were geotagged with coordinates by Twitter

- **51 180** (**0.31%**) of the total 16.6 million users

NUTS-3 regions (districts or major cities) with the fewest users based on Twitter geotags:

.small[
|NUTS-3 |Name              | Users|NUTS-3 |Name              | Users|NUTS-3 |Name                        | Users|
|:------|:-----------------|-----:|:------|:-----------------|-----:|:------|:---------------------------|-----:|
|DEB3G  |Kusel             |     6|DE247  |Coburg            |    11|DE23A  |Tirschenreuth               |    12|
|DE255  |Schwabach         |     9|DE267  |Haßberge          |    11|DEB37  |Pirmasens, kreisfreie Stadt |    12|
|DEG0D  |Sömmerda          |     9|DEG0N  |Eisenach, Stadt   |    11|DEG0M  |Altenburger Land            |    13|
|DE272  |Kaufbeuren        |    10|DE234  |Amberg-Sulzbach   |    12|DEG0L  |Greiz                       |    13|
|DE926  |Holzminden        |    11|DEG06  |Eichsfeld         |    12|DE231  |Amberg                      |    13|
|DE22C  |Dingolfing-Landau |    11|DEG0A  |Kyffhäuserkreis   |    12|DE277  |Dillingen a.d.Donau         |    13|
]

---

### Profile locations

- **569 million** (**65.66%**) of the collected tweets were posted by users who provided a profile location

- **9.2 million** users (**59.15%**)

---

### Profile locations

.pull-left[
```
Domsühl, Deutschland 
AUETAL               
Hitzacker, Germany   
58710 Menden         
Salem, Deutschland   
Harlingerode         
Leichlingen Allemagne
Taunusstein Bleidenstadt
Burtscheid, Deutschland 
Drögen                  
Groß Leuthen            
Dotzheim, Wiesbaden     
48.478008,13.176936     
Wessum                  
Germany, Heinsberg          
Schiltberg, Bavaria, Germany
Tönisvorst, DE              
Germany, Niedersachsen,     
```
]

.pull-right[
```
They/Them | Ze/Zir | He/Him  
Old Man Kelsey's Woods       
she//her 💓                  
loving sangie ♡              
Seo Soojin is the definition of sexiness and cuteness
robworld                     
harley she/they queer 17     
exo planet | vivi's mom 🐕   
Side View                    
💥🍸🐇                       
Minding My Business Blvd.    
Out here init                
starving somewhere           
Avocado Toast                
she / they ; 18 ; ar 55 (na) 
To na sua kkj
she | ᵃᵇᵇˢ
𝐭|𝐧|𝐯|𝐤|𝐤|𝐥|𝐦|𝐤|𝐚
```
]

---

.pull-left[
```
Alemanha - Berlim
Alemanha - Berlin 
Alemania(Berlin)
Alemania, Berlin
Alemania/Berlin
Allemagne Berlin
Allemagne, Berlin
almanya berlin
almanya, berlin
almanya/berlin
bärlin
bärlin ♥
bÄrlin
🐻Bärlin
Bärlin
Bärlin 😏
```
]

.pull-right[
```
Berlino, Germania 🏡
Berlino, Germanio
Berlino, Germanujo
Berlino, Germany
Deutschland 🇩🇪, Berlin
Deutschland 🇪🇺🇩🇪 Berlin
Deutschland Berlin
Deutschland, Berlin
Deutschland, Berlin.
Deutschland,Berlin
Deutschland- Berlin
Deutschland-Berlin
Βερολίνο
берлин
برلين
ベルリン
```
]

- Challenge: generate usable regional indicators from the free text in the profile location

---
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# Geocoding

---

[**Nominatim**](https://nominatim.openstreetmap.org): text search engine for [OpenStreetMap](https://openstreetmap.org) data

.smaller[*Demo: Public Nominatim instance at https://nominatim.openstreetmap.org*]

.center[
<iframe src="https://nominatim.openstreetmap.org/ui/search.html" width="96%" height="450px" data-external="1"></iframe>
]

---

### Self-hosted Nominatim database

... to make geocoding more efficient

- Public Nominatim has a rate limit of 1 query per second

→ It would take years to geocode the hundreds of millions of user profile locations

- Tailor the OpenStreetMap database used for geocoding to our needs

- Flexible access to geodata in the database

- Geocoding results not limited by API output
  
  - (Spatial) joins directly in the database

---
class: highlight-last

### Implementation details

- Normalisation of the profile location text

- Places with the same name are ordered according to Nominatim search ranking and Wikipedia importance
  
  Example: New York the US city > New York the hair salon in Munich

- Locations matched at the level of street addresses are excluded (except train stations) to protect user privacy

- Geocoding output: corresponding **spatial geometry** ("shape") for each profile location string

---

#### Determine suitable aggregation levels for regional analyses:

- **Spatial join** of the geometries of the profile locations with the geometries of German administrative regions at NUTS-1, NUTS-2, and NUTS-3 level.
  
  → Match if the geometry of the profile location lies entirely within the geometry of the administrative region ([ST_CoveredBy](https://postgis.net/docs/ST_CoveredBy.html))

.center[
<img src="https://gisgeography.com/wp-content/uploads/2019/04/Spatial-Join-Completely-Within.png" width="400px" style="display: block; margin: auto;" />

.smaller[Source: https://gisgeography.com/spatial-join]
]

---

### Results

|Profile location            |NUTS-1 |NUTS-2 |NUTS-3 |
|:---------------------------|------:|------:|------:|
|Titisee-Neustadt, Germany   |DE1    |DE13   |DE132  |
|fRaNkFuRt                   |DE7    |DE71   |DE712  |
|Deutschland Aalen           |DE1    |DE11   |DE11D  |
|Saarland / Ensheim          |DEC    |DEC0   |DEC01  |
|Hardegsen, Niedersachsen    |DE9    |DE91   |DE918  |
|hh.                         |DE6    |DE60   |DE600  |
|Wartjenstedt                |DE9    |DE91   |DE91B  |
|nrw*                        |DE2    |*NA*   |*NA*   |
|Usingen, Deutschland        |DE7    |DE71   |DE718  |
|Hochzoll-Süd, Augsburg      |DE2    |DE27   |DE271  |

---

### Results

- **229 million** (**26.42%**) tweets

- 15 000% increase for the number of geolocated tweets

- **970 631** users (**6.23%**)

- Explanation: Seemingly more active users (in our dataset!) are more likely to provide geocodable profile locations

|Geoinformation     |  Mean| Median|    SD|    Max|
|:------------------|-----:|------:|-----:|------:|
|geocoded by us     | 230.0|      9|  1939| 792298|
|Twitter geotag     |  29.8|      2|  1108| 226900|
|*NA*               |  42.9|      1|   669| 447564|

---
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background-color: white

---
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# Evaluation

---
background-color: white

### Accuracy of geocoding

Gold standard: Twitter GPS geotags[1]

.center[
<img src="./img/geocoding-accuracy.png" width="80%" style="display: block; margin: auto;" />
]

.footnote.small[
[1] Tweet geotags are aggregated at user level. Only users are selected whose majority of geotags (at least 2) are in the same NUTS-3 region. For users with multiple unique geotags, centroid is calculated.
]

---
background-color: white

### Spatial distribution of geocoded users

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519","Landshut N users: 745","Passau N users: 1015","Straubing N users: 425","Deggendorf N users: 473","Freyung-Grafenau N users: 208","Kelheim N users: 354","Landshut N users: 312","Passau N users: 473","Regen N users: 255","Rottal-Inn N users: 379","Straubing-Bogen N users: 243","Dingolfing-Landau N users: 234","Amberg N users: 307","Regensburg N users: 3016","Weiden i.d.OPf. N users: 168","Amberg-Sulzbach N users: 217","Cham N users: 374","Neumarkt i.d.OPf. N users: 494","Neustadt a.d.Waldnaab N users: 244","Regensburg N users: 367","Schwandorf N users: 430","Tirschenreuth N users: 189","Bamberg N users: 1568","Bayreuth N users: 1057","Coburg N users: 571","Hof N users: 432","Bamberg N users: 306","Bayreuth N users: 290","Coburg N users: 198","Forchheim N users: 409","Hof N users: 305","Kronach N users: 198","Kulmbach N users: 310","Lichtenfels N users: 212","Wunsiedel i.Fichtelgebirge N users: 293","Ansbach N users: 422","Erlangen N users: 1801","Fürth N users: 1270","Nürnberg N users: 10113","Schwabach N users: 234","Ansbach N users: 687","Erlangen-Höchstadt N users: 444","Fürth N users: 388","Nürnberger Land N users: 767","Neustadt a.d.Aisch-Bad Windsheim N users: 1293","Roth N users: 428","Weißenburg-Gunzenhausen N users: 241","Aschaffenburg N users: 1232","Schweinfurt N users: 536","Würzburg N users: 3228","Aschaffenburg N users: 525","Bad Kissingen N users: 318","Rhön-Grabfeld N users: 194","Haßberge N users: 292","Kitzingen N users: 328","Miltenberg N users: 441","Main-Spessart N users: 378","Schweinfurt N users: 228","Würzburg N users: 475","Augsburg N users: 4572","Kaufbeuren N users: 224","Kempten (Allgäu) N users: 675","Memmingen N users: 298","Aichach-Friedberg N users: 389","Augsburg N users: 621","Dillingen a.d.Donau N users: 216","Günzburg N users: 404","Neu-Ulm N users: 699","Lindau (Bodensee) N users: 430","Ostallgäu N users: 688","Unterallgäu N users: 420","Donau-Ries N users: 484","Oberallgäu N users: 606","Berlin, Stadt N users: 143367","Brandenburg an der Havel, Stadt N users: 267","Cottbus, Stadt N users: 986","Frankfurt (Oder), Stadt N users: 461","Potsdam, Stadt N users: 3563","Barnim N users: 794","Dahme-Spreewald N users: 900","Elbe-Elster N users: 401","Havelland N users: 757","Märkisch-Oderland N users: 590","Oberhavel N users: 836","Oberspreewald-Lausitz N users: 423","Oder-Spree N users: 579","Ostprignitz-Ruppin N users: 394","Potsdam-Mittelmark N users: 842","Prignitz N users: 281","Spree-Neiße N users: 397","Teltow-Fläming N users: 623","Uckermark N users: 487","Bremen, Stadt N users: 11789","Bremerhaven, Stadt N users: 1229","Hamburg, Freie und Hansestadt N users: 63971","Darmstadt, Wissenschaftsstadt N users: 3699","Frankfurt am Main, Stadt N users: 31980","Offenbach am Main, Stadt N users: 1229","Wiesbaden, Landeshauptstadt N users: 4270","Bergstraße N users: 1193","Darmstadt-Dieburg N users: 1257","Groß-Gerau N users: 1200","Hochtaunuskreis N users: 1354","Main-Kinzig-Kreis N users: 2244","Main-Taunus-Kreis N users: 1085","Odenwaldkreis N users: 337","Offenbach N users: 1662","Rheingau-Taunus-Kreis N users: 1061","Wetteraukreis N users: 1583","Gießen N users: 2184","Lahn-Dill-Kreis N users: 1181","Limburg-Weilburg N users: 843","Marburg-Biedenkopf N users: 1986","Vogelsbergkreis N users: 354","Kassel, documenta-Stadt N users: 4580","Fulda N users: 1214","Hersfeld-Rotenburg N users: 370","Kassel N users: 685","Schwalm-Eder-Kreis N users: 634","Waldeck-Frankenberg N users: 561","Werra-Meißner-Kreis N users: 701","Rostock N users: 3349","Schwerin N users: 1185","Mecklenburgische Seenplatte N users: 1242","Landkreis Rostock N users: 684","Vorpommern-Rügen N users: 1407","Nordwestmecklenburg N users: 706","Vorpommern-Greifswald N users: 1350","Ludwigslust-Parchim N users: 666","Braunschweig, Stadt N users: 4099","Salzgitter, Stadt N users: 622","Wolfsburg, Stadt N users: 1560","Gifhorn N users: 651","Goslar N users: 841","Helmstedt N users: 375","Northeim N users: 557","Peine N users: 555","Wolfenbüttel N users: 502","Göttingen N users: 3360","Diepholz N users: 844","Hameln-Pyrmont N users: 949","Hildesheim N users: 1601","Holzminden N users: 250","Nienburg (Weser) N users: 468","Schaumburg N users: 731","Region Hannover N users: 18467","Celle N users: 1030","Cuxhaven N users: 1084","Harburg N users: 1064","Lüchow-Dannenberg N users: 135","Lüneburg N users: 1614","Osterholz N users: 363","Rotenburg (Wümme) N users: 656","Heidekreis N users: 870","Stade N users: 1535","Uelzen N users: 480","Verden N users: 616","Delmenhorst, Stadt N users: 471","Emden, Stadt N users: 484","Oldenburg (Oldenburg), Stadt N users: 2498","Osnabrück, Stadt N users: 3410","Wilhelmshaven, Stadt N users: 870","Ammerland N users: 570","Aurich N users: 1220","Cloppenburg N users: 582","Emsland N users: 1897","Friesland N users: 616","Grafschaft Bentheim N users: 732","Leer N users: 809","Oldenburg N users: 493","Osnabrück N users: 1027","Vechta N users: 554","Wesermarsch N users: 461","Wittmund N users: 277","Düsseldorf, Stadt N users: 20686","Duisburg, Stadt N users: 5407","Essen, Stadt N users: 7762","Krefeld, Stadt N users: 2170","Mönchengladbach, Stadt N users: 1966","Mülheim an der Ruhr, Stadt N users: 1019","Oberhausen, Stadt N users: 1783","Remscheid, Stadt N users: 784","Solingen, Klingenstadt N users: 1351","Wuppertal, Stadt N users: 3848","Kleve N users: 1741","Mettmann N users: 2974","Rhein-Kreis Neuss N users: 3031","Viersen N users: 1766","Wesel N users: 2705","Bonn, Stadt N users: 9285","Köln, Stadt N users: 42718","Leverkusen, Stadt N users: 1504","Düren N users: 1574","Rhein-Erft-Kreis N users: 2039","Euskirchen N users: 951","Heinsberg N users: 1358","Oberbergischer Kreis N users: 1340","Rheinisch-Bergischer Kreis N users: 1412","Rhein-Sieg-Kreis N users: 3407","Städteregion Aachen N users: 7093","Bottrop, Stadt N users: 763","Gelsenkirchen, Stadt N users: 1680","Münster, Stadt N users: 6614","Borken N users: 1790","Coesfeld N users: 845","Recklinghausen N users: 3625","Steinfurt N users: 2039","Warendorf N users: 994","Bielefeld, Stadt N users: 5429","Gütersloh N users: 1751","Herford N users: 1278","Höxter N users: 567","Lippe N users: 1529","Minden-Lübbecke N users: 1768","Paderborn N users: 2864","Bochum, Stadt N users: 5371","Dortmund, Stadt N users: 12684","Hagen, Stadt der FernUniversität N users: 1338","Hamm, Stadt N users: 1251","Herne, Stadt N users: 1111","Ennepe-Ruhr-Kreis N users: 2076","Hochsauerlandkreis N users: 1382","Märkischer Kreis N users: 2070","Olpe N users: 604","Siegen-Wittgenstein N users: 1893","Soest N users: 1677","Unna N users: 2241","Koblenz, kreisfreie Stadt N users: 2400","Ahrweiler N users: 1031","Altenkirchen (Westerwald) N users: 500","Bad Kreuznach N users: 798","Birkenfeld N users: 452","Mayen-Koblenz N users: 975","Neuwied N users: 850","Rhein-Lahn-Kreis N users: 888","Westerwaldkreis N users: 1146","Cochem-Zell N users: 269","Rhein-Hunsrück-Kreis N users: 550","Trier, kreisfreie Stadt N users: 2153","Bernkastel-Wittlich N users: 499","Eifelkreis Bitburg-Prüm N users: 828","Vulkaneifel N users: 609","Trier-Saarburg N users: 523","Frankenthal (Pfalz), kreisfreie Stadt N users: 222","Kaiserslautern, kreisfreie Stadt N users: 1514","Landau in der Pfalz, kreisfreie Stadt N users: 368","Ludwigshafen am Rhein, kreisfreie Stadt N users: 843","Mainz, kreisfreie Stadt N users: 5239","Neustadt an der Weinstraße, kreisfreie Stadt N users: 291","Pirmasens, kreisfreie Stadt N users: 269","Speyer, kreisfreie Stadt N users: 504","Worms, kreisfreie Stadt N users: 605","Zweibrücken, kreisfreie Stadt N users: 207","Alzey-Worms N users: 538","Bad Dürkheim N users: 527","Donnersbergkreis N users: 255","Germersheim N users: 444","Kaiserslautern N users: 369","Kusel N users: 175","Südliche Weinstraße N users: 343","Rhein-Pfalz-Kreis N users: 503","Mainz-Bingen N users: 918","Südwestpfalz N users: 338","Regionalverband Saarbrücken N users: 3227","Merzig-Wadern N users: 385","Neunkirchen N users: 273","Saarlouis N users: 760","Saarpfalz-Kreis N users: 492","St. Wendel N users: 278","Dresden, Stadt N users: 10816","Bautzen N users: 1029","Görlitz N users: 984","Meißen N users: 734","Sächsische Schweiz-Osterzgebirge N users: 778","Chemnitz, Stadt N users: 2892","Erzgebirgskreis N users: 935","Mittelsachsen N users: 907","Vogtlandkreis N users: 864","Zwickau N users: 1315","Leipzig, Stadt N users: 15081","Leipzig N users: 710","Nordsachsen N users: 592","Dessau-Roßlau, Stadt N users: 514","Halle (Saale), Stadt N users: 3121","Magdeburg, Landeshauptstadt N users: 3797","Altmarkkreis Salzwedel N users: 303","Anhalt-Bitterfeld N users: 580","Jerichower Land N users: 171","Börde N users: 399","Burgenlandkreis N users: 618","Harz N users: 878","Mansfeld-Südharz N users: 350","Saalekreis N users: 623","Salzlandkreis N users: 666","Stendal N users: 406","Wittenberg N users: 394","Flensburg, Stadt N users: 1535","Kiel, Landeshauptstadt N users: 5606","Lübeck, Hansestadt N users: 293","Neumünster, Stadt N users: 539","Dithmarschen N users: 673","Herzogtum Lauenburg N users: 998","Nordfriesland N users: 1335","Ostholstein N users: 1055","Pinneberg N users: 1375","Plön N users: 486","Rendsburg-Eckernförde N users: 1240","Schleswig-Flensburg N users: 908","Segeberg N users: 1348","Steinburg N users: 743","Stormarn N users: 1075","Erfurt, Stadt N users: 3234","Gera, Stadt N users: 688","Jena, Stadt N users: 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---

### Content of the geocoded tweets

Comparison of geolocated vs. non-geolocated tweets as bags of words

- Cosine similarity: 0.996
  
- Jaccard coefficient: 0.935

---
class: inverse center middle

# Example use cases

---
background-color: white

#### Support for the German Green Party[2]

.pull-left.w35[
<img src="./img/gruene-hashtags.png" width="446" style="display: block; margin: auto;" />
]

.pull-right.w60[

Correlation with Green votes per inhabitant:

.footnote.small[[2] During the one-month period leading to the 2021 German federal election]
]

---
background-color: white

#### Usage of gender-inclusive language: urban vs rural

.pull-left.w35[
<img src="./img/gendered-speech.png" width="446" style="display: block; margin: auto;" />
]

.pull-right.w65[
.center[Regression models of the proportion of users who tweeted with gender-inclusive language[3]]

.footnote.smaller[[3] Model 4: <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">y</mi><mo>=</mo><mi mathvariant="bold">X</mi><mi>β</mi><mo>+</mo><mi mathvariant="bold">u</mi></mrow><annotation encoding="application/x-tex">\mathbf{y} = \mathbf{X}\beta + \mathbf{u}</annotation></semantics></math>y=Xβ+u, <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">u</mi><mo>=</mo><mi>λ</mi><mrow><mi mathvariant="bold">W</mi><mi mathvariant="bold">u</mi></mrow><mo>+</mo><mi>ε</mi></mrow><annotation encoding="application/x-tex">\mathbf{u} = \lambda\mathbf{Wu} + \varepsilon</annotation></semantics></math>u=λWu+ε where <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">W</mi></mrow><annotation encoding="application/x-tex">\mathbf{W}</annotation></semantics></math>W is the spatial neighbour weights matrix]
]

---
class: inverse center middle

# Discussion

---

- Potential for filling data gaps when analysing small regions

- Usable for certain research questions

- Benefits of standardised output as official region identifiers:

- Easily combine with data from other sources
  
  - Less privacy-sensitive compared to exact point coding

- For the users who don't have profile location:

- More complex geocoding methods available, e.g. using follower network or tweet content
  
  - Much more computationally expensive and time consuming; much more difficult to validate

---

### Open science

- Code will be made public for reproduction

- Geocoding results with tweet IDs can be released for rehydration

- R package [{nutscoder}](https://github.com/long39ng/nutscoder) (https://github.com/long39ng/nutscoder)

- input: text strings; output: administrative regions (not limited to NUTS regions in Germany)

``` r
library(nutscoder)
nuts_geocode(c("Hamburgo", "هامبورغ", "HH", "Berlin", "🐻Bärlin", "ベルリン"))
#> # A tibble: 8 × 5
#> location name nuts_1 nuts_2 nuts_3
#> <chr> <chr> <chr> <chr> <chr> 
#> 1 Hamburgo Hamburg DE6 DE60 DE600 
#> 2 هامبورغ Hamburg DE6 DE60 DE600 
#> 3 HH Hamburg DE6 DE60 DE600 
#> 4 Berlin Berlin DE3 DE30 DE300 
#> 5 🐻Bärlin Berlin DE3 DE30 DE300 
#> 6 ベルリン Berlin DE3 DE30 DE300 
```

---
class: center middle

## Thank you for your attention!