Simple Thematic Mapping in Stata
1st Italian Stata Users Group Meeting Roma, 25 October 2004
Maurizio Pisati University of Milano Bicocca – Italy [email protected]
Thematic maps
ò Thematic maps represent the spatial distribution of one or more variables of interest within a given geographical unit
1 Thematic maps
ò Examples: – A sociologist could use a choropleth map (a.k.a. shaded map) to show how the percentage of families below the poverty line varies across the states or the provinces of a given country – A police officer could be interested in analyzing a dot map showing the locations of drug markets within a given city
Software for thematic mapping
ò Usually, to produce state-of-the-art thematic maps one has to resort to specialized software (e.g., ArcView, MapInfo) ò In some cases, however, it is possible to exploit the graphical engine of a general- purpose statistical package to draw simple but effective thematic maps
2 Stata’s mapping capabilities
ò Up until version 7, Stata offered very limited mapping capabilities ò On the other hand, the graphical engine introduced in Stata 8 is quite flexible and makes it possible to draw several kinds of maps in a relatively simple manner
The tmap package
ò The tmap package is a suite of Stata programs designed to draw five kinds of thematic map: – Choropleth maps – Proportional symbol maps – Deviation maps – Dot maps – Label maps
3 The tmap package
ò Choropleth, proportional symbol, and deviation maps are intended to depict area data ò Dot maps are suitable for representing point data ò Label maps can be used to show data of both types
The tmap package
ò The tmap package exploits the possibility – offered by the new Stata graphical engine – to overlay a large number of different graphs, each of which is used to create a distinct element of the desired map
4 The tmap package
ò Specifically: – graph twoway area is used to draw the outlines of the geographical areas of interest and to fill them with the appropriate colors – graph twoway scatter is used to plot the proper symbols or labels when required
tmap choropleth
ò tmap choropleth represents the spatial distribution of area data by means of choropleth maps, i.e., maps where each of n sub-areas is colored (or shaded) according to a discrete scale based on the value taken on by a quantitative variable of interest in that sub- area
5 tmap choropleth
ò The number of classes that make up the discrete scale must be between 2 and 9 ò The corresponding class breaks can be based on four different criteria: – Quantiles – Equal intervals – Standard deviates – Custom
tmap propsymbol
ò tmap propsymbol represents the spatial distribution of area data by means of proportional symbol maps, i.e., maps where the value taken on by a quantitative variable of interest in each of n sub-areas is represented by a symbol whose size is proportional to the value itself
6 tmap deviation
ò tmap deviation represents the spatial distribution of area data by means of deviation maps, a particular kind of proportional symbol maps where: – symbol size expresses the absolute deviation of the quantitative variable of interest from its mean or median – symbol fill expresses the sign of the deviation (positive or negative)
tmap dot
ò tmap dot represents the spatial distribution of point data by means of dot maps, i.e., maps where the locations at which some “events” of interest have occurred are indicated by symbols whose color or shape can vary according to the type of “event”
7 tmap label
ò tmap label is an auxiliary program that allows the user to superimpose onto a base map the values taken on by a numeric or string variable at different locations ò This program can be used, for example, to plot sub-area names or to represent the spatial distribution of a given quantitative variable of interest in numeric form
Base maps
ò All the programs included in the tmap package require that the boundaries of the whole geographical unit of interest R or of its sub- areas be stored in an external file
8 Base maps
ò This file must always include the following three variables: – _ID, which contains the numeric identifier of the polygon(s) representing R or its sub-areas – _X, which contains the x-coordinates of the polygon(s) – _Y, which contains the y-coordinates of the polygon(s)
Base maps
ò The coordinates of each polygon must be arranged so as to correspond to consecutive nodes ò Each polygon must be “closed”, i.e., the last pair of coordinates of each polygon must be equal to the first pair
9 Base maps: example
_ID _X _Y 1 514396 5036528 1 514393 5036473 … … … 1 514396 5036528 2 516654 5039135 2 516726 5039090 … … … 2 516654 5039135
Choropleth maps: examples tmap choropleth foreign01, /// id(id) /// map("Milano-AreaMap.dta") /// clmethod(quantile) /// clnumber(4) /// palette(Reds)
10 Percentage foreign population, by administrative district.
Milano, 2001
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Choropleth maps: examples
tmap choropleth foreign01, /// id(id) /// map("Milano-AreaMap.dta") /// clmethod(quantile) /// clnumber(4) /// palette(Custom) /// colors(eltblue midblue /// ebblue edkblue) /// ocolor(white) /// osize(medium) /// legtitle("% foreign pop.") /// legformat("%4.1f“)
11 Percentage foreign population, by administrative district.
Milano, 2001
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% foreign pop.
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Choropleth maps: examples
tmap choropleth foreign01, /// id(id) /// map("Milano-AreaMap.dta") /// clmethod(quantile) /// clnumber(4) /// palette(Custom) /// colors(eltblue midblue /// ebblue edkblue) /// ocolor(none) /// osize(none) /// legtitle("% foreign pop.") /// legformat("%4.1f“)
12 Percentage foreign population, by administrative district.
Milano, 2001
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 83 83 83 83 83 83 83 83 83 83 83 3 3 3 3 3 30 30 30 30 30 30 30 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 83 83 83 83 83 83 83 83 83 83 83 3 3 3 3 3 30 30 30 30 30 30 30 30 0 0 0 0 0 0 0 0A 0A 0A 0A 0A 0A 0A A A A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 9 9 9 9 9 9 9 9 9
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 38 38 38 38C 38C 38C 38C 38C 38C 38C 38C 3C 3C 3C 3C 3C 30C 30C 30C 30C 30C 30C 30 30 0 0 0 0 0 0 0 0A 0A 0A 0A 0A 0A 0A A A A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 9 9 9 9 9 9 9 9 9
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 86 86 86 86 86 86 86 86 86 86 86 86 86 86 86 86 86 86 86 86 86 86 386 386 386 38C6 38C6 38C6 38C 38C 38C 38C 38C 3C 3C 3C 3C 3C 30C 30C 30C? 30C? 30C? 30C? 30? 30? 0? 0? 0? 0? 0? 0? 0? 0A? 0A? 0A? 0A? 0A? 0A? 0A A A A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 A9 9 9 9 9 9 9 9 9 9
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2 2 2 2 2 2 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62 672 672 672 672 672 672 672 672 672 672 672 672 672 672 672 672 672 672 672 672 672 67 67 >67 >67 >67 >67 >67 >7 > > >@ >@ >@ >@ >@ >@ >@ >@ >@ >@ @ @ @ @ @ @ @B: @B: @B: @B: @B: @B: B: B: =B: =B: =: =: =: =: =: 9=4: 9=4: 9=4: 9=4: 9=4: 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 9 9 9
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 7 7 >7 >7 >7 >7 >7< >7< >< >< >@< >@< >@< >@< >@< >@< >@< >@< >@< >@< @< @< @< @< @< @< @:< @:< @:< @:< @:< @: : : =: =: =: =: =: =: =: =4: =4: =4: =4: =4: 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 72 72 72 72 72 72 72 72 72 72 72 72 72 712 712 712 712 712 712 712 712 71 71 71 71 71 71 7<1 7<1 <15 <15 @<15 @<15 @<15 @<15 @<15 @<15 @<15 @<5 @<5 @<5 @<5 @<5 @<5; @<5; @<5; @<5; @<:5; @<:5; @<:5; @<:5; @<:5; @:; :; :; :; :; :; :; :; :; :; 4:; 4:; 4:; 4:; 4:; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4 4 4 4
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 72 72 72 72 72 72 72 72 72 72 72 72 72 712 712 712 712 712 712 712 712 71 71 71 71 71 71 7<1 7<1 <15 <15 <15 <15 <15 <15 <15 <15 <15 <5 <5 <5 <5 <5 <5; <5; <5; <5; <5; <5; <5; <5; <5; ; ; ; ; ; ; ; ; ; ; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4; 4 4 4 4
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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 15 15 15 15 15 15 15 15 5 5 5 5 5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 15 15 15 15 15 15 15 15 5 5 5 5 5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
D D D D 5 5 5 5 5 5 5 5 5 5 5 5 5 5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
% foreign pop.
EFGD EFGD EFGD EFGD 5 5 5 5 5 5 5 5 5 5 5 5 5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ;5 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; [4.6,6.6] 5 (6.6,9.0]
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Choropleth maps: examples
tmap choropleth foreign01, /// id(id) /// map("Milano-AreaMap.dta") /// clmethod(stdev) /// clnumber(5)
13 Percentage foreign population, by administrative district.
Milano, 2001
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J J J J J J J J J J J J J J J J J J J J J J J J OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJI OJI OJI OJI OJI OJI OJI OJI OI OI OI OI OI OI OTI OTI OTIM TIM TIM TIM TIM TIM TIM TIM TIM TIM TM TM TM TM TMS TMS TMS TMS TMS TRMS TRMS TRMS TRMS RMS RS RS RS RS RS RS RS RS RS RLS RLS RLS RLS RLS LS LS LS LS LS LS LS LS LS LS LS L L L L L
J J J J J J J J J J J J J J J J J J J J J J J J OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OIJ OIJ OIJ OIJ OIJ OIJ OIJ OIJ OI OI OI OI OI OI OI OI OIM IM IM IM IM IM IM IM IM IM M M M M MS MS MS MS MS MS MS MS MS MS S S S S S S S S S LS LS LS LS LS LS LS LS LS LS LS LS LS LS LS LS L L L L L
I I I I I I I I I I I I I I I I IM IM IM IM IM IM IM IM IM IM M M M M SM SM SM SM SM SM SM SM SM SM S S S S S S S S S S S S S S S S S S S S S S S S S
I I I I I I I I I I I I I I I I IM IM IM IM IM IM IM IM IM IM M M M M SM SM SM SM SM SM SM SM SM SM S S S S S S S S S S S S S S S S S S S S S S S S S
\ \ \ \ \ I I I I I I I I I I I I I I I I IM IM IM IM IM IM IM IM IM IM M M M M SM SM SM SM SM SM SM SM SM SM S S S S S S S S S S S S S S S S S S S S S S S S S
]^\ ]^\ ]^\ ]^\ ]^\ M M M M M M M M M M M M M SM SM SM SM SM SM SM SM SM SM S S S S S S S S S S S S S S S S S S S S S S S S S [4.61,5.78] M (5.78,7.85]
(7.85,9.92]
_` _` _` _` _` M M M M M M M M M M M M M M M M M M M M M M M M (9.92,11.99] (11.99,13.65]
Prop. symbol maps: examples
tmap propsymbol foreign01, /// x(x) y(y) /// map("Milano-GeneralMap.dta")
14 Percentage foreign population, by administrative district. Milano, 2001
Symbol size proportional to variable value
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
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a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a
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Prop. symbol maps: examples
tmap propsymbol foreign01, /// x(x) y(y) /// map("Milano-GeneralMap.dta") /// sshape(S) /// scolor(navy) /// ocolor(dknavy) /// fcolor(ltbluishgray)
15 Percentage foreign population, by administrative district. Milano, 2001
Symbol size proportional to variable value
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bj bj bj bj bj b b b b b b b b b b bk bk bk bk b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bv bv bv bv bv bv b b b b b b b b b b b b b b b b b b b b b b b b b b b bk bk bk bk b b b b b b b b b bl bl bl bl bl bl bl bl b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bv bv bv bv bv bv b b b b b b b b b b bi bi bi bi bi bi bi bi bi b b b b b b b b b b b b b b b b b b b b b bl bl bl bl bl bl bl bl b b bn bn bn bn bn bn bn b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b bu bu bu bu bu b b b b b b b b b b b b b b b b b b b b b b bi bi bi bi bi bi bi bi bi b b b b b b bd bd bd bd bd bd bd bd b b b b b b b b b b b b b b b b b bn bn bn bn bn bn bn b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b bu bu bu bu bu b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bd bd bd bde bde bde bde bde be be be b b bm bm bm bm bm bm bm b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bh bh bh bh bh bh bh b b b bc bc bc bc bc bc bc b b be be be be be be be be b b bm bm bm bm bm bm bm b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b bt bt bt bt b b b b b b b b b b b b b b b b b b b b b b b b b b b b bh bh bh bh bh bh bh b b b bc bc bc bc bc bc bc b b b b b b b b bf bf bf bf bf bf b b b b b b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b bt bt bt bt b b b b b b b b b b b bs bs bs bs bs bs b b b b b b b b b b b b b b b b b b bg bg bg bg bg bg bg b b b b b b b b b b b bf bf bf bf bf bf b b b b b b b b b bo bo bo bo bo bo b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bs bs bs bs bs bs b b b b b b b b b b b b b b b b b b bg bg bg bg bg bg bg b b b b b b b b b b b b b b b b b b b b b b b b b b bo bo bo bo bo bo b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b br br br br b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bp bp bp bp bp bp bp b b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bq bq bq bq bq b b b b b b b b b b b b b b bp bp bp bp bp bp bp b b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bq bq bq bq bq b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
Deviation maps: example
tmap deviation foreign01, /// x(x) y(y) /// map("Milano-GeneralMap.dta") /// scolor(red)
16 Percentage foreign population, by administrative district: Deviations from overall mean. Milano 2001 Solid symbols=positive deviations - Hollow symbols=negative deviations
Symbol size proportional to absolute value of deviations
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Label maps: example
tmap label district, /// x(x) y(y) /// map("Milano-GeneralMap.dta") /// llength(30) /// lsize(0.8) /// lcolor(navy)
17
Administrative districts of Milano
Niguarda-CàGranda-Bicocca
Vialba-Certosa-Quarto Oggiaro Monza-Padova
Bovisa-Dergano
Feltre-Carnia-Cimiano-Ortica-L
Centro Direzionale-Greco-Zara
San Siro-QT8-Gallaratese
Venezia-Buenos Ayres
Magenta-Sempione Centro Studi-Argonne
Centro Storico
Baggio-Forze Armate
Vittoria-Romana-Molise Lorenteggio-Inganni Forlanini-Taliedo
Ticinese-Genova
Barona-Ronchetto
Corvetto-Rogoredo-Vigentina
Chiesa Rossa-Gratosoglio
Point maps: examples tmap dot, /// x(x) y(y) /// map("Milano-GeneralMap.dta")
18 Location of police stations.
Milano, 2004
¢ ¢ ¢ ¡ ¡ ¡
¡ ¡ ¡
£ £
¤ ¤
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Point maps: examples tmap dot, /// x(x) y(y) /// map("Milano-GeneralMap.dta") /// by(type)
19 Location of police stations, by police force.
Milano, 2004
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ÉÊ ¦ÉÊ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ Polizia di stato Carabinieri
Ackowledgments
ò The color schemes used in tmap choropleth were designed by Dr. Cynthia A. Brewer, Department of Geography, The Pennsylvania State University, University Park, Pennsylvania, USA. The color schemes are used with Dr. Brewer’s permission and are from the ColorBrewer map design tool available at ColorBrewer.org
20 Ackowledgments
ò I wish to thank an anonymous reviewer and Nick Cox for their valuable suggestions and for helping improve the tmap package ò Any remaining errors are mine
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