COMIC: A tool for composite indices evaluation

COMIC: A tool for composite indices

evaluation

P. Massoli, M. Mazziotta, A. Pareto, C. Rinaldelli

Padua, 17th -18th September 2015

Contents

1. Objectives

2. Software requisites

3. What the software can do?

4. Implemented methods

5. Directory tree

6. Input data

Graphical user interface

7. Output data

The “Table of Contents” file

Plots & Tables

8. Further developments

COMIC: A tool for composite indices evaluation


1

Objectives

2

COMIC = COMposite Indices Creator

It has been entirely developed by the authors who are members of the

BES Committee at the Italian Institute of Statistics - ISTAT

This software enables the user to:

calculate composite indices and their subsequent ranks

compare differnt methods of calculation in order to choose the most

appropriate one with ease

Write efficient reports about the results obtained



Software requisites

3

COMIC has been requested to be entirely written in SAS in order to allow experts within the BES Committee to partecipate actively in the implementation and integration of the methods of composition.

COMIC is relatively easy to use and it doesn’t necessitate installation: one simply copies the software on their computer (indipendently of the operative system: Windows, Linux, Unix, ...).

No particular skills are needed to run the software.

COMIC has been developed by using a SAS System Base setup and thus, no particular and specific SAS packages are required as these could hinder its use.



What the software can do?

4

It deals with data pertaining to any type of statistical unit. It currently optimizes

calculations when dealing with statistical units like: regions and groups thereof

(macroregions)

It performs exploratory analysis of the input data (Correlation matrox, ACP,

Factor analysis, communalities, scree plots, matrix plots, …)

It evaluates the rank for each synthesys method or composite index selected

It creates geographical maps of the values of the composite indices (solely for

those statistical units for which it makes sense)

It creates historical series of the composite indices (solely in the case of input

data relevant to two or more time periods)

It creates “speed-acceleration plots (if both a static and a dynamic methods are

selected)

It compares the methods selected by means of cograduation matrices and

scatterplots

It performs an Influence analysus (reports and plots)



Implemented methods (1/6)

5

Data la matrice X={xijt} di n righe (unità statistiche), m colonne (indicatori) e p strati (anni), si

calcola la matrice trasformata R={rijt}, con:

negativa; polarità ha indicatorel' se )Min(Max

)(Max

positiva; polarità ha indicatorel' se )Min(Max

)Min(

jx

jx

r

jj

j

jj

j

xx

ijtx

xx

xijt

ijt

dove jxMin e

jxMax sono, rispettivamente, il minimo e il massimo dell’indicatore j, tra le n

unità statistiche, nei p anni considerati o dei valori forniti dall’esterno.

L’indice sintetico, per l’unità i al tempo t, è dato dalla formula:

m

rm

j ijt

it

11-0M .

Algebraic mean of 0-1 indices (Media indici 0-1)




6


calcola la matrice trasformata Z={zijt}, con:

negativa; polarità ha indicatorel' se S

)M(

positiva; polarità ha indicatorel' se S

)M(

jx

jx

z

jt

jt

jt

jt

x

xijt

x

xijt

ijt

dove jtxM e

jtxS sono, rispettivamente, la media e lo scostamento quadratico medio

dell’indicatore j al tempo t.


m

zm

j ijtz

it

1M .

Algebraic mean of z-scores (Media z-scores)




7


calcola la matrice trasformata Z={zijt}, con:

negativa; polarità ha indicatorel' se 10 S

)M(100

positiva; polarità ha indicatorel' se 10S

)M(100

jx

jx

z

jt

jt

jt

jt

x

xijt

x

xijt

ijt

dove jtxM e

jtxS sono, rispettivamente, la media e lo scostamento quadratico medio

dell’indicatore j al tempo t. L’indice sintetico, per l’unità i al tempo t, è dato dalla formula:

itzzit ititcvSMMPI -/

dove m

zm

j ijt

zit

1M ;

m

zm

j zijt

z

it

it

1

2)M(S ;

it

it

z

z

itM

Scv .

MPI (Mazziotta-Pareto Index)



Implementedmethods (4/6)

8



negativa; polarità ha indicatorel' se 7060)Min(Max

)(Max

positiva; polarità ha indicatorel' se 7060)Min(Max

)Min(

jx

jx

r

jtjt

j

jtjt

jt

xx

ijtx

xx

xijt

ijt

dove jtxMin e

jtxMax sono, rispettivamente, il minimo e il massimo dell’indicatore j, tra le n

unità statistiche, nei p anni considerati o dei valori calcolati in modo da porre uguale a 100 un

valore di riferimento (per es., la media nazionale nell’anno base).


itrrit ititcvSMMPI -/

.

AMPI (Adjusted MPI)




9

Data la matrice X={xijt} di n righe (unità statistiche), m colonne (indicatori) e p strati (anni),

l’indice sintetico ‘statico’, per l’unità i al tempo t, è dato dalla formula:

m

j

m

bjt

ijt

itx

x

1

1

100JS

dove bjtx è il valore base dell’indicatore j al tempo t (per es., la media nazionale nell’anno di

riferimento). L’indice sintetico ‘dinamico’, per l’unità i al tempo t, è dato dalla formula:

m

j

m

tij

ijt

itx

x

1

1

)1(

100JD

dove )1( tijx è il valore dell’indicatore j, per l’unità i al tempo t-1.

Jevons index: static and dynamic




10



negativa; polarità ha indicatorel' se 1198)Min(Max

)(Max

positiva; polarità ha indicatorel' se 1198)Min(Max

)Min(

jx

jx

r

jtjt

j

jtjt

jt

xx

ijtx

xx

xijt

ijt

dove jtxMin e

jtxMax sono, rispettivamente, il minimo e il massimo dell’indicatore j, tra le n

unità statistiche, nei p anni considerati o dei valori calcolati in modo da porre uguale a 100 un

valore di riferimento (per es., la media nazionale nell’anno base).


m

j

mijtit r

1

1

IMG .

IMG (Indice Media Geometrica)



Directory tree

11

COMIC is distributed by means of a compressed archive. When it is

uncompressed, the directory tree is as follows:

Directory DATI which contains the following predefined sub-directories:

Input: input data can be stored here (or in any other directory

selected by the user);

Maps: where COMIC searches for all the necessary data in order

to create a geographical map;

Output: output data can be sored here (or in any other directory

selected by the user);

Directory PGM (where all the SAS macros are stored)

Directory SETTINGS (where all execution parameters are stored in

order to facilitate repeated runs)



Input data (1/2)

12

Four input data set types can be selected:

Microsoft Excel Worksheet (.xls not .xlsx)

ASCII - Comma Separated Values (.csv)

ASCII - Tab Separated Values (.txt)

SAS data set

Metodi per la costruzione di indici sintetici: teoria e pratica – P. Massoli

Roma, 6-7 novembre 2014

Input data (2/2)

13 COMIC: A tool for composite indices evaluation


Region year type wgt ind1 ind2 ind3 ind4 Piemonte 2006 2 1 68,6 7,1 27 10,4 Valle d'Aosta 2006 2 1 70,8 5,4 27 24,2 Liguria 2006 2 1 65,9 8,8 34,1 18,3 Lombardia 2006 2 1 70,4 6,9 25,3 16,7 Bolzano/Bo. 2006 2 1 73,6 3,8 33,5 25,9 Trento 2006 2 1 69,4 6 19 17,6 Veneto 2006 2 1 69,3 7,2 22,5 13,5 Friuli-V.G. 2006 2 1 68,3 7,1 14,9 16,6 Emilia-Rom. 2006 2 1 73,1 6,2 26,4 19,8 Toscana 2006 2 1 68,7 8,7 17,1 16,6 Umbria 2006 2 1 66,9 10,6 25,2 19,3 Marche 2006 2 1 68,2 8,8 30,9 8,5 Lazio 2006 2 1 63,5 14,4 16 23,6 Abruzzo 2006 2 1 62 13,1 17,7 18 Molise 2006 2 1 56,6 20,9 13,4 17,8 Campania 2006 2 1 48,3 29,6 17,2 25,7 Puglia 2006 2 1 49,6 25,8 22,9 22,2 Basilicata 2006 2 1 54,7 23,3 19,6 26,2 Calabria 2006 2 1 49,9 30,1 13,3 36,5 Sicilia 2006 2 1 49,1 29,8 16,2 29,3 Sardegna 2006 2 1 56 21,6 10,2 18,4 Italia 2006 2 62,5 14,5 21,1 20,3 Piemonte 2007 2 1 68,8 7,9 17,5 11,5 Valle d'Aosta 2007 2 1 72,1 5,4 21,8 26,9

Graphical User Interface (1/6)

14

In order that COMIC may be used even by users with low software skills,

a simple but effective graphic user interface has been created:

The %WINDOW/%DISPLAY SAS Base macro facility has been

implemented in order to catch all the variables/parameters necessary

for a correct COMIC run.

Users communicate with COMIC only by using the GUI (no SAS code

needs to be written).

Many calculations take place automatically and all the data caught by

using the GUI is saved in ASCII files in the SETTINGS directory.



Graphical User Interface: menu (2/6)



Graphical User Interface: base indicators (3/6)



Graphical User Interface: weights (4/6)



Graphical User Interface: min/max values (5/6)



Graphical User Interface: data time periods (6/6)



Output data

20

While the software is running, an output sub-directory by the same name

as that of the input data file is created automatically (or overwritten if it

already exists). The directory in question is created within the parent

directory DATI\output or any other directory selected by the user. The

output directory tree in question is as follows:

• Dati: where all the output datasets SAS are saved (ranks, historical

series, …);

• Word: where all the reports in rich text format (rtf) are saved;

• Html: where all the reports written in html language are saved;

In order to facilitate navigation among the reports, a hypertextual “table of

contents” file written in html (sommario.html) is automatically created in

the output directory;



Table of contents (1/4)



Plots and tables (1/11)



Further developments



Some other SAS procedure can be implemented to

enhance exploratory analysis of input data;

World and Europe geograèhical mapping feature will

be added to those already existing;

Another robustness analysis will be added to the

already existing influence analysis in order to better

investigate the implemented methods robustness.

COMIC: A tool for composite indices evaluation

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