<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0188-4611</journal-id>
<journal-title><![CDATA[Investigaciones geográficas]]></journal-title>
<abbrev-journal-title><![CDATA[Invest. Geog]]></abbrev-journal-title>
<issn>0188-4611</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Geografía]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0188-46112022000300105</article-id>
<article-id pub-id-type="doi">10.14350/rig.60615</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Alternativas de estandarización para índices compuestos espacio-temporales. El caso del rezago educativo en los estados de México, 2000 a 2020]]></article-title>
<article-title xml:lang="en"><![CDATA[Standardization alternatives for space-time composite indices. The case of educational backwardness in the states of Mexico from 2000 to 2020]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Treviño Cantú]]></surname>
<given-names><![CDATA[Jesús Antonio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma de Nuevo León Facultad de arquitectura ]]></institution>
<addr-line><![CDATA[Ciudad Guadalupe Nuevo León]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<numero>109</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0188-46112022000300105&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0188-46112022000300105&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0188-46112022000300105&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Los investigadores de índices compuestos han detectado y tratado de eliminar, con poco éxito hasta ahora, la ponderación implícita de los datos porque generan índices distorsionados. El origen de esta distorsión suele adjudicarse a las variables con distinto rango de valores, al valor máximo y mínimo desigual entre ellas o a la de asimetría de cada variable. El procedimiento para abordar este triple reto es la estandarización de los datos. A la fecha no hay un procedimiento de este tipo que corrija simultáneamente este triple problema y, con ello, la ponderación implícita. El igual máximo y mínimo entre variables resuelve el problema de rangos desiguales, pero no corrige la asimetría en cada una de ellas. El rango igual entre variables no implica igual máximo y mínimo entre ellas ni garantiza simetría en cada variable. Finalmente, la corrección de la asimetría en cada variable no implica igual máximo y mínimo ni igual rango entre variables. El objetivo del presente estudio es sugerir e ilustrar un procedimiento de estandarización de variables que elimina la ponderación implícita de cada variable. Las estandarizaciones revisadas en este trabajo para elaborar índices compuestos resuelven solo de forma parcial el problema de la ponderación implícita por lo que este trabajo propone un procedimiento de estandarización que resuelve simultáneamente el triple reto impuesto por los rangos disparejos, los máximos y mínimos desiguales y la asimetría. El nuevo procedimiento propuesto, la estandarización balanceada, soluciona el problema de la ponderación implícita en el tiempo y el espacio, en la agregación transversal y longitudinal de las variables de las distintas unidades de observación. Este trabajo ilustra el procedimiento de estandarización propuesto con las variables del rezago educativo en los estados de México. La metodología propuesta es aplicable a cualquier tema donde la estandarización espacio temporal sea necesaria.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Researchers of composite indexes have detected and attempted to eliminate the implicit weighting of data because it leads to biased indexes, with little success so far. This bias is usually attributed to variables having different ranges of values, unequal maximum and minimum values between variables, or the asymmetry of each variable. The procedure for addressing this triple challenge is data standardization. No procedure is currently available that simultaneously solves this triple issue and, with it, implicit weighting. Equal maximum and minimum values between variables solve the unequal-range issue but do not correct the asymmetry of each variable. An equal range between variables does not imply equal maximum and mínimum values between them, nor does it guarantee the symmetry of each variable. Finally, correcting the asymmetry of each variable does not imply equal maximum and minimum values or equal ranges between variables. The objective of this study is to suggest and illustrate a variable standardization procedure that eliminates the implicit weighting of each variable. The standardizations reviewed in this paper to elaborate composite indexes solve only partially the implicit weighting issue. Thus, this paper proposes a standardization procedure that simultaneously solves the triple challenge imposed by unequal ranges, unequal maxima and minima, and asymmetry. The propose new procedure, balanced standardization, solves the issue of implicit weighting in time and space in the cross-sectional and longitudinal aggregation of variables of the different observation units. This work illustrates the proposed standardization procedure with variables related to the educational lag in the states of Mexico. The methodology proposed herein is applicable to any topic requiring spatio-temporal standardization.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[procedimientos de estandarización]]></kwd>
<kwd lng="es"><![CDATA[ponderación implícita]]></kwd>
<kwd lng="es"><![CDATA[rangos desiguales]]></kwd>
<kwd lng="es"><![CDATA[valores máximo y mínimo distintos]]></kwd>
<kwd lng="es"><![CDATA[asimetría]]></kwd>
<kwd lng="en"><![CDATA[standardization procedures]]></kwd>
<kwd lng="en"><![CDATA[implicit weighting]]></kwd>
<kwd lng="en"><![CDATA[unequal ranges]]></kwd>
<kwd lng="en"><![CDATA[different minimum and maximum values]]></kwd>
<kwd lng="en"><![CDATA[asymmetry]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Angoa]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Pérez-Mendoza]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Polèse]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Los tres Méxicos: Análisis de la distribución espacial del empleo en la industria y los servicios superiores, por tamaño urbano y por región]]></article-title>
<source><![CDATA[EURE]]></source>
<year>2009</year>
<volume>35</volume>
<numero>104</numero>
<issue>104</issue>
<publisher-loc><![CDATA[Santiago ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Acharya]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Porwal]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A vulnerability index for the management of and response to the COVID-19 epidemic in India: An ecological study]]></article-title>
<source><![CDATA[The Lancet Global Health]]></source>
<year>2020</year>
<volume>8</volume>
<numero>9</numero>
<issue>9</issue>
<page-range>e1142-51</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Balcerzak]]></surname>
<given-names><![CDATA[A. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Multiple-criteria Evaluation of Quality of Human Capital in the European Union Countries]]></article-title>
<source><![CDATA[Economics and Sociology]]></source>
<year>2016</year>
<volume>9</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>11-26</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Brimicombe]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Constructing and evaluating contextual indices using GIS: A case of primary school performance tables]]></article-title>
<source><![CDATA[Environment and Planning A: Economy and Space]]></source>
<year>2000</year>
<volume>32</volume>
<numero>11</numero>
<issue>11</issue>
<page-range>1909-33</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="">
<collab>CONEVAL</collab>
<collab>Consejo Nacional de Evaluación de la Política de Desarrollo Social</collab>
<source><![CDATA[Índice de rezago social 2020 a nivel nacional, estatal, municipal y localidades]]></source>
<year>2021</year>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="">
<collab>CONEVAL</collab>
<collab>Consejo Nacional de Evaluación de la Política de Desarrollo Social</collab>
<source><![CDATA[Los mapas de pobreza en México. Anexo técnico metodológico]]></source>
<year>2007</year>
<publisher-loc><![CDATA[México ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cutillo]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Mazziotta]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Pareto]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A composite index of economic well-being for the european union countries]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Perna]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Salvati]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Schirripa]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Conference of the societá italiana di statistica (SIS)]]></source>
<year>2021</year>
<page-range>546-51</page-range><publisher-name><![CDATA[Pearson]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dasgupta]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Weale]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On measuring the quality of life]]></article-title>
<source><![CDATA[World Development]]></source>
<year>1992</year>
<volume>20</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>119-31</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Exeter]]></surname>
<given-names><![CDATA[D. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Boyle]]></surname>
<given-names><![CDATA[P. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Norman]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Deprivation (im)mobility and cause-specific premature mortality in Scotland]]></article-title>
<source><![CDATA[Social Science &amp; Medicine]]></source>
<year>2011</year>
<volume>72</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>389-97</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Flanagan]]></surname>
<given-names><![CDATA[B. E.]]></given-names>
</name>
<name>
<surname><![CDATA[Gregory]]></surname>
<given-names><![CDATA[E. W.]]></given-names>
</name>
<name>
<surname><![CDATA[Hallisey]]></surname>
<given-names><![CDATA[E. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Heitgerd]]></surname>
<given-names><![CDATA[J. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Lewis]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A social vulnerability index for disaster management]]></article-title>
<source><![CDATA[Journal of Homeland Security and Emergency Management]]></source>
<year>2011</year>
<volume>8</volume>
<numero>1</numero>
<issue>1</issue>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gilthorpe]]></surname>
<given-names><![CDATA[M. S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The importance of normalisation in the construction of deprivation indices]]></article-title>
<source><![CDATA[Journal of Epidemiology &amp; Community Health]]></source>
<year>1995</year>
<volume>49</volume>
<numero>^s2</numero>
<issue>^s2</issue>
<supplement>2</supplement>
<page-range>S45-50</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Heinrich]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Huber]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Rinner]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Making Area-based Composite Indices Comparable across Time-The Role of Standardization and Outlier Removal]]></article-title>
<source><![CDATA[URISA Journal]]></source>
<year>2017</year>
<volume>27</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>37-49</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mazziotta]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Pareto]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Everything you always wanted to know about normalization (but were affraid to ask)]]></article-title>
<source><![CDATA[Rivista Italiana di Economia Demografia e Statistica]]></source>
<year>2021</year>
<volume>75</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>41-52</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mazziotta]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Pareto]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Normalization methods for spatio&#8208;temporal analysis of environmental performance: Revisiting the Min-Max method]]></article-title>
<source><![CDATA[Environmetrics]]></source>
<year>2022</year>
<volume>33</volume>
<numero>5</numero>
<issue>5</issue>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Norman]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Identifying change over time in small area socio-economic deprivation]]></article-title>
<source><![CDATA[Applied Spatial Analysis and Policy]]></source>
<year>2010</year>
<volume>3</volume>
<numero>2-3</numero>
<issue>2-3</issue>
<page-range>107-38</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Norman]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The changing geography of deprivation in Britain: exploiting small area census data 1971 to 2011]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Malleson]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Addis]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Durham]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Heppenstall]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Lovelace]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Norman]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Oldroyd]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[GIS Research UK (GISRUK) 2015 Proceedings]]></source>
<year>2015</year>
<page-range>465-74</page-range><publisher-name><![CDATA[School of Geography, University of Leeds]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<collab>OECD</collab>
<source><![CDATA[Handbook on constructing composite indicators. Methodology and user guide]]></source>
<year>2008</year>
<publisher-loc><![CDATA[Paris ]]></publisher-loc>
<publisher-name><![CDATA[OECD Publications]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ricketts Hein]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ilbery]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Kneafsey]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Distribution of local food activity in England and Wales: An index of food relocalization]]></article-title>
<source><![CDATA[Regional Studies]]></source>
<year>2006</year>
<volume>40</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>289-301</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rinner]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Pietropaolo]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Tracking area-based composite indices over time: change indicators vs. jointly rescaled indicators]]></article-title>
<source><![CDATA[Geomatica]]></source>
<year>2021</year>
<volume>75</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>51-64</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sibley]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Spatial Applications of Exploratory Data Analysis]]></source>
<year>1987</year>
<publisher-loc><![CDATA[Norwich ]]></publisher-loc>
<publisher-name><![CDATA[Geo Books]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
