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<!DOCTYPE html>
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<title>Chapter 7 Identifying the poor group | Multidimensional poverty measurement: A statistical approach with applications</title>
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<div class="book without-animation with-summary font-size-2 font-family-1" data-basepath=".">
<div class="book-summary">
<nav role="navigation">
<ul class="summary">
<li class="chapter" data-level="" data-path="preface.html"><a href="preface.html"><i class="fa fa-check"></i>Preface</a></li>
<li class="chapter" data-level="1" data-path="Chapter-1.html"><a href="Chapter-1.html"><i class="fa fa-check"></i><b>1</b> Poverty and measurement theory principles</a><ul>
<li class="chapter" data-level="1.1" data-path="Chapter-1.html"><a href="Chapter-1.html#the-concept-of-poverty"><i class="fa fa-check"></i><b>1.1</b> The Concept of Poverty</a></li>
<li class="chapter" data-level="1.2" data-path="Chapter-1.html"><a href="Chapter-1.html#Chapter-1-dimensions"><i class="fa fa-check"></i><b>1.2</b> Theoretical dimensions of poverty</a></li>
<li class="chapter" data-level="1.3" data-path="Chapter-1.html"><a href="Chapter-1.html#the-measurement-of-poverty-and-its-challenges"><i class="fa fa-check"></i><b>1.3</b> The measurement of poverty and its challenges</a><ul>
<li class="chapter" data-level="1.3.1" data-path="Chapter-1.html"><a href="Chapter-1.html#challenges-in-selection-of-dimensions-contents-cut-offs-and-weights"><i class="fa fa-check"></i><b>1.3.1</b> Challenges in selection of dimensions, contents, cut offs and weights</a></li>
<li class="chapter" data-level="1.3.2" data-path="Chapter-1.html"><a href="Chapter-1.html#challenges-in-aggregation-and-identification-of-the-poor"><i class="fa fa-check"></i><b>1.3.2</b> Challenges in aggregation and identification of the poor</a></li>
</ul></li>
<li class="chapter" data-level="1.4" data-path="Chapter-1.html"><a href="Chapter-1.html#the-poor-and-the-not-poor-the-poverty-line"><i class="fa fa-check"></i><b>1.4</b> The poor and the not poor: The poverty line</a></li>
<li class="chapter" data-level="1.5" data-path="Chapter-1.html"><a href="Chapter-1.html#a-brief-on-multidimensional-poverty-measurement"><i class="fa fa-check"></i><b>1.5</b> A brief on multidimensional poverty measurement</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="Chapter-2.html"><a href="Chapter-2.html"><i class="fa fa-check"></i><b>2</b> Poverty and measurement theory: A statistical framework</a><ul>
<li class="chapter" data-level="2.1" data-path="Chapter-2.html"><a href="Chapter-2.html#workflow-in-poverty-measurement-a-falsifiable-framework"><i class="fa fa-check"></i><b>2.1</b> Workflow in poverty measurement: A falsifiable framework</a></li>
<li class="chapter" data-level="2.2" data-path="Chapter-2.html"><a href="Chapter-2.html#samplingspace"><i class="fa fa-check"></i><b>2.2</b> Identification of the sampling space</a></li>
<li class="chapter" data-level="2.3" data-path="Chapter-2.html"><a href="Chapter-2.html#selection-of-dimensions-and-indicators"><i class="fa fa-check"></i><b>2.3</b> Selection of dimensions and indicators</a></li>
<li class="chapter" data-level="2.4" data-path="Chapter-2.html"><a href="Chapter-2.html#aggregation-and-weighting"><i class="fa fa-check"></i><b>2.4</b> Aggregation and weighting</a><ul>
<li class="chapter" data-level="2.4.1" data-path="Chapter-2.html"><a href="Chapter-2.html#splitting-the-population-into-meaningful-groups"><i class="fa fa-check"></i><b>2.4.1</b> Splitting the population into meaningful groups</a></li>
</ul></li>
<li class="chapter" data-level="2.5" data-path="Chapter-2.html"><a href="Chapter-2.html#measurement-theory-as-an-statistical-framework"><i class="fa fa-check"></i><b>2.5</b> Measurement theory as an statistical framework</a></li>
<li class="chapter" data-level="2.6" data-path="Chapter-2.html"><a href="Chapter-2.html#poverty-and-error-in-measurement"><i class="fa fa-check"></i><b>2.6</b> Poverty and error in measurement</a></li>
<li class="chapter" data-level="2.7" data-path="Chapter-2.html"><a href="Chapter-2.html#measurement-model-for-poverty"><i class="fa fa-check"></i><b>2.7</b> Measurement model for poverty</a></li>
<li class="chapter" data-level="2.8" data-path="Chapter-2.html"><a href="Chapter-2.html#Chapter-2-blueprint"><i class="fa fa-check"></i><b>2.8</b> Blueprints and poverty measurement models</a></li>
<li class="chapter" data-level="2.9" data-path="Chapter-2.html"><a href="Chapter-2.html#measurement-theory-and-principles"><i class="fa fa-check"></i><b>2.9</b> Measurement theory and principles</a><ul>
<li class="chapter" data-level="2.9.1" data-path="Chapter-2.html"><a href="Chapter-2.html#origins-of-measurement-theory"><i class="fa fa-check"></i><b>2.9.1</b> Origins of measurement theory</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="3" data-path="Chapter-3.html"><a href="Chapter-3.html"><i class="fa fa-check"></i><b>3</b> Reliability in poverty measurement</a><ul>
<li class="chapter" data-level="3.1" data-path="Chapter-3.html"><a href="Chapter-3.html#intuition-to-the-concept-of-reliability"><i class="fa fa-check"></i><b>3.1</b> Intuition to the concept of reliability</a></li>
<li class="chapter" data-level="3.2" data-path="Chapter-3.html"><a href="Chapter-3.html#reliability-theory"><i class="fa fa-check"></i><b>3.2</b> Reliability theory</a></li>
<li class="chapter" data-level="3.3" data-path="Chapter-3.html"><a href="Chapter-3.html#Chapter-3-measuresrel"><i class="fa fa-check"></i><b>3.3</b> Statistical measures of reliability</a></li>
<li class="chapter" data-level="3.4" data-path="Chapter-3.html"><a href="Chapter-3.html#itemlevelrel"><i class="fa fa-check"></i><b>3.4</b> Item-level reliability and weighting</a></li>
<li class="chapter" data-level="3.5" data-path="Chapter-3.html"><a href="Chapter-3.html#relestimation"><i class="fa fa-check"></i><b>3.5</b> Estimation of Reliability</a><ul>
<li class="chapter" data-level="3.5.1" data-path="Chapter-3.html"><a href="Chapter-3.html#overall-reliability"><i class="fa fa-check"></i><b>3.5.1</b> Overall reliability</a></li>
<li class="chapter" data-level="3.5.2" data-path="Chapter-3.html"><a href="Chapter-3.html#Chapter-3-expoverel"><i class="fa fa-check"></i><b>3.5.2</b> Exploratory (non-model based) estimation of overall reliability</a></li>
<li class="chapter" data-level="3.5.3" data-path="Chapter-3.html"><a href="Chapter-3.html#model-based-estimation-of-overall-reliability"><i class="fa fa-check"></i><b>3.5.3</b> Model-based estimation of overall reliability</a></li>
<li class="chapter" data-level="3.5.4" data-path="Chapter-3.html"><a href="Chapter-3.html#overall-reliability-and-population-orderings"><i class="fa fa-check"></i><b>3.5.4</b> Overall reliability and population orderings</a></li>
<li class="chapter" data-level="3.5.5" data-path="Chapter-3.html"><a href="Chapter-3.html#item-level-reliability"><i class="fa fa-check"></i><b>3.5.5</b> Item-level reliability</a></li>
</ul></li>
<li class="chapter" data-level="3.6" data-path="Chapter-3.html"><a href="Chapter-3.html#multidimensional-item-reliability-evaluation"><i class="fa fa-check"></i><b>3.6</b> Multidimensional item-reliability evaluation</a><ul>
<li class="chapter" data-level="3.6.1" data-path="Chapter-3.html"><a href="Chapter-3.html#item-reliability-and-monotonicity"><i class="fa fa-check"></i><b>3.6.1</b> Item-reliability and monotonicity</a></li>
</ul></li>
<li class="chapter" data-level="3.7" data-path="Chapter-3.html"><a href="Chapter-3.html#real-data-example"><i class="fa fa-check"></i><b>3.7</b> Real data example</a><ul>
<li class="chapter" data-level="3.7.1" data-path="Chapter-3.html"><a href="Chapter-3.html#overall-reliability-1"><i class="fa fa-check"></i><b>3.7.1</b> Overall reliability</a></li>
<li class="chapter" data-level="3.7.2" data-path="Chapter-3.html"><a href="Chapter-3.html#item-level-reliability-1"><i class="fa fa-check"></i><b>3.7.2</b> Item-level reliability</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="4" data-path="Chapter-4.html"><a href="Chapter-4.html"><i class="fa fa-check"></i><b>4</b> Validity in poverty measurement</a><ul>
<li class="chapter" data-level="4.1" data-path="Chapter-4.html"><a href="Chapter-4.html#intuition-to-the-concept-of-validity"><i class="fa fa-check"></i><b>4.1</b> Intuition to the concept of validity</a></li>
<li class="chapter" data-level="4.2" data-path="Chapter-4.html"><a href="Chapter-4.html#theory-of-validity"><i class="fa fa-check"></i><b>4.2</b> Theory of validity</a></li>
<li class="chapter" data-level="4.3" data-path="Chapter-4.html"><a href="Chapter-4.html#methods-for-the-analysis-validity"><i class="fa fa-check"></i><b>4.3</b> Methods for the analysis validity</a><ul>
<li class="chapter" data-level="4.3.1" data-path="Chapter-4.html"><a href="Chapter-4.html#criterion-validity"><i class="fa fa-check"></i><b>4.3.1</b> Criterion validity</a></li>
<li class="chapter" data-level="4.3.2" data-path="Chapter-4.html"><a href="Chapter-4.html#construct-validity"><i class="fa fa-check"></i><b>4.3.2</b> Construct validity</a></li>
</ul></li>
<li class="chapter" data-level="4.4" data-path="Chapter-4.html"><a href="Chapter-4.html#validity-assessment"><i class="fa fa-check"></i><b>4.4</b> Validity assessment</a><ul>
<li class="chapter" data-level="4.4.1" data-path="Chapter-4.html"><a href="Chapter-4.html#criterion-validity-1"><i class="fa fa-check"></i><b>4.4.1</b> Criterion Validity</a></li>
<li class="chapter" data-level="4.4.2" data-path="Chapter-4.html"><a href="Chapter-4.html#construct-validity-1"><i class="fa fa-check"></i><b>4.4.2</b> Construct Validity</a></li>
<li class="chapter" data-level="4.4.3" data-path="Chapter-4.html"><a href="Chapter-4.html#a-joint-assessment-criterion-and-construct-validity"><i class="fa fa-check"></i><b>4.4.3</b> A joint assessment: Criterion and construct validity</a></li>
<li class="chapter" data-level="4.4.4" data-path="Chapter-4.html"><a href="Chapter-4.html#real-data-example-1"><i class="fa fa-check"></i><b>4.4.4</b> Real-data example</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="5" data-path="Chapter-5.html"><a href="Chapter-5.html"><i class="fa fa-check"></i><b>5</b> Comparability in poverty measurement</a><ul>
<li class="chapter" data-level="5.1" data-path="Chapter-5.html"><a href="Chapter-5.html#measurement-invariance"><i class="fa fa-check"></i><b>5.1</b> Measurement invariance</a></li>
<li class="chapter" data-level="5.2" data-path="Chapter-5.html"><a href="Chapter-5.html#introduction-to-key-aspects-of-measurement-invariance"><i class="fa fa-check"></i><b>5.2</b> Introduction to key aspects of measurement invariance</a></li>
<li class="chapter" data-level="5.3" data-path="Chapter-5.html"><a href="Chapter-5.html#methods-for-the-assessment-of-measurement-invariance"><i class="fa fa-check"></i><b>5.3</b> Methods for the assessment of Measurement Invariance</a><ul>
<li class="chapter" data-level="5.3.1" data-path="Chapter-5.html"><a href="Chapter-5.html#multiple-group-factor-analysis"><i class="fa fa-check"></i><b>5.3.1</b> Multiple Group Factor Analysis</a></li>
<li class="chapter" data-level="5.3.2" data-path="Chapter-5.html"><a href="Chapter-5.html#the-alignment-method"><i class="fa fa-check"></i><b>5.3.2</b> The alignment method</a></li>
</ul></li>
<li class="chapter" data-level="5.4" data-path="Chapter-5.html"><a href="Chapter-5.html#real-data-analysis-of-measurement-invariance"><i class="fa fa-check"></i><b>5.4</b> Real-data analysis of Measurement Invariance</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html"><i class="fa fa-check"></i><b>6</b> Scale equating and linking</a><ul>
<li class="chapter" data-level="6.1" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#intuition-to-scale-equating"><i class="fa fa-check"></i><b>6.1</b> Intuition to scale equating</a></li>
<li class="chapter" data-level="6.2" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#theory-of-scale-equating-theoryequating"><i class="fa fa-check"></i><b>6.2</b> Theory of scale equating [#Theoryequating]</a><ul>
<li class="chapter" data-level="6.2.1" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#workflow-in-scale-equating"><i class="fa fa-check"></i><b>6.2.1</b> Workflow in scale equating</a></li>
<li class="chapter" data-level="6.2.2" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#theory-of-irt-scale-equating"><i class="fa fa-check"></i><b>6.2.2</b> Theory of IRT scale equating</a></li>
</ul></li>
<li class="chapter" data-level="6.3" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#data-and-designs-in-test-equating"><i class="fa fa-check"></i><b>6.3</b> Data and designs in test equating</a><ul>
<li class="chapter" data-level="6.3.1" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#single-group-design"><i class="fa fa-check"></i><b>6.3.1</b> Single group design</a></li>
<li class="chapter" data-level="6.3.2" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#equivalent-groups-design"><i class="fa fa-check"></i><b>6.3.2</b> Equivalent groups design</a></li>
<li class="chapter" data-level="6.3.3" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#non-equivalent-groups-with-anchor-test-design"><i class="fa fa-check"></i><b>6.3.3</b> Non Equivalent Groups with Anchor test Design</a></li>
<li class="chapter" data-level="6.3.4" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#non-equivalent-groups-with-covariates-design"><i class="fa fa-check"></i><b>6.3.4</b> Non Equivalent Groups with Covariates Design</a></li>
</ul></li>
<li class="chapter" data-level="6.4" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#example-of-irt-equating-neat-design-with-simulated-data-in-r"><i class="fa fa-check"></i><b>6.4</b> Example of IRT equating (NEAT design) with simulated data in R</a></li>
<li class="chapter" data-level="6.5" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#real-data-example-2"><i class="fa fa-check"></i><b>6.5</b> Real-data example</a><ul>
<li class="chapter" data-level="6.5.1" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#step-1-finding-the-anchors.-mi-analysis"><i class="fa fa-check"></i><b>6.5.1</b> Step 1: Finding the anchors. MI Analysis</a></li>
<li class="chapter" data-level="6.5.2" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#step-2-extract-irt-parameters-for-each-of-10-indices"><i class="fa fa-check"></i><b>6.5.2</b> Step 2: Extract IRT parameters for each of 10 indices</a></li>
<li class="chapter" data-level="6.5.3" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#step-3-estimating-the-constants-for-equating"><i class="fa fa-check"></i><b>6.5.3</b> Step 3: Estimating the constants for equating</a></li>
<li class="chapter" data-level="6.5.4" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#step-4-applying-the-constants-and-obtaning-equated-scores"><i class="fa fa-check"></i><b>6.5.4</b> Step 4: Applying the constants and obtaning equated scores</a></li>
<li class="chapter" data-level="6.5.5" data-path="scale-equating-and-linking.html"><a href="scale-equating-and-linking.html#finding-equated-poverty-lines"><i class="fa fa-check"></i><b>6.5.5</b> Finding equated poverty lines</a></li>
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<li class="chapter" data-level="7" data-path="identifying-the-poor-group.html"><a href="identifying-the-poor-group.html"><i class="fa fa-check"></i><b>7</b> Identifying the poor group</a><ul>
<li class="chapter" data-level="7.1" data-path="identifying-the-poor-group.html"><a href="identifying-the-poor-group.html#the-poverty-line"><i class="fa fa-check"></i><b>7.1</b> The poverty line</a></li>
<li class="chapter" data-level="7.2" data-path="identifying-the-poor-group.html"><a href="identifying-the-poor-group.html#perspectives-on-the-poverty-line-union-and-intersection-approaches"><i class="fa fa-check"></i><b>7.2</b> Perspectives on the poverty line: Union and intersection approaches</a></li>
<li class="chapter" data-level="7.3" data-path="identifying-the-poor-group.html"><a href="identifying-the-poor-group.html#the-human-rights-based-approach"><i class="fa fa-check"></i><b>7.3</b> The human rights-based approach</a></li>
<li class="chapter" data-level="7.4" data-path="identifying-the-poor-group.html"><a href="identifying-the-poor-group.html#the-ubn-weighted-approach"><i class="fa fa-check"></i><b>7.4</b> The UBN weighted approach</a></li>
<li class="chapter" data-level="7.5" data-path="identifying-the-poor-group.html"><a href="identifying-the-poor-group.html#the-partially-weighted-approach"><i class="fa fa-check"></i><b>7.5</b> The partially-weighted approach</a></li>
<li class="chapter" data-level="7.6" data-path="identifying-the-poor-group.html"><a href="identifying-the-poor-group.html#the-bristol-optimal-approach"><i class="fa fa-check"></i><b>7.6</b> The Bristol Optimal approach</a></li>
<li class="chapter" data-level="7.7" data-path="identifying-the-poor-group.html"><a href="identifying-the-poor-group.html#example-with-simulated-data"><i class="fa fa-check"></i><b>7.7</b> Example with simulated data</a></li>
<li class="chapter" data-level="7.8" data-path="identifying-the-poor-group.html"><a href="identifying-the-poor-group.html#real-data-analysis"><i class="fa fa-check"></i><b>7.8</b> Real-data analysis</a></li>
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<li class="chapter" data-level="8" data-path="final-thoughts.html"><a href="final-thoughts.html"><i class="fa fa-check"></i><b>8</b> Final thoughts</a><ul>
<li class="chapter" data-level="8.1" data-path="final-thoughts.html"><a href="final-thoughts.html#the-future-of-data-production-in-multidimensional-poverty-measurement"><i class="fa fa-check"></i><b>8.1</b> The future of data production in multidimensional poverty measurement</a></li>
<li class="chapter" data-level="8.2" data-path="final-thoughts.html"><a href="final-thoughts.html#advanced-topics-in-multidimensional-poverty-measurement"><i class="fa fa-check"></i><b>8.2</b> Advanced topics in multidimensional poverty measurement</a></li>
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<li class="chapter" data-level="9" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i><b>9</b> References</a></li>
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<i class="fa fa-circle-o-notch fa-spin"></i><a href="./">Multidimensional poverty measurement: A statistical approach with applications</a>
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<div id="identifying-the-poor-group" class="section level1">
<h1><span class="header-section-number">Chapter 7</span> Identifying the poor group</h1>
<div id="the-poverty-line" class="section level2">
<h2><span class="header-section-number">7.1</span> The poverty line</h2>
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<div id="perspectives-on-the-poverty-line-union-and-intersection-approaches" class="section level2">
<h2><span class="header-section-number">7.2</span> Perspectives on the poverty line: Union and intersection approaches</h2>
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<div id="the-human-rights-based-approach" class="section level2">
<h2><span class="header-section-number">7.3</span> The human rights-based approach</h2>
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<div id="the-ubn-weighted-approach" class="section level2">
<h2><span class="header-section-number">7.4</span> The UBN weighted approach</h2>
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<div id="the-partially-weighted-approach" class="section level2">
<h2><span class="header-section-number">7.5</span> The partially-weighted approach</h2>
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<div id="the-bristol-optimal-approach" class="section level2">
<h2><span class="header-section-number">7.6</span> The Bristol Optimal approach</h2>
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<div id="example-with-simulated-data" class="section level2">
<h2><span class="header-section-number">7.7</span> Example with simulated data</h2>
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<div id="real-data-analysis" class="section level2">
<h2><span class="header-section-number">7.8</span> Real-data analysis</h2>
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