MULTIPLE CORRESPONDENCE ANALYSIS MCA

12 E D I S I 0 2 T A H U N X V I I 2 0 1 1 gap α=2 individuals receive higher weight the larger their poverty gaps are. For α0 it satisfies monotonicity sensitive to the depth of poverty while if α0 it satisfies transfer sensitive to the distribution among the poor. In multidimensional context, distributional data are presented in a matrix size , in which every typical element corresponds to the achievement of individuali in dimensionj. Following Sen 1976, it is required to identify the poor. The most common approach in the analysis is to define first a threshold level for each dimensionj,under which a person is considered to be deprived. The aggregation of these thresholds can be expressed in a vector of poverty lines . In this way, whether a person is considered in deprived situation or not in every dimension could be defined. This research computes poverty line using two-step FGT method as follows: The non-normalised FGT index is estimated as: 3 where z is the poverty line and x + = maxx,0. The usual normalised FGT index is estimated as 4 The next decision is important to judge someone as multidimensionally poor. A common starting point is to consider all those deprived in at least one dimension, also called union approach. However, stricter criteria can be used, even to the extreme of requiring deprivation in all considered dimensions, the so called intersection approach. According to Alkire and Foster 2008, this constructs a second cut-off: the number of dimensions in which someone is required to be deprived so as to be identified as multidimensionallypoor. This cut-off is named afterk. If is the amount of deprivations suffered by individual i, then he will be considered multidimensionally poor if . Multidimensional poverty indicators are possibly heterogenous in the nature of quantitative indicators income, number of assets or qualitative or categorical indicators ordinal, e.g. level of education and non-ordinal, e.g. occupation, geographical region. This paper assumes variables are either quantitative or qualitative. A variable which has no meaningful ordinal structure cannot be used as poverty or welfare indicator. The first step consists in defining a unique numerical indicator C as a composite of the K primary indicators Ik, computable for each population unit Ui, and significant as generating a complete ordering of the populationU. A composite poverty indicator C takes the value CiIik, k=1,K for a given set of elementary population unit Ui.

V. MULTIPLE CORRESPONDENCE ANALYSIS MCA

In multivariate statistics, MCA is is basically a data analysis technique for nominal or categorical data, used to detect and represent underlying structures in a data set. It works by representing data as points in a low-dimensional Euclidean spaceAsselin and Anh, 2008. It is an extension of simple correspondence analysis CA which is applicable to a large set of variables. Instead of analysing the contingency table or cross-tabulation, as PCA does, MCA analyses an indicator matrix consists of an Individuals × Variables matrix. MCA allows to analyse the pattern of relationships of several categorical dependent variables Asselin, 2002. Each nominal variable comprises several levels, and each of these is coded as a binary variable. Studies based on MCA to generate composite poverty indices include the works of Asselin and Anh 2004 in Vietnam; Ki et al. 2005 in Senegal; Ndjanyou 2006 and Njong 2007 both for the Cameroon case.Technically MCA is resulted from a standard correspondence analysis on anindicator matrix i.e., a matrix whose entries are 0 or 1. The ultimate aim of MCA in addition todatareduction is to generate a composite indicator for each household. The axiom means that if ahousehold i improves its situation for a given variable, then its composite index of poverty CIPi increases: its poverty level decreases larger values mean less poverty orequivalently, welfare improvement. The monotonicity axiom must be translated into the FirstAxis Ordering Consistency FAOC principle Asselin, 2002 so that the firstaxis must have growing factorial scores indicating a movement from poor to non-poorsituation. For each of the ordinal variables, the MCA calculates a discrimination measureon each of the factorial axes. It is the variance of the factorial scores of all the modalitiesof the variable on the axis and measures the intensity with which the variable explains theaxis. 5 Where Wp = the weight score of the first standardised axis of category p. Ip = binary indicator 01, in which values 1 when the household has themodality and 0 otherwise. The CIP value reflects the average global welfare level of ahousehold.Asselin 2002 expresses this average minimal weight as: 6

VI. INEQUALITY