# p. 2

· in this presentation we will extend the correspondence analysis to the case of symbolic multi-valued variables and then we will apply it to process multiplechoice multiple questionnaire questionnaire · but the first question is what is a symbolic multi-valued variable multiuniversity of costa rica

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# p. 3

eyes-color hair-color · a symbolic variable y is called multi-valued if its multivalues yk are all finite subsets yk green,blue · so there is imprecise information in the input data that will be represented in the two dimensional plane as a rectangle instead of a point university of costa rica

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# p. 4

relationship between two symbolic multi-valued variables · as it is very well know in classic correspondence analysis a contingency table associated with two qualitative variables is build · example 1 if there are two qualitative variables x =eyes-color with 3 modalities green blue and brown and y hair-color with 2 modalities blond and black university of costa rica

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# p. 5

· if we have 5 individuals the following disjunctive complete tables could be obtained · then the crossed or contingency table between the variables x and y is university of costa rica

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# p. 6

symbolic case · example 1 if x1 eyes-color1 green or x1 eyes-color1 blue if y3 hair-color3 blond or y3 hair-color3 black · in this case there are two possible disjunctive complete tables for the variable x and two for y university of costa rica

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# p. 7

· using this information we have 4 possible contingency tables between the variable x and y university of costa rica

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# p. 8

· taking the minimum and the maximum of the components of these 4 matrices an interval contingency data table is obtained university of costa rica

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# p. 9

there is a problem · the construction of the matrix k requires too many calculations · in fact it requires pmnm matrix products · the following theorem reduces the calculation to only two matrix multiplications · before presenting the theorem the following definition must be given university of costa rica

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# p. 10

definition · the minimum possibilities matrix meet matrix is · the maximum possibilities matrix join matrix is university of costa rica

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# p. 11

example 2 using the same variables x and y from example 1 we have the following result university of costa rica

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# p. 13

then university of costa rica

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# p. 14

correspondence analysis between two multi-valued variable then we can start with the following matrix the idea of the method is to transform the matrix k to the matrix kc and then to apply a classical ca to kc in order to project there the interval profiles university of costa rica

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