# [Blueboard] Lecture on Multiple Correspondence Analysis (MCA)

Editha V. Bagtas ebagtas at ateneo.edu
Mon Sep 2 16:02:12 PHT 2013

```The Ateneo de Manila University
Mathematics Department

cordially invites you to a talk on

Applications of Multiple Correspondence Analysis

by

Anthony R. Zosa, MS
Mathematics Department
School of Science and Engineering

on Monday, September 9, 2013
4:30 - 6:00 pm at SECA 303.

Abstract

Multiple Correspondence Analysis (MCA), a nonparametric approach to
data reduction, is normally applied to multidimensional scaling of
categorical variables.  MCA, designed for nominally scaled variables,
is the counterpart of the metric-based factor and principal component
analyses.  Thus, it is suitable for contingency tables and frequency
matrices.  MCA uses the centroid principle governed by a squared loss
function.  The squared canonical correlations are the eigenvalues
derived from the singular value decomposition (SVD) D-1/2CD-1/2  with
C as the matrix of bivariate marginals.  These eigenvalues, in turn,
suggests the relevant dimensions.  Hence, SVD is used to
simultaneously approximate all possible two-dimensional subtables of a
multidimensional table.  This aggregation technique is used to
determine latent variables from several variables.

Like the principal component analysis, MCA is normally used as a
preliminary analysis of categorical data; thus, it can be used without
any statistical inference.  The statistical properties of MCA hinges
on (a) the principle of linearizing its statistics and using the delta
method to approximate the standard errors, and (b) the assumption that
with large samples, the eigenvalues are distributed asymptotically as
eigenvalues of a matrix with independent standard normal in each of
the off diagonal blocks.

MCA is used to analyze data from an on-going project on media killings
in the Philippines.  The study aims to identify the determinants of
media killings, given the prevailing socio-economic and political
situations in the different locations of the Philippines.  Since most
variables are nominal in nature (e.g., politics, insurgency, criminal
activities, and peace and order assessment), MCA is the most viable
approach in reducing the number of variables to be used in the model.
A computational example using R is used on the data set.

MCA is highly applicable to many AMF related projects where banks
require students to find out the determinants of “good” or “bad” loans
from an array of categorical variables.
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