1,721,007 research outputs found
Correspondence analysis: theory, practice and new strategies
No full textA comprehensive overview of the internationalisation of correspondence analysis Correspondence Analysis: Theory, Practice and New Strategies examines the key issues of correspondence analysis, and discusses the new advances that have been made over the last 20 years. The main focus of this book is to provide a comprehensive discussion of some of the key technical and practical aspects of correspondence analysis, and to demonstrate how they may be put to use. Particular attention is given to the history and mathematical links of the developments made. These links include not just those maj
A general similarity measure for simple correspondence analysis
No full textThis article presents a general similarity measure for comparing different variants of simple correspondence analysis when analysing the association using the Cressie-Read family of divergence statistics (Beh and Lombardo 2024, International Statistical Review). It includes, as special cases, the similarity measures that have been proposed in the correspondence analysis literature for assessing the similarities and differences between the traditional approach to simple correspondence analysis and new approaches like the log-ratio analysis, and the Hellinger distance method. This article describes six further properties that show how the proposed general similarity measure can be expanded upon
Correspondence analysis and the Freeman–Tukey statistic: A study of archaeological data.
No full textTraditionally, simple correspondence analysis is performed by decomposing a matrix of
standardised residuals using singular value decomposition where the sum-of-squares of
these residuals gives Pearson’s chi-squared statistic. Such residuals, which are treated as
being asymptotically normally distributed, arise by assuming that the cell frequencies
are Poisson random variables so that their mean and variance are the same. However,
studies in the past reveal that this is not the case and that the cell frequencies are prone to
overdispersion. There are a growing number of remedies that have been proposed in the
statistics, and allied, literature. One such remedy, and the focus of this paper, is to stabilise
the variance using the Freeman–Tukey transformation. Therefore, the properties that stem
from performing correspondence analysis will be examined by decomposing the Freeman–
Tukey residuals of a two-way contingency table. The application of this strategy shall be
made by studying one large, and sparse, set of archaeological data
Familywise decompositions of Pearson’s chi-square statistic in the analysis of contingency tables.
No full textPearson’s chi-square statistic is well established for testing goodness-of-fit of various
hypotheses about observed frequency distributions in contingency tables. A general
formula for ANOVA-like decompositions of Pearson’s statistic is given under the
independence assumption along with their extensions to higher-order tables. Mathematically,
it makes the terms in the partitions and orthogonality among them obvious.
Practically, it enables simultaneous analyses of marginal and joint probabilities in
contingency tables under a variety of hypotheses about the marginal probabilities.
Specifically, this framework accommodates the specification of theoretically driven
probabilities as well as the well known cases in which the marginal probabilities
are fixed or estimated from the data. The former allows tests of prescribed marginal
probabilities, while the latter allows tests of the associations among variables after
eliminating the marginal effects. Mixtures of these two cases are also permitted. Examples
are given to illustrate the tests
Assessing Satisfaction with Public Transport Service by Ordered Multiple Correspondence Analysis (online 2018)
No full textThis paper provides a composite indicator for comparing the perceived service of satisfac-tion of public transport by residents of a southern Italian city across three time periods spanning 2008–2012. Data were collected from 400 respondents that rated their agreement with 15 attribute-related statements regarding local public transport services. This study identifies passenger satisfaction in terms of the various quality aspects of public transport services using features of ordered multiple correspondence analysis. Such a method com-bines dimension reduction and cluster analysis for categorical data by objectively assigning individuals to clusters and identifying optimal scaling values to each of the categories. The main findings of our study indicate that there are differences in how public transport is per-ceived during the period of time studied
Multiple and multiway correspondence analysis
No full textOne of the most popular, and versatile, ways of visually analyzing the associating between categorical data is to perform a correspondence analysis on the contingency table that is formed from their cross-classification. Traditionally the analysis of multiple categorical variables involves transforming such a table into a two-way form through “flattening,” stacking or by some other means; doing so leads to simple or multiple correspondence analysis. Although such a transformation does not always preserve some of the truly multivariate nature of the association. Therefore one may instead adopt the less common multiway correspondence analysis. This paper will briefly explore the development, literature, and possible research opportunities of multiple and multiway correspondence analysis. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Dimension Reduction Data: Types and Structures > Categorical Data
Analysis of three-way non-symmetrical association of food concepts in cross-cultural marketing (online 2018)
No full textThis paper analyses the non-symmetrical association among some key-words
in a food context, given the European countries and gender of participants to a survey. The
aim is to understand the meaning of the food concepts traditional and innovation associated
to selected key-words in cross-cultural marketing. For studying the association among
three categorical variables, usually, one can refer to Pearson’s three-way statistic, but in
case of non-symmetrical association we prefer to consider Marcotorchino’s three-way predictability
index and its related CM-statistic. Doing so, we present a generalisation of threeway
non-symmetrical correspondence analysis to portray the predictability of food concepts
given the knowledge of participants’country and gende
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