CODAWORK’03http://hdl.handle.net/10256/6162014-11-24T22:57:58Z2014-11-24T22:57:58ZValidation of order rank scales based on compositional data analysis: a proposalMalpica Lander, ClaudiaGalindo Villardón, Purificaciónhttp://hdl.handle.net/10256/6962012-06-28T12:30:36Z2003-10-17T00:00:00ZValidation of order rank scales based on compositional data analysis: a proposal
Malpica Lander, Claudia; Galindo Villardón, Purificación
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
Usually, psychometricians apply classical factorial analysis to evaluate construct validity of order rank
scales. Nevertheless, these scales have particular characteristics that must be taken into account: total
scores and rank are highly relevant
2003-10-17T00:00:00ZRefinement criteria for global illumination using convex funcionsRigau Vilalta, JaumeFeixas Feixas, MiquelSbert, Mateuhttp://hdl.handle.net/10256/6952012-06-28T12:30:36Z2003-10-17T00:00:00ZRefinement criteria for global illumination using convex funcions
Rigau Vilalta, Jaume; Feixas Feixas, Miquel; Sbert, Mateu
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
In several computer graphics areas, a refinement criterion is often needed to decide whether to go
on or to stop sampling a signal. When the sampled values are homogeneous enough, we assume that
they represent the signal fairly well and we do not need further refinement, otherwise more samples are
required, possibly with adaptive subdivision of the domain. For this purpose, a criterion which is very
sensitive to variability is necessary. In this paper, we present a family of discrimination measures, the
f-divergences, meeting this requirement. These convex functions have been well studied and successfully
applied to image processing and several areas of engineering. Two applications to global illumination
are shown: oracles for hierarchical radiosity and criteria for adaptive refinement in ray-tracing. We
obtain significantly better results than with classic criteria, showing that f-divergences are worth further
investigation in computer graphics. Also a discrimination measure based on entropy of the samples for
refinement in ray-tracing is introduced. The recursive decomposition of entropy provides us with a natural
method to deal with the adaptive subdivision of the sampling region
2003-10-17T00:00:00ZAlternative ways to estimate change points in multinomial sequences. An application to an authorship attribution problemRiba, AlexGinebra, Josephttp://hdl.handle.net/10256/6942012-06-28T12:30:36Z2003-10-17T00:00:00ZAlternative ways to estimate change points in multinomial sequences. An application to an authorship attribution problem
Riba, Alex; Ginebra, Josep
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
The statistical analysis of literary style is the part of stylometry that compares measurable characteristics
in a text that are rarely controlled by the author, with those in other texts. When the
goal is to settle authorship questions, these characteristics should relate to the author’s style and
not to the genre, epoch or editor, and they should be such that their variation between authors is
larger than the variation within comparable texts from the same author.
For an overview of the literature on stylometry and some of the techniques involved, see for example
Mosteller and Wallace (1964, 82), Herdan (1964), Morton (1978), Holmes (1985), Oakes (1998) or
Lebart, Salem and Berry (1998).
Tirant lo Blanc, a chivalry book, is the main work in catalan literature and it was hailed to be
“the best book of its kind in the world” by Cervantes in Don Quixote. Considered by writters
like Vargas Llosa or Damaso Alonso to be the first modern novel in Europe, it has been translated
several times into Spanish, Italian and French, with modern English translations by Rosenthal
(1996) and La Fontaine (1993). The main body of this book was written between 1460 and 1465,
but it was not printed until 1490.
There is an intense and long lasting debate around its authorship sprouting from its first edition,
where its introduction states that the whole book is the work of Martorell (1413?-1468), while at
the end it is stated that the last one fourth of the book is by Galba (?-1490), after the death of
Martorell. Some of the authors that support the theory of single authorship are Riquer (1990),
Chiner (1993) and Badia (1993), while some of those supporting the double authorship are Riquer
(1947), Coromines (1956) and Ferrando (1995). For an overview of this debate, see Riquer (1990).
Neither of the two candidate authors left any text comparable to the one under study, and therefore
discriminant analysis can not be used to help classify chapters by author. By using sample texts
encompassing about ten percent of the book, and looking at word length and at the use of 44
conjunctions, prepositions and articles, Ginebra and Cabos (1998) detect heterogeneities that might
indicate the existence of two authors. By analyzing the diversity of the vocabulary, Riba and
Ginebra (2000) estimates that stylistic boundary to be near chapter 383.
Following the lead of the extensive literature, this paper looks into word length, the use of the most
frequent words and into the use of vowels in each chapter of the book. Given that the features
selected are categorical, that leads to three contingency tables of ordered rows and therefore to
three sequences of multinomial observations.
Section 2 explores these sequences graphically, observing a clear shift in their distribution. Section 3
describes the problem of the estimation of a suden change-point in those sequences, in the following
sections we propose various ways to estimate change-points in multinomial sequences; the method
in section 4 involves fitting models for polytomous data, the one in Section 5 fits gamma models
onto the sequence of Chi-square distances between each row profiles and the average profile, the
one in Section 6 fits models onto the sequence of values taken by the first component of the
correspondence analysis as well as onto sequences of other summary measures like the average
word length. In Section 7 we fit models onto the marginal binomial sequences to identify the
features that distinguish the chapters before and after that boundary. Most methods rely heavily
on the use of generalized linear models
2003-10-17T00:00:00ZA compositional statistical analysis of capital stockLarrosa, Juan M.http://hdl.handle.net/10256/6932012-06-28T12:30:36Z2003-10-17T00:00:00ZA compositional statistical analysis of capital stock
Larrosa, Juan M.
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
Most of economic literature has presented its analysis under the assumption of homogeneous capital stock.
However, capital composition differs across countries. What has been the pattern of capital composition
associated with World economies? We make an exploratory statistical analysis based on compositional data
transformed by Aitchinson logratio transformations and we use tools for visualizing and measuring statistical
estimators of association among the components. The goal is to detect distinctive patterns in the composition.
As initial findings could be cited that:
1. Sectorial components behaved in a correlated way, building industries on one side and , in a less
clear view, equipment industries on the other.
2. Full sample estimation shows a negative correlation between durable goods component and
other buildings component and between transportation and building industries components.
3. Countries with zeros in some components are mainly low income countries at the bottom of the
income category and behaved in a extreme way distorting main results observed in the full
sample.
4. After removing these extreme cases, conclusions seem not very sensitive to the presence of
another isolated cases
2003-10-17T00:00:00ZThe agreement between ipsative and normative questionnaires using compositional data analysis techniquesDe Vries, Anton L.M.http://hdl.handle.net/10256/6922012-06-28T12:30:36Z2003-10-17T00:00:00ZThe agreement between ipsative and normative questionnaires using compositional data analysis techniques
De Vries, Anton L.M.
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
The main instrument used in psychological measurement is the self-report questionnaire. One of its major
drawbacks however is its susceptibility to response biases. A known strategy to control these biases has
been the use of so-called ipsative items. Ipsative items are items that require the respondent to make
between-scale comparisons within each item. The selected option determines to which scale the weight of
the answer is attributed. Consequently in questionnaires only consisting of ipsative items every
respondent is allotted an equal amount, i.e. the total score, that each can distribute differently over the
scales. Therefore this type of response format yields data that can be considered compositional from its
inception.
Methodological oriented psychologists have heavily criticized this type of item format, since the resulting
data is also marked by the associated unfavourable statistical properties. Nevertheless, clinicians have
kept using these questionnaires to their satisfaction. This investigation therefore aims to evaluate both
positions and addresses the similarities and differences between the two data collection methods. The
ultimate objective is to formulate a guideline when to use which type of item format.
The comparison is based on data obtained with both an ipsative and normative version of three
psychological questionnaires, which were administered to 502 first-year students in psychology according
to a balanced within-subjects design. Previous research only compared the direct ipsative scale scores
with the derived ipsative scale scores. The use of compositional data analysis techniques also enables one
to compare derived normative score ratios with direct normative score ratios. The addition of the second
comparison not only offers the advantage of a better-balanced research strategy. In principle it also allows
for parametric testing in the evaluation
2003-10-17T00:00:00ZOn the use of principal components in contemporany population genetics: a case studyGasparini, MauroDi Gaetano, C.http://hdl.handle.net/10256/6892012-06-28T12:30:36Z2003-10-17T00:00:00ZOn the use of principal components in contemporany population genetics: a case study
Gasparini, Mauro; Di Gaetano, C.
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
In human Population Genetics, routine applications of principal component techniques are often
required. Population biologists make widespread use of certain discrete classifications of human
samples into haplotypes, the monophyletic units of phylogenetic trees constructed from several
single nucleotide bimorphisms hierarchically ordered. Compositional frequencies of the haplotypes
are recorded within the different samples. Principal component techniques are then required as a
dimension-reducing strategy to bring the dimension of the problem to a manageable level, say two,
to allow for graphical analysis.
Population biologists at large are not aware of the special features of compositional data and normally make use of the crude covariance of compositional relative frequencies to construct principal
components. In this short note we present our experience with using traditional linear principal
components or compositional principal components based on logratios, with reference to a specific
dataset
2003-10-17T00:00:00ZCompositional ideas in the bayesian analysis of categorical data with application to dose finding clinical trialsGasparini, MauroEisele, J.http://hdl.handle.net/10256/6862012-06-28T12:30:36Z2003-10-17T00:00:00ZCompositional ideas in the bayesian analysis of categorical data with application to dose finding clinical trials
Gasparini, Mauro; Eisele, J.
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
Compositional random vectors are fundamental tools in the Bayesian analysis of categorical data.
Many of the issues that are discussed with reference to the statistical analysis of compositional
data have a natural counterpart in the construction of a Bayesian statistical model for categorical
data.
This note builds on the idea of cross-fertilization of the two areas recommended by Aitchison (1986)
in his seminal book on compositional data. Particular emphasis is put on the problem of what
parameterization to use
2003-10-17T00:00:00ZThe allometry of non-employment. What can compositional data analysis tell us about labour market performance across the UK's regions?Anyadike Danes, Michaelhttp://hdl.handle.net/10256/6842012-06-28T12:30:36Z2003-10-17T00:00:00ZThe allometry of non-employment. What can compositional data analysis tell us about labour market performance across the UK's regions?
Anyadike Danes, Michael
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
The low levels of unemployment recorded in the UK in recent years are widely cited as
evidence of the country’s improved economic performance, and the apparent convergence of unemployment rates across the country’s regions used to suggest that the longstanding divide in living standards between the relatively prosperous ‘south’ and the more depressed ‘north’ has been substantially narrowed. Dissenters from these
conclusions have drawn attention to the greatly increased extent of non-employment
(around a quarter of the UK’s working age population are not in employment) and the
marked regional dimension in its distribution across the country. Amongst these dissenters it is generally agreed that non-employment is concentrated amongst older
males previously employed in the now very much smaller ‘heavy’ industries (e.g. coal,
steel, shipbuilding).
This paper uses the tools of compositiona l data analysis to provide a much richer picture of non-employment and one which challenges the conventional analysis wisdom about UK labour market performance as well as the dissenters view of the nature of the
problem. It is shown that, associated with the striking ‘north/south’ divide in nonemployment rates, there is a statistically significant relationship between the size of the non-employment rate and the composition of non-employment. Specifically, it is shown that the share of unemployment in non-employment is negatively correlated with the overall non-employment rate: in regions where the non-employment rate is high the share of unemployment is relatively low. So the unemployment rate is not a very reliable indicator of regional disparities in labour market performance. Even more importantly from a policy viewpoint, a significant positive relationship is found between the size of
the non-employment rate and the share of those not employed through reason of sickness
or disability and it seems (contrary to the dissenters) that this connection is just as strong for women as it is for men
2003-10-17T00:00:00ZCompositional hypotheses of subcompositional stability and specific perturbation change and their testingAitchison, JohnNg, K.W.http://hdl.handle.net/10256/6802012-06-28T12:30:36Z2003-10-17T00:00:00ZCompositional hypotheses of subcompositional stability and specific perturbation change and their testing
Aitchison, John; Ng, K.W.
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes.
Against this background the relevance of perturbations and subcompositions can be
clearly seen. Moreover we can identify a number of hypotheses of interest involving
the specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate analysis. We then develop appropriate estimation and testing procedures for a complete lattice of relevant compositional hypotheses
2003-10-17T00:00:00ZMajor-elements trends in cenozoic volcanites of HungaryMartín Fernández, Josep AntoniBarceló i Vidal, CarlesPawlowsky-Glahn, VeraKovács, L.Ó.Kovács, G.P.http://hdl.handle.net/10256/6792012-11-19T08:56:18Z2003-10-16T00:00:00ZMajor-elements trends in cenozoic volcanites of Hungary
Martín Fernández, Josep Antoni; Barceló i Vidal, Carles; Pawlowsky-Glahn, Vera; Kovács, L.Ó.; Kovács, G.P.
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
Hungary lies entirely within the Carpatho-Pannonian Region (CPR), a dominant tectonic unit of eastern Central Europe. The CPR consists of the Pannonian Basin system, and the arc of the Carpathian Mountains surrounding the lowlands in the north, east, and southeast. In the west, the CPR is bounded by the Eastern Alps, whereas in the south, by the Dinaridic belt. (...)
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