What is "clinical data"? Why and how can they be collected during field surveys on medicinal plants?

ETHNOPHARMACOLOGICAL RELEVANCE: "Reverse pharmacology", also called "bedside-to-bench" or "field to pharmacy" approach, is a research process starting with documentation of clinical outcome as observed by patients with different therapeutic regimens. The treatment most significantly associated with cure is selected for future studies: first, clinical safety and efficacy; then in vivo and vitro studies. Some clinical data, i.e. details on patient status and progress, can be collected during ethnobotanical surveys; they will help clinical researchers and, once effectiveness and safety are established, will also help users of traditional medicine make safer and more effective choices. To gather clinical data successfully, ethnopharmacologists need to be backed by an appropriate team of specialists in medicine and epidemiology. Ethnopharmacologists can also gather important data on traditional medicine safety. MATERIALS AND METHODS: The first step is to create a consensus on the meaning of "clinical data", their interest and importance. An understanding of why "a cure is not a proof of effectiveness" is a starting point to avoid faulty interpretation of the clinical observations. RESULTS: Experience showed that, with the "bedside-to-bench" approach, a treatment derived from traditional recipe can be scientifically validated (in terms of safety and effectiveness) with a cost of less than a million euros, thus providing an end-product that is affordable, available and sustainable. CONCLUSIONS: With rigorous clinical study results, medicinal plant users gain the possibility to refine heath strategies. The field surveyor may gain a better relationship with the population, once she/he is seen as bringing information useful for the quality of care in the community.

Estimating the basic reproductive number from viral sequence data.

Epidemiological processes leave a fingerprint in the pattern of genetic structure of virus populations. Here, we provide a new method to infer epidemiological parameters directly from viral sequence data. The method is based on phylogenetic analysis using a birth-death model (BDM) rather than the commonly used coalescent as the model for the epidemiological transmission of the pathogen. Using the BDM has the advantage that transmission and death rates are estimated independently and therefore enables for the first time the estimation of the basic reproductive number of the pathogen using only sequence data, without further assumptions like the average duration of infection. We apply the method to genetic data of the HIV-1 epidemic in Switzerland.

Focused time-lapse inversion of radio and audio magnetotelluric data

Geoelectrical techniques are widely used to monitor groundwater processes, while surprisingly few studies have considered audio (AMT) and radio (RMT) magnetotellurics for such purposes. In this numerical investigation, we analyze to what extent inversion results based on AMT and RMT monitoring data can be improved by (1) time-lapse difference inversion; (2) incorporation of statistical information about the expected model update (i.e., the model regularization is based on a geostatistical model); (3) using alternative model norms to quantify temporal changes (i.e., approximations of l(1) and Cauchy norms using iteratively reweighted least-squares), (4) constraining model updates to predefined ranges (i.e., using Lagrange Multipliers to only allow either increases or decreases of electrical resistivity with respect to background conditions). To do so, we consider a simple illustrative model and a more realistic test case related to seawater intrusion. The results are encouraging and show significant improvements when using time-lapse difference inversion with non l(2) model norms. Artifacts that may arise when imposing compactness of regions with temporal changes can be suppressed through inequality constraints to yield models without oscillations outside the true region of temporal changes. Based on these results, we recommend approximate l(1)-norm solutions as they can resolve both sharp and smooth interfaces within the same model. (C) 2012 Elsevier B.V. All rights reserved.

Int��gration de m��thodes de data mining dans le renseignement criminel : analyse par des structures issues de la th��orie des graphes dans le profilage des stup��fiants

Data mining can be defined as the extraction of previously unknown and potentially useful information from large datasets. The main principle is to devise computer programs that run through databases and automatically seek deterministic patterns. It is applied in different fields of application, e.g., remote sensing, biometry, speech recognition, but has seldom been applied to forensic case data. The intrinsic difficulty related to the use of such data lies in its heterogeneity, which comes from the many different sources of information. The aim of this study is to highlight potential uses of pattern recognition that would provide relevant results from a criminal intelligence point of view. The role of data mining within a global crime analysis methodology is to detect all types of structures in a dataset. Once filtered and interpreted, those structures can point to previously unseen criminal activities. The interpretation of patterns for intelligence purposes is the final stage of the process. It allows the researcher to validate the whole methodology and to refine each step if necessary. An application to cutting agents found in illicit drug seizures was performed. A combinatorial approach was done, using the presence and the absence of products. Methods coming from the graph theory field were used to extract patterns in data constituted by links between products and place and date of seizure. A data mining process completed using graphing techniques is called ``graph mining''. Patterns were detected that had to be interpreted and compared with preliminary knowledge to establish their relevancy. The illicit drug profiling process is actually an intelligence process that uses preliminary illicit drug classes to classify new samples. Methods proposed in this study could be used \textit{a priori} to compare structures from preliminary and post-detection patterns. This new knowledge of a repeated structure may provide valuable complementary information to profiling and become a source of intelligence.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Some last thoughts on compositional data analysis

One of the disadvantages of old age is that there is more past than future: this,however, may be turned into an advantage if the wealth of experience and, hopefully,wisdom gained in the past can be reflected upon and throw some light on possiblefuture trends. To an extent, then, this talk is necessarily personal, certainly nostalgic,but also self critical and inquisitive about our understanding of the discipline ofstatistics. A number of almost philosophical themes will run through the talk: searchfor appropriate modelling in relation to the real problem envisaged, emphasis onsensible balances between simplicity and complexity, the relative roles of theory andpractice, the nature of communication of inferential ideas to the statistical layman, theinter-related roles of teaching, consultation and research. A list of keywords might be:identification of sample space and its mathematical structure, choices betweentransform and stay, the role of parametric modelling, the role of a sample spacemetric, the underused hypothesis lattice, the nature of compositional change,particularly in relation to the modelling of processes. While the main theme will berelevance to compositional data analysis we shall point to substantial implications forgeneral multivariate analysis arising from experience of the development ofcompositional data analysis���

Compositional Data in Biomedical Research

Modern methods of compositional data analysis are not well known in biomedical research.Moreover, there appear to be few mathematical and statistical researchersworking on compositional biomedical problems. Like the earth and environmental sciences,biomedicine has many problems in which the relevant scienti c information isencoded in the relative abundance of key species or categories. I introduce three problemsin cancer research in which analysis of compositions plays an important role. Theproblems involve 1) the classi cation of serum proteomic pro les for early detection oflung cancer, 2) inference of the relative amounts of di erent tissue types in a diagnostictumor biopsy, and 3) the subcellular localization of the BRCA1 protein, and it'srole in breast cancer patient prognosis. For each of these problems I outline a partialsolution. However, none of these problems is \solved". I attempt to identify areas inwhich additional statistical development is needed with the hope of encouraging morecompositional data analysts to become involved in biomedical research

Crash Data Validation: An Iowa Case Study, February, 2007

With the quickening pace of crash reporting, the statistical editing of data on a weekly basis, and the ability to provide working databases to users at CTRE/Iowa Traffic Safety Data Service, the University of Iowa, and the Iowa DOT, databases that would be considered incomplete by past standards of static data files are in ���public use��� even as the dynamic nature of the central DOT database allows changes to be made to both the aggregate of data and to the individual crashes already reported. Moreover, ���definitive��� analyses of serious crashes will, by their nature, lag seriously behind the preliminary data files. Even after these analyses, the dynamic nature of the mainframe data file means that crash numbers can continue to change long after the incident year. The Iowa DOT, its Office of Driver Services (the ���data owner���), and institutional data users/distributors must establish data use, distribution, and labeling protocols to deal with the new, dynamic nature of data. In order to set these protocols, data must be collected concerning the magnitude of difference between database records and crash narratives and diagrams. This study determines the difference between database records and crash narratives for the Iowa Department of Transportation���s Office of Traffic and Safety crash database and the impacts of this difference.

Mapping of Environmental Data Using Kernel-Based Methods

Recently, kernel-based Machine Learning methods have gained great popularity in many data analysis and data mining fields: pattern recognition, biocomputing, speech and vision, engineering, remote sensing etc. The paper describes the use of kernel methods to approach the processing of large datasets from environmental monitoring networks. Several typical problems of the environmental sciences and their solutions provided by kernel-based methods are considered: classification of categorical data (soil type classification), mapping of environmental and pollution continuous information (pollution of soil by radionuclides), mapping with auxiliary information (climatic data from Aral Sea region). The promising developments, such as automatic emergency hot spot detection and monitoring network optimization are discussed as well.

Nucleation and growth of metamorphic minerals in contact aureoles

THESIS ABSTRACT Nucleation and growth of metamorphic minerals are the consequence of changing P-T-X-conditions. The thesis presented here focuses on processes governing nucleation and growth of minerals in contact metamorphic environments using a combination of geochemical analytics (chemical-, isotope-, and trace element composition), statistical treatments of spatial data, and numerical models. It is shown, that a combination of textural modeling and stable isotope analysis allows a distinction between several possible reaction paths for olivine growth in a siliceous dolomite contact aureole. It is suggested that olivine forms directly from dolomite and quartz. The formation of olivine from this metastable reaction implies metamorphic crystallization far from equilibrium. As a major consequence, the spatial distribution of metamorphic mineral assemblages in a contact aureole cannot be interpreted as a proxy for the temporal evolution of a single rock specimen, because each rock undergoes a different reaction path, depending on temperature, heating rate, and fluid-infiltration rate. A detailed calcite-dolomite thermometry study was initiated on multiple scales ranging from aureole scale to the size of individual crystals. Quantitative forward models were developed to evaluate the effect of growth zoning, volume diffusion and the formation of submicroscopic exsolution lamellae (<1 ��m) on the measured Mg-distribution in individual calcite crystals and compare the modeling results to field data. This study concludes that Mg-distributions in calcite grains of the Ubehebe Peak contact aureole are the consequence of rapid crystal growth in combination with diffusion and exsolution. The crystallization history of a rock is recorded in the chemical composition, the size and the distribution of its minerals. Near the Cima Uzza summit, located in the southern Adamello massif (Italy), contact metamorphic brucite bearing dolomite marbles are exposed as xenoliths surrounded by mafic intrusive rocks. Brucite is formed retrograde pseudomorphing spherical periclase crystals. Crystal size distributions (CSD's) of brucite pseudomorphs are presented for two profiles and combined with geochemistry data and petrological information. Textural analyses are combined with geochemistry data in a qualitative model that describes the formation periclase. As a major outcome, this expands the potential use of CSD's to systems of mineral formation driven by fluid-infiltration. RESUME DE LA THESE La nucl��ation et la croissance des min��raux m��tamorphiques sont la cons��quence de changements des conditions de pression, temp��rature et composition chimique du syst��me (PT-X). Cette th��se s'int��resse aux processus gouvernant la nucl��ation et la croissance des min��raux au cours d'un ��pisode de m��tamorphisme de contact, en utilisant la g��ochimie analytique (composition chimique, isotopique et en ��l��ments traces), le traitement statistique des donn��es spatiales et la mod��lisation num��rique. Il est montr�� que la combinaison d'un mod��le textural avec des analyses en isotopes stables permet de distinguer plusieurs chemins de r��actions possibles conduisant �� la croissance de l'olivine dans une aur��ole de contact riche en Silice et dolomite. Il est sugg��r�� que l'olivine se forme directement �� partir de la dolomie et du quartz. Cette r��action m��tastable de formation de l'olivine implique une cristallisation m��tamorphique loin de l'��quilibre. La principale cons��quence est que la distribution spatiale des assemblages de min��raux m��tamorphiques dans une aur��ole de contact ne peut pas ��tre consid��r��e comme un t��moin de l'��volution temporelle d'un type de roche donn��, puisque chaque type de roche suit diff��rents chemins de r��actions, en fonction de la temp��rature, la vitesse de r��chauffement et le taux d'infiltration du fluide. Une ��tude thermom��trique calcite-dolomite d��taill��e a ��t�� r��alis��e �� diverses ��chelles, depuis l'��chelle de l'aur��ole de contact jusqu'�� l'��chelle du cristal. Des mod��les num��riques quantitatifs ont ��t�� d��velopp��s pour ��valuer l'effet des zonations de croissance, de la diffusion volumique et de la formation de lamelles d'exsolution submicroscopiques (<1��m) sur la distribution du magn��sium mesur�� dans des cristaux de calcite individuels. Les r��sultats de ce mod��le ont ��t�� compar��s �� des ��chantillons naturels. Cette ��tude montre que la distribution du Mg dans les grains de calcite de l'aur��ole de contact de l'Ubehebe Peak (USA) r��sulte d'une croissance cristalline rapide, associ��e aux processus de diffusion et d'exsolution. L'histoire de cristallisation d'une roche est enregistr��e dans la composition chimique, la taille et la distribution de ses min��raux. Pr��s du sommet Cima Uzza situ�� au sud du massif d'Adamello (Italie), des marbres dolomitiques �� brucite du m��tamorphisme de contact forment des x��nolithes dans une intrusion mafique. La brucite constitue des pseudomorphes r��trogrades du p��riclase. Les distributions de taille des cristaux (CSD) des pseudomorphes de brucite sont pr��sent��es pour deux profiles et sont combin��es aux donn��es g��ochimiques et p��trologiques. Les analyses textorales sont combin��es aux donn��es g��ochimiques dans un mod��le qualitatif qui d��crit la formation du p��riclase. Ceci ��largit l'utilisation potentielle de la C5D aux syst��mes de formation de min��raux control��s par les infiltrations fluides. THESIS ABSTRACT (GENERAL PUBLIC) Rock textures are essentially the result of a complex interaction of nucleation, growth and deformation as a function of changing physical conditions such as pressure and temperature. Igneous and metamorphic textures are especially attractive to study the different mechanisms of texture formation since most of the parameters like pressure-temperature-paths are quite well known for a variety of geological settings. The fact that textures are supposed to record the crystallization history of a rock traditionally allowed them to be used for geothermobarometry or dating. During the last decades the focus of metamorphic petrology changed from a static point of view, i.e. the representation of a texture as one single point in the petrogenetic grid towards a more dynamic view, where multiple metamorphic processes govern the texture formation, including non-equilibrium processes. This thesis tries to advance our understanding on the processes governing nucleation and growth of minerals in contact metamorphic environments and their dynamic interplay by using a combination of geochemical analyses (chemical-, isotope-, and trace element composition), statistical treatments of spatial data and numerical models. In a first part the thesis describes the formation of metamorphic olivine porphyroblast in the Ubehebe Peak contact aureole (USA). It is shown that not the commonly assumed succession of equilibrium reactions along a T-t-path formed the textures present in the rocks today, but rather the presence of a meta-stable reaction is responsible for forming the olivine porphyroblast. Consequently, the spatial distribution of metamorphic minerals within a contact aureole can no longer be regarded as a proxy for the temporal evolution of a single rock sample. Metamorphic peak temperatures for samples of the Ubehebe Peak contact aureole were determined using calcite-dolomite. This geothermometer is based on the temperature-dependent exchange of Mg between calcite and dolomite. The purpose of the second part of this thesis was to explain the interfering systematic scatter of measured Mg-content on different scales and thus to clarify the interpretation of metamorphic temperatures recorded in carbonates. Numerical quantitative forward models are used to evaluate the effect of several processes on the distribution of magnesium in individual calcite crystals and the modeling results were then compared to measured field. Information about the crystallization history is not only recorded in the chemical composition of grains, like isotope composition or mineral zoning. Crystal size distributions (CSD's) provide essential information about the complex interaction of nucleation and growth of minerals. CSD's of brucite pseudomorphs formed retrograde after periclase of the southern Adamello massif (Italy) are presented. A combination of the textural 3D-information with geochemistry data is then used to evaluate reaction kinetics and to constrain the actual reaction mechanism for the formation of periclase. The reaction is shown to be the consequence of the infiltration of a limited amount of a fluid phase at high temperatures. The composition of this fluid phase is in large disequilibrium with the rest of the rock resulting in very fast reaction rates. RESUME DE LA THESE POUR LE GRAND PUBLIC: La texture d'une roche r��sulte de l'interaction complexe entre les processus de nucl��ation, croissance et d��formation, en fonction des variations de conditions physiques telles que la pression et la temp��rature. Les textures ign��es et m��tamorphiques pr��sentent un int��r��t particulier pour l'��tude des diff��rents m��canismes �� l'origine de ces textures, puisque la plupart des param��tres comme les chemin pression-temp��rature sont relativement bien contraints dans la plupart des environnements g��ologiques. Le fait que les textures soient suppos��es enregistrer l'histoire de cristallisation des roches permet leur utilisation pour la datation et la g��othermobarom��trie. Durant les derni��res d��cennies, la recherche en p��trologie m��tamorphique a ��volu�� depuis une visualisation statique, c'est-��-dire qu'une texture donn��e correspondait �� un point unique de la grille p��trog��n��tique, jusqu'�� une visualisation plus dynamique, o�� les multiples processus m��tamorphiques qui gouvernent 1a formation d'une texture incluent des processus hors ��quilibre. Cette th��se a pour but d'am��liorer les connaissances actuelles sur les processus gouvernant la nucl��ation et la croissance des min��raux lors d'��pisodes de m��tamorphisme de contact et l'interaction dynamique existant entre nucl��ation et croissance. Pour cela, les analyses g��ochimiques (compositions chimiques en ��l��ments majeurs et traces et composition isotopique), le traitement statistique des donn��es spatiales et la mod��lisation num��rique ont ��t�� combin��s. Dans la premi��re partie, cette th��se d��crit la formation de porphyroblastes d'olivine m��tamorphique dans l'aur��ole de contact de l'Ubehebe Peak (USA). Il est montr�� que la succession g��n��ralement admise des r��actions d'��quilibre le long d'un chemin T-t ne peut pas expliquer les textures pr��sentes dans les roches aujourd'hui. Cette th��se montre qu'il s'agirait plut��t d'une r��action m��tastable qui soit responsable de la formation des porphyroblastes d'olivine. En cons��quence, la distribution spatiale des min��raux m��tamorphiques dans l'aur��ole de contact ne peut plus ��tre interpr��t��e comme le t��moin de l'��volution temporelle d'un ��chantillon unique de roche. Les pics de temp��rature des ��chantillons de l'aur��ole de contact de l'Ubehebe Peak ont ��t�� d��termin��s gr��ce au g��othermom��tre calcite-dolomite. Celui-ci est bas�� sur l'��change du magn��sium entre la calcite et la dolomite, qui est fonction de la temp��rature. Le but de la deuxi��me partie de cette th��se est d'expliquer la dispersion syst��matique de la composition en magn��sium �� diff��rentes ��chelles, et ainsi d'am��liorer l'interpr��tation des temp��ratures du m��tamorphisme enregistr��es dans les carbonates. Des mod��les num��riques quantitatifs ont permis d'��valuer le r��le de diff��rents processus sur la distribution du magn��sium dans des cristaux de calcite individuels. Les r��sultats des mod��les ont ��t�� compar��s aux ��chantillons naturels. La composition chimique des grains, comme la composition isotopique ou la zonation min��rale, n'est pas le seul t��moin de l'histoire de la cristallisation. La distribution de la taille des cristaux (CSD) fournit des informations essentielles sur les interactions entre nucl��ation et croissance des min��raux. La CSD des pseudomorphes de brucite retrograde form��s apr��s le p��riclase dans le sud du massif Adamello (Italie) est pr��sent��e dans la troisi��me partie. La combinaison entre les donn��es textorales en trois dimensions et les donn��es g��ochimiques a permis d'��valuer les cin��tiques de r��action et de contraindre les m��canismes conduisant �� la formation du p��riclase. Cette r��action est pr��sent��e comme ��tant la cons��quence de l'infiltration d'une quantit�� limit��e d'une phase fluide �� haute temp��rature. La composition de cette phase fluide est en grand d��s��quilibre avec le reste de la roche, ce qui permet des cin��tiques de r��actions tr��s rapides.

Psychogenic seizures and frontal disconnection: EEG synchronisation study.

Objective Psychogenic non-epileptic seizures (PNES) are paroxysmal events that, in contrast to epileptic seizures, are related to psychological causes without the presence of epileptiform EEG changes. Recent models suggest a multifactorial basis for PNES. A potentially paramount, but currently poorly understood factor is the interplay between psychiatric features and a specific vulnerability of the brain leading to a clinical picture that resembles epilepsy. Hypothesising that functional cerebral network abnormalities may predispose to the clinical phenotype, the authors undertook a characterisation of the functional connectivity in PNES patients. Methods The authors analysed the whole-head surface topography of multivariate phase synchronisation (MPS) in interictal high-density EEG of 13 PNES patients as compared with 13 age- and sex-matched controls. MPS mapping reduces the wealth of dynamic data obtained from high-density EEG to easily readable synchronisation maps, which provide an unbiased overview of any changes in functional connectivity associated with distributed cortical abnormalities. The authors computed MPS maps for both Laplacian and common-average-reference EEGs. Results In a between-group comparison, only patchy, non-uniform changes in MPS survived conservative statistical testing. However, against the background of these unimpressive group results, the authors found widespread inverse correlations between individual PNES frequency and MPS within the prefrontal and parietal cortices. Interpretation PNES appears to be associated with decreased prefrontal and parietal synchronisation, possibly reflecting dysfunction of networks within these regions.

Geographical effects on the accuracy of textile trade data:an international approach for 1913

Foreign trade statistics are the main data source to the study of international trade.However its accuracy has been under suspicion since Morgernstern published hisfamous work in 1963. Federico and Tena (1991) have resumed the question arguing thatthey can be useful in an adequate level of aggregation. But the geographical assignmentproblem remains unsolved. This article focuses on the spatial variable through theanalysis of the reliability of textile international data for 1913. A geographical biasarises between export and import series, but because of its quantitative importance it canbe negligible in an international scale.

Further evidence on the statistical properties of real GNP

The well-known lack of power of unit root tests has often been attributed to the shortlength of macroeconomic variables and also to DGP s that depart from the I(1)-I(0)alternatives. This paper shows that by using long spans of annual real GNP and GNPper capita (133 years) high power can be achieved, leading to the rejection of both theunit root and the trend-stationary hypothesis. This suggests that possibly neither modelprovides a good characterization of these data. Next, more flexible representations areconsidered, namely, processes containing structural breaks (SB) and fractional ordersof integration (FI). Economic justification for the presence of these features in GNP isprovided. It is shown that the latter models (FI and SB) are in general preferred to theARIMA (I(1) or I(0)) ones. As a novelty in this literature, new techniques are appliedto discriminate between FI and SB models. It turns out that the FI specification ispreferred, implying that GNP and GNP per capita are non-stationary, highly persistentbut mean-reverting series. Finally, it is shown that the results are robust when breaksin the deterministic component are allowed for in the FI model. Some macroeconomicimplications of these findings are also discussed.

Hybrid consumption paths in the attribute space: A model and application with scanner data

This paper presents and estimates a dynamic choice model in the attribute space considering rational consumers. In light of the evidence of several state-dependence patterns, the standard attribute-based model is extended by considering a general utility function where pure inertia and pure variety-seeking behaviors can be explained in the model as particular linear cases. The dynamics of the model are fully characterized by standard dynamic programming techniques. The model presents a stationary consumption pattern that can be inertial, where the consumer only buys one product, or a variety-seeking one, where the consumer shifts among varied products.We run some simulations to analyze the consumption paths out of the steady state. Underthe hybrid utility assumption, the consumer behaves inertially among the unfamiliar brandsfor several periods, eventually switching to a variety-seeking behavior when the stationary levels are approached. An empirical analysis is run using scanner databases for three different product categories: fabric softener, saltine cracker, and catsup. Non-linear specifications provide the best fit of the data, as hybrid functional forms are found in all the product categories for most attributes and segments. These results reveal the statistical superiority of the non-linear structure and confirm the gradual trend to seek variety as the level of familiarity with the purchased items increases.