Factorial Maps Research Articles

Empirical Modeling of Soil Loss and Yield Utilizing RUSLE and SYI: A Geospatial Study in South Sikkim, Teesta Basin

Soil erosion and subsequent sedimentation pose significant challenges in the Sikkim Himalayas. In this study, we conducted an assessment of the impact of rainfall-induced soil erosion and sediment loss in South Sikkim, which falls within the Teesta Basin, employing Revised Universal Soil Loss Equation (RUSLE) and Sediment Yield Index (SYI) models. Leveraging mean annual precipitation data, a detailed soil map, geomorphological landforms, Digital Elevation Models (DEMs), and LANDSAT 8 OLI data were used to prepare the factorial maps of South Sikkim. The results of the RUSLE and SYI models revealed annual soil loss >200 t ha−1 yr−1, whereas mean values were estimated to be 93.42 t ha−1 yr−1 and 70.3 t ha−1 yr−1, respectively. Interestingly, both models displayed similar degrees of soil loss in corresponding regions under the various severity classes. Notably, low-severity erosion <50 t ha−1 yr−1 was predominantly observed in the valley sides in low-elevation zones, while areas with severe erosion rates >200 t ha−1 yr−1were concentrated in the upper reaches, characterized by steep slopes. These findings underscore the strong correlation between erosion rates and topography, which makes the region highly vulnerable to erosion. The prioritization of such regions and potential conservation methods need to be adopted to protect such precious natural resources in mountainous regions.

Differentiation of Synanthropic Fleas from Andalusia (Spain) through Geometric Morphometrics Analysis.

Fleas (Siphonaptera) are ectoparasitic hematophagous insects responsible for causing bites and itchy skin conditions in both humans and animals. Furthermore, they can act as vectors of different pathogens of a wide variety of diseases worldwide, including bartonellosis, rickettsiosis, and bubonic plague. Accurate identification of fleas is necessary for the study of their epidemiology, prevention, and control. In addition to traditional morphological classification approaches and molecular biology techniques, geometric morphometrics is increasingly proving to be a useful complementary tool for discriminating between Siphonaptera taxa. With the objective of determining the capacity of this technique to identify and differentiate synanthropic fleas, a principal component analysis was carried out on populations of Ctenocephalides felis, Pulex irritans, and Archaeopsylla erinacei collected in distinct regions of Andalusia (Spain). The analysis carried out on 81 male and female specimens revealed factorial maps that allowed the differentiation of the populations under study, with only partial overlaps that did not prevent their correct identification. Global size differences were also detected, with a slightly larger size in P. irritans males and a bigger size in A. erinacei females. Therefore, the present study emphasizes the role of geometric morphometrics as a useful complementary technique in taxonomic studies of arthropods, especially in the case of flea specimens lacking representative morphological features.

ICT Usage in Enterprises in the Years 2010–2019 – Poland in Comparison with Other European Union Countries

As Eurostat’s glossary explains, the term Information and Communication Technologies (ICT): ‘covers all technical means used to handle information and aid communication. This includes both computer and network hardware, as well as their software.’ In both local and global perspective, the ICT impact on modern economies and societies is undeniable. Moreover, it is growing, as the usability and technical capabilities are expanding. The researchers recognised that the ICT expansion in enterprises is a stimulant for economic development, as it strengthens competitiveness and innovation. Its impact on labour markets is significant, and constantly increasing demand for digital competences and ICT specialists can be observed. In both global and local perspective, the ICT sector is growing dynamically along with its value share in GDP. Monitoring the development of ICT usage as well as analysing how it stimulates socio‑economic transformations and growth are crucial for global leaders, governments and local authorities all over the world in order to formulate policy at all levels. Also, it plays a significant role in modern businesses expansion, as it strengthens innovativeness and competitiveness. The main objective of the paper is to study the ICT usage development in Poland against other EU countries from the enterprises’ perspective in the years 2010–2019 (before the COVID–19 pandemic and Brexit). The research presented was based on Eurostat data. The variables were selected on the basis of the literature review on ICT usage, as well as the criterion of data availability and comprehensiveness. The exploratory data analysis methods dealing with three‑way data structures, i.e. the between and within‑class principal component analysis, were used, and the presentation of the results was supported by factorial maps (scatterplots and biplots). In the analysed period, enterprises in all the European Union Member States intensified their ICT usage. Despite the positive trend from 2010 to 2019, Poland remained far behind the leading countries, and more precisely, was in the group of the least developed ones.

A unified framework for the integration of multiple hierarchical clusterings or networks from multi-source data

BackgroundIntegrating data from different sources is a recurring question in computational biology. Much effort has been devoted to the integration of data sets of the same type, typically multiple numerical data tables. However, data types are generally heterogeneous: it is a common place to gather data in the form of trees, networks or factorial maps, as these representations all have an appealing visual interpretation that helps to study grouping patterns and interactions between entities. The question we aim to answer in this paper is that of the integration of such representations.ResultsTo this end, we provide a simple procedure to compare data with various types, in particular trees or networks, that relies essentially on two steps: the first step projects the representations into a common coordinate system; the second step then uses a multi-table integration approach to compare the projected data. We rely on efficient and well-known methodologies for each step: the projection step is achieved by retrieving a distance matrix for each representation form and then applying multidimensional scaling to provide a new set of coordinates from all the pairwise distances. The integration step is then achieved by applying a multiple factor analysis to the multiple tables of the new coordinates. This procedure provides tools to integrate and compare data available, for instance, as tree or network structures. Our approach is complementary to kernel methods, traditionally used to answer the same question.ConclusionOur approach is evaluated on simulation and used to analyze two real-world data sets: first, we compare several clusterings for different cell-types obtained from a transcriptomics single-cell data set in mouse embryos; second, we use our procedure to aggregate a multi-table data set from the TCGA breast cancer database, in order to compare several protein networks inferred for different breast cancer subtypes.

On the potential for using selected PCA-based methods to analyze the crime rate in Poland

The aim of the paper is to assess the potential for using some selected PCA-based methods to analyze the spatial diversity of crime in Poland during 2000-2017. Classical principal components analysis (PCA) deals with two-way matrices, usually taking into account objects and variables. In the case of data analyzed in the study, apart from two dimensions (objects – voivodships, variables – criminal offences), there is also the dimension of time, so the dataset can be seen as data cube: objects × variables × time. Therefore, this type of data requires the use of methods handling three-way data structures. In the paper the variability of some selected categories of criminal offences in time (2000–2017) and space (according to voivodships) is analyzed using the between-class and the within-class principal component analysis. The advantage of these methods is, among others, the possibility of the graphical presentation of the results in two-dimensional space with the use of factorial maps.

Corporate Entrepreneurship and International Performance: a Cross-Country Study

The overall purpose of this article is to examine the theoretical connections between Corporate Entrepreneurship-CE and International Performance-IP. More specifically, we address two main research questions: (1) How do different dimensions of CE influence IP and (2) To what extent the context of host country matters? Using a two-case study approach, we employ hybrid qualitative–quantitative analyses to address the effects of different dimensions of CE on IP. We adopted four statistical techniques: descriptive statistics, decision tree, cluster analysis, and principal components (factorial maps). The results show that country matters for the perception of the relationship between CE and IP. They show that it is meaningful to separate the different dimensions of CE (innovative behavior, new business ventures, competitive aggressiveness, product/service and process innovation, self-renewal, proactiveness, and risk taking) when examining their influence on IP. The paper focuses on three level of the organization: the production sector (staff), middle management (managers), and top management (CEO and directors). Such perspective allows to explore the role of first-level managers in a “bottom-up” process of corporate entrepreneurship. Furthermore, we distinguished between two levels of corporate entrepreneurship: results and entrepreneurial behavior.

Multiple Subject Barycentric Discriminant Analysis (MUSUBADA): How to Assign Scans to Categories without Using Spatial Normalization

We present a new discriminant analysis (DA) method called Multiple Subject Barycentric Discriminant Analysis (MUSUBADA) suited for analyzing fMRI data because it handles datasets with multiple participants that each provides different number of variables (i.e., voxels) that are themselves grouped into regions of interest (ROIs). Like DA, MUSUBADA (1) assigns observations to predefined categories, (2) gives factorial maps displaying observations and categories, and (3) optimally assigns observations to categories. MUSUBADA handles cases with more variables than observations and can project portions of the data table (e.g., subtables, which can represent participants or ROIs) on the factorial maps. Therefore MUSUBADA can analyze datasets with different voxel numbers per participant and, so does not require spatial normalization. MUSUBADA statistical inferences are implemented with cross-validation techniques (e.g., jackknife and bootstrap), its performance is evaluated with confusion matrices (for fixed and random models) and represented with prediction, tolerance, and confidence intervals. We present an example where we predict the image categories (houses, shoes, chairs, and human, monkey, dog, faces,) of images watched by participants whose brains were scanned. This example corresponds to a DA question in which the data table is made of subtables (one per subject) and with more variables than observations.

Functional changes in culturable microbial communities during a co-composting process: Carbon source utilization and co-metabolism

Microbial communities in sewage sludge and green waste co-composting were investigated using culture-dependent methods and community level physiological profiles (CLPP) with Biolog Microplate. Different microbial groups characterized each stage of composting. Bacterial densities were high from beginning to end of composting, whereas actinomycete densities increased only after bio-oxidation phase i. e. after 40 days. Fungal populations become particularly high during the last stage of decomposition. Cluster analyses of metabolic profiles revealed a similar separation between two groups of composts at 67 days for bacteria and fungi. Principal component analysis (PCA) applied to bacterial and fungal CLPP data showed a chronological distribution of composts with two phases. The first one (before 67 days), where the composts were characterized by the rapid decomposition of non-humic biodegradable organic matter, was significantly correlated to the decrease of C, C/N, organic matter (OM), fulvic acid (FA), respiration, cellulase, protease, phenoloxidase, alkaline and acid phosphatases activities. The second phase corresponding to the formation of polycondensed humic-like substances was significantly correlated to humic acid (HA) content, pH and HA/FA. The influent substrates selected on both factorial maps showed that microbial communities could adapt their metabolic capacities to the particular environment. The first phase seems to be focused on easily degradable substrate utilization whereas the maturation phase appears as multiple metabolisms, which induce the release of metabolites and their polymerization leading to humification processes.

Designing erosion management plans in Lebanon using remote sensing, GIS and decision-tree modeling

Soil erosion by water represents a serious threat to the natural and human environment in Mediterranean countries, including Lebanon, which represents a good case study. This research deals with how to use Geographic Information Systems (GIS), remote sensing, and, more specifically, structural classification techniques and decision-tree modeling to map erosion risks and design priority management planning over a representative region of Lebanon. The structural classification organization and analysis of spatial structures (OASIS) of Landsat TM satellite imagery (30 m) was used to define landscapes that prevail in this area and their boundaries, depending on their spectral appearance. The landscape map produced was overlaid sequentially with thematic erosion factorial maps (i.e., slope gradient, drainage density, rainfall quantity, vegetal cover, soil infiltration, soil erodibility, rock infiltration and rock movement). The overlay was visual and conditional using three visual interpretation rules (dominance, unimodality and scarcity conservation), and landscape properties were produced. Rills and gullies were measured in the field, and a decision-tree regression model was developed on the landscapes to statistically explain gully occurrence. This model explained 88% of the variability in field gully measurements. The erosion risk map produced corresponds well to field observations (accuracy of 82%). The landscapes were prioritized according to anti-erosive remedial measures: preventive (Pre), protective (Pro), and restorative (Res). This approach seems useful in Lebanon, but can also serve in other countries with similar geo-environmental conditions or those lacking detailed geospatial data.

Assessing soil erosion in Mediterranean karst landscapes of Lebanon using remote sensing and GIS

Maps showing the potential for soil erosion at 1:100,000 scale are produced in a study area within Lebanon that can be used for evaluating erosion of Mediterranean karstic terrain with two different sets of impact factors built into an erosion model. The first set of factors is: soil erodibility, morphology, land cover/use and rainfall erosivity. The second is obtained by the first adding a fifth factor, rock infiltration. High infiltration can reflect high recharge, therefore decreasing the potential of surface runoff and hence the quantity of transported materials. Infiltration is derived as a function of lithology, lineament density, karstification and drainage density, all of which can be easily extracted from satellite imagery. The influence of these factors is assessed by a weight/rate approach sharing similarities between quantitative and qualitative methods and depending on pair-wise comparison matrix. The main outcome was the production of factorial maps and erosion susceptibility maps (scale 1:100,000). Spatial and attribute comparison of erosion maps indicates that the model that includes a measure of rock infiltration better represents erosion potential. Field investigation of rills and gullies shows 87.5% precision of the model with rock infiltration. This is 17.5% greater than the precision of the model without rock infiltration. These results indicate the necessity and importance of integrating information on infiltration of rock outcrops to assess soil erosion in Mediterranean karst landscapes.

Evaluation of Chemical Parameters in Soft Mold-Ripened Cheese During Ripening by Mid-Infrared Spectroscopy

The suitability of mid-infrared spectroscopy (MIR) to follow the evolution throughout ripening of specific physicochemical parameters in Camembert-type cheeses was evaluated. The infrared spectra were obtained directly from raw cheese samples deposited on an attenuated total reflectance crystal. Significant correlations were observed between physicochemical data, pH, acid-soluble nitrogen, nonprotein nitrogen, ammonia (NH4+), lactose, and lactic acid. Dry matter showed significant correlation only with lactose and nonprotein nitrogen. Principal components analysis factorial maps of physicochemical data showed a ripening evolution in 2 steps, from d 1 to d 7 and from d 8 to d 27, similar to that observed previously from infrared spectral data. Partial least squares regressions made it possible to obtain good prediction models for dry matter, acid-soluble nitrogen, nonprotein nitrogen, lactose, lactic acid, and NH4+ values from spectral data of raw cheese. The values of 3 statistical parameters (coefficient of determination, root mean square error of cross validation, and ratio prediction deviation) are satisfactory. Less precise models were obtained for pH.

A NEW TECHNIQUE FOR ORDERING ASYMMETRICAL THREE-DIMENSIONAL DATA SETS IN ECOLOGY

The aim of this paper is to tackle the problem that arises from asymmetrical data cubes formed by two crossed factors fixed by the experimenter (factor A and factor B, e.g., sites and dates) and a factor which is not controlled for (the species). The entries of this cube are densities in species. We approach this kind of data by the comparison of patterns, that is to say by analyzing first the effect of factor B on the species-factor A pattern, and second the effect of factor A on the species-factor B pattern. The analysis of patterns instead of individual responses requires a correspondence analysis. We use a method we call Foucart's correspondence analysis to coordinate the correspondence analyses of several independent matrices of species x factor A (respectively B) type, corresponding to each modality of factor B (respectively A). Such coordination makes it possible to evaluate the effect of factor B (respectively A) on the species-factor A (respectively B) pattern. The results obtained by such a procedure are much more insightful than those resulting from a classical single correspondence analysis applied to the global matrix that is obtained by simply unrolling the data cube, juxtaposing for example the individual species x factor A matrices through modalities of factor B. This is because a single global correspondence analysis combines three effects of factors in a way that cannot be determined from factorial maps (factor A, factor B, and factor A x factor B interaction) whereas the applications of Foucart's correspondence analysis clearly discriminate two different issues. Using two data sets, we illustrate that this technique proves to be particularly powerful in the analyses of ecological convergence which include several distinct data sets and in the analyses of spatiotemporal variations of species distributions.

Signature biologique du dopage : un avenir pour la détection ?

Introduction. – Fighting doping is permitted thanks to detection of forbidden molecules, not on detection of induced metabolic deviations, what is possible now using metabonomics. Results. – From studies performed on bovines treated with different anabolics, it is possible with urinary fingerprinting obtained by 2D-NMR, to produce factorial maps summarising main part of the relevant metabolic information. From such a specific biological signature of anabolic response, it is possible to interpret some of these biochemical disruptions. Conclusion. – Tracking down doping in sportsmen could be reinforced as promisingly shown in cattle thanks to a prior detection of the suspected family of anabolics.

Behaviours promoting grouping or dispersal of mother and neonates in ovoviviparous cockroaches

The nature of early relationships between mother and nymphs and among siblings was compared in four cockroach species belonging to the same ovoviviparous family (Zetoborinae) in order to characterise the behavioural interactions favouring dispersal or maintenance of the group of neonates. Behavioural interactions between mothers and their new-born nymphs and between two sibling neonates were video recorded and analysed with flow charts on factorial maps. In the solitary species Thanatophyllum akinetum, nymphs dispersed a few hours after birth without aggressiveness between siblings or between mother and offspring. In contrast females of Schultesia lampyridiformis displayed a behaviour never previously observed in cockroaches: aggression towards their own neonate nymphs, which could contribute to their dispersal. In Phortioeca nimbata and Lanxoblatta emarginata, nymphs stayed with their mother for 10 days, but social interactions differed between the two sp ecies: P. nimbata mothers actively searched for their nymphs, this behaviour being favoured by an active search for mutual contact by the nymphs themselves, while L. emarginata nymphs sought more actively the proximity of their mother but less contact between themselves. Thus, different species of Zetoborinae presented two types of dispersal of the young and two types of maintenance of the birth group, both achieved by specific behavioural interactions. The relevance of behavioural interactions for the characterisation of early gregarism and parental care is discussed.

Measurement for Solitariness and Gregarism: Analysing Spacing, Attraction and Interactions in Four Species of Zetoborinae (Blattaria)

Abstract Distinguishing gregarism based on attraction between conspecifics from aggregation based on environmental factors is not a trivial task. In this paper, we propose a laboratory experimental design for characterizing gregarism, using Zetoborine cockroaches as a model. Three complementary tests were used: the classical spacing and attraction tests, complemented by analyses of social interactions with flow charts on factorial maps. Convergent results from the three tests allowed a tentative characterization of solitariness and different degrees of gregarism. These elements were used to improve the interpretation of spacing patterns of four species of cockroaches observed in the field.

Cluster Analysis of Gallstone FT-IR Spectra: Tests on Simulated Mixture Spectra and Comparison between Spectral and Morphological Classification of Human Gallstones

Sixty-four combination spectra of three major gallstone components [i.e., cholesterol, calcium bilirubinate, and calcium carbonate (aragonite)] were simulated in accordance with a “fractal” ternary diagram. Comparison between the original pattern of composition and factorial maps of pretreated spectra makes it possible to show the effects of different normalization procedures (Euclidean norm, spectrum maximum, and area under spectrum set to 1). Cluster analysis of these spectra, depending on different agglomerative links (single linkage, complete linkage, average linkage, and Ward's criterion), was carried out. All the resultant trees yield the same groups, but Ward's criterion best preserves the pattern of the data. More than 100 gallstones from France and Vietnam were classified by using cluster analysis of their FT-IR spectra with Ward's criterion. Seven homogeneous groups of spectra were extracted, which have been significantly correlated to the four morphological types of gallstones: pure cholesterol, mixed cholesterol, brown pigment, and black pigment stones. This analysis also reveals that the morphological groups are not homogeneous in composition, in particular for black pigment stones.

Simultaneous Determination of Sugars by Multivariate Analysis Applied to Mid-Infrared Spectra of Biological Samples

We have investigated the use of principal component analysis (PCA) to describe and assess mid-infrared spectral data obtained from complex biological samples containing sucrose, fructose, and glucose. The correlation coefficients between spectral data and chemical values of each variable (sucrose, glucose, fructose, total sugars, and reducing sugars) showed that in each case, axes 1, 3, 4, and 5 had the highest values. These values also indicated which axes each variable was mostly correlated with. The results also showed that the samples were distributed according to their sucrose concentrations (or total sugars) along a concentration gradient in the projection plan formed between axes 1 and 3. No clear discrimination according to concentration was observed with other factorial maps. Prediction equations that linked sucrose, fructose, glucose, total sugar, and reducing sugars concentrations to the spectral data were established by regression on the principal component. Very high correlation coefficients values between the first 10 axes and the chemical values were obtained (between 0.9757 and 0.998). From such aqueous biological samples containing a ternary mixture of sucrose, fructose, and glucose, it was possible to (1) identify the characteristic IR bands of these different sugars (and their combination: reducing sugars/total sugars) and (2) to specifically measure their concentrations with a relatively good accuracy.

Gram-Schmidt Orthogonalization and Elimination of the Effect of Unwanted Component Spectra Applied to a Biological Mid-infrared Spectra Collection

Abstract Near Infrared spectroscopy (NIR) is the most widely used technique for the analysis of major biochemical constituents in food products. The Mid-infrared range spectroscopy is also being more and more studied in the field of food analysis. This range was primarily applied to qualitative analysis of food components, but with the advent of new techniques such as Attenuated Total Reflectance (ATR) together with the possibility of combination with powerful micro-computers, MIR is now more and more used for quantitative analysis. In addition to baseline deformations, interference by unwanted compounds are major sources of problems that are encountered in analyses. We have previously proposed (Cadet et al., 1991) the use of multidimensional statistical analysis combined with Mid-FTIR spectroscopy for the prediction of sucrose concentrations in biological solutions containing three sugars: sucrose, fructose and glucose. In this paper, a least-squares method has been used to assess the elimination of the component spectra associated to the fructose (the unwanted components were first orthogonal zed and normalized by the Gram-Schmidt orthogonalization method). This procedure permitted the automatic subtraction of discriminant spectral patterns representative of fructose concentration before application of Principal Component Analysis (PCA) and Principal Component Regression (PCR). PCA was applied independently before and after spectral correction of the collections. It is found that when the factorial maps obtained before and after correction are compared, the elimination procedure improves significantly the classification of solutions according to their sucrose content. However the bias and standard deviation (SD) values that are associated with the sucrose content predicted values are not influenced by the correction method used: bias and SD are 3.62×10−2 and 3.097×10−1 before correction and after correction they were respectively 3.60×10−2 and 3.104×10−1. This could be explained by the fact that the presence of fructose in solution does not interfere with caracteristic absorption bands of sucrose and that sucrose and fructose concentrations are strongly correlated. The absorbtions bands of the spectral representation of the principal component, which is identified to be that associated with sucrose, are identical before and after correction.

Study of the Effects of Basic Di‐ and Tri‐phenyl Derivatives on Malignant Cell Proliferation: An Example of the Application of Correspondence Factor Analysis to Structure‐Activity Relationships (SAR)

AbstractThe descriptive multivariate method known as Correspondence Factor Analysis (CFA) was used to establish correlations between the structures of three chemical classes of compounds (triphenyl‐acrylonitriles (TPEs), diphenylethylenes (DPEs), and diphenylalkyls) substituted in the para position by either hydroxy or basic groups and their responses in a battery of three biochemical tests, namely the induction of the proliferation of the MCF7 human breast cancer cell‐line, the estrogen‐irreversible inhibition of MCF7 cell proliferation (herein denoted cytotoxicity), and binding to the estrogen receptor (ER). The power of CFA was illustrated by performing several analyses: (a) Construction of factorial maps that described only the specificity of the response of the TPE population in the tests or both the specificity and amplitude of the response; (b) Use of the factorial maps as mathematical models for the introduction of new variables. These variables were either further biochemical tests (cytotoxicity under different conditions, inhibition of the activation of protein kinase C) on which the TPE population had been screened or further compounds (DPEs and diphenylalkyls). Relationships among the different tests were thus assessed as well as affiliations of the new compounds with TPEs. The analyses revealed the importance of the presence and configuration of hydroxy groups in ER binding and cell proliferation, but also the ability of non‐hydroxylated compounds to induce cell growth independently of their relative affinity for ER. Cytotoxicity could be related to the presence of basic groups but also to resonance of conjugated bis‐para‐hydroxy diphenyl derivatives. Overall, the analyses stressed the complexity of the relationships between growth‐promoting and growth‐inhibitory potential of the test‐compound populations and suggested the involvement of multiple mechanisms of action.

A multivariate approach to the description of patient populations. An example of the analysis of the hormone profiles of patients with advanced prostate cancer

In view of the multifactorial nature of the endocrine dysfunctions that may develop during prostate cancer and the unsuitability of the most widely used statistical methods to study such dysfunction, we have in the present study examined the relationships among 17 biological variables in 26 patients with advanced prostate cancer by two complementary multivariate methods, correspondence factorial analysis (CFA) and a hierarchical automatic classification procedure. The 17 variables included 14 hormones, their precursors or metabolites [LH, FSH, estradiol (E2), testosterone, dihydrotestosterone (DHT), androstenedione (A), androstenediol (Ediol), dehydroepiandrosterone (DHA), DHA-sulphate (DS), cortisol (CORT), 17α-hydroxyprogesterone (17-OH-PROG), pregnenolone (PREG), 17α-hydroxy-pregnenolone (17-OH-PREG), and androstanediol glucuronide (ADG)], one plasma binding protein, namely, sex-hormone-binding protein (SHBG) and two tumour markers, prostatic acid phosphatase (PAP) and prostate-specific antigen (PSA). The originality of these multivariate methods is that they do not preselect a dependent variable nor perform two-by-two correlations as in stepwise multiple regression analysis but describe the patient population by extracting layers of correlations (from strong to weak) from amid confounding variables. Compared to principal component analysis which is based on covariance, CFA, based on the χ2-metric, enables the licit representation of both tests and patients on the same factorial maps. From an examination of proximity among variables, it is possible to deduce which tests are related, which groups of patients have similar hormone profiles, and which tests vary most in which patients. The most discriminant factors in this particular population of patients were PSA and PAP levels, which were, however, not strongly correlated and were apparently selectively associated with certain hormones. PAP seemed the more pathological marker; PSA was somewhat anticorrelated to the adrenal androgen (DHA and DS) and PREG levels. The hormones with the lowest variance were A, Ediol and CORT reflecting their key roles in metabolism. A number of patients were hypogonadic. SHBG levels were not closely related to total T levels but anticorrelated with ADG suggesting that, in the patients concerned, SHBG decreases the bioavailable T fraction. There was no correlation between ADG and precursor hormones (PREG, DHA, DS) but a slight anticorrelation between these precursors and DHT. Therefore the source of ADG in these patients does not seem to be increased levels of precursor hormones nor of DHT but increased peripheral tissue metabolism of androgens. In future, descriptive multivariate analyses of large patient cohorts should help to define subpopulations with distinctive hormone profiles for prospective clinical studies.