Dynamic perceptual mapping

Perceptual maps have been used for decades by market researchers to illuminatethem about the similarity between brands in terms of a set of attributes, to position consumersrelative to brands in terms of their preferences, or to study how demographic and psychometricvariables relate to consumer choice. Invariably these maps are two-dimensional and static. Aswe enter the era of electronic publishing, the possibilities for dynamic graphics are opening up.We demonstrate the usefulness of introducing motion into perceptual maps through fourexamples. The first example shows how a perceptual map can be viewed in three dimensions,and the second one moves between two analyses of the data that were collected according todifferent protocols. In a third example we move from the best view of the data at the individuallevel to one which focuses on between-group differences in aggregated data. A final exampleconsiders the case when several demographic variables or market segments are available foreach respondent, showing an animation with increasingly detailed demographic comparisons.These examples of dynamic maps use several data sets from marketing and social scienceresearch.

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods.

Measuring subcompositional incoherence

Subcompositional coherence is a fundamental property of Aitchison s approach to compositional data analysis, and is the principal justification for using ratios of components. We maintain, however, that lack of subcompositional coherence, that is incoherence, can be measured in an attempt to evaluate whether any given technique is close enough, for all practical purposes, to being subcompositionally coherent. This opens up the field to alternative methods, which might be better suited to cope with problems such as data zeros and outliers, while being only slightly incoherent. The measure that we propose is based on the distance measure between components. We show that the two-part subcompositions, which appear to be the most sensitive to subcompositional incoherence, can be used to establish a distance matrix which can be directly compared with the pairwise distances in the full composition. The closeness of these two matrices can be quantified using a stress measure that is common in multidimensional scaling, providing a measure of subcompositional incoherence. The approach is illustrated using power-transformed correspondence analysis, which has already been shown to converge to log-ratio analysis as the power transform tends to zero.

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

Building adaptive capacity and resilience to climate change in the water sector in Cape Verde

Purpose of the evaluation This is a scheduled standard mid-term evaluation (MTR) of a UNDP implemented GEF LDCF co-financed project. It is conducted by a team of an international and a national independent evaluator. The objective of the MTR, as set out in the Terms of Reference (TORs; Annex 1), is to provide an independent analysis of the progress of the project so far. The MTR aims to:  identify potential project design problems,  assess progress towards the achievement of the project objective and outcomes,  identify and document lessons learned (including lessons that might improve design and implementation of other projects, including UNDP-GEF supported projects), and  make recommendations regarding specific actions that should be taken to improve the project. The MTR is intended to assess signs of project success or failure and identify the necessary changes to be made. The project commenced its implementation in the first half of 2010 with the recruitment of project staff. According to the updated project plan, it is due to close in July 201410 with operations scaling down in December 2013 due to funding limits. Because of a slow implementation start, the mid-term evaluation was delayed to July 201311 The intended target audience of the evaluation are:  The project team and decision makers in the INGRH  The GEF and UNFCCC Operational Focal Points  The project partners and beneficiaries  UNDP in Cape Verde as well as the regional and headquarter (HQ) office levels  The GEF Secretariat.

Total curvature and total torsion of knotted polymers

Previous work on radius of gyration and average crossing number has demonstrated that polymers with fixed topology show a different scaling behavior with respect to these characteristics than polymers with unrestricted topology. Using numerical simulations, we show here that the difference in the scaling behavior between polymers with restricted and unrestricted topology also applies to the total curvature and total torsion. For each knot type, the equilibrium length with respect to a given spatial characteristic is the number of edges at which the value of the characteristic is the same as the average for all polygons. This number appears to be correlated to physical properties of macromolecules, for example gel mobility as measured by the separation between distinct knot types. We also find that, on average, closed polymers require slightly more total curvature and slightly less total torsion than open polymers with the corresponding number of monomers.

GPS analysis of human locomotion: further evidence for long-range correlations in stride-to-stride fluctuations of gait parameters.

During free walking, gait is automatically adjusted to provide optimal mechanical output and minimal energy expenditure; gait parameters, such as cadence, fluctuate from one stride to the next around average values. It was described that this fluctuation exhibited long-range correlations and fractal-like patterns. In addition, it was suggested that these long-range correlations disappeared if the participant followed the beep of metronome to regulate his or her pace. Until now, these fractal fluctuations were only observed for stride interval, because no technique existed to adequately analyze an extended time of free walking. The aim of the present study was to measure walking speed (WS), step frequency (SF) and step length (SL) with high accuracy (<1 cm) satellite positioning method (global positioning system or GPS) in order to detect long-range correlations in the stride-to-stride fluctuations. Eight participants walked 30 min under free and constrained (metronome) conditions. Under free walking conditions, DFA (detrended fluctuation analysis) and surrogate data tests showed that the fluctuation of WS, SL and SF exhibited a fractal pattern (i.e., scaling exponent alpha: 0.5 < alpha < 1) in a large majority of participants (7/8). Under constrained conditions (metronome), SF fluctuations became significantly anti-correlated (alpha < 0.5) in all participants. However, the scaling exponent of SL and WS was not modified. We conclude that, when the walking pace is controlled by an auditory signal, the feedback loop between the planned movement (at supraspinal level) and the sensory inputs induces a continual shifting of SF around the mean (persistent anti-correlation), but with no effect on the fluctuation dynamics of the other parameters (SL, WS).

Tying up the loose ends in simple correspondence analysis

Although correspondence analysis is now widely available in statistical software packages and applied in a variety of contexts, notably the social and environmental sciences, there are still some misconceptions about this method as well as unresolved issues which remain controversial to this day. In this paper we hope to settle these matters, namely (i) the way CA measures variance in a two-way table and how to compare variances between tables of different sizes, (ii) the influence, or rather lack of influence, of outliers in the usual CA maps, (iii) the scaling issue and the biplot interpretation of maps,(iv) whether or not to rotate a solution, and (v) statistical significance of results.

Weighted Euclidean biplots

We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots.

Dung beetle (Coleoptera, Scarabaeidae) assemblage of a highly fragmented landscape of Atlantic forest: from small to the largest fragments of northeastern Brazilian region

Human activities in tropical forests are the main causes of forest fragmentation. According to historical factor in deforestation processes, forest remnants exhibit different sizes and shapes. The aim of the present study was to evaluate the dung beetle assemblage on fragments of different degree of sizes. Sampling was performed during rainy and dry season of 2010 in six fragments of Atlantic forest, using pitfall traps baited with excrement and carrion. Also, we used two larger fragments as control. We used General Linear Models to determine whether the fragments presented distinguished dung beetle abundance and richness. Analysis of Similarities and Non-Metric Multidimensional Scaling were used to determine whether the dung beetle assemblage was grouped according to species composition. A total of 3352 individuals were collected and 19 species were identified in the six fragments sampled. Dung beetle abundance exhibited a shift according to fragment size; however, richness did not change among fragments evaluated. Also, fragments sampled and the two controls exhibited distinct species composition. The distinction on abundance of dung beetles among fragments may be related to different amount of resource available in each one. It is likely that the dung beetle richness did not distinguish among the different fragments due to the even distribution of the mammal communities in these patches, and consequent equal dung diversity. We conclude that larger fragments encompass higher abundance of dung beetle and distinct species. However, for a clearer understanding of effects of fragmentation on dung beetles in Atlantic forest, studies evaluating narrower variations of larger fragments should be conducted.

Biomass estimation of Triplectides egleri Sattler (Trichoptera, Leptoceridae) in a stream at Ducke Reserve, Central Amazonia

ABSTRACT Biomass is a fundamental measure for understanding the structure and functioning (e.g. fluxes of energy and nutrients in the food chain) of aquatic ecosystems. We aim to provide predictive models to estimate the biomass of Triplectides egleri Sattler, 1963, in a stream in Central Amazonia, based on body and case dimensions. We used body length, head-capsule width, interocular distance and case length and width to derive biomass estimations. Linear, exponential and power regression models were used to assess the relationship between biomass and body or case dimensions. All regression models used in the biomass estimation of T. egleri were significant. The best fit between biomass and body or case dimensions was obtained using the power model, followed by the exponential and linear models. Body length provided the best estimate of biomass. However, the dimensions of sclerotized structures (interocular distance and head-capsule width) also provided good biomass predictions, and may be useful in estimating biomass of preserved and/or damaged material. Case width was the dimension of the case that provided the best estimate of biomass. Despite the low relation, case width may be useful in studies that require low stress on individuals.

Bias related to body mass index in pediatric echocardiographic z scores.

In pediatric echocardiography, cardiac dimensions are often normalized for weight, height, or body surface area (BSA). The combined influence of height and weight on cardiac size is complex and likely varies with age. We hypothesized that increasing weight for height, as represented by body mass index (BMI) adjusted for age, is poorly accounted for in Z scores normalized for weight, height, or BSA. We aimed to evaluate whether a bias related to BMI was introduced when proximal aorta diameter Z scores are derived from bivariate models (only one normalizing variable), and whether such a bias was reduced when multivariable models are used. We analyzed 1,422 echocardiograms read as normal in children ≤18 years. We computed Z scores of the proximal aorta using allometric, polynomial, and multivariable models with four body size variables. We then assessed the level of residual association of Z scores and BMI adjusted for age and sex. In children ≥6 years, we found a significant residual linear association with BMI-for-age and Z scores for most regression models. Only a multivariable model including weight and height as independent predictors produced a Z score free of linear association with BMI. We concluded that a bias related to BMI was present in Z scores of proximal aorta diameter when normalization was done using bivariate models, regardless of the regression model or the normalizing variable. The use of multivariable models with weight and height as independent predictors should be explored to reduce this potential pitfall when pediatric echocardiography reference values are evaluated.

Crecimiento de Platyxanthus orbignyi "Cangrejo violaceo" procedente de la caleta de Huanchaco - La Libertad durante el 2015

Esta investigación se realizó para determinar el crecimiento de Platyxanthus orbignyi “cangrejo violáceo” capturados en la caleta de Huanchaco, ubicado en el distrito de Huanchaco, Provincia de Trujillo, Departamento La Libertad, durante el 2015. El objetivo fue determinar el crecimiento de P. orbignyi, la muestra estuvo constituida por 1477 ejemplares procedentes de las capturas que realizan los pescadores artesanales empleando caballitos de totora y trampas denominadas nasas. Estos muestreos fueron mensuales durante el año 2015. La relación entre longitud cefalotorácica (mm) y ancho cefalotorácico (mm) presentó diferencia estadística entre las líneas de regresión de ambos sexos, la relación entre el ancho cefalotorácico (mm) y peso total (g) mostró alometría en el crecimiento de hembras y machos, estadísticamente no se encontró diferencia entre los sexos. Mediante el método de Bhattacharya (1967) modificado por Pauly y Caddy (1985) se establecieron siete estados de muda para las hembras y nueve estados de muda para los machos. Según el criterio de Kurata (1962) se estableció que el crecimiento en ambos sexos es de tipo geométrico retrogresivo. Los parámetros calculados se ajustaron a la ecuación de von Bertalanffy.

Relationships between soil class and nutritional status of coffee plantations

Farm planning requires an assessment of the soil class. Research suggest that the Diagnosis and Recommendation Integrated System (DRIS) has the capacity to evaluate the nutritional status of coffee plantations, regardless of environmental conditions. Additionally, the use of DRIS could reduce the costs for farm planning. This study evaluated the relationship between the soil class and nutritional status of coffee plants (Coffea canephora Pierre) using the Critical Level (CL) and DRIS methods, based on two multivariate statistical methods (discriminant and multidimensional scaling analyses). During three consecutive years, yield and foliar concentration of nutrients (N, P, K, Ca, Mg, S, B, Zn, Mn, Fe and Cu) were obtained from coffee plantations cultivated in Espírito Santo state. Discriminant analysis showed that the soil class was an important factor determining the nutritional status of the coffee plants. The grouping separation by the CL method was not as effective as the DRIS one. The bidimensional analysis of Euclidean distances did not show the same relationship between plant nutritional status and soil class. Multidimensional scaling analysis by the CL method indicated that 93.3 % of the crops grouped into one cluster, whereas the DRIS method split the fields more evenly into three clusters. The DRIS method thus proved to be more consistent than the CL method for grouping coffee plantations by soil class.

Fractal temporal organisation of motricity is altered in major depression.

OBJECTIVE: Motor changes in major depression (MD) may represent potential markers of treatment response. Physiological rhythms (heart rate/gait cycle/hand movements) have been recently shown to be neither random nor regular but to display a fractal temporal organisation, possibly reflecting a unique central "internal clock" control. Sleep and mood circadian rhythm modifications observed in MD also suggest a role for this "internal clock". We set out to examine the fractal pattern of motor activity in MD. METHODS: Ten depressed patients (46±20 years) and ten age- and gender-matched healthy controls (48±21 years) underwent a 6-h ambulatory monitoring of spontaneous hand activity with a validated wireless device. Fractal scaling exponent (α) was analysed. An α value close to 1 means the pattern is fractal. RESULTS: Healthy controls displayed a fractal pattern of spontaneous motor hand activity (α: 1.0±0.1), whereas depressed patients showed an alteration of that pattern (α:1.2±0.15, p<0.01), towards a smoother organisation. CONCLUSION: The alteration of fractal pattern of hand activity by depression further supports the role of a central internal clock in the temporal organisation of movements. This novel way of studying motor changes in depression might have an important role in the detection of endophenotypes and potential predictors of treatment response.