Power transformations in correspondence analysis

Power transformations of positive data tables, prior to applying the correspondence analysis algorithm, are shown to open up a family of methods with direct connections to the analysis of log-ratios. Two variations of this idea are illustrated. The first approach is simply to power the original data and perform a correspondence analysis this method is shown to converge to unweighted log-ratio analysis as the power parameter tends to zero. The second approach is to apply the power transformation to thecontingency ratios, that is the values in the table relative to expected values based on the marginals this method converges to weighted log-ratio analysis, or the spectral map. Two applications are described: first, a matrix of population genetic data which is inherently two-dimensional, and second, a larger cross-tabulation with higher dimensionality, from a linguistic analysis of several books.

Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data

We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices to analyse the ratios of the data values. The usual approach to dimension reduction in compositional data analysis is to perform principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence. We show that by introducing weights for the rows and columns, the method achieves this desirable property. This weighted log-ratio analysis is theoretically equivalent to spectral mapping , a multivariate method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra. The close relationship between spectral mapping and correspondence analysis is also explained, as well as their connection with association modelling. The weighted log-ratio methodology is applied here to frequency data in linguistics and to chemical compositional data in archaeology.

Comparing correspondence analysis and the log-ratio alternative for representing categorical data

We compare correspondance análisis to the logratio approach based on compositional data. We also compare correspondance análisis and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. These three methods of representation can produce quite similar results. One illustrative example is given

A unified approach for representing rows and columns in contingency tables

By using suitable parameters, we present a uni¯ed aproach for describing four methods for representing categorical data in a contingency table. These methods include:correspondence analysis (CA), the alternative approach using Hellinger distance (HD),the log-ratio (LR) alternative, which is appropriate for compositional data, and theso-called non-symmetrical correspondence analysis (NSCA). We then make an appropriate comparison among these four methods and some illustrative examples are given.Some approaches based on cumulative frequencies are also linked and studied usingmatrices.Key words: Correspondence analysis, Hellinger distance, Non-symmetrical correspondence analysis, log-ratio analysis, Taguchi inertia

Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.

Comparing correspondence analysis and the log-ratio alternative for representing categorical data

We compare correspondance análisis to the logratio approach based on compositional data. We also compare correspondance análisis and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. These three methods of representation can produce quite similar results. One illustrative example is given

A unified approach for representing rows and columns in contingency tables

By using suitable parameters, we present a uni¯ed aproach for describing four methods for representing categorical data in a contingency table. These methods include: correspondence analysis (CA), the alternative approach using Hellinger distance (HD), the log-ratio (LR) alternative, which is appropriate for compositional data, and the so-called non-symmetrical correspondence analysis (NSCA). We then make an appropriate comparison among these four methods and some illustrative examples are given. Some approaches based on cumulative frequencies are also linked and studied using matrices. Key words: Correspondence analysis, Hellinger distance, Non-symmetrical correspondence analysis, log-ratio analysis, Taguchi inertia

Waist-to-height Ratio Percentiles And Cutoffs For Obesity: A Cross-sectional Study In Brazilian Adolescents.

This study aimed to describe the distribution of waist-to-height ratio (WHtR) percentiles and cutoffs for obesity in Brazilian adolescents. A cross-sectional study including adolescents aged 10 to 15 years was conducted in the city of São Paulo, Brazil; anthropometric measurements (weight, height, and waist-circumference) were taken, and WHtRs were calculated and then divided into percentiles derived by using Least Median of Squares (LMS) regression. The receiver operating characteristic (ROC) curve was used in determining cutoffs for obesity (BMI ≥ 97th percentile) and Mann-Whitney and Kruskal-Wallis tests were used for comparing variables. The study included 8,019 adolescents from 43 schools, of whom 54.5% were female, and 74.8% attended public schools. Boys had higher mean WHtR than girls (0.45 ± 0.06 vs 0.44 ± 0.05; p=0.002) and higher WHtR at the 95th percentile (0.56 vs 0.54; p<0.05). The WHtR cutoffs according to the WHO criteria ranged from 0.467 to 0.506 and 0.463 to 0.496 among girls and boys respectively, with high sensitivity (82.8-95%) and specificity (84-95.5%). The WHtR was significantly associated with body adiposity measured by BMI. Its age-specific percentiles and cutoffs may be used as additional surrogate markers of central obesity and its co-morbidities.

Evaluation Of Characteristic-to-total Spectrum Ratio: Comparison Between Experimental And A Semi-empirical Model.

Primary X-ray spectra were measured in the range of 80-150kV in order to validate a computer program based on a semiempirical model. The ratio between the characteristic and total air Kerma was considered to compare computed results and experimental data. Results show that the experimental spectra have higher first HVL and mean energy than the calculated ones. The ratios between the characteristic and total air Kerma for calculated spectra are in good agreement with experimental results for all filtrations used.

Impact Of Drug Formulation And Free Platinum/cisplatin Ratio On Hypersensitivity Reactions To Cisplatin: Formulation Matters.

Use of cisplatin can induce type I hypersensitivity reactions that may also be linked to the quality of the drug utilized. We observed cases of hypersensitivity that appeared to be associated with the brand of cisplatin used. The aim of this study was to compare two different brands of cisplatin in relation to type I hypersensitivity reactions. Brand A was used in a tertiary care teaching hospital until 2012, and use of brand B started from January 2013, when the first hypersensitivity cases were observed. Patients were categorized based on symptom. Cisplatin of both brands was analysed by high-performance liquid chromatography (HPLC) and high-resolution electrospray ionization mass spectrometry (ESI-(+)-MS) and characterized according to US Pharmacopeia. There were no cases of hypersensitivity associated with the use of cisplatin brand A, whereas four of 127 outpatients that used cisplatin brand B were affected. The two brands were in accordance with the US Pharmacopeia parameters, and there was no significant difference in the total platinum levels between the two brands when analysed by HPLC. However, high-resolution ESI-(+)-MS analyses show that brand B contains approximately 2.7 times more hydrolysed cisplatin than brand A. The increase in the hydrolysed form of cisplatin found in brand B may be the cause of the hypersensitivity reaction observed in a subset of patients. We present the first study of the quality of drugs by high-resolution ESI-(+)-MS. Drug regulatory agencies and manufacturers should consider including measurement of hydrolysed cisplatin as a quality criterion for cisplatin formulations.

Florivory and sex ratio in Annona dioica St. Hil. (Annonaceae) in the Pantanal at Nhecolândia, southwestern Brazil

Annona dioica St. Hil. is a species that grows to approximately 2 m tall and is very widespread in the cerrados. Individual plants of this androdioecious species produce numerous hermaphroditic or male flowers, but few fruits. The aim of this study was to determine the sex ratio among the plants and to compare the frequency of herbivory between male and hermaphroditic flowers. The fieldwork was done by studying flowering plants in grasslands used as pasture for cattle at Fazenda Nhumirim. One hundred and forty-seven male plants and 71 hermaphroditic plants were examined and produced a total of 194 and 94 flowers, respectively, during the study period. The male:hermaphrodite sex ratio was 2.07:1, and was similar to the male:hermaphrodite flower ratio of 2.06:1. The frequency of florivory rate in hermaphrodites was significantly higher than in male flowers (33.0%, n = 31, and 25.7%, n = 50, respectively; G = 14.83; d.f. = 1; p < 0.001). The mean fresh weights of male and hermaphroditic flowers were significantly different (8.38 ± 2.40 g vs. 6.93 ± 2.68 g, respectively; 0 ± SEM; n = 50 each; t = 2.479; d.f. = 49; p = 0.017). These results indicate that the low fruit set in this species can be explained by the sex ratio, the greater herbivory of hermaphroditic flowers and the probable absence of pollinators.

Sex ratio and morphological characteristics of rufous gnateaters, Conopophaga lineata (Aves, Passeriformes) in Atlantic forest fragments

Unequal sex ratios lead to the loss of genetic variability, decreasing the viability of populations in the long term. Anthropogenic activities often disturb the natural habitats and can cause alterations in sex ratio and morphological characteristics of several species. Forest fragmentation is a major conservation concern, so that understanding its effects in natural populations is essential. In this study, we evaluated the sex ratio and the morphological characteristics of Rufous Gnateaters (Conopophaga lineata (Wied, 1831)) in small and large forest fragments in Minas Gerais, Brazil. Birds (n = 89) were sexed by plumage characteristics and molecular markers. The molecular analysis showed that plumage is not a totally reliable method for sexing Rufous Gnateaters. We observed that sex ratio did not differ between large and small forest fragments, but birds in small fragments had larger wings and tarsus. Wing and tarsus changes may affect the movement ability of individuals within and among forest fragments. In conclusion, Rufous Gnateaters have been able to survive in both small and large Atlantic rain forest fragments without altering their sex ratio, but morphological changes can be prejudicial to their long term survival.

Análise TG-ROC de testes de imunofluorescência no diagnóstico de leishmaniose visceral canina

OBJETIVO: Analisar a acurácia do diagnóstico de dois protocolos de imunofluorescência indireta para leishmaniose visceral canina. MÉTODOS: Cães provenientes de inquérito soroepidemiológico realizado em área endêmica nos municípios de Araçatuba e de Andradina, na região noroeste do estado de São Paulo, em 2003, e área não endêmica da região metropolitana de São Paulo, foram utilizados para avaliar comparativamente dois protocolos da reação de imunofluorescência indireta (RIFI) para leishmaniose: um utilizando antígeno heterólogo Leishmania major (RIFI-BM) e outro utilizando antígeno homólogo Leishmania chagasi (RIFI-CH). Para estimar acurácia utilizou-se a análise two-graph receiver operating characteristic (TG-ROC). A análise TG-ROC comparou as leituras da diluição 1:20 do antígeno homólogo (RIFI-CH), consideradas como teste referência, com as diluições da RIFI-BM (antígeno heterólogo). RESULTADOS: A diluição 1:20 do teste RIFI-CH apresentou o melhor coeficiente de contingência (0,755) e a maior força de associação entre as duas variáveis estudadas (qui-quadrado=124,3), sendo considerada a diluição-referência do teste nas comparações com as diferentes diluições do teste RIFI-BM. Os melhores resultados do RIFI-BM foram obtidos na diluição 1:40, com melhor coeficiente de contingência (0,680) e maior força de associação (qui-quadrado=80,8). Com a mudança do ponto de corte sugerido nesta análise para a diluição 1:40 da RIFI-BM, o valor do parâmetro especificidade aumentou de 57,5% para 97,7%, embora a diluição 1:80 tivesse apresentado a melhor estimativa para sensibilidade (80,2%) com o novo ponto de corte. CONCLUSÕES: A análise TG-ROC pode fornecer importantes informações sobre os testes de diagnósticos, além de apresentar sugestões sobre pontos de cortes que podem melhorar as estimativas de sensibilidade e especificidade do teste, e avaliá-los a luz do melhor custo-benefício.

Ratio of weight to height gain: a useful tool for identifying children at risk of becoming overweight or obese at preschool age

PURPOSE: To analyze the usefulness of the weight gain/height gain ratio from birth to two and three years of age as a predictive risk indicator of excess weight at preschool age. METHODS: The weight and height/length of 409 preschool children at daycare centers were measured according to internationally recommended rules. The weight values and body mass indices of the children were transformed into a z-score per the standard method described by the World Health Organization. The Pearson correlation coefficients (rP) and the linear regressions between the anthropometric parameters and the body mass index z-scores of preschool children were statistically analyzed (alpha = 0.05). RESULTS: The mean age of the study population was 3.2 years (± 0.3 years). The prevalence of excess weight was 28.8%, and the prevalence of overweight and obesity was 8.8%. The correlation coefficients between the body mass index z-scores of the preschool children and the birth weights or body mass indices at birth were low (0.09 and 0.10, respectively). There was a high correlation coefficient (rP = 0.79) between the mean monthly gain of weight and the body mass index z-score of preschool children. A higher coefficient (rP = 0.93) was observed between the ratio of the mean weight gain per height gain (g/cm) and the preschool children body mass index z-score. The coefficients and their differences were statistically significant. CONCLUSION: Regardless of weight or length at birth, the mean ratio between the weight gain per g/cm of height growth from birth presented a strong correlation with the body mass index of preschool children. These results suggest that this ratio may be a good indicator of the risk of excess weight and obesity in preschool-aged children.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.