Log-ratio Analysis Research Articles

A general similarity measure for simple correspondence analysis

This article presents a general similarity measure for comparing different variants of simple correspondence analysis when analysing the association using the Cressie-Read family of divergence statistics (Beh and Lombardo 2024, International Statistical Review). It includes, as special cases, the similarity measures that have been proposed in the correspondence analysis literature for assessing the similarities and differences between the traditional approach to simple correspondence analysis and new approaches like the log-ratio analysis, and the Hellinger distance method. This article describes six further properties that show how the proposed general similarity measure can be expanded upon.

Comparison of log-ratio and log10 chemical elemental data analysis of Central Amazonian pottery and archaeological implications

Comparison of log-ratio and log10 chemical elemental data analysis of Central Amazonian pottery and archaeological implications

Logratio analysis of components separated from grain‐size distributions and implications for sedimentary processes: An example of bottom surface sediments in a shallow lake

ABSTRACTThe grain‐size distributions of sediments can yield important information about sediment provenance and sedimentary processes; however, grain‐size distributions are frequently polymodal, rendering analyses difficult. To improve analyses of polymodal grain‐size data, the present study decomposed the grain‐size distributions of bottom surface sediments from Lake Kitaura, a shallow lake in Japan, into lognormal distributions and performed logratio analysis of their mixing proportions. The polymodal grain‐size distributions of the studied samples were separated into four common components at most sites. This logratio analysis revealed clear differences in the characteristics of the spatial distributions of the separated grain‐size components. The logratio values indicated that the three finer components were uniformly deposited within the lake, whereas the coarsest component was spatially diverse, reflecting differences in their sources and sedimentary processes. These results demonstrate the effectiveness of decomposition and logratio analysis of polymodal grain‐size distributions for estimating sedimentary processes. This method can be applied to modern sediments and for palaeoenvironmental reconstructions using sediment cores.

Advancing forensic research: An examination of compositional data analysis with an application on petrol fraud detection

In recent years, numerous studies have examined the chemical compounds of petrol and petrol data for forensic research. Standard quantitative methods often assume that the variables or compounds do not have compositional constraints or are not part of a constrained whole, operating within an Euclidean vector space. However, chemical compounds are typically part of a whole, and the appropriate vector space for their analysis is the simplex. Biased and arbitrary results result when statistical analysis are applied on such data without proper pre-processing of such data. Compositional analysis of data has not yet been considered in forensic science. Therefore, we compare classical statistical analysis as applied in forensic research and the new proposed paradigm of compositional data analysis (CoDa). It is demonstrated how such analysis improves the analysis in petrol and forensic science. Our study shows how principal component analysis (PCA) and classification results are affected by the preprocessing steps performed on the raw data.Our results indicate that results from a log ratio analysis provides a better separation between subgroups of the data and leads to an easier interpretation of the results. In addition, with a compositional analysis a higher classification accuracy is obtained. Even a non-linear classification method - in our case a random forest - was shown to perform poorly when applied without using compositional methods. Moreover, normalization of samples due to laboratory/unit-of-measurement effects is no longer necessary, since the composition of an observation is in compositional thinking equivalent to a multiple of it, because the used (log) ratios on raw and log ratio transformed data are equal.Petrol data from different petrol stations in Brazil are used for the demonstration. This data is highly susceptible to counterfeit petrol. Forensic analysis of its chemical elements requires non-biased statistical analysis designed for compositional data to detect fraud.Based on these results, we recommend the use of compositional data methods for gasoline and petrol chemical element analysis and gasoline product characterization, authentication and fraud detection in forensic sciences.

Taxicab Correspondence Analysis and Taxicab Logratio Analysis: A Comparison on Contingency Tables and Compositional Data

In this paper, we attempt to see further by relating theory with practice: First, we review the principles on which three interrelated well developed methods for the analysis and visualization of contingency tables and compositional data are erected: Correspondence analysis based on Benzécri’s principle of distributional equivalence, Goodman’s RC association model based on Yule’s principle of scale invariance, and compositional data analysis based on Aitchison’s principle of subcompositional coherence. Second, we introduce a novel index named intrinsic measure of the quality of the signs of the residuals for the choice of the method. The criterion is based on taxicab singular value decomposition, on which the package TaxicabCA in R is developed. We present a minimal R script thatcan be executed to obtain the numerical results and the maps in this paper. Third, we introduce a flexible method based on the novel index for the choice of the constant to be added to contingency tables with zero counts so that logratio methods can be applied.

Determination of Effect Sizes for Power Analysis for Microbiome Studies Using Large Microbiome Databases.

Herein, we present a tool called Evident that can be used for deriving effect sizes for a broad spectrum of metadata variables, such as mode of birth, antibiotics, socioeconomics, etc., to provide power calculations for a new study. Evident can be used to mine existing databases of large microbiome studies (such as the American Gut Project, FINRISK, and TEDDY) to analyze the effect sizes for planning future microbiome studies via power analysis. For each metavariable, the Evident software is flexible to compute effect sizes for many commonly used measures of microbiome analyses, including α diversity, β diversity, and log-ratio analysis. In this work, we describe why effect size and power analysis are necessary for computational microbiome analysis and show how Evident can help researchers perform these procedures. Additionally, we describe how Evident is easy for researchers to use and provide an example of efficient analyses using a dataset of thousands of samples and dozens of metadata categories.

Selective pivot logratio coordinates for partial least squares discriminant analysis modelling with applications in metabolomics

Data resulting from high‐throughput biological experiments are frequently of relative nature. This implies that the most relevant information is on the shape of the data distribution over the biological features more than on the size of the measurements themselves. One well‐established way to acknowledge this in statistical processing is through logratio analysis. In the current work, we introduce selective pivot logratio coordinates as a new type of orthonormal logratio coordinate representation for high‐dimensional relative (a.k.a. compositional) data. This proposal is aimed to enhance the identification of biomarkers in the context of binary classification problems, which is a common setting of scientific studies in the field. These logratio coordinates are constructed so that the pivot coordinate representing a certain compositional part aggregates all pairwise logratios of that part to the rest but, unlike in the ordinary formulation, excludes those deviating from the main pattern. This novel coordinate system is embedded within a partial least squares discriminant analysis (PLS‐DA) model for its practical application. Based on both synthetic and real‐world metabolomic data sets, we demonstrate the enhanced performance of the novel approach when compared with other methods used in the area.

Quality parameters and fatty acid and triacylglycerol profiles of directly brined table olive fat throughout processing and shelf life

The transformations that may suffer directly brined table olive fat during processing were studied using cracked Aloreña de Málaga olive as a model. The classical studies showed that storage increased acidity and K270, but not peroxide value, K232 and ΔK. FA profiles, nutritional fat subclasses, and TAGs suffered several significant changes along processing, although some could be spurious. Compositional data (CoDa) analysis identified C18:2n-6 and C18:1c, and their corresponding TAGs as the most affected compounds, conclusion that was particularly evident after weighted CoDa log-ratio analysis (LRA). Thus, CoDa analysis is a promising alternative statistical tool to study table olive FA, TAG profiles and fats in general. Most of the quality parameters’ values and FA and TAG concentrations were compatible with Virgin Olive Oil (VOO), showing that the fat quality and nutritional characteristics of natural green olives in brine could be comparable to that of VOO.

Development of LR-PCA Based Fusion Approach to Detect the Changes in Mango Fruit Crop by Using Landsat 8 OLI Images

Change detection (CD) is the process of detecting changes from multi-temporal satellite images that have undergone spatial changes due to natural phenomena and/or human-induced activities. Mango is a major fruit crop in India, but detection of changes in mango crops remains a challenging task because the reason that many perennial crops have similar reflectance profiles. Therefore, a potent change detection technique is required for different applications such as the rate of deforestation, urban developments, damage evaluation, and resource monitoring. Compared to annual and seasonal crops, relatively few studies have been conducted on change detection in perennial fruit crops. In this study, a novel change detection technique (i.e., LR-PCA) is developed using the fusion of log-ratio (LR) and principal component analysis (PCA) images derived from bi-temporal soil adjusted vegetation index (SAVI) images to extract meaningful information and detect temporal changes in the mango fruit crop areas with high change detection accuracy. The proposed approach comprised two steps: (1) SAVI images from 2015 and 2019 were used to retrieve the log-ratio (LR) and principal component (PC) images, respectively, and both the images were fused by applying the pixel-by-pixel fusion approach. (2) Fused images were classified into three classes: “positive change”, “no change”, and “negative change” using a derived threshold value. The results show that the LR-PCA method of change detection yields a high change detection accuracy of 92% in comparison with the other change detection methods viz. vegetation image differencing, image ratioing, PCA, and log-ratio. To validate the adaptability of the proposed algorithm, experiments with two sets of bi-temporal SAVI indices images belonging to the Sitapur district of Uttar Pradesh State determine that the proposed change detection method performs well as compared to the existing individual methods for detection of changes in mango fruit crop. The proposed method is expected to be useful for detecting changes in the area of perennial crops. In the future, an accurate and efficient change detection analysis may be helpful for developing a real-time mango fruit crop monitoring system at the national level.

Fatty acid ratio analysis identifies changes in competent meroplanktonic larvae sampled over different supply events

Planktonic communities are a cornerstone of ocean food webs. Early benthic performance of meroplanktonic organisms is shaped by their life stages in planktonic communities. Fatty acid profiles of marine invertebrates are a good indicator of their nutritional state and allow inferring how dietary regimes experienced during larval pelagic life may drive their pre- and post-metamorphosis performance. Fatty acid profiles of Carcinus maenas megalopae were analysed during four larval supply events in two consecutive years to better understand the variability in their nutritional state at settlement. The logratio analysis of fatty acids showed differences between the four larval supply events, with five ratios explaining 83.1% of the variance. The ratios that contributed to separate larval supply events presented a combination of essential, de novo synthetized and diet origin fatty acids (e.g., phytanate/20:4 n-6, 16:0/18:2 n-4). The high fatty acid signature dispersion found within the same supply event suggests that larvae settling at Ria de Aveiro (Portugal) developed through different planktonic feeding zones and experienced contrasting feeding regimes. The fatty acid profile of megalopae demonstrated a high contribution of diatoms, flagellates and bacteria in the larval diet of C. maenas. The present study demonstrated differences between supply events, although a high variability of larval phenotypes was recorded within the same supply event.

Statistical Analysis of Chemical Element Compositions in Food Science: Problems and Possibilities.

In recent years, many analyses have been carried out to investigate the chemical components of food data. However, studies rarely consider the compositional pitfalls of such analyses. This is problematic as it may lead to arbitrary results when non-compositional statistical analysis is applied to compositional datasets. In this study, compositional data analysis (CoDa), which is widely used in other research fields, is compared with classical statistical analysis to demonstrate how the results vary depending on the approach and to show the best possible statistical analysis. For example, honey and saffron are highly susceptible to adulteration and imitation, so the determination of their chemical elements requires the best possible statistical analysis. Our study demonstrated how principle component analysis (PCA) and classification results are influenced by the pre-processing steps conducted on the raw data, and the replacement strategies for missing values and non-detects. Furthermore, it demonstrated the differences in results when compositional and non-compositional methods were applied. Our results suggested that the outcome of the log-ratio analysis provided better separation between the pure and adulterated data and allowed for easier interpretability of the results and a higher accuracy of classification. Similarly, it showed that classification with artificial neural networks (ANNs) works poorly if the CoDa pre-processing steps are left out. From these results, we advise the application of CoDa methods for analyses of the chemical elements of food and for the characterization and authentication of food products.

A Compositional Model to Predict the Aggregated Isotope Distribution for Average DNA and RNA Oligonucleotides.

Structural modifications of DNA and RNA molecules play a pivotal role in epigenetic and posttranscriptional regulation. To characterise these modifications, more and more MS and MS/MS- based tools for the analysis of nucleic acids are being developed. To identify an oligonucleotide in a mass spectrum, it is useful to compare the obtained isotope pattern of the molecule of interest to the one that is theoretically expected based on its elemental composition. However, this is not straightforward when the identity of the molecule under investigation is unknown. Here, we present a modelling approach for the prediction of the aggregated isotope distribution of an average DNA or RNA molecule when a particular (monoisotopic) mass is available. For this purpose, a theoretical database of all possible DNA/RNA oligonucleotides up to a mass of 25 kDa is created, and the aggregated isotope distribution for the entire database of oligonucleotides is generated using the BRAIN algorithm. Since this isotope information is compositional in nature, the modelling method is based on the additive log-ratio analysis of Aitchison. As a result, a univariate weighted polynomial regression model of order 10 is fitted to predict the first 20 isotope peaks for DNA and RNA molecules. The performance of the prediction model is assessed by using a mean squared error approach and a modified Pearson’s χ2 goodness-of-fit measure on experimental data. Our analysis has indicated that the variability in spectral accuracy contributed more to the errors than the approximation of the theoretical isotope distribution by our proposed average DNA/RNA model. The prediction model is implemented as an online tool. An R function can be downloaded to incorporate the method in custom analysis workflows to process mass spectral data.

Making the most of expert knowledge to analyse archaeological data: a case study on Parthian and Sasanian glazed pottery

Chemical compositional data sets of archaeological artefacts are often analysed using standard statistical procedures. Adopting a different approach, we examine the major element oxides found in Parthian and Sasanian glazed pottery by identifying statistically important ratios of oxides in conjunction with the expert knowledge of the archaeological scientist during, rather than after, the identification process. This results in meaningful ratios, both statistically and archaeologically, which help identify the recipes and production practices used by Mesopotamian glass and glaze producers. The application of logratio analysis to interrogate the chronological groups suggests that the silica sources used for glazes were significantly purer in later periods and exhibited less variation. Comparing the expert-assisted selection of ratios derived from a legacy data set to the ratios from compositional data of Parthian glazed pottery recovered at the early 3rd century CE Roman military outpost of Ain Sinu in northern Iraq supports the hypothesis that there was a shift to more standardised recipes in the production of glass used for glazes. If this translates to a centralised glass-making industry, it would suggest that there are, as yet, undiscovered glass production centres, potentially in areas associated with increased urbanisation in southern Mesopotamia around the time of the Parthian–Sasanian transition.

Influence of genetic background and dietary oleic acid on gut microbiota composition in Duroc and Iberian pigs.

BackgroundPhenotypic variability for productive and meat quality traits has been largely studied in Iberian pigs, especially in genetic selection and nutritional experiments. Complex interactions among genetic background, diet composition and gut microbiota hinder the correct assessment of each factor’s contribution on phenotypes. In order to disentangle these interactions, we evaluated changes in gut microbiota composition comparing 48 Iberian and Duroc pigs fed diets with different energy source (standard diet with carbohydrates vs sunflower oil-enriched diet with high oleic acid content).ResultsA higher richness was observed for Iberian pigs (p < 0.05) and compositional analysis was applied for beta-diversity, differential abundance and pairwise log-ratio analyses. We found significant differences in overall microbiota composition between breeds, and also between diets inside breeds, to a lesser extent. Differential abundance analysis revealed that Duroc animals have more proportion of Actinobacteria and Prevotella, while Iberian replace those microorganisms with other more variable taxa. According to dietary differences, high-oleic fed animals were richer in Prevotella. We also found microbial ratios capable of separating animals by breeds and diets, mostly related to Actinobacteria.ConclusionThis study reveals that both genetic background and diet composition might have a relevant impact in gut microbiota composition. The application of compositional data analysis has facilitated the identification of microorganisms and ratios as possibly related to metabolic changes due to genetic background and, to a lower extent, to dietary changes. This may lead to a relevant progress in the knowledge of interactions between pig genetics, environment and gut microbiota.

Log-ratio analysis of microbiome data with many zeroes is library size dependent.

Microbiome composition data collected through amplicon sequencing are count data on taxa in which the total count per sample (the library size) is an artefact of the sequencing platform, and as a result, such data are compositional. To avoid library size dependency, one common way of analysing multivariate compositional data is to perform a principal component analysis (PCA) on data transformed with the centred log‐ratio, hereafter called a log‐ratio PCA. Two aspects typical of amplicon sequencing data are the large differences in library size and the large number of zeroes. In this study, we show on real data and by simulation that, applied to data that combine these two aspects, log‐ratio PCA is nevertheless heavily dependent on the library size. This leads to a reduction in power when testing against any explanatory variable in log‐ratio redundancy analysis. If there is additionally a correlation between the library size and the explanatory variable, then the type 1 error becomes inflated. We explore putative solutions to this problem.

Assessing the Italian tax courts system by weighted three-way log-ratio analysis

Deciding on what should be the most suitable reforms of a national judicial system, whether this means reorganising a courts' structure or offering incetives to judges, requires more empirical evidence. The efficiency of the public judicial system is important to any functioning democracy as it affects several aspects of citizens’ life. As a consequence, new statistical methodologies are required for further valuable insights into the issues that affect the effectiveness of a judicial system.The current study attempts to fill this gap by introducing a new statistical method to investigate the heterogeneity among Italian judicial courts. Here we propose a generalisation of log-ratio analysis for the analysis of the association between the variables of a three-way contingency table. Our focus of this investigation will be on the tax court system of the Italian judicial system.Log-ratio analysis presents many advantages, two of which are the computation and the visual representation of the odds ratios on which the analysis is based. For three-way tables, a conditional odds ratio reflects the likelihood that an event (say tax disputes) will take place in a particular geographical area (say North Italy) instead of an another (say South Italy) given a specific condition (type of justice court).Interestingly, the three-way log-ratio analysis presented in this paper allows one to visually describe these conditional odds-ratios in terms of point distances in a biplot between the types of justice court located in different geographical areas of Italy.

Mineral–nutrient relationships in African soils assessed using cluster analysis of X-ray powder diffraction patterns and compositional methods

Soil mineral compositions are often complex and spatially diverse, with each mineral exhibiting characteristic chemical properties that determine the intrinsic total concentration of soil nutrients and their phyto-availability. Defining soil mineral-nutrient relationships is therefore important for understanding the inherent fertility of soils for sustainable nutrient management, and data-driven approaches such as cluster analysis allow for these relations to be assessed in new detail.Here the fuzzy-c-means clustering algorithm was applied to an X-ray powder diffraction (XRPD) dataset of 935 soils from sub-Saharan Africa, with each diffractogram representing a digital signature of a soil’s mineralogy. Nine mineralogically distinct clusters were objectively selected from the soil mineralogy continuum by retaining samples exceeding the 75% quantile of the membership coefficients in each cluster, yielding a dataset of 239 soils. As such, samples within each cluster represented mineralogically similar soils from different agro-ecological environments of sub-Saharan Africa. Mineral quantification based on the mean diffractogram of each cluster illustrated substantial mineralogical diversity between the nine groups with respect to quartz, K-feldspar, plagioclase, Fe/Al/Ti-(hydr)oxides, phyllosilicates (1:1 and 2:1), ferromagnesians, and calcite.Mineral–nutrient relationships were defined using the clustered XRPD patterns and corresponding measurements of total and/or extractable (Mehlich-3) nutrient concentrations (B, Mg, K, Ca, Mn, Fe, Ni, Cu and Zn) in combination with log-ratio compositional data analysis. Fe/Al/Ti/Mn-(hydr)oxides and feldspars were found to be the primary control of total nutrient concentrations, whereas 2:1 phyllosilicates were the main source of all extractable nutrients except for Fe and Zn. Kaolin minerals were the most abundant phyllosilicate group within the dataset but did not represent a nutrient source, which reflects the lack of nutrients within their chemical composition and their low cation exchange capacity. Results highlight how the mineral composition controls the total nutrient reserves and their phyto-availability in soils of sub-Saharan Africa. The typical characterisation of soils and their parent material based on the clay particle size fraction (i.e. texture) and/or the overall silica component (i.e. acid and basic rock types) alone may therefore mask the intricacies of mineral contributions to soil nutrient concentrations.

Callous-unemotional traits with mental disorders in adolescents by two-way Log-ratio analysis

Psychopathy is complex phenomenon associate to personality disorder that manifests at a relatively early age and tends to be relatively stable throughout life. Psychopathy in adolescents is currently being studied using the approach of callous-unemotional (CU) traits. Recent studies have shown that adolescents with these traits have different causal factors leading to their behavior problems and mental disorders. Here I propose to use the log-ratio analysis, for two-way contingency table, for assessing the correlation between CU traits and mental disorders in adolescents. The data are provided by H.E.R.A.C.L.E. Lab (Unicusano research center on health education) and obtained submitting to a sample of 689 high school students two questionnaires: The Inventory of Callous-Unemotional Traits (ICU) and The Strengths and Difficulties Questionnaire (SDQ)). In two-way tables obtained, an odds ratio reflects the likelihood that a ICU trait (callousness, uncaring and unemotional) will have with SDQ values (normal, borderline and abnormal). Log-ratio analysis presents many advantages, among which the computation and the visual representation in a biplot map of the odds ratio that allows the correlation in terms of distances between points.

Counts: an outstanding challenge for log-ratio analysis of compositional data in the molecular biosciences.

Thanks to sequencing technology, modern molecular bioscience datasets are often compositions of counts, e.g. counts of amplicons, mRNAs, etc. While there is growing appreciation that compositional data need special analysis and interpretation, less well understood is the discrete nature of these count compositions (or, as we call them, lattice compositions) and the impact this has on statistical analysis, particularly log-ratio analysis (LRA) of pairwise association. While LRA methods are scale-invariant, count compositional data are not; consequently, the conclusions we draw from LRA of lattice compositions depend on the scale of counts involved. We know that additive variation affects the relative abundance of small counts more than large counts; here we show that additive (quantization) variation comes from the discrete nature of count data itself, as well as (biological) variation in the system under study and (technical) variation from measurement and analysis processes. Variation due to quantization is inevitable, but its impact on conclusions depends on the underlying scale and distribution of counts. We illustrate the different distributions of real molecular bioscience data from different experimental settings to show why it is vital to understand the distributional characteristics of count data before applying and drawing conclusions from compositional data analysis methods.

Identification of diagnostic metabolic signatures in clear cell renal cell carcinoma using mass spectrometry imaging.

Clear cell renal cell carcinoma (ccRCC) is the most common and lethal subtype of kidney cancer. Intraoperative frozen section (IFS) analysis is used to confirm the diagnosis during partial nephrectomy. However, surgical margin evaluation using IFS analysis is time consuming and unreliable, leading to relatively low utilization. In our study, we demonstrated the use of desorption electrospray ionization mass spectrometry imaging (DESI-MSI) as a molecular diagnostic and prognostic tool for ccRCC. DESI-MSI was conducted on fresh-frozen 23 normal tumor paired nephrectomy specimens of ccRCC. An independent validation cohort of 17 normal tumor pairs was analyzed. DESI-MSI provides two-dimensional molecular images of tissues with mass spectra representing small metabolites, fatty acids and lipids. These tissues were subjected to histopathologic evaluation. A set of metabolites that distinguish ccRCC from normal kidney were identified by performing least absolute shrinkage and selection operator (Lasso) and log-ratio Lasso analysis. Lasso analysis with leave-one-patient-out cross-validation selected 57 peaks from over 27,000 metabolic features across 37,608 pixels obtained using DESI-MSI of ccRCC and normal tissues. Baseline Lasso of metabolites predicted the class of each tissue to be normal or cancerous tissue with an accuracy of 94 and 76%, respectively. Combining the baseline Lasso with the ratio of glucose to arachidonic acid could potentially reduce scan time and improve accuracy to identify normal (82%) and ccRCC (88%) tissue. DESI-MSI allows rapid detection of metabolites associated with normal and ccRCC with high accuracy. As this technology advances, it could be used for rapid intraoperative assessment of surgical margin status.