An Examination of Transformation Techniques to Investigate and Interpret Multivariate Geochemical Data Analysis: Tellus Case Study

This research aims to use the multivariate geochemical dataset, generated by the Tellus project, to investigate the appropriate use of transformation methods to maintain the integrity of geochemical data and inherent constrained behaviour in multivariate relationships. The widely used normal score transform is compared with the use of a stepwise conditional transform technique. The Tellus Project, managed by GSNI and funded by the Department of Enterprise Trade and Development and the EU’s Building Sustainable Prosperity Fund, involves the most comprehensive geological mapping project ever undertaken in Northern Ireland. Previous study has demonstrated spatial variability in the Tellus data but geostatistical analysis and interpretation of the datasets requires use of an appropriate methodology that reproduces the inherently complex multivariate relations. Previous investigation of the Tellus geochemical data has included use of Gaussian-based techniques. However, earth science variables are rarely Gaussian, hence transformation of data is integral to the approach. The multivariate geochemical dataset generated by the Tellus project provides an opportunity to investigate the appropriate use of transformation methods, as required for Gaussian-based geostatistical analysis. In particular, the stepwise conditional transform is investigated and developed for the geochemical datasets obtained as part of the Tellus project. The transform is applied to four variables in a bivariate nested fashion due to the limited availability of data. Simulation of these transformed variables is then carried out, along with a corresponding back transformation to original units. Results show that the stepwise transform is successful in reproducing both univariate statistics and the complex bivariate relations exhibited by the data. Greater fidelity to multivariate relationships will improve uncertainty models, which are required for consequent geological, environmental and economic inferences.

Qualitative data analysis:A practical example

The aim of this paper is to equip readers with an understanding of the principles of qualitative data analysis and offer a practical example of how analysis might be undertaken in an interview-based study.

Helping the most vulnerable out of the poverty trap and reducing inequality: Policies, strategies, and services for individuals with Autism Spectrum Disorder, including intellectual and neurodevelopmental disabilities: Benchmarking Autism Services Efficacy: BASE Project (Volume 3) Secondary Data analysis

1) Executive Summary
Legislation (Autism Act NI, 2011), a cross-departmental strategy (Autism Strategy 2013-2020) and a first action plan (2013-2016) have been developed in Northern Ireland in order to support individuals and families affected by Autism Spectrum Disorder (ASD) without a prior thorough baseline assessment of need. At the same time, there are large existing data sets about the population in NI that had never been subjected to a secondary data analysis with regards to data on ASD. This report covers the first comprehensive secondary data analysis and thereby aims to inform future policy and practice.
Following a search of all existing, large-scale, regional or national data sets that were relevant to the lives of individuals and families affected by Autism Spectrum Disorder (ASD) in Northern Ireland, extensive secondary data analyses were carried out. The focus of these secondary data analyses was to distill any ASD related data from larger generic data sets. The findings are reported for each data set and follow a lifespan perspective, i.e., data related to children is reported first before data related to adults.
Key findings:
Autism Prevalence:
Of children born in 2000 in the UK,
• 0.9% (1:109) were reported to have ASD, when they were 5-year old in 2005;
• 1.8% (1:55) were reported to have ASD, when they were 7-years old in 2007;
• 3.5% (1:29) were reported to have ASD, when they were 11-year old in 2011.
In mainstream schools in Northern Ireland
• 1.2% of the children were reported to have ASD in 2006/07;
• 1.8% of the children were reported to have ASD in 2012/13.

Economic Deprivation:
• Families of children with autism (CWA) were 9%-18% worse off per week than families of children not on the autism spectrum (COA).
• Between 2006-2013 deprivation of CWA compared to COA nearly doubled as measured by eligibility for free school meals (from near 20 % to 37%)
• In 2006, CWA and COA experienced similar levels of deprivation (approx. 20%), by 2013, a considerable deprivation gap had developed, with CWA experienced 6% more deprivation than COA.
• Nearly 1/3 of primary school CWA lived in the most deprived areas in Northern Ireland.
• Nearly ½ of children with Asperger’s Syndrome who attended special school lived in the most deprived areas.

Unemployment:
• Mothers of CWA were 6% less likely to be employed than mothers of COA.
• Mothers of CWA earned 35%-56% less than mothers of COA.
• CWA were 9% less likely to live in two income families than COA.

Health:
• Pre-diagnosis, CWA were more likely than COA to have physical health problems, including walking on level ground, speech and language, hearing, eyesight, and asthma.
• Aged 3 years of age CWA experienced poorer emotional and social health than COA, this difference increased significantly by the time they were 7 years of age.
• Mothers of young CWA had lower levels of life satisfaction and poorer mental health than mothers of young COA.
Education:
• In mainstream education, children with ASD aged 11-16 years reported less satisfaction with their social relationships than COA.
• Younger children with ASD (aged 5 and 7 years) were less likely to enjoy school, were bullied more, and were more reluctant to attend school than COA.
• CWA attended school 2-3 weeks less than COA .
• Children with Asperger’s Syndrome in special schools missed the equivalent of 8-13 school days more than children with Asperger’s Syndrome in mainstream schools.
• Children with ASD attending mainstream schooling were less likely to gain 5+ GCSEs A*-C or subsequently attend university.



Further and Higher Education:
• Enrolment rates for students with ASD have risen in Further Education (FE), from 0% to 0.7%.
• Enrolment rates for students with ASD have risen in Higher Education (HE), from 0.28% to 0.45%.
• Students with ASD chose to study different subjects than students without ASD, although other factors, e.g., gender, age etc. may have played a part in subject selection.
• Students with ASD from NI were more likely than students without ASD to choose Northern Irish HE Institutions rather than study outside NI.

Participation in adult life and employment:
• A small number of adults with ASD (n=99) have benefitted from DES employment provision over the past 12 years.
• It is unknown how many adults with ASD have received employment support elsewhere (e.g. Steps to Work).
•
Awareness and Attitudes in the General Population:
• In both the 2003 and 2012 NI Life and Times Survey (NILTS), NI public reported positive attitudes towards the inclusion of children with ASD in mainstream education (see also BASE Project Vol. 2).

Gap Analysis Recommendations:
This was the first comprehensive secondary analysis with regards to ASD of existing large-scale data sets in Northern Ireland. Data gaps were identified and further replications would benefit from the following data inclusion:
• ASD should be recorded routinely in the following datasets:
o Census;
o Northern Ireland Survey of Activity Limitation (NISALD);
o Training for Success/Steps to work; Steps to Success;
o Travel survey;
o Hate crime; and
o Labour Force Survey.
• Data should be collected on the destinations/qualifications of special school leavers.
• NILT Survey autism module should be repeated in 5 years time (2017) (see full report of 1st NILT Survey autism module 2012 in BASE Project Report Volume 2).
• General public attitudes and awareness should be assessed for children and young people, using the Young Life and Times Survey (YLT) and the Kids Life and Times Survey (KLT); (this work is underway, Dillenburger, McKerr, Schubolz, & Lloyd, 2014-2015).
 

Expansion of pulse responses from temporal analysis of products (TAP) pulse responses for more accurate data analysis

TAP pulse responses are normally analysed using moments, which are integrals of the full TAP pulse response. However, in some cases the entire pulse response may not be recorded due to technical reasons, thereby compromising any data analysis due to moments generated from incomplete pulse responses. The current work discloses the development of a function which mathematically expands the tail of a TAP pulse response, so that the TAP data analysis can be accurately conducted. This newly developed analysis method has been applied to the oxidative dehydrogenation of ethane over Co–Cr–Sn–WOx/α-Al2O3 and Co–Cr–Sn–WOx/α-Al2O3 catalysts as a case study.

Historical data reveal power-law dispersal patterns of invasive aquatic species

Understanding how invasive species spread is of particular concern in the current era of globalisation and rapid environmental change. The occurrence of super-diffusive movements within the context of Lévy flights has been discussed with respect to particle physics, human movements, microzooplankton, disease spread in global epidemiology and animal foraging behaviour. Super-diffusive movements provide a theoretical explanation for the rapid spread of organisms and disease, but their applicability to empirical data on the historic spread of organisms has rarely been tested. This study focuses on the role of long-distance dispersal in the invasion dynamics of aquatic invasive species across three contrasting areas and spatial scales: open ocean (north-east Atlantic), enclosed sea (Mediterranean) and an island environment (Ireland). Study species included five freshwater plant species, Azolla filiculoides, Elodea canadensis, Lagarosiphon major, Elodea nuttallii and Lemna minuta; and ten species of marine algae, Asparagopsis armata, Antithamnionella elegans, Antithamnionella ternifolia, Codium fragile, Colpomenia peregrina, Caulerpa taxifolia, Dasysiphonia sp., Sargassum muticum, Undaria pinnatifida and Womersleyella setacea. A simulation model is constructed to show the validity of using historical data to reconstruct dispersal kernels. Lévy movement patterns similar to those previously observed in humans and wild animals are evident in the re-constructed dispersal pattern of invasive aquatic species. Such patterns may be widespread among invasive species and could be exacerbated by further development of trade networks, human travel and environmental change. These findings have implications for our ability to predict and manage future invasions, and improve our understanding of the potential for spread of organisms including infectious diseases, plant pests and genetically modified organisms.

Special condition wind power forecasting based on Gaussian process and similar historical data

Due to the variability of wind power, it is imperative to accurately and timely forecast the wind generation to enhance the flexibility and reliability of the operation and control of real-time power. Special events such as ramps, spikes are hard to predict with traditional methods using solely recently measured data. In this paper, a new Gaussian Process model with hybrid training data taken from both the local time and historic dataset is proposed and applied to make short-term predictions from 10 minutes to one hour ahead. A key idea is that the similar pattern data in history are properly selected and embedded in Gaussian Process model to make predictions. The results of the proposed algorithms are compared to those of standard Gaussian Process model and the persistence model. It is shown that the proposed method not only reduces magnitude error but also phase error.

RMA with quantile normalization mixes biological signals between different sample groups in microarray data analysis

Quantile normalization (QN) is a technique for microarray data processing and is the default normalization method in the Robust Multi-array Average (RMA) procedure, which was primarily designed for analysing gene expression data from Affymetrix arrays. Given the abundance of Affymetrix microarrays and the popularity of the RMA method, it is crucially important that the normalization procedure is applied appropriately. In this study we carried out simulation experiments and also analysed real microarray data to investigate the suitability of RMA when it is applied to dataset with different groups of biological samples. From our experiments, we showed that RMA with QN does not preserve the biological signal included in each group, but rather it would mix the signals between the groups. We also showed that the Median Polish method in the summarization step of RMA has similar mixing effect. RMA is one of the most widely used methods in microarray data processing and has been applied to a vast volume of data in biomedical research. The problematic behaviour of this method suggests that previous studies employing RMA could have been misadvised or adversely affected. Therefore we think it is crucially important that the research community recognizes the issue and starts to address it. The two core elements of the RMA method, quantile normalization and Median Polish, both have the undesirable effects of mixing biological signals between different sample groups, which can be detrimental to drawing valid biological conclusions and to any subsequent analyses. Based on the evidence presented here and that in the literature, we recommend exercising caution when using RMA as a method of processing microarray gene expression data, particularly in situations where there are likely to be unknown subgroups of samples.

Compositional Data Analysis in Forensic Geoscience

Statistics are regularly used to make some form of comparison between trace evidence or deploy the exclusionary principle (Morgan and Bull, 2007) in forensic investigations. Trace evidence are routinely the results of particle size, chemical or modal analyses and as such constitute compositional data. The issue is that compositional data including percentages, parts per million etc. only carry relative information. This may be problematic where a comparison of percentages and other constraint/closed data is deemed a statistically valid and appropriate way to present trace evidence in a court of law. Notwithstanding an awareness of the existence of the constant sum problem since the seminal works of Pearson (1896) and Chayes (1960) and the introduction of the application of log-ratio techniques (Aitchison, 1986; Pawlowsky-Glahn and Egozcue, 2001; Pawlowsky-Glahn and Buccianti, 2011; Tolosana-Delgado and van den Boogaart, 2013) the problem that a constant sum destroys the potential independence of variances and covariances required for correlation regression analysis and empirical multivariate methods (principal component analysis, cluster analysis, discriminant analysis, canonical correlation) is all too often not acknowledged in the statistical treatment of trace evidence. Yet the need for a robust treatment of forensic trace evidence analyses is obvious. This research examines the issues and potential pitfalls for forensic investigators if the constant sum constraint is ignored in the analysis and presentation of forensic trace evidence. Forensic case studies involving particle size and mineral analyses as trace evidence are used to demonstrate the use of a compositional data approach using a centred log-ratio (clr) transformation and multivariate statistical analyses.