Regression and hypothesis tests for multivariate GNSS state time series

A satellite based observation system can continuously or repeatedly generate a user state vector time series that may contain useful information. One typical example is the collection of International GNSS Services (IGS) station daily and weekly combined solutions. Another example is the epoch-by-epoch kinematic position time series of a receiver derived by a GPS real time kinematic (RTK) technique. Although some multivariate analysis techniques have been adopted to assess the noise characteristics of multivariate state time series, statistic testings are limited to univariate time series. After review of frequently used hypotheses test statistics in univariate analysis of GNSS state time series, the paper presents a number of T-squared multivariate analysis statistics for use in the analysis of multivariate GNSS state time series. These T-squared test statistics have taken the correlation between coordinate components into account, which is neglected in univariate analysis. Numerical analysis was conducted with the multi-year time series of an IGS station to schematically demonstrate the results from the multivariate hypothesis testing in comparison with the univariate hypothesis testing results. The results have demonstrated that, in general, the testing for multivariate mean shifts and outliers tends to reject less data samples than the testing for univariate mean shifts and outliers under the same confidence level. It is noted that neither univariate nor multivariate data analysis methods are intended to replace physical analysis. Instead, these should be treated as complementary statistical methods for a prior or posteriori investigations. Physical analysis is necessary subsequently to refine and interpret the results.

Predicting loss and fragmentation of habitat of the vulnerable subtropical rainforest tree Macadamia integrifolia with models developed from compiled ecological data

Habitat models are widely used in ecology, however there are relatively few studies of rare species, primarily because of a paucity of survey records and lack of robust means of assessing accuracy of modelled spatial predictions. We investigated the potential of compiled ecological data in developing habitat models for Macadamia integrifolia, a vulnerable mid-stratum tree endemic to lowland subtropical rainforests of southeast Queensland, Australia. We compared performance of two binomial models—Classification and Regression Trees (CART) and Generalised Additive Models (GAM)—with Maximum Entropy (MAXENT) models developed from (i) presence records and available absence data and (ii) developed using presence records and background data. The GAM model was the best performer across the range of evaluation measures employed, however all models were assessed as potentially useful for informing in situ conservation of M. integrifolia, A significant loss in the amount of M. integrifolia habitat has occurred (p < 0.05), with only 37% of former habitat (pre-clearing) remaining in 2003. Remnant patches are significantly smaller, have larger edge-to-area ratios and are more isolated from each other compared to pre-clearing configurations (p < 0.05). Whilst the network of suitable habitat patches is still largely intact, there are numerous smaller patches that are more isolated in the contemporary landscape compared with their connectedness before clearing. These results suggest that in situ conservation of M. integrifolia may be best achieved through a landscape approach that considers the relative contribution of small remnant habitat fragments to the species as a whole, as facilitating connectivity among the entire network of habitat patches.

Non-invasive, quantitative analysis of drug mixtures in containers using spatially offset Raman spectroscopy (SORS) and multivariate statistical analysis

In this paper, spatially offset Raman spectroscopy (SORS) is demonstrated for non-invasively investigating the composition of drug mixtures inside an opaque plastic container. The mixtures consisted of three components including a target drug (acetaminophen or phenylephrine hydrochloride) and two diluents (glucose and caffeine). The target drug concentrations ranged from 5% to 100%. After conducting SORS analysis to ascertain the Raman spectra of the concealed mixtures, principal component analysis (PCA) was performed on the SORS spectra to reveal trends within the data. Partial least squares (PLS) regression was used to construct models that predicted the concentration of each target drug, in the presence of the other two diluents. The PLS models were able to predict the concentration of acetaminophen in the validation samples with a root-mean-square error of prediction (RMSEP) of 3.8% and the concentration of phenylephrine hydrochloride with an RMSEP of 4.6%. This work demonstrates the potential of SORS, used in conjunction with multivariate statistical techniques, to perform non-invasive, quantitative analysis on mixtures inside opaque containers. This has applications for pharmaceutical analysis, such as monitoring the degradation of pharmaceutical products on the shelf, in forensic investigations of counterfeit drugs, and for the analysis of illicit drug mixtures which may contain multiple components.

A hybrid approach to combining CART and logistic regression for stock ranking

The benefits of applying tree-based methods to the purpose of modelling financial assets as opposed to linear factor analysis are increasingly being understood by market practitioners. Tree-based models such as CART (classification and regression trees) are particularly well suited to analysing stock market data which is noisy and often contains non-linear relationships and high-order interactions. CART was originally developed in the 1980s by medical researchers disheartened by the stringent assumptions applied by traditional regression analysis (Brieman et al. [1984]). In the intervening years, CART has been successfully applied to many areas of finance such as the classification of financial distress of firms (see Frydman, Altman and Kao [1985]), asset allocation (see Sorensen, Mezrich and Miller [1996]), equity style timing (see Kao and Shumaker [1999]) and stock selection (see Sorensen, Miller and Ooi [2000])...

Bivariate genome-wide association study of genetically correlated neuroimaging phenotypes from DTI and MRI through a seemingly unrelated regression model

Large multisite efforts (e.g., the ENIGMA Consortium), have shown that neuroimaging traits including tract integrity (from DTI fractional anisotropy, FA) and subcortical volumes (from T1-weighted scans) are highly heritable and promising phenotypes for discovering genetic variants associated with brain structure. However, genetic correlations (rg) among measures from these different modalities for mapping the human genome to the brain remain unknown. Discovering these correlations can help map genetic and neuroanatomical pathways implicated in development and inherited risk for disease. We use structural equation models and a twin design to find rg between pairs of phenotypes extracted from DTI and MRI scans. When controlling for intracranial volume, the caudate as well as related measures from the limbic system - hippocampal volume - showed high rg with the cingulum FA. Using an unrelated sample and a Seemingly Unrelated Regression model for bivariate analysis of this connection, we show that a multivariate GWAS approach may be more promising for genetic discovery than a univariate approach applied to each trait separately.