Data analysis methods in optometry Part 7: multiple linear regression

Multiple regression analysis is a complex statistical method with many potential uses. It has also become one of the most abused of all statistical procedures since anyone with a data base and suitable software can carry it out. An investigator should always have a clear hypothesis in mind before carrying out such a procedure and knowledge of the limitations of each aspect of the analysis. In addition, multiple regression is probably best used in an exploratory context, identifying variables that might profitably be examined by more detailed studies. Where there are many variables potentially influencing Y, they are likely to be intercorrelated and to account for relatively small amounts of the variance. Any analysis in which R squared is less than 50% should be suspect as probably not indicating the presence of significant variables. A further problem relates to sample size. It is often stated that the number of subjects or patients must be at least 5-10 times the number of variables included in the study.5 This advice should be taken only as a rough guide but it does indicate that the variables included should be selected with great care as inclusion of an obviously unimportant variable may have a significant impact on the sample size required.

Do board contacts matter? : an analysis of the relationship between boards of directors’ ties and the performance of Australia’s largest companies.

Boards of directors are thought to provide access to a wealth of knowledge and resources for the companies they serve, and are considered important to corporate governance. Under the Resource Based View (RBV) of the firm (Wernerfelt, 1984) boards are viewed as a strategic resource available to firms. As a consequence there has been a significant research effort aimed at establishing a link between board attributes and company performance. In this thesis I explore and extend the study of interlocking directorships (Mizruchi, 1996; Scott 1991a) by examining the links between directors’ opportunity networks and firm performance. Specifically, I use resource dependence theory (Pfeffer & Salancik, 1978) and social capital theory (Burt, 1980b; Coleman, 1988) as the basis for a new measure of a board’s opportunity network. I contend that both directors’ formal company ties and their social ties determine a director’s opportunity network through which they are able to access and mobilise resources for their firms. This approach is based on recent studies that suggest the measurement of interlocks at the director level, rather than at the firm level, may be a more reliable indicator of this phenomenon. This research uses publicly available data drawn from Australia’s top-105 listed companies and their directors in 1999. I employ Social Network Analysis (SNA) (Scott, 1991b) using the UCINET software to analyse the individual director’s formal and social networks. SNA is used to measure a the number of ties a director has to other directors in the top-105 company director network at both one and two degrees of separation, that is, direct ties and indirect (or ‘friend of a friend’) ties. These individual measures of director connectedness are aggregated to produce a board-level network metric for comparison with measures of a firm’s performance using multiple regression analysis. Performance is measured with accounting-based and market-based measures. Findings indicate that better-connected boards are associated with higher market-based company performance (measured by Tobin’s q). However, weaker and mostly unreliable associations were found for accounting-based performance measure ROA. Furthermore, formal (or corporate) network ties are a stronger predictor of market performance than total network ties (comprising social and corporate ties). Similarly, strong ties (connectedness at degree-1) are better predictors of performance than weak ties (connectedness at degree-2). My research makes four contributions to the literature on director interlocks. First, it extends a new way of measuring a board’s opportunity network based on the director rather than the company as the unit of interlock. Second, it establishes evidence of a relationship between market-based measures of firm performance and the connectedness of that firm’s board. Third, it establishes that director’s formal corporate ties matter more to market-based firm performance than their social ties. Fourth, it establishes that director’s strong direct ties are more important to market-based performance than weak ties. The thesis concludes with implications for research and practice, including a more speculative interpretation of these results. In particular, I raise the possibility of reverse causality – that is networked directors seek to join high-performing companies. Thus, the relationship may be a result of symbolic action by companies seeking to increase the legitimacy of their firms rather than a reflection of the social capital available to the companies. This is an important consideration worthy of future investigation.

Mapping of multiple quantitative trait loci affecting bovine spongiform encephalopathy

A whole-genome scan was conducted to map quantitative trait loci (QTL) for BSE resistance or susceptibility. Cows from four half-sib families were included and 173 microsatellite markers were used to construct a 2835-cM (Kosambi) linkage map covering 29 autosomes and the pseudoautosomal region of the sex chromosome. Interval mapping by linear regression was applied and extended to a multiple-QTL analysis approach that used identified QTL on other chromosomes as cofactors to increase mapping power. In the multiple-QTL analysis, two genome-wide significant QTL (BTA17 and X/Y ps) and four genome-wide suggestive QTL (BTA1, 6, 13, and 19) were revealed. The QTL identified here using linkage analysis do not overlap with regions previously identified using TDT analysis. One factor that may explain the disparity between the results is that a more extensive data set was used in the present study. Furthermore, methodological differences between TDT and linkage analyses may affect the power of these approaches.

Fusion of Multisensor Data:Review and Comparative Analysis

Image fusion is a formal framework which is expressed as means and tools for the alliance of multisensor, multitemporal, and multiresolution data. Multisource data vary in spectral, spatial and temporal resolutions necessitating advanced analytical or numerical techniques for enhanced interpretation capabilities. This paper reviews seven pixel based image fusion techniques - intensity-hue-saturation, brovey, high pass filter (HPF), high pass modulation (HPM), principal component analysis, fourier transform and correspondence analysis.Validation of these techniques on IKONOS data (Panchromatic band at I m spatial resolution and Multispectral 4 bands at 4 in spatial resolution) reveal that HPF and HPM methods synthesises the images closest to those the corresponding multisensors would observe at the high resolution level.

Juvenile fish assemblages collected on unconsolidated sediments of the southeast United States continental shelf

Patterns were investigated in juvenile fish use of unconsolidated sediments on the southeast United States continental shelf off Georgia. Juvenile fish and environmental data were sampled at ten stations along a 110-km cross-shelf transect, including four stations surrounding Gray’s Reef National Marine Sanctuary (Gray’s Reef NMFS). Cross-shelf stations were sampled approximately quarterly from spring 2000 to winter 2002. Additional stations were sampled on three transects inshore of Gray’s Reef NMS and four transects offshore of the Sanctuary during three cruises to investigate along-shelf patterns in the juvenile fish assemblages. Samples were collected in beam trawls, and 121 juvenile taxa, of which 33 were reef-associated species, were identified. Correspondence analysis on untransformed juvenile fish abundance indicated a cross-shelf gradient in assemblages, and the station groupings and assemblages varied seasonally. During the spring, fall, and winter, three cross-shelf regions were identified: inner-shelf, mid-shelf, and outer-shelf regions. In the summer, the shelf consisted of a single juvenile fish assemblage. Water depth was the primary environmental variable correlated with cross-shelf assemblages. However, salinity, density, and water column stratification also correlated with the distribution of assemblages during the spring, fall, and winter, and along with temperature likely influenced the distribution of juvenile fish. No along-shelf spatial patterns were found in the juvenile fish assemblages, but the along-shelf dimension sampled was small (~60 km). Our results revealed that a number of commercially and recreationally important species used unconsolidated sediments on the shelf off Georgia as juvenile habitat. We conclude that management efforts would be improved through a greater recognition of the importance of these habitats to fish production and the interconnectedness of multiple habitats in the southeast U.S. continental shelf ecosystem.

Economic analysis of fish farming in Ogun State

This study examined the economic potential of fish farming in Abeokuta zone of Ogun State in the 2003 production season. Descriptive statistics cost returns and multiple regression analysis were used in analyzing the data. The farmers predominantly practiced monoculture. Inefficiency in the use of pond size, lime and labour with over-utilization of fingerlings stocked was revealed by the study. The average variable cost of N124.67 constituted 45% of the total while average fixed cost was N149.802.67 per average farm size. Fish farming was found to be a profitable venture in the study area with a net income of N761, 400.58 for an average pond size of 301.47sq.m. Based on these findings, it is suggested that for profit maximization, the fish farm will have to increase the level of their use of fingerlings and fertilizers and decrease the use of lime labour and pond size

Analytical techniques for indentation of viscoelastic materials

Indentation of linearly viscoelastic materials is explored using elastic-viscoelastic correspondence analysis for both conical-pyramidal and spherical indentation. Boltzmann hereditary integrals are used to generate displacement-time solutions for loading at constant rate and creep following ramp loading. Experimental data for triangle- and trapezoidal-loading are examined for commercially-available polymers and compared with analytical solutions. Emphasis is given to the use of multiple experiments to test the fidelity and predictive capability of the obtained material creep function. Plastic deformation occurs in sharp indentation of glassy polymers and is found to complicate the viscoelastic analysis. A new method is proposed for estimating a material time-constant from peak displacement or hardness data obtained in pyramidal indentation tests performed at different loading rates.

PCR-DGGE Fingerprinting Analysis of Plankton Communities and Its Relationship to Lake Trophic Status

Plankton communities in eight lakes of different trophic status near Yangtze, China were characterized by using denatured gradient gel electrophoresis (DGGE). Various water quality parameters were also measured at each collection site. Following extraction of DNA from plankton communities, 16S rRNA and 18S rRNA genes were amplified with specific primers for prokaryotes and eukaryotes, respectively; DNA profiles were developed by DGGE. The plankton community of each lake had its own distinct DNA profile. The total number of bands identified at 34 sampling stations ranged from 37 to 111. Both prokaryotes and eukaryotes displayed complex fingerprints composed of a large number of bands: 16 to 59 bands were obtained with the prokaryotic primer set; 21 to 52 bands for the eukaryotic primer set. The DGGE-patterns were analyzed in relation to water quality parameters by canonical correspondence analysis (CCA). Temperature, pH, alkalinity, and the concentration of COD, TP and TN were strongly correlated with the DGGE patterns. The parameters that demonstrated a strong correlation to the DGGE fingerprints of the plankton community differed among lakes, suggesting that differences in the DGGE fingerprints were due mainly to lake trophic status. Results of the present study suggest that PCR-DGGE fingerprinting is an effective and precise method of identifying changes to plankton community composition, and therefore could be a useful ecological tool for monitoring the response of aquatic ecosystems to environmental perturbations.

Soil microbial community analysis using terminal restriction fragment length polymorphisms

Terminal restriction fragment length polymorphism (T-RFLP) analysis is a polymerase chain reaction (PCR)-fingerprinting method that is commonly used for comparative microbial community analysis. The method can be used to analyze communities of bacteria, archaea, fungi, other phylogenetic groups or subgroups, as well as functional genes. The method is rapid, highly reproducible, and often yields a higher number of operational taxonomic units than other, commonly used PCR-fingerprinting methods. Sizing of terminal restriction fragments (T-RFs) can now be done using capillary sequencing technology allowing samples contained in 96- or 384-well plates to be sized in an overnight run. Many multivariate statistical approaches have been used to interpret and compare T-RFLP fingerprints derived from different communities. Detrended correspondence analysis and the additive main effects with multiplicative interaction model are particularly useful for revealing trends in T-RFLP data. Due to biases inherent in the method, linking the size of T-RFs derived from complex communities to existing sequence databases to infer their taxonomic position is not very robust. This approach has been used successfully, however, to identify and follow the dynamics of members within very simple or model communities. The T-RFLP approach has been used successfully to analyze the composition of microbial communities in soil, water, marine, and lacustrine sediments, biofilms, feces, in and on plant tissues, and in the digestive tracts of insects and mammals. The T-RFLP method is a user-friendly molecular approach to microbial community analysis that is adding significant information to studies of microbial populations in many environments.

Correlation analysis of the structures and stability constants of gadolinium(III) complexes

To simplify the abstraction of descriptors, for the correlation analysis of the stability constants of gadolinium(III) complexes and their ligand structures, aiming at gadolinium(III) complexes, we only considered the ligands and ignored the common parts of the structures, i.e., the metal ions. Quantum-chemical descriptors and topological indices were calculated to describe the structures of the ligands. Multiple regression analysis and neural networks were applied to construct the models between the ligands and the stability constants of gadolinium(III) complexes and satisfactory results were obtained.

Quantitative structure-property relationships for colour reagents and their colour reactions with ytterbium using regression analysis and computational neural networks

In this paper, the new topological indices A(x1)-A(x3) suggested in our laboratory and molecular connectivity indices have been applied to multivariate analysis in structure-property studies. The topological indices of twenty asymmetrical phosphono bisazo derivatives of chromotropic acid have been calculated. The structure-property relationships between colour reagents and their colour reactions with ytterbium have been studied by A(x1)-A(x3) indices and molecular connectivity indices with satisfactory results. Multiple regression analysis and neural networks were employed simultaneously in this study.

Developing a model of innovation implementation for UK SMEs: A path analysis and explanatory case analysis

Continuous large-scale changes in technology and the globalization of markets have resulted in the need for many SMEs to use innovation as a means of seeking competitive advantage where innovation includes both technological and organizational perspectives (Tapscott, 2009). However, there is a paucity of systematic and empirical research relating to the implementation of innovation management in the context of SMEs. The aim of this article is to redress this imbalance via an empirical study created to develop and test a model of innovation implementation in SMEs. This study uses Structural Equation Modelling (SEM) to test the plausibility of an innovation model, developed from earlier studies, as the basis of a questionnaire survey of 395 SMEs in the UK. The resultant model and construct relationship results are further probed using an explanatory multiple case analysis to explore ‘how’ and ‘why’ type questions within the model and construct relationships. The findings show that the
effects of leadership, people and culture on innovation implementation are mediated by business improvement activities relating to Total Quality Management/Continuous Improvement (TQM/CI) and product and process developments. It is concluded that SMEs have an opportunity to leverage existing quality and process improvement activities to move beyond continuous
improvement outcomes towards effective innovation implementation. The article concludes by suggesting areas suitable for further research.

Application of Redundancy Analysis for Aerobiological Data

An aerobiological survey was conducted through five consecutive years (2006–2010) at Worcester (England).The concentration of 20 allergenic fungal spore types was measured using a 7-day volumetric spore trap. The relationship between investigated fungal spore genera and selected meteorological parameters (maximum, minimum, mean and dew point temperatures, rainfall, relative humidity, air pressure,wind direction) was examined using an ordination method(redundancy analysis) to determine which environmental factors favoured their most abundance in the air and whether it would be possible to detect similarities between different genera in their distribution pattern. Redundancy analysis provided additional information about the biology of the studied fungi through the results of the Spearman’s rank correlation. Application of the variance inflation factor in canonical correspondence analysis indicated which explanatory variables were auto-correlated and needed to be excluded from further analyses. Obtained information will be consequently implemented in the selection of factors that will be a foundation for forecasting models for allergenic fungal spores in the future.

Some reflections on acquisition, processing and analysis of statistical data in forest soils

Beyond the classical statistical approaches (determination of basic statistics, regression analysis, ANOVA, etc.) a new set of applications of different statistical techniques has increasingly gained relevance in the analysis, processing and interpretation of data concerning the characteristics of forest soils. This is possible to be seen in some of the recent publications in the context of Multivariate Statistics. These new methods require additional care that is not always included or refered in some approaches. In the particular case of geostatistical data applications it is necessary, besides to geo-reference all the data acquisition, to collect the samples in regular grids and in sufficient quantity so that the variograms can reflect the spatial distribution of soil properties in a representative manner. In the case of the great majority of Multivariate Statistics techniques (Principal Component Analysis, Correspondence Analysis, Cluster Analysis, etc.) despite the fact they do not require in most cases the assumption of normal distribution, they however need a proper and rigorous strategy for its utilization. In this work, some reflections about these methodologies and, in particular, about the main constraints that often occur during the information collecting process and about the various linking possibilities of these different techniques will be presented. At the end, illustrations of some particular cases of the applications of these statistical methods will also be presented.

L’utilisation des services de centre de jour par les personnes âgées qui présentent des incapacités

Contexte: Les centres de jour offrent des interventions de groupe à des personnes âgées qui présentent des incapacités, dans le but de favoriser leur maintien à domicile. Des études récentes tendent à démontrer qu’une utilisation régulière du service serait nécessaire pour induire des effets bénéfiques. Objectifs: Cette recherche visait à documenter l’utilisation des centres de jour par des personnes âgées qui présentent des incapacités. Elle comportait trois principaux objectifs: 1) Caractériser les utilisateurs de centre de jour et ce qui les distingue des non-utilisateurs et analyser les déterminants de l’utilisation du centre de jour. 2) Explorer l’adéquation entre les activités offertes par les centres de jour et les caractéristiques d’autonomie et de santé des utilisateurs. 3) Définir les facteurs associés à la régularité de la participation. Méthodes: Cette recherche s’appuie sur une analyse secondaire de données recueillies auprès de 723 personnes âgées qui ont participé au projet de démonstration SIPA (Services intégrés pour personnes âgées) implanté dans deux CLSC de la région de Montréal. L’utilisation du centre de jour a été documentée pendant une période de six mois, auprès des cinq centres de jour existant sur ce même territoire. Des informations sur le fonctionnement des centres de jour ont été obtenues par des entrevues et des rencontres de groupe auprès de coordonnateurs de ces centres. Les données ont été analysées à l’aide de statistiques descriptives, d’analyses en regroupement et d’analyses de régression logistique et multiple. Résultats: Les résultats sont présentés dans trois articles, soit un pour chacun des objectifs. Article 1: La proportion d’utilisateurs de centre de jour est de 18,8% (IC-0,95: 16,0 à 21,7%). Les facteurs suivants augmentent la probabilité d’utiliser le centre de jour: être plus jeune (RC: 1,12; IC-0,95: 1,06 à 1,19); ne pas avoir une éducation universitaire (RC: 1,92; IC-0,95: 1,04 à 3,57); recevoir l’aide du CLSC pour les activités de vie quotidienne plus d’une fois par semaine (RC: 1,73 et 2,48 pour aide de deux à cinq fois par semaine et aide de six à sept fois par semaine respectivement; IC-0,95: 1,06 à 2,80 et 1,22 à 5,06); faire partie du bassin de desserte d’un centre de jour dont les coûts sont moins élevés (RC: 1,054 ; IC-0,95: 1,001 à 1,108 pour chaque augmentation de 1$); et pour les hommes seulement, avoir déjà subi un accident vasculaire cérébral et présenter davantage d’incapacités fonctionnelles (interaction entre le sexe et la présence d’un AVC: RC: 0,298; IC-0,95: 0,108 à 0,825; interaction entre le sexe et les capacités fonctionnelles mesurées à l’OARS: RC: 1,096; IC-0,95: 1,019 à 1,178). De plus, on observe une plus grande probabilité d’utiliser le centre de jour chez les personnes qui cohabitent avec une personne de soutien. Toutefois, cette relation ne s’observe que chez les personnes nées au Canada (interaction entre la cohabitation avec la personne de soutien et le pays de naissance: RC: 0,417; IC-0,95: 0,185 à 0,938). Article 2: Des analyses en regroupement ont permis de distinguer quatre profils de participants ayant des caractéristiques similaires: 1) les personnes fragilisées par un âge avancé et un grand nombre de problèmes de santé; 2) les participants plus jeunes et plus autonomes que la moyenne, qui semblent des utilisateurs précoces; 3) les personnes qui présentent des incapacités d’origine cognitive; et 4) celles qui présentent des incapacités d’origine motrice. Les activités de groupe des centres de jour ont été regroupées en huit catégories: exercices physiques; groupe spécifique pour un diagnostic ou un problème fonctionnel commun; activités fonctionnelles; stimulation cognitive; activités musicales ou de réminiscence; sports et jeux physiques; intégration sociale; prévention et promotion de la santé. Les activités les plus fréquentes sont les exercices physiques et les activités d’intégration sociale auxquelles ont participé plus de 90% des utilisateurs de centre de jour, et ce en moyenne à respectivement 78% (±23%) et 72% (±24%) de leurs présences au centre de jour. Les autres catégories d’activités rejoignent de 45% à 77% des participants, et ce en moyenne à 35% (±15%) à 46% (±33%) de leurs présences. La participation aux diverses catégories d’activités a été étudiée pour chaque profil d’utilisateurs et comparée aux activités recommandées pour divers types de clientèle. On observe une concordance partielle entre les activités offertes et les besoins des utilisateurs. Cette concordance apparaît plus grande pour les participants qui présentent des problèmes de santé physique ou des incapacités d’origine motrice et plus faible pour ceux qui présentent des symptômes dépressifs ou des atteintes cognitives. Article 3: Les participants au centre de jour y sont inscrits en moyenne à raison de 1,56 (±0,74) jours par semaine mais sont réellement présents à 68,1% des jours attendus. Les facteurs suivants sont associés à une participation plus régulière au centre de jour en termes de taux de présences réelles / présences attendues: ne pas avoir travaillé dans le domaine de la santé (b: ,209; IC-0,95: ,037 à ,382); recevoir de l’aide du CLSC les jours de fréquentation du centre de jour (b: ,124; IC-0,95: ,019 à ,230); être inscrit pour la journée plutôt que la demi-journée (b: ,209: IC-0,95: ,018 à ,399); lors de ses présences au centre de jour, avoir une moins grande proportion d’activités de prévention et promotion de la santé (b: ,223; IC-0,95: ,044 à ,402); et enfin, avoir un aidant qui présente un fardeau moins élevé pour les personnes avec une atteinte cognitive et un fardeau plus élevé pour les personnes sans atteinte cognitive (interaction entre la présence d’atteinte cognitive et le fardeau de l’aidant: b: -,008; IC-0,95: -,014 à -,044). Conclusion: Conformément à leur mission, les centres de jour rejoignent une bonne proportion des personnes âgées qui présentent des incapacités. Cette étude fait ressortir les caractéristiques des personnes les plus susceptibles d’y participer. Elle suggère la nécessité de revoir la planification des activités pour assurer une offre de services qui tienne davantage compte des besoins des participants, en particulier de ceux qui présentent des atteintes cognitives et des symptômes de dépression. Elle démontre aussi que l’intensité d’exposition au service semble faible, ce qui soulève la question des seuils d’exposition nécessaires pour induire des effets favorables sur le maintien à domicile et sur la qualité de vie de la clientèle cible.