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.

Determinants of health costs due to farmers’ exposure to pesticides : an empirical analysis

It is now well known that pesticide spraying by farmers has an adverse impact on their health. This is especially so in developing countries where pesticide spraying is undertaken manually. The estimated health costs are large. Studies to date have examined farmers’ exposure to pesticides, the costs of ill-health and their determinants based on information provided by farmers. Hence, some doubt has been cast on the reliability of such studies. In this study, we rectify this situation by conducting surveys among two groups of farmers. Farmers who perceive that their ill-health is due to exposure to pesticides and obtained treatment and farmers whose ill-health have been diagnosed by doctors and who have been treated in hospital for exposure to pesticides. In the paper, cost comparisons between the two groups of farmers are made. Furthermore, regression analysis of the determinants of health costs show that the quantity of pesticides used per acre per month, frequency of pesticide use and number of pesticides used per hour per day are the most important determinants of medical costs for both samples. The results have important policy implications.

Identification of early-stage colorectal cancer patients at risk of relapse post-resection by immunobead reverse transcription-PCR analysis of peritoneal lavage fluid for malignant cells

Purpose: Colorectal cancer patients diagnosed with stage I or II disease are not routinely offered adjuvant chemotherapy following resection of the primary tumor. However, up to 10% of stage I and 30% of stage II patients relapse within 5 years of surgery from recurrent or metastatic disease. The aim of this study was to determine if tumor-associated markers could detect disseminated malignant cells and so identify a subgroup of patients with early-stage colorectal cancer that were at risk of relapse. Experimental Design: We recruited consecutive patients undergoing curative resection for early-stage colorectal cancer. Immunobead reverse transcription-PCR of five tumor-associated markers (carcinoembryonic antigen, laminin γ2, ephrin B4, matrilysin, and cytokeratin 20) was used to detect the presence of colon tumor cells in peripheral blood and within the peritoneal cavity of colon cancer patients perioperatively. Clinicopathologic variables were tested for their effect on survival outcomes in univariate analyses using the Kaplan-Meier method. A multivariate Cox proportional hazards regression analysis was done to determine whether detection of tumor cells was an independent prognostic marker for disease relapse. Results: Overall, 41 of 125 (32.8%) early-stage patients were positive for disseminated tumor cells. Patients who were marker positive for disseminated cells in post-resection lavage samples showed a significantly poorer prognosis (hazard ratio, 6.2; 95% confidence interval, 1.9-19.6; P = 0.002), and this was independent of other risk factors. Conclusion: The markers used in this study identified a subgroup of early-stage patients at increased risk of relapse post-resection for primary colorectal cancer. This method may be considered as a new diagnostic tool to improve the staging and management of colorectal cancer. © 2006 American Association for Cancer Research.

Indications for early hip revision surgery in the UK : A re-analysis of NJR data

This study determined the rate and indication for revision between cemented, uncemented, hybrid and resurfacing groups from NJR (6 th edition) data. Data validity was determined by interrogating for episodes of misclassification. We identified 6,034 (2.7%) misclassified episodes, containing 97 (4.3%) revisions. Kaplan-Meier revision rates at 3 years were 0.9% cemented, 1.9% for uncemented, 1.2% for hybrids and 3.0% for resurfacings (significant difference across all groups, p<0.001, with identical pattern in patients <55 years). Regression analysis indicated both prosthesis group and age significantly influenced failure (p<0.001). Revision for pain, aseptic loosening, and malalignment were highest in uncemented and resurfacing arthroplasty. Revision for dislocation was highest in uncemented hips (significant difference between groups, p<0.001). Feedback to the NJR on data misclassification has been made for future analysis. © 2012 Wichtig Editore.

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])...

Determinants of health costs due to farmers’ exposure to pesticides: an empirical analysis

Pesticide spraying by farmers has an adverse impact on their health. However, in studies to date examining farmers’ exposure to pesticides, the costs of ill health and their determinants have been based on information provided by farmers themselves. Some doubt has therefore been cast on the reliability of these estimates. In this study, we address this by conducting surveys among two groups of farmers who use pesticides on a regular basis. The first group is made up of farmers who perceive that their ill health is due to exposure to pesticides and have obtained at least some form of treatment (described in this article as the ‘general farmer group’). The second group is composed of farmers whose ill health has been diagnosed by doctors and who have been treated in hospital for exposure to pesticides (described here as the ‘hospitalised farmer group’). Cost comparisons are made between the two groups of farmers. Regression analysis of the determinants of health costs show that the most important determinants of medical costs for both samples are the defensive expenditure, the quantity of pesticides used per acre per month, frequency of pesticide use and number of pesticides used per hour per day. The results have important policy implications.

Analysis of environmental efficiency variation : a materials balance approach

Recent literature has argued that environmental efficiency (EE), which is built on the materials balance (MB) principle, is more suitable than other EE measures in situations where the law of mass conversation regulates production processes. In addition, the MB-based EE method is particularly useful in analysing possible trade-offs between cost and environmental performance. Identifying determinants of MB-based EE can provide useful information to decision makers but there are very few empirical investigations into this issue. This article proposes the use of data envelopment analysis and stochastic frontier analysis techniques to analyse variation in MB-based EE. Specifically, the article develops a stochastic nutrient frontier and nutrient inefficiency model to analyse determinants of MB-based EE. The empirical study applies both techniques to investigate MB-based EE of 96 rice farms in South Korea. The size of land, fertiliser consumption intensity, cost allocative efficiency, and the share of owned land out of total land are found to be correlated with MB-based EE. The results confirm the presence of a trade-off between MB-based EE and cost allocative efficiency and this finding, favouring policy interventions to help farms simultaneously achieve cost efficiency and MP-based EE.

A broad-scale analysis of links between coastal fisheries production and mangrove extent : a case-study for northeastern Australia

The paradigm that mangroves are critical for sustaining production in coastal fisheries is widely accepted, but empirical evidence has been tenuous. This study showed that links between mangrove extent and coastal fisheries production could be detected for some species at a broad regional scale (1000s of kilometres) on the east coast of Queensland, Australia. The relationships between catch-per-unit-effort for different commercially caught species in four fisheries (trawl, line, net and pot fisheries) and mangrove characteristics, estimated from Landsat images were examined using multiple regression analyses. The species were categorised into three groups based on information on their life history characteristics, namely mangrove-related species (banana prawns Penaeus merguiensis, mud crabs Scylla serrata and barramundi Lates calcarifer), estuarine species (tiger prawns Penaeus esculentus and Penaeus semisulcatus, blue swimmer crabs Portunus pelagicus and blue threadfin Eleutheronema tetradactylum) and offshore species (coral trout Plectropomus spp.). For the mangrove-related species, mangrove characteristics such as area and perimeter accounted for most of the variation in the model; for the non-mangrove estuarine species, latitude was the dominant parameter but some mangrove characteristics (e.g. mangrove perimeter) also made significant contributions to the models. In contrast, for the offshore species, latitude was the dominant variable, with no contribution from mangrove characteristics. This study also identified that finer scale spatial data for the fisheries, to enable catch information to be attributed to a particular catchment, would help to improve our understanding of relationships between mangroves and fisheries production.

Analysis of risk management disclosures by Australian publicly listed companies

In the aftermath of the global financial crisis, effective risk management (RM) and its communication to stakeholders are now considered essential components in corporate governance. However, despite the importance of RM communication, it is still unclear how and to what extent disclosures in financial reports can achieve effective communication of RM activities. The situation is hampered by the paucity of international RM Research that captures institution differences in corporate governance standards. The Australian setting provides an ideal environment in which to examine RM communication because the Australian Securities Exchange (ASX) has since 2007 recommended RM disclosures under its principle-based governance rules. The recommendations are contained in Principle 7 of the Corporate Governance Principles and recommendations (ASX CGPR). Accordingly, to assess the effectiveness of the AXS's RM governance principle, this study examines the nature and extent of RM disclosures reported by major ASX-listed firms. Using a mixed method approach (thematic content analysis and a series of regression analysis) we find widespread divergence in disclosure practices and low conformance with the Principle 7 recommendations. Certain corporate governance mechanisms appear to influence some categories of RM dislcosure but equity risk has surprisingly little explanatory power. These results suggest that the RM disclosures practices observed in the Australian setting may not be meeting the objectives of regulators and the needs of stakeholders.

Regional avian species declines estimated from volunteer-collected long-term data using List Length Analysis

Long-term systematic population monitoring data sets are rare but are essential in identifying changes in species abundance. In contrast, community groups and natural history organizations have collected many species lists. These represent a large, untapped source of information on changes in abundance but are generally considered of little value. The major problem with using species lists to detect population changes is that the amount of effort used to obtain the list is often uncontrolled and usually unknown. It has been suggested that using the number of species on the list, the "list length," can be a measure of effort. This paper significantly extends the utility of Franklin's approach using Bayesian logistic regression. We demonstrate the value of List Length Analysis to model changes in species prevalence (i.e., the proportion of lists on which the species occurs) using bird lists collected by a local bird club over 40 years around Brisbane, southeast Queensland, Australia. We estimate the magnitude and certainty of change for 269 bird species and calculate the probabilities that there have been declines and increases of given magnitudes. List Length Analysis confirmed suspected species declines and increases. This method is an important complement to systematically designed intensive monitoring schemes and provides a means of utilizing data that may otherwise be deemed useless. The results of List Length Analysis can be used for targeting species of conservation concern for listing purposes or for more intensive monitoring. While Bayesian methods are not essential for List Length Analysis, they can offer more flexibility in interrogating the data and are able to provide a range of parameters that are easy to interpret and can facilitate conservation listing and prioritization. © 2010 by the Ecological Society of America.