Collinearity refers to the non independence of predictor variables, usually in a regression-type analysis. It is a common feature of any descriptive ecological data set and can be a problem for parameter estimation because it inflates the variance of regression parameters and hence potentially leads to the wrong identification of relevant predictors in a statistical model. Collinearity is a severe problem when a model is trained on data from one region or time, and predicted to another with a different or unknown structure of collinearity. To demonstrate the reach of the problem of collinearity in ecology, we show how relationships among predictors differ between biomes, change over spatial scales and through time. Across disciplines, different approaches to addressing collinearity problems have been developed, ranging from clustering of predictors, threshold-based pre-selection, through latent variable methods, to shrinkage and regularisation. Using simulated data with five predictor-response relationships of increasing complexity and eight levels of collinearity we compared ways to address collinearity with standard multiple regression and machine-learning approaches. We assessed the performance of each approach by testing its impact on prediction to new data. In the extreme, we tested whether the methods were able to identify the true underlying relationship in a training dataset with strong collinearity by evaluating its performance on a test dataset without any collinearity. We found that methods specifically designed for collinearity, such as latent variable methods and tree based models, did not outperform the traditional GLM and threshold-based pre-selection. Our results highlight the value of GLM in combination with penalised methods (particularly ridge) and threshold-based pre-selection when omitted variables are considered in the final interpretation. However, all approaches tested yielded degraded predictions under change in collinearity structure and the ‘folk lore’-thresholds of correlation coefficients between predictor variables of |r| >0.7 was an appropriate indicator for when collinearity begins to severely distort model estimation and subsequent prediction. The use of ecological understanding of the system in pre-analysis variable selection and the choice of the least sensitive statistical approaches reduce the problems of collinearity, but cannot ultimately solve them.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1600-0587.2012.07348.x

Collinearity: a review of methods to deal with it and a simulation study evaluating their performance

Using the means-end framework as a theoretical foundation, this article conceptualizes, constructs, refines, and tests a multiple-item scale (E-S-QUAL) for measuring the service quality delivered b...

/pdf/e-s-qual-a-multiple-item-scale-for-assessing-electronic-2f9xy8ot5i.pdf

E-S-QUAL: A Multiple-Item Scale for Assessing Electronic Service Quality

This study examines the response rates for surveys used in organizational research. We analysed 1607 studies published in the years 2000 and 2005 in 17 refereed academic journals, and we identified 490 different studies that utilized surveys. We examined the response rates in these studies, which covered more than 100,000 organizations and 400,000 individual respondents. The average response rate for studies that utilized data collected from individuals was 52.7 percent with a standard deviation of 20.4, while the average response rate for studies that utilized data collected from organizations was 35.7 percent with a standard deviation of 18.8. Key insights from further analysis include relative stability in response rates in the past decade and higher response rates for journals published in the USA. The use of incentives was not found to be related to response rates and, for studies of organizations, the use of reminders was associated with lower response rates. Also, electronic data collection efforts (e.g. email, phone, web) resulted in response rates as high as or higher than traditional mail methodology. We discuss a number of implications and recommendations.

Survey response rate levels and trends in organizational research

A comparison is undertaken between scale development and index construction procedures to trace the implications of adopting a reflective versus formative perspective when creating multi-item measures for organizational research. Focusing on export coordination as an illustrative construct of interest, the results show that the choice of measurement perspective impacts on the content, parsimony and criterion validity of the derived coordination measures. Implications for practising researchers seeking to develop multi-item measures of organizational constructs are considered.

https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=950400

Formative Versus Reflective Indicators in Organizational Measure Development: A Comparison and Empirical Illustration

Patterns of attachment

Chapter 3 deals with probability distributions, discrete and continuous densities, distribution functions, bivariate distributions, means, variances, covariance, correlation, and some random process material. Chapter 4 is a detailed study of the concept of utility including the psychological aspects, risk, attributes, rules for utilities, multidimensional utility, and normal form of analysis. Chapter 5 treats games and optimization, linear optimization, and mixed strategies. Entropy is the topic of Chapter 6 with sections devoted to entropy, disorder, information, Shannon’s theorem, demon’s roulette, Maxwell– Boltzmann distribution, Schrodinger’s nutshell, maximum entropy probability distributions, blackbodies, and Bose–Einstein distribution. Chapter 7 is standard statistical fare including transformations of random variables, characteristic functions, generating functions, and the classic limit theorems such as the central limit theorem and the laws of large numbers. Chapter 8 is about exchangeability and inference with sections on Bayesian techniques and classical inference. Partial exchangeability is also treated. Chapter 9 considers such things as order statistics, extreme value, intensity, hazard functions, and Poisson processes. Chapter 10 covers basic elements of risk and reliability, while Chapter 11 is devoted to curve fitting, regression, and Monte Carlo simulation. There is an ample number of exercises at the ends of the chapters with answers or comments on many of them in an appendix in the back of the book. Other appendices are on the common discrete and continuous distributions and mathematical aspects of integration.

Xianggui Qu

Papers

Multivariate Data Analysis