Non-spatial and Spatial Linear Regression

This chapter gives an introduction to the workhorse of quantitative statistical analysis, linear regression analysis, assuming minimal background knowledge of the reader. We give a broad overview of linear regression analysis using one predictor variable and then turn to regression with multiple predictor variables and key assumptions, which segues into regression analysis of areal units that include spatial dependence. Throughout we use the statistical programming environment R, and we try to summarize the most important challenges that an applied researcher will face. As this is just an introduction to the topic, we provide references to sources that are highly recommended for any researcher who aims to understand or apply (spatial) linear regression analysis.

A Comparison of Reliability Coefficients for Ordinal Rating Scales

Kappa coefficients are commonly used for quantifying reliability on a categorical scale, whereas correlation coefficients are commonly applied to assess reliability on an interval scale. Both types of coefficients can be used to assess the reliability of ordinal rating scales. In this study, we compare seven reliability coefficients for ordinal rating scales: the kappa coefficients included are Cohen’s kappa, linearly weighted kappa, and quadratically weighted kappa; the correlation coefficients included are intraclass correlation ICC(3,1), Pearson’s correlation, Spearman’s rho, and Kendall’s tau-b. The primary goal is to provide a thorough understanding of these coefficients such that the applied researcher can make a sensible choice for ordinal rating scales. A second aim is to find out whether the choice of the coefficient matters. We studied to what extent we reach the same conclusions about inter-rater reliability with different coefficients, and to what extent the coefficients measure agreement in a similar way, using analytic methods, and simulated and empirical data. Using analytical methods, it is shown that differences between quadratic kappa and the Pearson and intraclass correlations increase if agreement becomes larger. Differences between the three coefficients are generally small if differences between rater means and variances are small. Furthermore, using simulated and empirical data, it is shown that differences between all reliability coefficients tend to increase if agreement between the raters increases. Moreover, for the data in this study, the same conclusion about inter-rater reliability was reached in virtually all cases with the four correlation coefficients. In addition, using quadratically weighted kappa, we reached a similar conclusion as with any correlation coefficient a great number of times. Hence, for the data in this study, it does not really matter which of these five coefficients is used. Moreover, the four correlation coefficients and quadratically weighted kappa tend to measure agreement in a similar way: their values are very highly correlated for the data in this study.

Light Transport Simulation and Realistic Rendering: State of the Art Report

The field of light transport simulation quickly growths in last decades. Nowadays there are about hundreds of books and papers that are quite difficult to cover for applied researcher or developer. Unlike similar surveys, in this paper we make attempt to provide short roadmap to select the best method for some light transport problem based on scene and calculated phenomena constraints. In our paper we propose several classifications for light transport simulation algorithms based on their mathematical properties, robustness and required scene constraints. These classifications help to understand advantages, disadvantages and limitations of the methods. In this paper we use not only a survey of existing works but also our own experience with the methods that we have implemented over the last decade in different software products. Some results of our experiments are shown in the paper. Finally, we propose a short guide for method selection in form of block scheme.

Should I Allow my Confirmatory Factors to Correlate During Factor Extraction? Implications for the Applied Researcher

With complex models becoming increasingly popular in the social sciences, many researchers have begun using latent variable modeling in multiple-steps, saving, estimating, or otherwise extracting factor scores from one confirmatory factor analysis (CFA) for use in a second inferential analysis. With two or more factors identified in a CFA, there exist few practical guidelines as to how researchers should proceed. In Study 1, we examine two common practices when CFAs have two or more factors. Some researchers estimate each factor orthogonally, fitting a separate CFAs to each, while others allow factors to correlate in the model used for extraction. We provide a simulation study measuring the bias introduced in each of the two approaches. Study 1 demonstrates the extent to which between-factor correlations are generally underestimated when factors are estimated in separate CFAs, and overestimated when factors are allowed to correlate. In Study 2, we demonstrate that this bias can be mitigated through the use of a different estimator. Ten Berge estimation shows near zero bias on the critical correlations between factors. Finally, we demonstrate this with an example dataset, advise researchers against the practice of factor score extraction without using Ten Berge methods, and encourage researchers to interpret previous findings using such methods with caution.

Quantitative Synthesis of Research Evidence: Multilevel Meta-Analysis

Multilevel meta-analysis is an innovative synthesis technique used for the quantitative integration of effect size estimates across participants and across studies. The quantitative summary allows for objective, evidence-based, and informed decisions in research, practice, and policy. Based on previous methodological work, the technique results in powerful, unbiased, and precise effect size estimates. However, its use in practice is limited and its full potential is not yet fully understood. This article aims to bring the multilevel meta-analytic model closer to the applied researcher by introducing the technique at a conceptual level and discussing its full potential and relevance to the field. The procedure of multilevel meta-analysis is illustrated using a recent single-case meta-analytic dataset. Software codes, output tables, interpretations, and graphical displays of effect size estimates are given such that the reader can repeat the analysis independently.