Logits and tigers and bears, oh my! A brief look at the simple math of logistic regression and how it can improve dissemination of results

Logistic regression is slowly gaining acceptance in the social sciences, and fills an important niche in the researcher’s toolkit: being able to predict important outcomes that are not continuous in nature. While OLS regression is a valuable tool, it cannot routinely be used to predict outcomes that are binary or categorical in nature. These outcomes represent important social science lines of research: retention in, or dropout from school, using illicit drugs, underage alcohol consumption, antisocial behavior, purchasing decisions, voting patterns, risky behavior, and so on. The goal of this paper is to briefly lead the reader through the surprisingly simple mathematics that underpins logistic regression: probabilities, odds, odds ratios, and logits. Anyone with spreadsheet software or a scientific calculator can follow along, and in turn, this knowledge can be used to make much more interesting, clear, and accurate presentations of results (especially to non-technical audiences). In particular, I will share an example of an interaction in logistic regression, how it was originally graphed, and how the graph was made substantially more user-friendly by converting the original metric (logits) to a more readily interpretable metric (probability) through three simple steps. Accessed 7,862 times on https://pareonline.net from June 06, 2012 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Normality of residuals is a continuous variable, and does seem to influence the trustworthiness of confidence intervals : A response to, and appreciation of, Williams, Grajales, and Kurkiewicz (2013)

Osborne and Waters (2002) focused on checking some of the assumptions of multiple linear regression. In a critique of that paper, Williams, Grajales, and Kurkiewicz correctly clarify that regression models estimated using ordinary least squares require the assumption of normally distributed errors, but not the assumption of normally distributed response or predictor variables.They go on to discuss estimate bias and provide a helpful summary of the assumptions of multiple regression when using ordinary least squares. While we were not as precise as we could have been when discussing assumptions of normality, the critical issue of the 2002 paper remains -researchers often do not check on or report on the assumptions of their statistical methods. This response expands on the points made by Williams, advocates a thorough examination of data prior to reporting results, and provides an example of how incremental improvements in meeting the assumption of normality of residuals incrementally improves the accuracy of confidence intervals. Accessed 6,654 times on https://pareonline.net from September 06, 2013 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

What is Rotating in Exploratory Factor Analysis?

Exploratory factor analysis (EFA) is one of the most commonly-reported quantitative methodology in the social sciences, yet much of the detail regarding what happens during an EFA remains unclear. The goal of this brief technical note is to explore what rotation is, what exactly is rotating, and why we use rotation when performing EFAs. Some commentary about the relative utility and desirability of different rotation methods concludes the narrative. Accessed 43,804 times on https://pareonline.net from January 07, 2015 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Bringing balance and technical accuracy to reporting odds ratios and the results of logistic regression analyses

Logistic regression and odds ratios (ORs) are powerful tools recently becoming more common in the social sciences. Yet few understand the technical challenges of correctly interpreting an odds ratio, and often it is done incorrectly in a variety of different ways. The goal of this brief note is to review the correct interpretation of the odds ratio, how to transform it into the more easily understood and intuitive relative risk (RRs) estimate, and a suggestion for dealing with odds ratios or relative risk estimates that are below 1.0 so that perceptually their magnitude is equivalent of Ors or RRs greater than 1.0. Accessed 37,451 times on https://pareonline.net from October 18, 2006 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Advantages of Hierarchical Linear Modeling

Accessed 124,217 times on https://pareonline.net from January 10, 2000 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Effect Sizes and the Disattenuation of Correlation and Regression Coefficients: Lessons from Educational Psychology

This paper presents an overview of the concept of disattenuation of correlation and multiple regression coefficients, some discussion of the pros and cons of this approach, and illustrates the effect of performing this procedure using data from a large survey of Educational Psychology research. Accessed 49,382 times on https://pareonline.net from May 27, 2003 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Prediction in Multiple Regression

Accessed 135,767 times on https://pareonline.net from March 10, 2000 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Fostering Students\u27 Identification with Mathematics and Science

Book Summary: Interest in Mathematics and Science Learning is the first volume to assemble findings on the role of interest in mathematics and science learning. As the contributors illuminate across the volume’s 22 chapters, interest provides a critical bridge between cognition and affect in learning and development. This volume will be useful to educators, researchers, and policy makers, especially those whose focus is mathematics, science, and technology education. Chapter Summary: The primary purpose of this chapter is to explore the process whereby students transition from a short-term, situational interest in mathematics or science to a more enduring individual interest in which they incorporate performance in mathematics or science into their self-definitions (e.g. I am a scientist ). We do so by examining the research related to domain identification, which is the extent to which students define themselves through a role or performance in a domain, such as mathematics or science. Understanding the process of domain identification is important because it can contribute to an understanding of how individual interest develops over time. The means through which students become highly domain identified involves many factors that are internal (e.g. goals and beliefs) and external (e.g. family environment and educational experiences) to them. Students who are more identified with an academic domain tend to demonstrate increased motivation, effort, perseverance (when faced with failure), and achievement. Importantly, students with lower domain identification tend to demonstrate less motivation, lower effort, and fewer desirable outcomes. Student outcomes in a domain can reciprocally influence domain identification by reinforcing or altering it. This feedback loop can help explain incremental changes in motivation, self-concept, individual interest, and, ultimately, important outcomes such as achievement, choice of college major, and career path. This dynamic model presents possible mechanisms for influencing student outcomes. Furthermore, assessing students\u27 domain identification can allow practitioners to intervene to prevent undesirable outcomes. Finally, we present research on how mathematics and science instructors could use the principles of the MUSIC Model of Academic Motivation to enhance students\u27 domain identification, by (a) empowering students, (b) demonstrating the usefulness of the domain, (c) supporting students\u27 success, (d) triggering students\u27 interests, and (e) fostering a sense of caring and belonging. We conclude that by using the MUSIC model, instructors can intentionally design educational experiences to help students progress from a situational interest to one that is more enduring and integrated into their identities

Four assumptions of multiple regression that researchers should always test

Most statistical tests rely upon certain assumptions about the variables used in the analysis. When these assumptions are not met the results may not be trustworthy, resulting in a Type I or Type II error, or over- or under-estimation of significance or effect size(s). As Pedhazur (1997, p. 33) notes, Knowledge and understanding of the situations when violations of assumptions lead to serious biases, and when they are of little consequence, are essential to meaningful data analysis . However, as Osborne, Christensen, and Gunter (2001) observe, few articles report having tested assumptions of the statistical tests they rely on for drawing their conclusions. This creates a situation where we have a rich literature in education and social science, but we are forced to call into question the validity of many of these results, conclusions, and assertions, as we have no idea whether the assumptions of the statistical tests were met. Our goal for this paper is to present a discussion of the assumptions of multiple regression tailored toward the practicing researcher. Several assumptions of multiple regression are “robust” to violation (e.g., normal distribution of errors), and others are fulfilled in the proper design of a study (e.g., independence of observations). Therefore, we will focus on the assumptions of multiple regression that are not robust to violation, and that researchers can deal with if violated. Specifically, we will discuss the assumptions of linearity, reliability of measurement, homoscedasticity, and normality. Accessed 630,254 times on https://pareonline.net from January 07, 2002 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

What is authorship, and what should it be? A survey of prominent guidelines for determining authorship in scientific publications

Before the mid 20th century most scientific writing was solely authored (Claxton, 2005; Greene, 2007) and thus it is only relatively recently, as science has grown more complex, that the ethical and procedural issues around authorship have arisen. Fields as diverse as medicine (International Committee of Medical Journal Editors, 2008), mathematics (e.g., American Statistical Association, 1999), the physical sciences (e.g., American Chemical Society, 2006), and the social sciences (e.g., American Psychological Association, 2002) have, in recent years, wrestled with what constitutes authorship and how to eliminate problematic practices such as honorary authorship and ghost authorship (e.g., Anonymous, 2004; Claxton, 2005; Manton & English, 2008). As authorship is the coin of the realm in academia (Louis, Holdsworth, Anderson, & Campbell, 2008), it is an ethical issue of singular importance. The goal of this paper is to review prominent and diverse guidelines concerning scientific authorship and to attempt to synthesize existing guidelines into recommendations that represent ethical practices for ensuring credit where (and only where) credit is due. Accessed 16,706 times on https://pareonline.net from July 20, 2009 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right