Hypotheses involving mediation are common in the behavioral sciences. Mediation exists when a predictor affects a dependent variable indirectly through at least one intervening variable, or mediator. Methods to assess mediation involving multiple simultaneous mediators have received little attention in the methodological literature despite a clear need. We provide an overview of simple and multiple mediation and explore three approaches that can be used to investigate indirect processes, as well as methods for contrasting two or more mediators within a single model. We present an illustrative example, assessing and contrasting potential mediators of the relationship between the helpfulness of socialization agents and job satisfaction. We also provide SAS and SPSS macros, as well as Mplus and LISREL syntax, to facilitate the use of these methods in applications.

https://link.springer.com/content/pdf/10.3758/BRM.40.3.879.pdf

Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models

Similarity breeds connection. This principle—the homophily principle—structures network ties of every type, including marriage, friendship, work, advice, support, information transfer, exchange, comembership, and other types of relationship. The result is that people's personal networks are homogeneous with regard to many sociodemographic, behavioral, and intrapersonal characteristics. Homophily limits people's social worlds in a way that has powerful implications for the information they receive, the attitudes they form, and the interactions they experience. Homophily in race and ethnicity creates the strongest divides in our personal environments, with age, religion, education, occupation, and gender following in roughly that order. Geographic propinquity, families, organizations, and isomorphic positions in social systems all create contexts in which homophilous relations form. Ties between nonsimilar individuals also dissolve at a higher rate, which sets the stage for the formation of niches (localize...

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Birds of a Feather: Homophily in Social Networks

So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

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Experimental Design and Data Analysis for Biologists

Mediation is said to occur when a causal effect of some variable X on an outcome Y is explained by some intervening variable M. The authors recommend that with small to moderate samples, bootstrap methods (B. Efron & R. Tibshirani, 1993) be used to assess mediation. Bootstrap tests are powerful because they detect that the sampling distribution of the mediated effect is skewed away from 0. They argue that R. M. Baron and D. A. Kenny's (1986) recommendation of first testing the X --> Y association for statistical significance should not be a requirement when there is a priori belief that the effect size is small or suppression is a possibility. Empirical examples and computer setups for bootstrap analyses are provided.

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Mediation in experimental and nonexperimental studies: New procedures and recommendations.

In 1885, Sir Francis Galton first defined the term “regression” and completed the theory of bivariate correlation. A decade later, Karl Pearson developed the index that we still use to measure correlation, Pearson's r. Our article is written in recognition of the 100th anniversary of Galton's first discussion of regression and correlation. We begin with a brief history. Then we present 13 different formulas, each of which represents a different computational and conceptual definition of r. Each formula suggests a different way of thinking about this index, from algebraic, geometric, and trigonometric settings. We show that Pearson's r (or simple functions of r) may variously be thought of as a special type of mean, a special type of variance, the ratio of two means, the ratio of two variances, the slope of a line, the cosine of an angle, and the tangent to an ellipse, and may be looked at from several other interesting perspectives.

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Thirteen ways to look at the correlation coefficient

Psychology advances knowledge by testing statistical hypotheses using empirical observations and data. The expectation is that most statistically significant findings can be replicated in new data and in new laboratories, but in practice many findings have replicated less often than expected, leading to claims of a replication crisis. We review recent methodological literature on questionable research practices, meta-analysis, and power analysis to explain the apparently high rates of failure to replicate. Psychologists can improve research practices to advance knowledge in ways that improve replicability. We recommend that researchers adopt open science conventions of preregi-stration and full disclosure and that replication efforts be based on multiple studies rather than on a single replication attempt. We call for more sophisticated power analyses, careful consideration of the various influences on effect sizes, and more complete disclosure of nonsignificant as well as statistically significant findings.

Psychology, Science, and Knowledge Construction: Broadening Perspectives from the Replication Crisis.

A quiet methodological revolution, a modeling revolution, has occurred over the past several decades, almost without discussion. In contrast, the 20th century ended with contentious argument over the utility of null hypothesis significance testing (NHST). The NHST controversy may have been at least partially irrelevant, because in certain ways the modeling revolution obviated the NHST argument. I begin with a history of NHST and modeling and their relation to one another. Next, I define and illustrate principles involved in developing and evaluating mathematical models. Following, I discuss the difference between using statistical procedures within a rule-based framework and building mathematical models from a scientific epistemology. Only the former is treated carefully in most psychology graduate training. The pedagogical implications of this imbalance and the revised pedagogy required to account for the modeling revolution are described. To conclude, I discuss how attention to modeling implies shifting statistical practice in certain progressive ways. The epistemological basis of statistics has moved away from being a set of procedures, applied mechanistically, and moved toward building and evaluating statistical and scientific models.

The epistemology of mathematical and statistical modeling: a quiet methodological revolution.

Previous studies have documented that smoking during pregnancy (SDP) is associated with offspring externalizing problems, even when measured covariates were used to control for possible confounds. However, the association may be because of nonmeasured environmental and genetic factors that increase risk for offspring externalizing problems. The current project used the National Longitudinal Survey of Youth and their children, ages 4-10 years, to explore the relations between SDP and offspring conduct problems (CPs), oppositional defiant problems (ODPs), and attention-deficit/hyperactivity problems (ADHPs) using methodological and statistical controls for confounds. When offspring were compared to their own siblings who differed in their exposure to prenatal nicotine, there was no effect of SDP on offspring CP and ODP. This suggests that SDP does not have a causal effect on offspring CP and ODP. There was a small association between SDP and ADHP, consistent with a causal effect of SDP, but the magnitude of the association was greatly reduced by methodological and statistical controls. Genetically informed analyses suggest that unmeasured environmental variables influencing both SDP and offspring externalizing behaviors account for the previously observed associations. That is, the current analyses imply that important unidentified environmental factors account for the association between SDP and offspring externalizing problems, not teratogenic effects of SDP.

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Smoking during pregnancy and offspring externalizing problems: An exploration of genetic and environmental confounds

Hundreds of research articles have addressed the relationship between birth order and intelligence. Virtually all have used cross-sectional data, which are fundamentally flawed in the assessment of within-family (including birth order) processes. Although within-family models have been based on patterns in cross-sectional data, a number of equally plausible between-family explanations also exist. Within-family (preferably intact-family) data are prerequisite for separating within- and between-family causal processes. This observation reframes an old issue in a way that can be easily addressed by studying graphical patterns. Sibling data from the National Longitudinal Survey of Youth are evaluated, and the results are compared with those from other studies using within-family data. It appears that although low-IQ parents have been making large families, large families do not make Iow-IQ children in modern U.S. society. The apparent relation between birth order and intelligence has been a methodological illusion.

Joseph Lee Rodgers

Papers

Thirteen ways to look at the correlation coefficient

Psychology, Science, and Knowledge Construction: Broadening Perspectives from the Replication Crisis.

The epistemology of mathematical and statistical modeling: a quiet methodological revolution.

Smoking during pregnancy and offspring externalizing problems: An exploration of genetic and environmental confounds

Resolving the debate over birth order, family size, and intelligence.