The analysis and identification of homologizer/moderator variables when the moderator is continuous: An illustration with anthropometric data

Challenging the association between health literacy and health: the role of conversion factors

Previous studies have found substantial correlations between health literacy and various health outcomes. However, the role of social and personal factors in those links remains understudied. Applying a moderation approach, we assume that these factors function as conversion factors on the associations between health literacy and health outcomes. Consequently, we test if associations between health literacy and health outcomes are stronger among young male adults who score high in conversion factors compared to those who score low. Cross-sectional data from the Young Adult Survey Switzerland were used for the analyses (n = 9339, age = 18-25). Multiple logistic regression analyses were applied to estimate associations between health literacy and health. Moderator analyses with three conversion factors and five health outcomes were conducted. For each health outcome at least one conversion factor moderated the association between health literacy and health according to the hypothesis. Although strength and form of the moderation effect differ across analyses, generally stronger associations were found among groups with beneficial social or personal factors. The present findings support the hypothesis that conversion factors play a crucial role in the associations between health literacy and health. The findings, thus, point towards a potential risk of linear health literacy approaches that assume equal benefits from increased health literacy. Individuals with beneficial social and personal factors (those already privileged) may enjoy greater health benefits from interventions improving health literacy.

A simple statistic for comparing moderation of slopes and correlations

Given a linear relationship between two continuous random variables X and Y that may be moderated by a third, Z, the extent to which the correlation ρ is (un)moderated by Z is equivalent to the extent to which the regression coefficients β_y and β_x are (un)moderated by Z iff the variance ratio σy2∕σx2 is constant over the range or states of Z. Otherwise, moderation of slopes and of correlations must diverge. Most of the literature on this issue focuses on tests for heterogeneity of variance in Y, and a test for this ratio has not been investigated. Given that regression coefficients are proportional to ρ via this ratio, accurate tests, and estimations of it would have several uses. This paper presents such a test for both a discrete and continuous moderator and evaluates its Type I error rate and power under unequal sample sizes and departures from normality. It also provides a unified approach to modeling moderated slopes and correlations with categorical moderators via structural equations models.

Studying Individual Differences in Predictability With Gamma Regression and Nonlinear Multilevel Models

Statistical prediction remains an important tool for decisions in a variety of disciplines. An equally important issue is identifying factors that contribute to more or less accurate predictions. The time series literature includes well developed methods for studying predictability and volatility over time. This article develops distribution-appropriate methods for studying individual differences in predictability for settings in psychological research. Specifically, 3 different approaches are discussed for modeling predictability. The 1st is a bivariate measure of predictability discussed previously in the psychology literature, the squared or absolute valued difference between criterion and predictor, which is shown to follow the gamma distribution. The 2nd method extended limitations of previous research and involved understanding predictability in regression models. The 3rd method used nonlinear multilevel models to study predictability in settings where participants are nested within clusters. An application was presented using SAS NLMIXED to understand the predictability of college grade point average by student demographic characteristics. The findings from the application suggest that the 1st-year college performance of English as a second language students were, on average, less predictable whereas females and Whites tended to demonstrate more predictable academic performance than their male or racial/ethnic minority counterparts.