Aaron B. Taylor

Tests of the Three-Path Mediated Effect:

In a three-path mediational model, two mediators intervene in a series between an independent and a dependent variable. Methods of testing for mediation in such a model are generalized from the more often used single-mediator model. Six such methods are introduced and compared in a Monte Carlo study in terms of their Type I error, power, and coverage. Based on its results, the joint significance test is preferred when only a hypothesis test is of interest. The percentile bootstrap and bias-corrected bootstrap are preferred when a confidence interval on the mediated effect is desired, with the latter having more power but also slightly inflated Type I error in some conditions.

Explanation of Two Anomalous Results in Statistical Mediation Analysis

Previous studies of different methods of testing mediation models have consistently found two anomalous results. The first result is elevated Type I error rates for the bias-corrected and accelerated bias-corrected bootstrap tests not found in nonresampling tests or in resampling tests that did not include a bias correction. This is of special concern as the bias-corrected bootstrap is often recommended and used due to its higher statistical power compared with other tests. The second result is statistical power reaching an asymptote far below 1.0 and in some conditions even declining slightly as the size of the relationship between X and M, a, increased. Two computer simulations were conducted to examine these findings in greater detail. Results from the first simulation found that the increased Type I error rates for the bias-corrected and accelerated bias-corrected bootstrap are a function of an interaction between the size of the individual paths making up the mediated effect and the sample size, such that elevated Type I error rates occur when the sample size is small and the effect size of the nonzero path is medium or larger. Results from the second simulation found that stagnation and decreases in statistical power as a function of the effect size of the a path occurred primarily when the path between M and Y, b, was small. Two empirical mediation examples are provided using data from a steroid prevention and health promotion program aimed at high school football players (Athletes Training and Learning to Avoid Steroids; Goldberg et al., 1996), one to illustrate a possible Type I error for the bias-corrected bootstrap test and a second to illustrate a loss in power related to the size of a. Implications of these findings are discussed.

R2 effect-size measures for mediation analysis

R2 effect-size measures are presented to assess variance accounted for in mediation models. The measures offer a means to evaluate both component paths and the overall mediated effect in mediation models. Statistical simulation results indicate acceptable bias across varying parameter and sample-size combinations. The measures are applied to a real-world example using data from a team-based health promotion program to improve the nutrition and exercise habits of firefighters. SAS and SPSS computer code are also provided for researchers to compute the measures in their own data.

Evaluating model fit for growth curve models: Integration of fit indices from SEM and MLM frameworks.

Evaluating overall model fit for growth curve models involves 3 challenging issues. (a) Three types of longitudinal data with different implications for model fit may be distinguished: balanced on time with complete data, balanced on time with data missing at random, and unbalanced on time. (b) Traditional work on fit from the structural equation modeling (SEM) perspective has focused only on the covariance structure, but growth curve models have four potential sources of misspecification: within-individual covariance matrix, between-individuals covariance matrix, marginal mean structure, and conditional mean structure. (c) Growth curve models can be estimated in both the SEM and multilevel modeling (MLM) frameworks; these have different emphases for the evaluation of model fit. In this article, the authors discuss the challenges presented by these 3 issues in the calculation and interpretation of SEM- and MLM-based fit indices for growth curve models and conclude by identifying some lines for future research.

The Effects of an Intensive Shared Book-Reading Intervention for Preschool Children at Risk for Vocabulary Delay

This study examined the effects of an intensive shared book-reading intervention on the vocabulary development of preschool children who were at risk for vocabulary delay. The participants were 125 children, who the researchers stratified by classroom and randomly assigned to one of two shared book-reading conditions (i.e., the experimental, Words of Oral Reading and Language Development [WORLD] intervention; or typical practice). Results on researcher-developed measures showed statistically and practically significant effects for the WORLD intervention with no differential effects for children with higher versus lower entry-level vocabulary knowledge. The researchers detected no statistically significant differences on standardized measures. Results suggest that a combination of instructional factors may be necessary to enhance the efficacy of shared book reading for children with early vocabulary difficulties.

Developing Low-Income Preschoolers’ Social Studies and Science Vocabulary Knowledge Through Content-Focused Shared Book Reading

Abstract This study evaluated the effects of integrating science and social studies vocabulary instruction into shared book reading with low-income preschool children. Twenty-one preschool teachers and 148 children from their classrooms were randomly assigned at the class level to either the Words of Oral Reading and Language Development (WORLD) intervention or a practice-as-usual condition. Children were screened and selected to approximate three vocabulary levels (15th, 30th, and 50th). WORLD teachers implemented the intervention in small groups of 5 to 6 students, 5 days per week, 20 minutes per session, for 18 weeks. Findings from multilevel models indicated statistically and practically significant effects of the WORLD intervention on standardized measures of receptive vocabulary (δT = 0.93) and on researcher-developed measures of expressive (δT = 1.01) and receptive vocabulary (δT = 1.41). The WORLD intervention had an overall main effect, regardless of entry-level vocabulary, a finding that speaks to its potential applicability in preschool classrooms.

Loss of Power in Logistic, Ordinal Logistic, and Probit Regression When an Outcome Variable Is Coarsely Categorized.

Variables that have been coarsely categorized into a small number of ordered categories are often modeled as outcome variables in psychological research. The authors employ a Monte Carlo study to investigate the effects of this coarse categorization of dependent variables on power to detect true effects using three classes of regression models: ordinary least squares (OLS) regression, ordinal logistic regression, and ordinal probit regression. Both the loss of power and the increase in required sample size to regain the lost power are estimated. The loss of power and required sample size increase were substantial under conditions in which the coarsely categorized variable is highly skewed, has few categories (e.g., 2, 3), or both. Ordinal logistic and ordinal probit regression protect marginally better against power loss than does OLS regression.

Effects of a Health Behavior Change Model—Based HIV/STI Prevention Intervention on Condom Use Among Heterosexual Couples: A Randomized Trial

This study examines an intervention for heterosexual couples to prevent human immunodeficiency virus/sexually transmitted infections. It also evaluates the effect of the intervention, which is based on current models of health behavior change, on intermediate outcomes (individual and relationship factors) and consistency of condom use. Eligible couples were administered a baseline interview and randomized to either a 3-session theory-based intervention or a 1-session standard of care comparison condition. Men and women completed 3-month interviews; only women completed 6-month interviews. No significant intervention effect on condom use was found among couples at 3 months (n = 212) or among women (n = 178) at 6 months. However, condom use increased significantly between baseline and 3 months and baseline and 6 months for participants in both treatment conditions. Intervention effects on condom use self-efficacy were found at 3 months and 6 months and on health-protective communication at 3 months. These findings provide valuable information for the design of future studies to help disentangle the effects of intervening with couples.

Effects of Supplemental Reading Interventions in Authentic Contexts: A Comparison of Kindergarteners' Response

This study compared the effects of 2 supplemental interventions on the beginning reading performance of kindergarteners identified as at risk of reading difficulty. Students (N = 206) were assigned randomly at the classroom level either to an explicit/systematic commercial program or to a school-designed practice intervention taught 30 min per day in small groups for approximately 100 sessions. Multilevel hierarchical linear analyses revealed statistically significant effects favoring the explicit/systematic intervention on alphabetic, phonemic, and untimed decoding skills with substantive effect sizes on all measures except word identification and passage comprehension. Group performance did not differ statistically on more advanced reading and spelling skills. Findings support the efficacy of both supplemental interventions and suggest the benefit of the more explicit/systematic intervention for children who are most at risk of reading difficulty.

Adjusting Beginning Reading Intervention Based on Student Performance: An Experimental Evaluation:

This experimental study evaluated a model in which the delivery of a supplemental beginning reading intervention was adjusted based on student performance. Kindergarten students identified as at risk for reading difficulties were assigned to one of two versions of the Early Reading Intervention (ERI; Pearson/Scott Foresman, 2004). Students assigned to the experimental condition received the intervention with systematic adjustments based on student performance. Students in the comparison condition received the same intervention without instructional modifications. The experimental group outperformed the comparison group on all posttest measures at the end of kindergarten. Follow-up analyses at the end of first grade revealed a continued advantage for the experimental group. Findings suggest that systematically adjusting intervention support in response to student performance may be feasible and efficacious.