Hierarchical Linear Modeling with Maximum Likelihood, Restricted Maximum Likelihood, and Fully Bayesian Estimation

Hierarchical linear modeling (HLM) is a useful tool when analyzing data collected from groups. There are many decisions to be made when constructing and estimating a model in HLM including which estimation technique to use. Three of the estimation techniques available when analyzing data with HLM are maximum likelihood, restricted maximum likelihood, and fully Bayesian estimation. Which estimation technique is employed determines how estimates can be interpreted and the models that may be compared. The purpose of this paper is to conceptually introduce and compare these methods of estimation in HLM and interpret the computer output that results from using them. This is done for the intraclass correlation, parameter estimates, and model fit indices using a simulated dataset that is available online. The statistical program R is utilized for all analyses and syntax is provided in Appendix 1. This paper is written to aid applied researchers who wish to better understand the differences between the estimation techniques and how to interpret their HLM results. Accessed 5,153 times on https://pareonline.net from April 12, 2017 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Physical Activity and Academic Achievement: An Analysis of Potential Student- and School-Level Moderators

Background: Many children do not engage in sufficient physical activity, and schools provide a unique venue for children to reach their recommended 60 daily minutes of moderate-to-vigorous physical activity (MVPA). Prior research examining effects of MVPA on academic achievement is inconclusive, and few studies have investigated potential moderators of this relationship. This study examined whether student-level characteristics (gender, race/ethnicity, free/reduced-price lunch status) and school-level characteristics (proportion of students qualifying for free/reduced-price lunch, physical activity environment and opportunities) moderate the relationship between MVPA and academic achievement. Methods: In a large, diverse metropolitan public school district in Georgia, 4,936 students in Grade 4 were recruited from 40 elementary schools. Students wore accelerometers to measure school-day MVPA for a total of 15 days across three semesters (fall 2018, spring 2019, fall 2019). Academic achievement data, including course marks (grades) for math, reading, spelling, and standardized test scores in writing, math, reading, and Lexile (reading assessment), were collected at baseline (Grade 3, ages 8–9) and at follow-up in Grade 4 (ages 9–10). Standardized test scores were not measured in Grade 5 (ages 10–11) due to COVID-19-related disruptions. Multilevel modeling assessed whether student-level and/or school-level characteristics were moderators in the cross-sectional and longitudinal MVPA-academic achievement relationship. Results: Cross sectional analyses indicated that the MVPA and AA relationship was moderated only by student Hispanic ethnicity for Grade 4 fall spelling marks (β = -0.159 p \u3c 0.001). The relationship for Grade 4 fall spelling marks was also moderated by school physical activity opportunities (β = -0.128 (p \u3c 0.001). Longitudinally, there was no significant moderation of the MVPA-academic achievement. A relationship by student gender, free/reduced-price lunch status, race/ethnicity; nor for school-level factors including proportion of students qualifying for free/reduced-price lunch, physical activity environment, and physical activity opportunities. Conclusions: Overall, our results did not suggest that student- or school-level characteristics moderate the MVPA-academic achievement relationship. While statistically significant results were observed for certain outcomes, practical differences were negligible. In this population, school-based MVPA does not appear to differently affect academic performance based on student gender, race/ethnicity, free/reduced-price lunch, nor school characteristics

A Meta-Analysis and Quality Review of Mathematics Interventions Conducted in Informal Learning Environments with Caregivers and Children

The purposes of this study included conducting a meta-analysis and reviewing the study reporting quality of math interventions implemented in informal learning environments (e.g., the home) by children’s caregivers. This meta-analysis included 25 preschool to third-grade math interventions with 83 effect sizes that yielded a statistically significant summary effect (g = 0.26, 95% CI [0.07, 0.45) on children’s math achievement. Significant moderators of the treatment effect included the intensity of caregiver training and type of outcome measure. There were larger average effects for interventions with caregiver training that included follow-up support and for outcomes that were comprehensive early numeracy measures. Studies met 58.0% of reporting quality indicators, and analyses revealed that quality of reporting has improved in recent years. The results of this study offer several recommendations for researchers and practitioners, particularly given the growing evidence base of math interventions conducted in informal learning environments

The Longitudinal Association Between Objectively-Measured School-Day Physical Activity and Academic Achievement in US Elementary School Students

Background: It is recommended that school-aged children accrue 30 minutes of daily moderate-to-vigorous physical activity (MVPA) in school. Current literature is inconclusive about the long-term associations between school-based physical activity and academic achievement. In this study, we use a large sample and longitudinal design to rigorously evaluate whether school-day MVPA is associated with academic achievement. Methods: In a diverse suburban public school district, 4936 Grade 4 students were recruited in 40 elementary schools. Students wore accelerometers to measure school-day MVPA for 15 days across three semesters. Academic performance data was collected across Grade 3 fall to Grade 5 spring, including teacher-assigned grades and standardized test scores. Multilevel modeling was conducted controlling for student demographics and school characteristics. Results: Cross-sectional analyses found small negative associations in Grade 4. Grade 4 full-year mean daily school-day MVPA had β = −-0.066, β = −-0.063, β = −-0.066, and β = −-0.058 associations (p \u3c  0.001) with Grade 4 math, reading, spelling, and writing grades respectively, and Grade 4 full-year mean daily school-day MVPA had β = −-0.206 and β = −-0.283 (p \u3c  0.001) associations with Grade 4 math and English Language Arts (ELA) standardized test scores respectively out of approximately 500 points. Longitudinal analyses found no significant associations between Grade 4 full-year mean daily school-day MVPA and Grade 5 Fall course grades. Results also indicated small negative associations for students attaining 30+ minutes of daily school-day MVPA compared to those attaining less than 15 minutes, but only in Grade 4 Fall cross-sectional analyses where teacher-assigned reading, spelling, and writing grades were − 1.666, − 1.638, and − 1.993 points lower respectively (p \u3c  0.001). Conlcusion: The cross-sectional findings, while statistically significant in a negative direction, have a negligible association when translated practically. For example, even if students attained twice the recommended amount of school-day MVPA – which would constitute an approximately 300% increase from current levels – results suggest that grades would only decrease by 2 points on a 100-point scale. Furthermore, longitudinal analyses suggest school-day MVPA does not have a predictive association with course grades or standardized test scores. Findings suggest school-based MVPA implemented in accordance with recommendations does not meaningfully detract from academic progress. Trial registration: ClinicalTrials.gov, NCT03765047. Registered 05 December 2018 - Retrospectively registered, https://clinicaltrials.gov/ct2/show/NCT0376504

Airborne bacterial emission fluxes from manure-fertilized agricultural soil

This is the first study to quantify the dependence on wind velocity of airborne bacterial emission fluxes from soil. It demonstrates that manure bacteria get aerosolized from fertilized soil more easily than soil bacteria, and it applies bacterial genomic sequencing for the first time to trace environmental faecal contamination back to its source in the chicken barn. We report quantitative, airborne emission fluxes of bacteria during and following the fertilization of agricultural soil with manure from broiler chickens. During the fertilization process, the concentration of airborne bacteria culturable on blood agar medium increased more than 600 000-fold, and 1 m3 of air carried 2.9 × 105 viable enterococci, i.e. indicators of faecal contamination which had been undetectable in background air samples. Trajectory modelling suggested that atmospheric residence times and dispersion pathways were dependent on the time of day at which fertilization was performed. Measurements in a wind tunnel indicated that airborne bacterial emission fluxes from freshly fertilized soil under local climatic conditions on average were 100-fold higher than a previous estimate of average emissions from land. Faecal bacteria collected from soil and dust up to seven weeks after fertilization could be traced to their origins in the poultry barn by genomic sequencing. Comparative analyses of 16S rRNA gene sequences from manure, soil and dust showed that manure bacteria got aerosolized preferably, likely due to their attachment to low-density manure particles. Our data show that fertilization with manure may cause substantial increases of bacterial emissions from agricultural land. After mechanical incorporation of manure into soil, however, the associated risk of airborne infection is low

Comparison of Heterogeneity and Heterogeneity Interval Estimators in Random-Effects Meta-Analysis

Meta-analyses are conducted to synthesize the quantitative results of related studies. The random-effects meta-analysis model is based on the assumption that a distribution of true effects exists in the population. This distribution is often assumed to be normal with a mean and variance. The population variance, also called heterogeneity, can be estimated numerous ways. Accurate estimation of heterogeneity is necessary as a description of the distribution and for determining weights applied in the estimation of the summary effect when using inverse-variance weighting. To evaluate a wide range of estimators, we compared 16 estimators (Bayesian and non-Bayesian) of heterogeneity with regard to bias and mean square error over conditions based on reviews of educational and psychological meta-analyses. Three simulation conditions were varied: (a) sample size per meta-analysis, (b) true heterogeneity, and (c) sample size per effect size within each meta-analysis. Confidence or highest density intervals can be calculated for heterogeneity. The heterogeneity estimators that performed best over the widest range of conditions were paired with heterogeneity interval estimators. Interval estimators were evaluated based on coverage probability, interval width, and coverage of the estimated value. The combination of the Paule Manel estimator and Q-Profile interval method is recommended when synthesizing standardized mean difference effect sizes

Early Math Interventions in Informal Learning Environments: Technical Report

The purpose of this technical report is to document the procedures of the National Science Foundation (NSF) funded grant (DUE #2000292), Investigating Effective Methods that Adults Use to Improve Children\u27s Math Achievement in Informal Learning Environments: A Meta Analysis. Specifically, this technical report documents the method and results of the literature search process, abstract screening, and full text-review. In addition, Appendix A includes our abstract screening protocol and Appendix B includes our full-text review protocol. This technical report also describes the article coding procedures and all the methods that senior personnel used to train graduate assistants (GAs) about each phase of the meta-analysis grant. This document represents the work of the first year of a 3-year meta-analysis project