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Over-time, repeated measures, or longitudinal data are terms referring to repeated measurements of the same variables within the same unit (e.g., person, family, team, company). Longitudinal data come from many sources, including self-reports, behaviors, observations, and physiology. Researchers collect repeated measures for a variety of reasons, such as wanting to model change in a process over time or wanting to increase measurement reliability. Whatever the reason for data collection, longitudinal methods pose unique challenges and opportunities. This chapter has three main goals: (1) to help researchers consider design decisions when developing a longitudinal study, (2) to describe the different decisions researchers have to make when analyzing longitudinal data, and (3) to consider the unique properties of longitudinal designs that researchers should be aware of when designing and analyzing longitudinal studies. We aim to provide a comprehensive overview of the major issues that researchers should consider, and we also point to more extensive resources.
In the models discussed here, there is a hierarchy of variation that corresponds to groupings within the data. For example, students may be sampled from different classes, that in turn are sampled from different schools. Or, rather than being nested, groups may be crossed. Important notions are those of fixed and random effects, and variance components. Analysis of data from designs that have the balance needed to allow an analysis of variance breakdown are a special case. Further types of mixed models are generalized linear mixed models and repeated measures models. Repeated measures models are multilevel models where measurements consist of multiple profiles in time or space, resulting in time or spatial dependence. Relative to the length of time series that is required for a realistic analysis, each individual repeated measures profile can and often will have values for a few time points only.
Chapter 4 presents methods of analysis of variance (ANOVA). Based on the GLM, it is shown that ANOVA differs from regression only in the nature of the independent variables. Whereas in regression, the independent variables are usually metric, in ANOVA, they are categorical. In univariate ANOVA, there is one factor (that is, independent variable). In factorial ANOVA, there are multiple factors. In multivariate ANOVA (MANOVA), there are multiple dependent variables. In addition, this chapter discusses ANOVA for repeated observations and ANOVA with metric covariates.
This chapter introduces the Conway–Maxwell–Poisson regression model, along with adaptations of the model to account for zero-inflation, censoring, and data clustering. Section 5.1 motivates the consideration and development of the various COM–Poisson regressions. Section 5.2 introduces the regression model and discusses related issues including parameter estimation, hypothesis testing, and statistical computing in R. Section 5.3 advances that work to address excess zeroes, while Section 5.4 describes COM–Poisson models that incorporate repeated measures and longitudinal studies. Section 5.5 focuses attention on the R statistical packages and functionality associated with regression analysis that accommodates excess zeros and/or clustered data as described in the two previous sections. Section 5.6 considers a general additive model based on COM–Poisson. Finally, Section 5.7 informs readers of other statistical computing softwares that are also available to conduct COM–Poisson regression, discussing their associated functionality. The chapter concludes with discussion.
Researchers in the decision making tradition usually analyze multiple decisions within experiments by aggregating choices across individuals and using the individual subject as the unit of analysis. This approach can mask important variations and patterns within the data. Specifically, it ignores variations in decisions across a task or game and possible influences of characteristics of the subject or the experiment on these variations. We demonstrate, by reanalyzing data from two previously published articles, how a mixed model analysis addresses these limitations. Our results, with a modified Iowa gambling task and a prisoner's dilemma game, illustrate the ways in which such an analysis can test hypotheses not possible with other techniques, is more parsimonious, and is more likely to be faithful to theoretical models.
We evaluated whether the association between deviant peer affiliation and onset of substance use is conditional upon sex and sympathetic nervous system (SNS) reactivity as measured by pre-ejection period (PEP). Community-sampled adolescents (N = 251; M = 15.78 years; 53% female; 66% White, 34% Black) participated in three waves. PEP reactivity was collected during a mirror star-tracer stress task. Alcohol, marijuana, tobacco, or any substance use, as well as binge drinking and sexual activity involving substance use were outcomes predicted by affiliation with deviant peers and two- and three-way interactions with sex and PEP reactivity. Probability of substance use increased over time, but this was amplified for adolescents with greater deviant peer affiliation in conjunction with blunted PEP reactivity. The same pattern of results was also found for prediction of binge drinking and sexual activity involving substance use. Findings are discussed in the context of biosocial models of adolescent substance use and health risk behaviors.
Primary schools contribute to promoting healthy eating behaviour and preventing overweight and obesity by providing nutrition education. Research highlights the importance of improving teachers’ programme implementation to enhance intervention effectiveness. An integrative approach has been suggested to reduce time barriers that teachers currently experience in teaching nutrition. This scoping review explores use and effectiveness of integrative teaching in primary-school-based nutrition education programmes. Six databases were searched for primary-school-based interventions on nutrition education. Papers reporting on integration of nutrition topics within core curriculum were included. Abstracts and full texts of potentially relevant articles were screened to determine eligibility. Next, data were extracted and tabulated. Findings were collated and summarised to describe intervention characteristics, subject integration and effectiveness of the included programmes. Data describing integration of nutrition into the primary school curriculum were extracted from 39 eligible papers. Nutrition education programmes often involve lessons about food groups and are frequently embedded within the mathematics, science or literacy syllabus. Although articles report on the integration of nutrition, the use of this approach was not commonly described in detail. Only seven papers discussed student outcomes related to the integration of nutrition education within core subjects. The ability to draw strong conclusions about school-based nutrition intervention effectiveness is limited by the current lack of programme description and methodological issues. Hence, more research is warranted to inform evidence on effectiveness of integrative nutrition education for both teacher and student outcomes. Future studies that include greater detail regarding the integrative approach are needed.
When herbicides are applied in mixture, and infestation by weeds is less than expected compared with when herbicides are applied alone, a synergistic effect is said to exist. The inverse response is described as being antagonistic. However, if the expected response is defined as a multiplicative, nonlinear function of the means for the herbicides when applied alone, then standard linear model methodology for tests of hypotheses does not apply directly. Consequently, nonlinear mixed-model methodology was explored using the nonlinear mixed-model procedure (PROC NLMIXED) of SAS System®. Generality of the methodology is illustrated using data from a randomized block design with repeated measures in time. Nonlinear mixed-model estimates and tests of synergistic and antagonistic effects were more sensitive in detecting significance, and PROC NLMIXED was a versatile tool for implementation.
Research examining racial/ethnic disparities in pollution exposure often relies on cross-sectional data. These analyses are largely insensitive to exposure trends and rarely account for broader contextual dynamics. To provide a more comprehensive assessment of racial-environmental inequality over time, we combine the 1990 to 2009 waves of the Panel Study of Income Dynamics (PSID) with spatially- and temporally-resolved measures of nitrogen dioxide (NO2) and particulate matter (PM2.5 and PM10) in respondents’ neighborhoods, as well as census data on the characteristics of respondents’ metropolitan areas. Results based on multilevel repeated measures models indicate that Blacks and Latinos are, on average, more likely to be exposed to higher levels of NO2, PM2.5, and PM10 than Whites. Despite nationwide declines in levels of pollution over time, racial and ethnic disparities persist and cannot be fully explained by individual-, household-, or metropolitan-level factors.
Based on the hypothesis that high-meat diets may increase breast cancer risk through hormonal pathways, the present analysis compared oestrogens in serum and urine by meat-eating status.
Design
Intervention with repeated measures.
Setting
Two randomized soya trials (BEAN1 and BEAN2) among premenopausal healthy women.
Subjects
BEAN1 participants completed seven unannounced 24 h dietary recalls and donated five blood and urine samples over 2 years. BEAN2 women provided seven recalls and three samples over 13 months. Serum samples were analysed for oestrone (E1) and oestradiol (E2) using RIA. Nine oestrogen metabolites were measured in urine by LC–MS. Semi-vegetarians included women who reported consuming <30 g of red meat, poultry and fish daily, and pescatarians those who reported consuming <20 g of meat/poultry but >10 g of fish daily. All other women were classified as non-vegetarians. We applied mixed models to compute least-square means by vegetarian status adjusted for potential confounders.
Results
The mean age of the 272 participants was 41·9 (sd 4·5) years. Serum E1 (85 v. 100 pg/ml, P = 0·04) and E2 (140 v. 154 pg/ml, P = 0·04) levels were lower in the thirty-seven semi-vegetarians than in the 235 non-vegetarians. The sum of the nine urinary oestrogen metabolites (183 v. 200 pmol/mg creatinine, P = 0·27) and the proportions of individual oestrogens and pathways did not differ by meat-eating status. Restricting the models to the samples collected during the luteal phase strengthened the associations.
Conclusions
Given the limitations of the study, the lower levels of serum oestrogens in semi-vegetarians than non-vegetarians need confirmation in larger populations.
Solving theoretical or empirical issues sometimes involves establishing the equality of two variables with repeated measures. This defies the logic of null hypothesis significance testing, which aims at assessing evidence against the null hypothesis of equality, not for it. In some contexts, equivalence is assessed through regression analysis by testing for zero intercept and unit slope (or simply for unit slope in case that regression is forced through the origin). This paper shows that this approach renders highly inflated Type I error rates under the most common sampling models implied in studies of equivalence. We propose an alternative approach based on omnibus tests of equality of means and variances and in subject-by-subject analyses (where applicable), and we show that these tests have adequate Type I error rates and power. The approach is illustrated with a re-analysis of published data from a signal detection theory experiment with which several hypotheses of equivalence had been tested using only regression analysis. Some further errors and inadequacies of the original analyses are described, and further scrutiny of the data contradict the conclusions raised through inadequate application of regression analyses.
Despite some evidence that genotype-environment interaction (G×E) effects may be involved in the variation observed in behavioral and biological traits, few attempts have been made to detect and quantify this component of genetic variation in humans. We propose that one way to achieve this goal is to challenge several genotypes in a similar manner, submitting both members of several MZ twin pairs to an ethically acceptable experimental treatment capable of inducing an adaptative response. In this situation, the G×E effect can be assessed with a two-way analysis of variance for repeated measures on one factor, the treatment effect. In this design, twins are considered nested within the pair, whereas the treatment effect is considered a fixed variable. The intrapair resemblance in the response to the treatment is quantified with an intraclass correlation coefficient computed with between-sibhips and within-sibhips means of squares. To illustrate this approach, changes induced by long-term endurance training were studied in 10 MZ twin pairs. Significant intrapair resemblance in the response of maximal oxygen uptake was observed, with about 7 to 8 times more variance between pairs than within pairs. This design with MZ twins may be helpful in the study of human variation for multifactorial phenotypes.
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