The hosts discuss the multilevel model and its cool extensions, while also mentioning topics like hostile federal judges, grievances, Sesame Street, distributional baguettes, naive standard errors, intra-class correlation, cross-classified models, and more.
Multi-level modeling allows for the analysis of data with nested or hierarchical structure and can be used to explore individual-level and group-level predictors.
MLM can handle complex research designs and examine the interplay between individual and contextual factors in various fields.
Hybrid models and fixed effects approaches offer alternative methods for addressing specific research questions in MLM.
Deep dives
Multi-level modeling explained
Multi-level modeling (MLM) is a statistical technique that allows for the analysis of data with nested or hierarchical structure. It involves breaking down the total variability of an outcome into within-group and between-group components. The within-group variability refers to the variability among individuals within a group, while the between-group variability refers to the variability among different groups. The intra-class correlation (ICC) is a key statistic used in MLM, which quantifies the proportion of total variability that can be attributed to between-group differences. It ranges from 0 to 1, with higher values indicating greater between-group variability. MLM can be used to answer a wide range of research questions, such as exploring the effects of individual-level and group-level predictors, investigating cross-level interactions, and analyzing longitudinal or repeated measures data.
Complexity and applications of MLM
Multi-level modeling can handle complex research designs involving multiple levels of nesting, such as students within classrooms within schools. It allows for the inclusion of predictors at different levels, making it possible to investigate the influences of individual-level, group-level, and even higher-level factors on outcomes. MLM can be applied to a variety of fields, including education, psychology, health sciences, and social sciences. It can be used to study topics like academic achievement, interpersonal relationships, health behaviors, organizational behavior, and much more. The flexibility of MLM makes it a powerful tool for examining the complex interplay between individual and contextual factors.
Hybrid models and fixed effects approach
In certain cases, researchers may need to use hybrid models or a fixed effects approach in MLM. Hybrid models combine random effects (allowing for group-level variability) with fixed effects (controlling for certain factors at the group level). This approach lets researchers strike a balance between accounting for between-group differences and examining within-group predictors. The fixed effects approach, on the other hand, focuses on removing or controlling for between-group differences by treating group membership as a predictor. These alternative models can be useful when the research question specifically requires treating certain factors as fixed or controlling for between-group variability.
Integration with structural equation modeling (SEM)
Multi-level modeling can be integrated with structural equation modeling (SEM) to handle more complex research questions involving latent variables and mediation analysis. However, this integration brings about additional challenges and considerations. Traditional SEM assumptions, such as perfect reliability, may not hold in the multi-level context, requiring the adaptation of models and estimation techniques. Multi-level SEM allows for the examination of relationships among latent variables, as well as the exploration of cross-level effects and mediated pathways. However, the use of multi-level SEM requires careful consideration and understanding of both multi-level modeling and SEM frameworks.
Conclusion
Multi-level modeling provides a powerful approach for analyzing data with a hierarchical or nested structure. It allows researchers to investigate the influences of individual-level and group-level predictors, explore cross-level interactions, and analyze longitudinal or repeated measures data. MLM is versatile and can be applied to various research fields and designs. Hybrid models and fixed effects approaches offer alternative ways of addressing specific research questions. Integration with structural equation modeling extends the applicability of MLM to complex latent variable models. Understanding and utilizing multi-level modeling can improve the depth and sophistication of statistical analysis in many areas of research.
In this week’s episode Greg and Patrick take advantage of the recent expiration of a statute of limitations that legally allows them to talk about the multilevel model: what it is, when we might use it, and extremely cool extensions that it allows. Along the way they also discuss hostile federal judges, McNeish, airing of grievances, Gauss and Markov’s corpses, Sesame Street, distributional baguettes, naivete, sentient GLMs, two pencil necks, Thor’s Hammer, Willy Sutton, Siren’s Song, peer groups of two, fighting good for an old guy, crazy town cool, 50 ducks, conceding a battle, and blushing corpses.
