Comparing cross-classified mixed effects and Bayesian structural equations modeling for stimulus sampling designs: A simulation study

Disaggregating level-specific effects in cross-classified multilevel models

In psychology and other fields, data often have a cross-classified structure, whereby observations are nested within multiple types of non-hierarchical clusters (e.g., repeated measures cross-classified by persons and stimuli). This paper discusses ways that, in cross-classified multilevel models, slopes of lower-level predictors can implicitly reflect an ambiguous blend of multiple effects (for instance, a purely observation-level effect as well as a unique between-cluster effect for each type of cluster). The possibility of conflating multiple effects of lower-level predictors is well recognized for non-cross-classified multilevel models, but has not been fully discussed or clarified for cross-classified contexts. Consequently, in published cross-classified modeling applications, this possibility is almost always ignored, and researchers routinely specify models that conflate multiple effects. In this paper, we show why this common practice can be problematic, and show how to disaggregate level-specific effects in cross-classified models. We provide a novel suite of options that include fully cluster-mean-centered, partially cluster-mean-centered, and contextual effect models, each of which provides a unique interpretation of model parameters. We further clarify how to avoid both fixed and random conflation, the latter of which is widely misunderstood even in non-cross-classified models. We provide simulation results showing the possible deleterious impact of such conflation in cross-classified models, and walk through pedagogical examples to illustrate the disaggregation of level-specific effects. We conclude by considering additional model complexities that can arise with cross-classification, providing guidance for researchers in choosing among model specifications, and describing newly available software to aid researchers who wish to disaggregate effects in practice.

How Do Spelling, Handwriting Speed, and Handwriting Quality Develop During Primary School? Cross-Classified Growth Curve Analysis of Children's Writing Development

Aim: Longitudinal studies are rare in the field of writing research, and little is known about the concurrent development of the two transcription skills: spelling and handwriting. This study was designed to provide a comprehensive picture of the development and the longitudinal relations between spelling, handwriting speed, and handwriting quality at the word level.

Method: Over a period of 3 years (coh1: Grades 2–4; coh2: Grades 3–5), 117 French-speaking children were assessed on a single-word dictation task. At each testing time, measures of spelling accuracy, handwriting speed, and handwriting quality were collected on 40 words. Words varied in both orthographic and graphic complexity, making it possible to investigate the influence of these levels of complexity on transcription abilities.

Results: Linear growth analyses using cross-classified Bayesian structural equation modeling (CC-BSEM) revealed that spelling and speed continued to improve until Grade 5, while handwriting quality reached an early plateau in Grade 2. In the younger cohort, graphic complexity had a significant influence on the pace of development of handwriting speed and on spelling and handwriting quality performance in Grade 2. In the older cohort, a positive relation between spelling and speed and a negative relation between handwriting speed and handwriting quality were found, indicating that fast handwriting is associated with high spelling ability and that fast handwriting is detrimental to handwriting quality. By providing a better understanding of writing development, this study yields innovative findings not only regarding the development of transcription skills but also regarding how spelling, handwriting speed, and handwriting quality can influence each other's performance throughout primary school.