Augmenting visual analysis in single-case research with hierarchical linear modeling.
Add hierarchical linear modeling to your single-case data analysis to detect hidden variability and strengthen claims of evidence-based practice.
01Research in Context
What this study did
The authors looked at single-case data from students with intellectual disability.
They added hierarchical linear modeling (HLM) on top of regular visual analysis.
HLM treats each student as a level so it can spot hidden differences between them.
What they found
Visual analysis alone said the intervention worked.
HLM agreed and also showed that baseline levels and growth rates varied a lot between students.
That hidden variability would have been missed without the extra model.
How this fits with other research
Falligant et al. (2022) extends this idea by testing simpler aids like conservative dual-criteria and fail-safe k. You can use these tools instead of, or with, HLM.
Landman et al. (2024) now supersedes the HLM push. Their new TLC index skips HLM’s math rules and works better when you have tiny datasets.
Shimp (1974) warned that old ANOVA mis-fits single-subject data. Cashon et al. (2013) answered that call by offering HLM as a better fit.
Why it matters
You can still trust your eyes, but one quick HLM run can show if one student is flat while another soars. If stats feel heavy, try the newer TLC index or the conservative dual-criteria sheet. Either way, you gain stronger evidence for your next IEP meeting.
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02At a glance
03Original abstract
The purpose of this article is to demonstrate how hierarchical linear modeling (HLM) can be used to enhance visual analysis of single-case research (SCR) designs. First, the authors demonstrated the use of growth modeling via HLM to augment visual analysis of a sophisticated single-case study. Data were used from a delayed multiple baseline design, across groups of participants, with an embedded changing criterion design in a single-case literacy project for students with moderate intellectual disabilities (MoID). Visual analysis revealed a functional relation between instruction and sight-word acquisition for all students. Growth HLM quantified relations at the group level and revealed additional information that included statistically significant variability among students at initial-baseline probe and also among growth trajectories within treatment subphases. Growth HLM showed that receptive vocabulary was a significant predictor of initial knowledge of sight words, and print knowledge significantly predicted growth rates in both treatment subphases. Next, to show the benefits of combining these methodologies to examine a different behavioral topography within a more commonly used SCR design, the authors used repeated-measures HLM and visual analysis to examine simulated data within an ABAB design. Visual analysis revealed a functional relation between a hypothetical intervention (e.g., token reinforcement) and a hypothetical dependent variable (e.g., performance of a target response). HLM supported the existence of a functional relation through tests of statistical significance and detected significant variance among participants' response to the intervention that would be impossible to identify visually. This study highlights the relevance of these procedures to the identification of evidence-based interventions.
Behavior modification, 2013 · doi:10.1177/0145445512453734