Improved analyses of single cases: Dynamic multilevel analysis

Ming Ming CHIU, Carly A. ROBERTS

Research output: Contribution to journalArticlespeer-review

7 Citations (Scopus)


This project identifies some difficulties when analyzing single-case data and showcases a new method, dynamic multilevel analysis (DMA). We re-analyze a published, meta-analysis of single-case interventions for participants with autism. Analytic difficulties include missing data, nested data, baseline trends, time periods, recency effects, many hypotheses’ false positives, interactions among explanatory variables, indirect effects (including false negatives), and sampling errors. Furthermore, non-overlapping analyses can yield contested results, overvalue data near overlap boundaries, lose statistical power, and lack estimates of explained variance or unexplained residuals. To address these difficulties, DMA integrates several methods, including multilevel and time-series analyses. DMA re-analysis not only showed robust intervention effects, but also time-, outcome-, and intervention component-specific effects. Moreover, DMA informs the suitability of time hypotheses or meta-analysis, and DMA’s components can be used separately, notably its time-series analyses for small samples (e.g., one participant). Hence, DMA can help researchers analyze single-case data more accurately. Copyright © 2016 Taylor & Francis.
Original languageEnglish
Pages (from-to)253-265
JournalDevelopmental Neurorehabilitation
Issue number4
Early online dateFeb 2016
Publication statusPublished - 2018


Chiu, M. M., & Roberts, C. A. (2018). Improved analyses of single cases: Dynamic multilevel analysis. Developmental Neurorehabilitation, 21(4), 253-265. doi: 10.3109/17518423.2015.1119904


  • Autism
  • Effect size
  • Hierarchical linear model
  • Meta-analysis
  • Single-case research design
  • Time-series analysis


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