Handling missing data in single-case studies
Open accessAbstract
Multiple imputation is illustrated for dealing with missing data in a published SCED study. Results were compared to those obtained from available data. Merits and issues of implementation are discussed. Recommendations are offered on primal/advanced readings, statistical software, and future research.
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Missing primary outcome data was handled using a multiple imputation approach.
“Missing primary outcome data was handled in line with recommendations by using a multiple imputation approach (Peng & Chen, 2018).”
From A single-case experimental evaluation of a new group-based intervention to enhance adjustment to life with acquired brain injury: VaLiANT (valued living after neurological trauma) (2022) · cites this paper as Peng & Chen, 2018
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Cites
Multiple Imputation for Nonresponse in Surveys
Rubin, D. B. (1987) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316696 · Cited by 20,701 · see citing works
Statistical Analysis With Missing Data
Lahiff, M., Little, R. J. A., & Rubin, D. B. (1989) · Journal of the American Statistical Association · doi:10.2307/2289883 · Cited by 17,384 · see citing works
Missing data: our view of the state of the art
Schafer, J. L., & Graham, J. W. (2002) · Psychological Methods · doi:10.1037/1082-989x.7.2.147 · Cited by 11,638 · see citing works
Multiple imputation using chained equations: Issues and guidance for practice
White, I. R., Royston, P., & Wood, A. M. (2011) · Statistics in Medicine · doi:10.1002/sim.4067 · Cited by 9,792 · see citing works
Analysis of Incomplete Multivariate Data
Schafer, J. L. (1997) · doi:10.1201/9781439821862 · Cited by 6,012 · see citing works
Schafer, J. L. (1999) · Statistical Methods in Medical Research · doi:10.1177/096228029900800102 · Cited by 3,949 · see citing works
The Use of Single-Subject Research to Identify Evidence-Based Practice in Special Education
Horner, R. H., Carr, E. G., Halle, J., McGee, G., Odom, S., & Wolery, M. (2005) · Exceptional Children · doi:10.1177/001440290507100203 · Cited by 3,368 · see citing works
Multiple imputation of discrete and continuous data by fully conditional specification
van Buuren, S. (2007) · Statistical Methods in Medical Research · doi:10.1177/0962280206074463 · Cited by 2,827 · see citing works
How Many Imputations are Really Needed? Some Practical Clarifications of Multiple Imputation Theory
Graham, J. W., Olchowski, A. E., & Gilreath, T. D. (2007) · Prevention Science · doi:10.1007/s11121-007-0070-9 · Cited by 2,795 · see citing works
Hays, W. (1983) · Contemporary Psychology · doi:10.1037/022267 · Cited by 2,399 · see citing works
A comparison of inclusive and restrictive strategies in modern missing data procedures.
Collins, L. M., Schafer, J. L., & Kam, C.-M. (2001) · Psychological Methods · doi:10.1037/1082-989x.6.4.330 · Cited by 2,389 · see citing works
Principled missing data methods for researchers
Dong, Y., & Peng, C.-Y. J. (2013) · SpringerPlus · doi:10.1186/2193-1801-2-222 · Cited by 2,208 · see citing works
Self-citationA multivariate technique for multiply imputing missing values using a sequence of regression models
Raghunathan, T. E., Lepkowski, J. M., Hoewyk, J. V., & Solenberger, P. W. (2001) · Survey methodology · Cited by 1,981 · see citing works
Multiple Imputation for Multivariate Missing-Data Problems: A Data Analyst's Perspective
Schafer, J. L., & Olsen, M. K. (1998) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3304_5 · Cited by 1,518 · see citing works
Combining nonoverlap and trend for single-case research: Tau-U
Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011) · Behavior Therapy · doi:10.1016/j.beth.2010.08.006 · Cited by 1,468 · see citing works
Fully conditional specification in multivariate imputation
Van Buuren, S., Brand, J. P. L., Groothuis-Oudshoorn, C. G. M., & Rubin, D. B. (2006) · Journal of Statistical Computation and Simulation · doi:10.1080/10629360600810434 · Cited by 1,217 · see citing works
Nonparametric and Distribution-Free Methods for the Social Sciences.
Bassler, J. F., Marascuilo, L. A., & McSweeney, M. (1978) · Journal of the American Statistical Association · doi:10.2307/2286625 · Cited by 997 · see citing works
Bradley, J. V. (1978) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1978.tb00581.x · Cited by 743 · see citing works
Ordered Hypotheses for Multiple Treatments: A Significance Test for Linear Ranks
Page, E. B. (1963) · Journal of the American Statistical Association · doi:10.1080/01621459.1963.10500843 · Cited by 688 · see citing works
Single-case experimental designs: a systematic review of published research and current standards
Smith, J. D. (2012) · Psychological Methods · doi:10.1037/a0029312 · Cited by 630 · cited 3× · see citing works
“Because the importance of SCED research in establishing and confirming evidence-based practices has been increasingly affirmed (Horner et al., 2005; Shadish & Sullivan, 2011; Smith, 2012), it is imperative that SCED research be conducted at the highest level of rigor to yield credible and generalizable results.”
BackgroundInfluentialHorton, N., & Kleinman, K. (2007) · American Statistician · doi:10.1198/000313007x172556 · Cited by 476 · see citing works
Characteristics of single-case designs used to assess intervention effects in 2008
Shadish, W. R., & Sullivan, K. J. (2011) · Behavior Research Methods · doi:10.3758/s13428-011-0111-y · Cited by 338 · see citing works
Partially parametric techniques for multiple imputation
Nathaniel Schenker, A., & Taylor, J. M. G. (1996) · Computational Statistics & Data Analysis · doi:10.1016/0167-9473(95)00057-7 · Cited by 335 · see citing works
Multiple Imputation for the Fatal Accident Reporting System
Heitjan, D. F., & Little, R. J. A. (1991) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.2307/2347902 · Cited by 227 · see citing works
A Potential for Bias When Rounding in Multiple Imputation
Horton, N. J., Lipsitz, S. R., & Parzen, M. I. (2003) · The American Statistician · doi:10.1198/0003130032314 · Cited by 224 · see citing works
Robustness of a multivariate normal approximation for imputation of incomplete binary data
Bernaards, C. A., Belin, T. R., & Schafer, J. L. (2006) · Statistics in Medicine · doi:10.1002/sim.2619 · Cited by 191 · see citing works
Demirtaş, H., Freels, S. A., & Yucel, R. M. (2008) · Journal of Statistical Computation and Simulation · doi:10.1080/10629360600903866 · Cited by 153 · see citing works
Lambert, M. C., Cartledge, G., Heward, W. L., & Lo, Y. (2006) · Journal of Positive Behavior Interventions · doi:10.1177/10983007060080020701 · Cited by 140 · see citing works
Bottom-up analysis of single-case research designs
Parker, R. I., & Vannest, K. J. (2012) · Journal of Behavioral Education · doi:10.1007/s10864-012-9153-1 · Cited by 117 · cited 5× · see citing works
“For advanced readings, consider Little and Rubin (2002), Rubin (1987), Schafer (1997), SAS Institute Inc. (2015), and Mächler (2015).”
BackgroundMethodInfluentialThe Average Spearman Rank Correlation Coefficient
Lyerly, S. B. (1952) · Psychometrika · doi:10.1007/bf02288917 · Cited by 101 · see citing works
The Single-Case Reporting Guideline In BEhavioural Interventions (SCRIBE) 2016 Statement
Tate, R., Perdices, M., Rosenkoetter, U., Shadish, W., Vohra, S., Barlow, D., Horner, R., Kazdin, A., Kratochwill, T., McDonald, S., et al. (2016) · Neuropsychological Rehabilitation · doi:10.1080/09602011.2016.1190533 · Cited by 82 · see citing works
Twenty Nonparametric Statistics And Their Large Sample Approximations
Fahoome, G. F. (2002) · Journal of Modern Applied Statistical Methods · doi:10.22237/jmasm/1036110540 · Cited by 50 · see citing works
Smith, J. D., Borckardt, J. J., & Nash, M. R. (2011) · Behavior Therapy · doi:10.1016/j.beth.2011.10.001 · Cited by 35 · see citing works
Computing Tools for Implementing Standards for Single-Case Designs
Chen, L.-T., Peng, C., & Chen, M. (2015) · Behavior Modification · doi:10.1177/0145445515603706 · Cited by 25 · see citing works
Self-citationvan de Wiel, M. A., & Bucchianico, A. D. (2001) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(00)00166-x · Cited by 25 · see citing works
Algorithms for Assessing Intervention Effects in Single-Case Studies
Peng, C. J., & Chen, L. (2015) · Journal of Modern Applied Statistical Methods · doi:10.22237/jmasm/1430454060 · Cited by 5 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 12
- Ake, C. F. (2005). Rounding after multiple imputation with non-binary categorical covariates. In Proceedings of the thirtieth annual SAS® Users Group International conference (paper 112-30). SAS Institute Inc., Cary, NC. Retrieved from http://www2.sas.com/proceedings/sugi30/112-30.pdf
- Allison, P. D. (2005). Imputation of categorical variables with PROC MI. In Proceedings of the thirtieth annual SAS® Users Group International conference (paper 113-30). SAS Institute Inc., Cary, NC. Retrieved from http://www2.sas.com/proceedings/sugi30/113-30.pdf
- Busk, P. L., & Marascuilo, L. A. (1992). Statistical analysis in single-case research: Issues, procedures, and recommendations, with applications to multiple behaviors. In T. R. Kratochwill & J. R. Levin (Eds.), Single-case research design and analysis: New directions for psychology and education (pp. 159-186).
- Carpenter, J., & Goldstein, H. (2004). Multiple imputation using MLwiN. Multilevel Modelling Newsletter, 16(2), 9-18. Retrieved from http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new16- 2.pdf
- Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Diggle, P. J., Heagerty, P., Liang, K. Y., & Zeger, S. L. (1995). Analysis of longitudinal data. New York, NY: Oxford University Press.
- Enders, C. K. (2010). Applied missing data analysis. New York, NY: The Guilford Press.
- Graham, J. W., & Schafer, J. L. (1999). On the performance of multiple imputation for multivariate data with small sample size. In R. Hoyle (Ed.), Statistical strategies for small sample research (pp. 1-29). Thousand Oaks, CA: Sage.
- Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data (2nd ed.). New York, NY: Wiley.
- Marascuilo, L. A., & Busk, P. L. (1988). Combining statistics for multiple- baseline AB and replicated ABAB designs across subjects. Behavioral Assessment, 10(1), 1-28.
- Peng, C.-Y. J., Harwell, M., Liou, S.-M., Ehman, L. H. (2006). Advances in missing data methods and implications for educational research. In S. Sawilowsky (Ed.), Real data analysis (pp. 31-78).
- Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Needham Heights, MA: Allyn & Bacon.
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A Priori Justification for Effect Measures in Single-Case Experimental Designs
Manolov, R., Moeyaert, M., & Fingerhut, J. E. (2022) · Perspectives on Behavior Science · doi:10.1007/s40614-021-00282-2 · Cited by 53 · see citing works
Sathananthan, N., Dimech-Betancourt, B., Morris, E., Vicendese, D., Knox, L., Gillanders, D., Das Nair, R., & Wong, D. (2022) · Neuropsychological Rehabilitation · doi:10.1080/09602011.2021.1971094 · Cited by 31 · see citing works
Handling missing data in randomization tests for single-case experiments: A simulation study
De, T. K., Michiels, B., Tanious, R., & Onghena, P. (2020) · Behavior Research Methods · doi:10.3758/s13428-019-01320-3 · Cited by 31 · see citing works
Somer, E., Gische, C., & Miočević, M. (2022) · Evaluation & the Health Professions · doi:10.1177/01632787211071136 · Cited by 16 · see citing works
Michiels, B., Tanious, R., De, T. K., & Onghena, P. (2020) · Behavior Research Methods · doi:10.3758/s13428-019-01266-6 · Cited by 23 · see citing works
Assessing Intervention Effects in the Presence of Missing Scores
Peng, C.-Y. J., & Chen, L.-T. (2021) · Education Sciences · doi:10.3390/educsci11020076 · Cited by 21 · see citing works
Self-citationAccounting for baseline trends in intervention studies: Methods, effect sizes, and software
Chen, L., Wu, P.-J., & Peng, C. J. (2019) · Cogent Psychology · doi:10.1080/23311908.2019.1679941 · Cited by 19 · see citing works
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Friedel, J. E., Cox, A. D., Galizio, A., Swisher, M., Small, M. L., & Perez, S. (2021) · Perspectives on Behavior Science · doi:10.1007/s40614-021-00318-7 · Cited by 10 · see citing works
van Diest, S. L., Oudsten, B. L. D., Aaronson, N. K., Beaulen, A. A. J. M., Verboon, P., Aarnoudse, B., & van Lankveld, J. J. D. M. (2023) · Frontiers in Psychology · doi:10.3389/fpsyg.2023.1123821 · Cited by 17 · see citing works
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- Authors
- Peng, C.-Y. J., & Chen, L.-T.
- Affiliations
- University of Nevada, Reno (US)
- Venue
- Journal of Modern Applied Statistical Methods
- Publisher
- Scilight Press Pty Ltd
- Published
- 2018-06-07
- Volume
- 17
- Issue
- 1
- ISSN
- 1538-9472 (ISSN-L)
- OpenAlex
- W2805387321
- Cited by
- 22
- References
- 16
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 3 · 2023: 3 · 2022: 4 · 2021: 5 · 2020: 1 · 2019: 3
- FWCI
- 1.87
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Locations
- Journal of Modern Applied Statistical Methods (publishedVersion)
- Human Biology (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- missing data, single-case experimental design, multiple imputation, missing data imputation, statistical software
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