Multilevel modeling in single-case studies with count and proportion data: A demonstration and evaluation.

Abstract

The outcomes in single-case experimental designs (SCEDs) are often counts or proportions. In our study, we provided a colloquial illustration for a new class of generalized linear mixed models (GLMMs) to fit count and proportion data from SCEDs. We also addressed important aspects in the GLMM framework including overdispersion, estimation methods, statistical inferences, model selection methods by detecting overdispersion, and interpretations of regression coefficients. We then demonstrated the GLMMs with two empirical examples with count and proportion outcomes in SCEDs. In addition, we conducted simulation studies to examine the performance of GLMMs in terms of biases and coverage rates for the immediate treatment effect and treatment effect on the trend. We also examined the empirical Type I error rates significance tests. Finally, we provided recommendations about how to make sound statistical decisions to use GLMMs based on the findings from simulation studies. Our hope is that this article will provide SCED researchers with the basic information necessary to conduct appropriate statistical analysis of count and proportion data in their own research and outline the future agenda for methodologist to explore the full potential of GLMMs to analyze or metaanalyze SCED data.

The value of generalized linear mixed models for data analysis in the plant sciences

“…There are several reasons to use GLMMs for the analysis of non-normal data, some of which were discussed in this paper, with many more details in several references (Littell et al, 2006;Bolker et al, 2009;Zuur et al, 2009;Gbur et al, 2012;Stroup, 2013;Brown and Prescott, 2015;Stroup et al, 2018;Gianinetti, 2020;Li et al, 2023;Ruıź et al, 2015Ruıź et al, , 2023. Perhaps the biggest argument is that one is better off matching the model to the data with a GLMM rather than changing (i.e., transforming) the data to match the model, as with a LMM (Gbur et al, 2012;Stroup, 2013).…”

“…Several other references are valuable for learning more about GLMMs and for conducting analyses of a wide range of datasets from different experimental designs (Littell et al, 2006;Bolker et al, 2009;Zuur et al, 2009;Gbur et al, 2012;Stroup, 2013;Brown and Prescott, 2015;Stroup et al, 2018;Gianinetti, 2020;Li et al, 2023;Ruıź et al, 2015Ruıź et al, , 2023. For those who wish to learn more theory, as well as applications, Stroup (2013) is an indispensable reference.…”

“…We focus on an example involving the percentage of plants infected by a particular disease in a field study, although the methods can be applied to any discrete data where percentages can be calculated. Gianinetti (2020) and Li et al (2023) are other excellent references for the GLMM-based analysis of data expressed as percentages. Readers should refer to Gbur et al (2012); Stroup (2013), and Ruıź et al (2023) for details on the analysis of continuous data using GLMMs.…”

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“…There are several reasons to use GLMMs for the analysis of non-normal data, some of which were discussed in this paper, with many more details in several references (Littell et al, 2006;Bolker et al, 2009;Zuur et al, 2009;Gbur et al, 2012;Stroup, 2013;Brown and Prescott, 2015;Stroup et al, 2018;Gianinetti, 2020;Li et al, 2023;Ruıź et al, 2015Ruıź et al, , 2023. Perhaps the biggest argument is that one is better off matching the model to the data with a GLMM rather than changing (i.e., transforming) the data to match the model, as with a LMM (Gbur et al, 2012;Stroup, 2013).…”

“…Several other references are valuable for learning more about GLMMs and for conducting analyses of a wide range of datasets from different experimental designs (Littell et al, 2006;Bolker et al, 2009;Zuur et al, 2009;Gbur et al, 2012;Stroup, 2013;Brown and Prescott, 2015;Stroup et al, 2018;Gianinetti, 2020;Li et al, 2023;Ruıź et al, 2015Ruıź et al, , 2023. For those who wish to learn more theory, as well as applications, Stroup (2013) is an indispensable reference.…”