A randomization test wrapper for synthesizing single-case experiments using multilevel models: A Monte Carlo simulation study. 2020

Bart Michiels, and René Tanious, and Tamal Kumar De, and Patrick Onghena
Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium.

Multilevel models (MLMs) have been proposed in single-case research, to synthesize data from a group of cases in a multiple-baseline design (MBD). A limitation of this approach is that MLMs require several statistical assumptions that are often violated in single-case research. In this article we propose a solution to this limitation by presenting a randomization test (RT) wrapper for MLMs that offers a nonparametric way to evaluate treatment effects, without making distributional assumptions or an assumption of random sampling. We present the rationale underlying the proposed technique and validate its performance (with respect to Type I error rate and power) as compared to parametric statistical inference in MLMs, in the context of evaluating the average treatment effect across cases in an MBD. We performed a simulation study that manipulated the numbers of cases and of observations per case in a dataset, the data variability between cases, the distributional characteristics of the data, the level of autocorrelation, and the size of the treatment effect in the data. The results showed that the power of the RT wrapper is superior to the power of parametric tests based on F distributions for MBDs with fewer than five cases, and that the Type I error rate of the RT wrapper is controlled for bimodal data, whereas this is not the case for traditional MLMs.

UI MeSH Term Description Entries
D009010 Monte Carlo Method In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993) Method, Monte Carlo
D011897 Random Allocation A process involving chance used in therapeutic trials or other research endeavor for allocating experimental subjects, human or animal, between treatment and control groups, or among treatment groups. It may also apply to experiments on inanimate objects. Randomization,Allocation, Random
D003198 Computer Simulation Computer-based representation of physical systems and phenomena such as chemical processes. Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D015233 Models, Statistical Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc. Probabilistic Models,Statistical Models,Two-Parameter Models,Model, Statistical,Models, Binomial,Models, Polynomial,Statistical Model,Binomial Model,Binomial Models,Model, Binomial,Model, Polynomial,Model, Probabilistic,Model, Two-Parameter,Models, Probabilistic,Models, Two-Parameter,Polynomial Model,Polynomial Models,Probabilistic Model,Two Parameter Models,Two-Parameter Model
D016008 Statistical Distributions The complete summaries of the frequencies of the values or categories of a measurement made on a group of items, a population, or other collection of data. The distribution tells either how many or what proportion of the group was found to have each value (or each range of values) out of all the possible values that the quantitative measure can have. Distribution, Statistical,Distributions, Statistical,Statistical Distribution
D055361 Multilevel Analysis The statistical manipulation of hierarchically and non-hierarchically nested data. It includes clustered data, such as a sample of subjects within a group of schools. Prevalent in the social, behavioral sciences, and biomedical sciences, both linear and nonlinear regression models are applied. Analyses, Multilevel,Analysis, Multilevel,Multilevel Analyses

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