A comparison of a novel application of hierarchical linear modeling and nonparametric analysis for single-subject designs.

Abstract

Behavioral researchers commonly use single-subject experimental designs to evaluate treatment effects. Several methods of data analysis are used, each with its own set of methodological strengths and limitations. Visual inspection is a common method to assess variability, level, and trend both within and between conditions. To quantify treatment outcomes for particular participants, researchers use nonparametric indices such as percentage of nonoverlapping data points (PND) and percentage of data points exceeding the median (PEM). Increasing attention has been directed to parametric methods for analyzing single-subject time series data analysis, including the estimation of individual growth curves and related functions via hierarchical linear modeling (HLM). The present study compares and contrasts the use of PND, PEM, and HLM for estimating individual treatment effects. The example in question utilized a clinical data set involving 36 obsessive-compulsive behaviors across 17 participants. The specific implementation of the HLM model is discussed in detail to illustrate applicability to single-subject designs. Strengths and weaknesses of each method are discussed, including the accessibility of PEM-PND and the robust and sensitive indices provided by the individual growth-curve model. Overall, consistent effects for the treatment phase were demonstrated, with moderate agreement among methods. This application also shows how treatment effects can be modeled and provides 1 example of how individual differences in treatment can be characterized across participants within a study. In this case, the treatment appeared equally effective across the age range of participants, with age not being correlated with individual estimates of treatment response.

Behavior stability and individual differences in Pavlovian extended conditioning

“…When averaging, information on individuals is usually lost. This concern is not new and it was voiced already in early days of the discipline (Hayes, 1953;Merrill, 1931;Sidman, 1952) and retaken into consideration in recent years (Blanco and Moris, 2017;Gallistel, 2012;Gallistel et al, 2004;Glautier, 2013;Jaksic et al, 2018;Young, 2018; see especially the refreshing point of view of Smith and Little, 2018). As Sidman (1952) pessimistically put it, "[i]ntra-organism variability may be so great as to obscure any lawful relation."…”

Beyond Rescorla–Wagner: the Ups and Downs of Learning

“…The role of individual differences and response variations in conditioning models has long been of concern (Hayes, 1953;Merrill, 1931;Sidman, 1952, for initial publications;Blanco and Moris, 2018;Calcagni et al, 2020;Gallistel, 2012;Gallistel, Fairhurst, and Balsam, 2004;Glautier, 2013;Jaksic et al, 2018;Mazur and Hastie, 1978;Smith and Little, 2018;Young, 2018, for recent ones). These differences have provoked a range of attitudes as diverse as discarding them as statistical errors around a clean theoretical learning curve, or taking them as proof that theoretical models are mere artifacts.…”

Behavior Stability and Individual Differences in Pavlovian Extended Conditioning

“…When averaging, information on individuals is usually lost. This concern is not new and it was voiced already in early days of the discipline (Merrill, 1931;Sidman, 1952;Hayes, 1953) and retaken into consideration in recent years (Gallistel et al, 2004;Gallistel, 2012;Glautier, 2013;Blanco and Moris, 2018;Jaksic et al, 2018;Young, 2018; see especially Smith and Little, 2018). As Sidman (1952) pessimistically put it, "[i]ntra-organism variability may be so great as to obscure any lawful relation."…”