Analysis and meta-analysis of single-case designs: An introduction

The last 10 years have seen great progress in the analysis and meta-analysis of single-case designs (SCDs). This special issue includes five articles that provide an overview of current work on that topic, including standardized mean difference statistics, multilevel models, Bayesian statistics, and generalized additive models. Each article analyzes a common example across articles and presents syntax or macros for how to do them. These articles are followed by commentaries from single-case design researchers and journal editors. This introduction briefly describes each article and then discusses several issues that must be addressed before we can know what analyses will eventually be best to use in SCD research. These issues include modeling trend, modeling error covariances, computing standardized effect size estimates, assessing statistical power, incorporating more accurate models of outcome distributions, exploring whether Bayesian statistics can improve estimation given the small samples common in SCDs, and the need for annotated syntax and graphical user interfaces that make complex statistics accessible to SCD researchers. The article then discusses reasons why SCD researchers are likely to incorporate statistical analyses into their research more often in the future, including changing expectations and contingencies regarding SCD research from outside SCD communities, changes and diversity within SCD communities, corrections of erroneous beliefs about the relationship between SCD research and statistics, and demonstrations of how statistics can help SCD researchers better meet their goals.     

潜变量建模的贝叶斯方法

贝叶斯统计是统计学的两大流派之一,近年来贝叶斯统计在社会及行为科学领域日益流行。鉴于国内心理学界对贝叶斯统计应用仍不广泛,本文尝试从非技术性的角度对贝叶斯统计用于潜变量建模的过程进行简要介绍。主要涉及贝叶斯与频率论在统计学基本概念上的对比;贝叶斯统计的基本原理和分析过程。最后以一个验证性因子分析为例,简要介绍贝叶斯统计用于潜变量建模的分析过程。希望本文能为国内心理学者进行潜变量建模提供新的视角。     

Theoretically informed qualitative psychotherapy research: A primer

This paper presents an introduction to theoretically informed qualitative psychotherapy research (QPR). Although QPR researchers have traditionally remained silent on theory, we suggest this has resulted in an implicit and unacknowledged use of theory. We argue instead for a clear articulation of qualitative researchers' theory and outline how theory can be incorporated to inform the entire qualitative research process. This approach assumes the research problem is embedded in a clearly defined and articulated theoretical framework, which also informs data collection and data analysis. We outline how researchers can use explicit theoretical frameworks to inform research question formulation, data collection and data analysis and illustrate this with specific applications of the method in practice. We believe that starting from a declared theoretical framework sets up a dialogue between the research problem, the type of data required and their meaningful analysis and interpretation. This aims not only to achieve greater depth in the final product of research, but also to enhance its utility in terms of practice; it contributes to building, altering and differentiating theory; and it allows for greater transparency by openly articulating the theoretical framework that scaffolds the entirety of the research process.     

A Bayesian Model For The Estimation Of Latent Interaction And Quadratic Effects When Latent Variables Are Non-Normally Distributed

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent predictor variables are nonnormally distributed. The nonnormal predictor distribution is approximated by a finite mixture distribution. We conduct a simulation study that demonstrates the advantages of the proposed Bayesian model over contemporary approaches (Latent Moderated Structural Equations [LMS], Quasi-Maximum-Likelihood [QML], and the extended unconstrained approach) when the latent predictor variables follow a nonnormal distribution. The conventional approaches show biased estimates of the nonlinear effects; the proposed Bayesian model provides unbiased estimates. We present an empirical example from work and stress research and provide syntax for substantive researchers. Advantages and limitations of the new model are discussed.     

An introduction to Bayesian model selection for evaluating informative hypotheses

Most researchers have specific expectations concerning their research questions. These may be derived from theory, empirical evidence, or both. Yet despite these expectations, most investigators still use null hypothesis testing to evaluate their data, that is, when analysing their data they ignore the expectations they have. In the present article, Bayesian model selection is presented as a means to evaluate the expectations researchers have, that is, to evaluate so called informative hypotheses. Although the methodology to do this has been described in previous articles, these are rather technical and havemainly been published in statistical journals. The main objective of thepresent article is to provide a basic introduction to the evaluation of informative hypotheses using Bayesian model selection. Moreover, what is new in comparison to previous publications on this topic is that we provide guidelines on how to interpret the results. Bayesian evaluation of informative hypotheses is illustrated using an example concerning psychosocial functioning and the interplay between personality and support from family.     

A tutorial introduction to Bayesian models of cognitive development

We present an introduction to Bayesian inference as it is used in probabilistic models of cognitive development. Our goal is to provide an intuitive and accessible guide to the what, the how, and the why of the Bayesian approach: what sorts of problems and data the framework is most relevant for, and how and why it may be useful for developmentalists. We emphasize a qualitative understanding of Bayesian inference, but also include information about additional resources for those interested in the cognitive science applications, mathematical foundations, or machine learning details in more depth. In addition, we discuss some important interpretation issues that often arise when evaluating Bayesian models in cognitive science.     

Religion in Meaning Making and Boundary Work: Theoretical Explorations

Based on the articles brought together for this special issue, this article proposes a transversal analysis and theoretical elaboration of the question of the uses of religious elements for meaning making and boundary work. In order to do so, we will first propose a sociocultural psychological perspective to examine meaning making dynamics. Second, we will apply a boundary work perspective, as recently developed in the social sciences, on the organization of religious differences. The first considers religious elements as resources that can be used by people to orient themselves in time and the social space, to interpret and guide action, and to create new forms of life. The second approach proposes an analysis of uses of religious stuff in order to understand how boundaries between groups are created, transgressed or dissolved as well as to explore the link between religion and power. Our argument is that the articulation of these two approaches can itself offer a rich theoretical frame to apprehend religions in contemporary society.     

An introduction to Bayesian hierarchical models with an application in the theory of signal detection

Although many nonlinear models of cognition have been proposed in the past 50 years, there has been little consideration of corresponding statistical techniques for their analysis. In analyses with nonlinear models, unmodeled variability from the selection of items or participants may lead to asymptotically biased estimation. This asymptotic bias, in turn, renders inference problematic. We show, for example, that a signal detection analysis of recognition memory data leads to asymptotic underestimation of sensitivity. To eliminate asymptotic bias, we advocate hierarchical models in which participant variability, item variability, and measurement error are modeled simultaneously. By accounting for multiple sources of variability, hierarchical models yield consistent and accurate estimates of participant and item effects in recognition memory. This article is written in tutorial format; we provide an introduction to Bayesian statistics, hierarchical modeling, and Markov chain Monte Carlo computational techniques.     

Approximated adjusted fractional Bayes factors: A general method for testing informative hypotheses

Informative hypotheses are increasingly being used in psychological sciences because they adequately capture researchers’ theories and expectations. In the Bayesian framework, the evaluation of informative hypotheses often makes use of default Bayes factors such as the fractional Bayes factor. This paper approximates and adjusts the fractional Bayes factor such that it can be used to evaluate informative hypotheses in general statistical models. In the fractional Bayes factor a fraction parameter must be specified which controls the amount of information in the data used for specifying an implicit prior. The remaining fraction is used for testing the informative hypotheses. We discuss different choices of this parameter and present a scheme for setting it. Furthermore, a software package is described which computes the approximated adjusted fractional Bayes factor. Using this software package, psychological researchers can evaluate informative hypotheses by means of Bayes factors in an easy manner. Two empirical examples are used to illustrate the procedure.     

贝叶斯结构方程模型及其研究现状

在心理学研究中结构方程模型(Structural Equation Modeling, SEM)被广泛用于检验潜变量间的因果效应, 其估计方法有频率学方法(如, 极大似然估计)和贝叶斯方法两类。近年来由于贝叶斯统计的流行及其在结构方程建模中易于处理小样本、缺失数据及复杂模型等方面的优势, 贝叶斯结构方程模型发展迅速, 但其在国内心理学领域的应用不足。主要介绍了贝叶斯结构方程模型的方法基础和优良特性, 及几类常用的贝叶斯结构方程模型及其应用现状, 旨在为应用研究者介绍新的研究工具。     

The ABC’s of LGM: An Introductory Guide to Latent Variable Growth Curve Modeling

In recent years, we have witnessed an increase in the complexity of theoretical models that attempt to explain behavior from both contextual and developmental perspectives. This increase in the complexity of our theoretical propositions regarding behavior parallels recent methodological advances for the analysis of change. These new analysis techniques have fundamentally altered how we conceptualize and study change. Researchers have begun to identify larger frameworks to integrate our knowledge regarding the analysis of change. One such framework is latent growth modeling, perhaps the most important and influential statistical revolution to have recently occurred in the social and behavioral sciences. This study presents a basic introduction to a latent growth modeling approach for analyzing repeated measures data. Included is the specification and interpretation of the growth factors, primary extensions such as the analysis of growth in multiple populations, and structural models including both precursors of growth, and subsequent outcomes hypothesized to be influenced by the growth functions.     

We are All Bayesian,Everyone is Not a Bayesian

Medical research makes intensive use of statistics in order to support its claims. In this paper we make explicit an epistemological tension between the conduct of clinical trials and their interpretation: statistical evidence is sometimes discarded on the basis of an (often) underlined Bayesian reasoning. We suggest that acknowledging the potentiality of Bayesian statistics might contribute to clarify and improve comprehension of medical research. Nevertheless, despite Bayesianism may provide a better account for scientific inference with respect to the standard frequentist approach, Bayesian statistics is rarely adopted in clinical research. The main reason lies in the supposed subjective elements characterizing this perspective. Hence, we discuss this objection presenting the so-called Reference analysis, a formal method which has been developed in the context of objective Bayesian statistics in order to define priors which have a minimal or null impact on posterior probabilities. Furthermore, according to this method only available data are relevant sources of information, so that it resists the most common criticisms against Bayesianism.

     

Constraining bridges between levels of analysis: A computational justification for locally Bayesian learning

Different levels of analysis provide different insights into behavior: computational-level analyses determine the problem an organism must solve and algorithmic-level analyses determine the mechanisms that drive behavior. However, many attempts to model behavior are pitched at a single level of analysis. Research into human and animal learning provides a prime example, with some researchers using computational-level models to understand the sensitivity organisms display to environmental statistics but other researchers using algorithmic-level models to understand organisms’ trial order effects, including effects of primacy and recency. Recently, attempts have been made to bridge these two levels of analysis. Locally Bayesian Learning (LBL) creates a bridge by taking a view inspired by evolutionary psychology: Our minds are composed of modules that are each individually Bayesian but communicate with restricted messages. A different inspiration comes from computer science and statistics: Our brains are implementing the algorithms developed for approximating complex probability distributions. We show that these different inspirations for how to bridge levels of analysis are not necessarily in conflict by developing a computational justification for LBL. We demonstrate that a scheme that maximizes computational fidelity while using a restricted factorized representation produces the trial order effects that motivated the development of LBL. This scheme uses the same modular motivation as LBL, passing messages about the attended cues between modules, but does not use the rapid shifts of attention considered key for the LBL approximation. This work illustrates a new way of tying together psychological and computational constraints.     

贝叶斯统计方法的应用与现状

贝叶斯统计方法是心理学数据分析的热门方法。研究全面论述贝叶斯方法在心理学领域的应用与方向。现阶段贝叶斯方法以模拟研究为主,应用方向为心理学研究常用的项目反应理论、认知诊断、计算机自适应、结构方程模型。同时,评述发现贝叶斯方法正逐步被国内心理学研究者所接受。最后,文章讨论了当下贝叶斯统计在心理学研究中应用的局限性及可能的原因,建议统计学者开发界面友好的贝叶斯软件,并在心理学课程中加入贝叶斯知识。     

The Role of Randomization in Bayesian and Frequentist Design of Clinical Trial

A key role in inference is played by randomization, which has been extensively used in clinical trials designs. Randomization is primarily intended to prevent the source of bias in treatment allocation by producing comparable groups. In the frequentist framework of inference, randomization allows also for the use of probability theory to express the likelihood of chance as a source for the difference of end outcome. In the Bayesian framework, its role is more nuanced. The Bayesian analysis of clinical trials can afford a valid rationale for selective controls, pointing out a more limited role for randomization than it is generally accorded. This paper is aimed to offer a view of randomization from the perspective of both frequentist and Bayesian statistics and discussing the role of randomization also in theoretical decision models.

     

Experiments on Socio-Technical Systems: The Problem of Control

My aim is to question whether the introduction of new technologies in society may be considered to be genuine experiments. I will argue that they are not, at least not in the sense in which the notion of experiment is being used in the natural and social sciences. If the introduction of a new technology in society is interpreted as an experiment, then we are dealing with a notion of experiment that differs in an important respect from the notion of experiment as used in the natural and social sciences. This difference shows itself most prominently when the functioning of the new technological system is not only dependent on technological hardware but also on social ‘software’, that is, on social institutions such as appropriate laws, and actions of operators of the new technological system. In those cases we are not dealing with ‘simply’ the introduction of a new technology, but with the introduction of a new socio-technical system. I will argue that if the introduction of a new socio-technical system is considered to be an experiment, then the relation between the experimenter and the system on which the experiment is performed differs significantly from the relation in traditional experiments in the natural and social sciences. In the latter experiments it is assumed that the experimenter is not part of the experimental system and is able to intervene in and control the experimental system from the outside. With regard to the introduction of new socio-technical systems the idea that there is an experimenter outside the socio-technical system who intervenes in and controls that system becomes problematic. From that perspective we are dealing with a different kind of experiment.     

Bayesian power equivalence in latent growth curve models

Longitudinal studies are the gold standard for research on time-dependent phenomena in the social sciences. However, they often entail high costs due to multiple measurement occasions and a long overall study duration. It is therefore useful to optimize these design factors while maintaining a high informativeness of the design. Von Oertzen and Brandmaier (2013,Psychology and Aging, 28, 414) applied power equivalence to show that Latent Growth Curve Models (LGCMs) with different design factors can have the same power for likelihood-ratio tests on the latent structure. In this paper, we show that the notion of power equivalence can be extended to Bayesian hypothesis tests of the latent structure constants. Specifically, we show that the results of a Bayes factor design analysis (BFDA; Schönbrodt & Wagenmakers (2018,Psychonomic Bulletin and Review, 25, 128) of two power equivalent LGCMs are equivalent. This will be useful for researchers who aim to plan for compelling evidence instead of frequentist power and provides a contribution towards more efficient procedures for BFDA.     

An Introduction to Model Selection

This paper is an introduction to model selection intended for nonspecialists who have knowledge of the statistical concepts covered in a typical first (occasionally second) statistics course. The intention is to explain the ideas that generate frequentist methodology for model selection, for example the Akaike information criterion, bootstrap criteria, and cross-validation criteria. Bayesian methods, including the Bayesian information criterion, are also mentioned in the context of the framework outlined in the paper. The ideas are illustrated using an example in which observations are available for the entire population of interest. This enables us to examine and to measure effects that are usually invisible, because in practical applications only a sample from the population is observed. The problem of selection bias, a hazard of which one needs to be aware in the context of model selection, is also discussed. Copyright 2000 Academic Press.