A generalized least squares regression approach for computing effect sizes in single-case research: application examples

A new method for deriving effect sizes from single-case designs is proposed. The strategy is applicable to small-sample time-series data with autoregressive errors. The method uses Generalized Least Squares (GLS) to model the autocorrelation of the data and estimate regression parameters to produce an effect size that represents the magnitude of treatment effect from baseline to treatment phases in standard deviation units. In this paper, the method is applied to two published examples using common single case designs (i.e., withdrawal and multiple-baseline). The results from these studies are described, and the method is compared to ten desirable criteria for single-case effect sizes. Based on the results of this application, we conclude with observations about the use of GLS as a support to visual analysis, provide recommendations for future research, and describe implications for practice.     

Paired comparison,triple comparison,and ranking experiments as generalized linear models,and their implementation on GLIM

A wide variety of paired comparison, triple comparison, and ranking experiments may be viewed as generalized linear models. These include paired comparison models based on both the Bradley-Terry and Thurstone-Mosteller approaches, as well as extensions of these models that allow for ties, order of presentation effects, and the presence of covariates. Moreover, the triple comparison model of Pendergrass and Bradley, as well as models for complete rankings of more than three items, can also be represented as generalized linear models. All such models can be easily fit by maximum likelihood, using the widely available GLIM computer package. Additionally, GLIM enables the computation of likelihood ratio statistics for testing many hypotheses of interest. Examples are presented that cover a variety of cases, along with their implementation on GLIM.     

Stress and alcohol use: moderating effects of gender, coping, and alcohol expectancies.

A stressor vulnerability model of stress-induced drinking was tested in a stratified random sample of 1,316 Black and White adult drinkers. Stressors were highly predictive of both alcohol use and drinking problems among men who relied on avoidant forms of emotion coping or held strong positive expectancies for alcohol's effects and accounted for more than 35% of the variance in alcohol use among the subgroup of men who were high in both vulnerability factors. In contrast, stressors were negatively related among men who were low in both and were unrelated among women regardless of their coping or expectancies. These findings suggest that tension reduction theories of alcohol use are overly broad and that individual characteristics must be considered to account for stress-related effects on alcohol use and abuse.     

More on least squares estimation of the transition matrix in a stationary first-order markov process from sample proportions data

Miller suggested ordinary least squares estimation of a constant transition matrix; Madansky proposed a relatively more efficient weighted least squares estimator which corrects for heteroscedasticity. In this paper an efficient generalized least squares estimator is derived which utilizes the entire covariance matrix of the distrubances. This estimator satisfies the condition that each row of the transition matrix must sum to unity. Madansky noted that estimates of the variances could be negative; a method for obtaining consistent non-negative estimates of the variances is suggested in this paper. The technique is applied to the hypothetical sample data used by Miller and Madansky.I am indebted to a referee for his thoughtful suggestions on content and style.     

Testing the significance of a correlation with nonnormal data: Comparison of Pearson, Spearman, transformation, and resampling approaches

It is well known that when data are nonnormally distributed, a test of the significance of Pearson's r may inflate Type I error rates and reduce power. Statistics textbooks and the simulation literature provide several alternatives to Pearson's correlation. However, the relative performance of these alternatives has been unclear. Two simulation studies were conducted to compare 12 methods, including Pearson, Spearman's rank-order, transformation, and resampling approaches. With most sample sizes (n ≥ 20), Type I and Type II error rates were minimized by transforming the data to a normal shape prior to assessing the Pearson correlation. Among transformation approaches, a general purpose rank-based inverse normal transformation (i.e., transformation to rankit scores) was most beneficial. However, when samples were both small (n ≤ 10) and extremely nonnormal, the permutation test often outperformed other alternatives, including various bootstrap tests. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Feasibility,acceptability, and validity of crowdsourcing for collecting longitudinal alcohol use data

Challenges to conducting longitudinal research include financial, time, and geographic constraints. An emerging sampling method positioned to address these concerns is crowdsourcing. This study evaluated the feasibility, acceptability, and validity of collecting intensive longitudinal alcohol use data with the crowdsourcing platform, Amazon.com 's Mechanical Turk (mTurk). Participants (N = 278) recruited from mTurk provided weekly recordings of daily alcohol and soda use over an 18‐week period. Construct and external validity was evaluated using generalized linear mixed models describing associations of between‐subject (e.g., alcohol use severity) and within‐subject (e.g., day of week) variables with prospectively collected alcohol and soda use. High response rates were observed across the 18‐week period demonstrating feasibility (64.1%‐86.8%). The design was acceptable with 94% of participants indicating they were satisfied with the procedures. Multilevel models supported construct and external validity by replicating expected associations, such as more frequent and heavier drinking by individuals with higher AUDIT scores and on weekends. These effects were specific to alcohol use and did not extend to soda consumption. These data support the feasibility, acceptability, and validity of using mTurk for intensive longitudinal data collection. Future studies may leverage this platform to generate large, geographically diverse samples for prospective behavioral analytic research.     

Social phobia: a comparison of specific and generalized subtypes and avoidant personality disorder.

The validity of the social phobia subtype distinction was examined in a large sample of carefully diagnosed social phobics (N = 89). Generalized and specific subtypes were diagnosed reliably, and the generalized subtype showed a consistent pattern of greater symptom severity than did the specific subtype. In addition, generalized social phobics with and without avoidant personality disorder were compared, and a difference was found for only 1 of 4 parameters. The results are discussed in terms of the validity of subtyping in social phobia and the diagnostic boundary between social phobia and avoidant personality disorder.     

Adolescent psychosocial maturity and alcohol use: quantitative and qualitative analysis of longitudinal data

Based on a psyschosocial developmental framework, this study used a mixed model design, including both quantitative and qualitative methods, to examine the relationship between adolescents' psychosocial maturity and their alcohol use. A sample of 1,198 10th-grade students (51% female) was surveyed and followed up two years later. Both concurrent and longitudinal findings indicated that the more psychosocially mature adolescents were less likely to drink heavily than those who showed less maturity. At age 15 this relationship was even stronger for those whose peers also drank. Further, at age 17, this linear relationship was more pronounced for those who drank less heavily at age 15. Of the three psychosocial competencies examined, the construct of personal meaning was more strongly related to adolescent alcohol use than were the constructs of interpersonal understanding and interpersonal skills. To illustrate this construct, two of the adolescents were interviewed, a girl and a boy, individually at the end of both school years. Thematic and developmental analyses of the interviews revealed individual variations in how the adolescents made meaning of their drinking; these encourage speculations that go beyond the general pattern found in the study.     

The linear regression line as a judgmental aid in visual analysis of serially dependent A-B time-series data

The purpose of this study was to investigate the effects of different types and magnitudes of serial dependence (first-order moving average and autoregression) and of linear regression lines within experimental phases on the agreement between results of visual and results of statistical data analyses. The stimulus material consisted of computer-simulated A-B-design data graphs. The time series were generated with a constant variance, varying degrees of treatment effects (changes in level), five conditions of serial dependency, and with or without linear regression lines. The material was presented to three groups of student raters (n₁=52, n₂=14, n₃=17) who rated the treatment effect in the graphs on a five-point scale. These ratings were compared with statistical results (time-series analyses). Each group had to interpret 70 graphs, 35 of which had regression lines. Data were analyzed by means of two three-factor and one four-factor ANOVA and by graphic display. The linear regression lines generally enhanced the agreement between the raters' estimations and the statistical results. Serial dependency also increased the agreement between the two analysis methods. However, with strong autoregression processes in the data, the raters tended to overestimate treatment effects relative to time-series analysis.Parts of this study were presented at the World Congress on Behavior Therapy, Washington, DC, December 11, 1983. The authors wish to express their appreciation to Christoph Bonk and Willi Ecker for their extensive collaboration in data analysis and for their assistance in carrying out the study.     

Fraternity and sorority involvement, social influences, and alcohol use among college students: a prospective examination.

This study used latent growth curve modeling to investigate whether the effects of gender and Greek involvement on alcohol use and problems over the first 2 years of college are best characterized by selection, socialization, or reciprocal influence processes. Three social influences (alcohol offers, social modeling, and perceived norms) were examined as potential mediators of these effects. Undergraduate participants (N = 388) completed self-report measures prior to enrollment and in the spring of their freshmen and sophomore years. Male gender and involvement in the Greek system were associated with greater alcohol use and problems prior to college. Both gender and Greek involvement significantly predicted increases in alcohol use and problems over the first 2 years of college. Cross-domain analyses provided strong support for a mediational role of each of the social influence constructs on alcohol use and problems prior to matriculation, and prematriculation social modeling and alcohol offers mediated relations between Greek involvement and changes in alcohol use over time. Findings suggest that students, particularly men, who affiliate with Greek organizations constitute an at-risk group prior to entering college, suggesting the need for selected interventions with this population, which should take place before or during the pledging process.     

Recent models and findings in visual backward masking: a comparison, review, and update

Visual backward masking not only is an empirically rich and theoretically interesting phenomenon but also has found increasing application as a powerful methodological tool in studies of visual information processing and as a useful instrument for investigating visual function in a variety of specific subject populations. Since the dual-channel, sustained-transient approach to visual masking was introduced about two decades ago, several new models of backward masking and metacontrast have been proposed as alternative approaches to visual masking. In this article, we outline, review, and evaluate three such approaches: an extension of the dual-channel approach as realized in the neural network model of retino-cortical dynamics (Ogmen, 1993), the perceptual retouch theory (Bachmann, 1984, 1994), and the boundary contour system (Francis, 1997; Grossberg & Mingolla, 1985b). Recent psychophysical and electrophysiological findings relevant to backward masking are reviewed and, whenever possible, are related to the aforementioned models. Besides noting the positive aspects of these models, we also list their problems and suggest changes that may improve them and experiments that can empirically test them.     

Deviant peer affiliations,crime and substance use: a fixed effects regression analysis

The present study was designed to assess the influence of deviant peer affiliations on crime and substance use in adolescence/young adulthood. Data were used from a 21-year longitudinal study of health, development, and adjustment of a birth cohort of 1,265 New Zealand children. Annual assessments of deviant peer affiliations were obtained for the period from age 14–21 years, together with measures of psychosocial outcomes including, violent crime, property crime, alcohol abuse, cannabis abuse, and nicotine dependence. Affiliating with deviant peers was found to be significantly associated with each of these outcomes (p < .0001). Statistical control for confounding by both fixed and time dynamic factors reduced the strength of association between deviant peer affiliations and outcome measures. Nevertheless, deviant peer affiliations remained significantly associated (p < .0001) with all outcomes. For violent/property crime, cannabis and alcohol abuse there was significant evidence of age-related variation in the strength of association with deviant peer affiliations, with deviant peer affiliations having greater influence on younger participants (14–15 years) than older participants (20–21 years). These results suggest that deviant peer affiliations are associated with increased rates of a range of adjustment problems in adolescence/young adulthood with deviant peer affiliations being most influential at younger ages.     

Testing models of the redundant-signals effect: a warning concerning the combination-rule regression analysis.

The redundant-signals effect is the observed RT advantage for trials presenting two or more targets, as compared with trials with only one target. Two general classes of parallel-processing model have been proposed to explain this effect: race models (e.g., Raab, 1962) and coactivation models (e.g., Miller, 1982). Various distributional analyses have been used in work aimed at discriminating between these two model classes. The present study reexamined one of these tests--the combination-rule regression analysis based on variable-criterion theory (Grice, Canham, & Boroughs, 1984)--by applying it to the data from two sets of simulated experiments. One set of simulations assumed coactivation; the other set assumed an independent race on redundant-target trials. Nearly identical combination-rule values were observed in the two sets of simulations. This finding shows that the combination rule of variable-criterion theory does not discriminate between models capable of explaining the redundant-signals effect. The implications of this finding are briefly discussed.     

Decision making under uncertainty: a comparison of simple scalability, fixed-sample, and sequential-sampling models

The purpose of this article is to investigate the learning and memory processes involved in decision making under uncertainty. In two different experiments, subjects were given a choice between a certain alternative that produced a single known payoff and an uncertain alternative that produced a normal distribution of payoffs. Initially this distribution was unknown, and in the first experiment it was learned through feedback from past decisions, whereas in the second experiment it was learned by observing sample outcomes. In the first experiment, a response deadline was used to limit the amount of time available for making a decision. In the second experiment, an observation cost was used to limit the number of samples that could be purchased. The mean and variance of the uncertain alternative and the value of the certain alternative were factorially manipulated to study their joint effects on choice probability, choice response time (Experiment 1), and number of observations purchased (Experiment 2). Algebraic-deterministic theories developed for decision making with simple gambles fail to explain the present results. Two new models are developed and tested--fixed- and sequential-sampling models--that attempt to describe the learning and memory processes involved in decision making under uncertainty.     

Attitudes,knowledge, and use of alcohol in university students

This paper investigated attitudes towards alcohol, knowledge of alcohol, parents drinking behaviour, reasons for drinking and television viewing habits varied in relation to actual drinking behaviour. A sample of 106 University students completed a questionnaire which enabled their classification as non, light, medium and heavy drinkers on the basis of their self-reported consumption levels. Results revealed 9% to be non-drinkers, 22% to be light, 38% to be moderate and 31% to be heavy. They also showed that alcohol drinking habits differed significantly with age, sex, smoking habits and in particular with parents drinking habits. Alcohol drinking habits also differed significantly with knowledge of alcohol, heavier drinkers being found to have a better overall knowledge, but reasons for drinking and attitudes towards drinking did not show any overall difference between the drinking habit categories. Finally, there was no indication that television viewing independently contributed to alcohol beliefs, knowledge, attitudes or habits. The results are discussed in terms of future research implications.