A Gradual Effects Model for Single-Case Designs

Single-case designs are a class of repeated measures experiments used to evaluate the effects of interventions for small or specialized populations, such as individuals with low-incidence disabilities. There has been growing interest in systematic reviews and syntheses of evidence from single-case designs, but there remains a need to further develop appropriate statistical models and effect sizes for data from the designs. We propose a novel model for single-case data that exhibit nonlinear time trends created by an intervention that produces gradual effects, which build up and dissipate over time. The model expresses a structural relationship between a pattern of treatment assignment and an outcome variable, making it appropriate for both treatment reversal and multiple baseline designs. It is formulated as a generalized linear model so that it can be applied to outcomes measured as frequency counts or proportions, both of which are commonly used in single-case research, while providing readily interpretable effect size estimates such as log response ratios or log odds ratios. We demonstrate the gradual effects model by applying it to data from a single-case study and examine the performance of proposed estimation methods in a Monte Carlo simulation of frequency count data.     

Neighborhood Effects on Nonword Visual Processing in a Language with Shallow Orthography

Neighborhood size and neighborhood frequency were orthogonally varied in two experiments on Italian nonwords. In Experiment 1, an inhibitory effect of neighborhood frequency on visual lexical decision was found: The presence of one high-frequency neighbor increased response latencies and error rates to nonwords. By contrast, no effect of neighborhood size and no neighborhood size x neighborhood frequency interaction were found. In Experiment 2, a facilitatory effect of neighborhood size on nonword naming was shown: Naming latencies were faster when nonwords had a large neighborhood. In the naming experiment, there was no effect of neighbors' frequency and no neighborhood size x neighborhood frequency interaction. An additional role for bigram frequency was found whereas syllable frequency did not give any independent contribution. These results further corroborate the view that, in a language with transparent orthography like Italian, despite a substantial contribution of sublexical print-to-sound mapping due to the language's high regularity/consistency, reading aloud of nonlexical material may benefit from the contribution of the lexical component.     

Orthographic contributions to perceived word center

We have a surprising tendency to misperceive the center of visually presented words (). To understand the origin of this bias, four experiments assessed the impact of letter font, letter size, and grapheme-phoneme convergences on perceived stimulus center. Fourteen observers indicated the perceived centers of words, pseudowords, consonant strings, and lines with a mouse cursor. Visual orthographic factors had no effect on perceived word center but grapheme-phoneme convergence did: Observers compensated for strong grapheme-phoneme asymmetries in the letter strings. These findings support the idea that the cognitive representation of words is spatially distorted as a result of lexical access mechanisms.     

Concurrent disjoint and reciprocal classification by Cebus apella in seriation tasks: evidence for hierarchical organization

We report the results of a 4-year-long study of capuchin monkeys (Cebus apella ) on concurrent three-way classification and linear size seriation tasks using explicit ordering procedures, requiring subjects to select icons displayed on touch screens rather than manipulate and sort actual objects into groups. The results indicate that C. apella is competent to classify nine items concurrently, first into three disjoint classes where class exemplars are identical to one another, then into three reciprocal classes which share common exemplar (size) features. In the final phase we compare the relative efficiency of executive control under conditions where both hierarchical and/or linear organization can be utilized. Whilst this shows a superiority of categorical based size seriation for a nine item test set suggesting an adaptive advantage for hierarchical over linear organization, Cebus nevertheless achieved high levels of principled linear size seriation with sequence lengths not normally achieved by children below the age of six years.     

Some conditions affecting the choice to cooperate or compete

Three experiments investigated conditions affecting the choice to cooperate or compete. Experiment I compared the effects first of an individual activity, then of a competitive task as an alternative to cooperation. For both comparisons, subjects could earn more by cooperating. Choice of competition, but not individual activity, was found to depend on the task choice contingencies. Competition predominated when both subjects could compete if either or both chose competition. Previously competitive pairs cooperated when both subjects could cooperate if either or both chose cooperation. Experiment II investigated the effects of differences in magnitude of the reinforcers for cooperating or competing. Choice between the two alternatives was manipulated in all pairs by varying reinforcer difference. Competition was chosen over cooperation only within the limits within which competition was potentially profitable. Experiment III replicated the findings of Experiment II using triads. Subjects in triads, however, were more likely to withdraw from the experiment. Thus, the data for pairs and triads suggest an orderly relation between reinforcer difference for cooperating or competing and task choice. Motivation of subjects to maximize relative gain by competing can be overridden by moderate reinforcer differences favoring cooperation.     

Using the simultaneous protocol to study equivalence class formation: the facilitating effects of nodal number and size of previously established equivalence classes

The emergence of equivalence classes in college students is unlikely when all baseline relations are trained concurrently and all probes for emergent relations are then introduced concurrently (the simultaneous protocol). This experiment showed how the number of nodes and the size of previously established equivalence classes enhanced the emergence of new equivalence classes under the simultaneous protocol. First, one-node three-, five-, or seven-member classes or three-node five- or seven-member classes were established with college students. A sixth group received no pretraining. Then, the simultaneous protocol was used to establish new three-node five-member equivalence classes with all students. The speed and variability with which the baseline relations were established in the simultaneous protocol were inverse functions of number of nodes in the previously established classes, but not of their size. The percentage of subjects who showed the emergence of new equivalence classes under the simultaneous protocol was a direct function of number of nodes and size of pretrained classes. The additional time spent for pretraining greatly reduced the total training time needed to produce individuals who showed the emergence of classes under the simultaneous protocol. The total time saved was a direct function of number of nodes and number of stimuli in the pretrained classes.     

Effects of food-pellet size on rate,latency, and topography of autoshaped key pecks and gapes in pigeons.

Four pigeons responded under autoshaping contingencies in which different conditional stimuli (red or green keylights) were associated with unconditional stimuli of different magnitudes (large or small food pellets) over successive trials within a session. Both topography (beak opening or gape) and strength (rates and latencies of key pecks and gapes) of responding during the conditional stimuli depended on the magnitude of the correlated unconditional stimulus. Key-peck and gape rates were higher and latencies were shorter in large-pellet trials than in small-pellet trials. Gape amplitudes varied directly with pellet size, although conditional and unconditional gapes were larger than either pellet. These findings were replicated when the key colors were presented either on one or two keys and after reversals of the color-size correlations. Because the unconditional stimulus was varied through pellet size, magnitude was not confounded with food-access duration or quality. These results demonstrate the effects of the magnitude of the unconditional stimulus, in that rates and latencies of both key pecks (which are directed movements toward the key) and gapes (which are independent of the bird''s position and key properties) varied with pellet size. Gape measures were unique in that two dimensions (response strength and topography) of a single response class varied simultaneously with magnitude.     

Meta-analysis for single-case consultation outcomes: Applications to research and practice

The application of meta-analysis holds much appeal for single-case consultation outcome research. We review a meta-analytic method for using within-study treatment effect sizes in reporting consultation outcomes. The strengths and limitations of traditional group design meta-analysis are examined. Various methods for analyzing single-case outcomes are discussed briefly, followed by an examination of the use of meta-analysis in single-case reviews across independent studies. Within-study meta-analytic results are presented that were derived from treatments implemented in consultations in natural settings. To conclude the article, an illustration is offered of a single-case data analysis display that incorporates meta-analytic results along with other indices of treatment outcome. Recommendations are provided for using meta-analytic methods to evaluate outcomes of single-case consultation treatment.     

A Comparison of ML,WLSMV, and Bayesian Methods for Multilevel Structural Equation Models in Small Samples: A Simulation Study

Multilevel structural equation models are increasingly applied in psychological research. With increasing model complexity, estimation becomes computationally demanding, and small sample sizes pose further challenges on estimation methods relying on asymptotic theory. Recent developments of Bayesian estimation techniques may help to overcome the shortcomings of classical estimation techniques. The use of potentially inaccurate prior information may, however, have detrimental effects, especially in small samples. The present Monte Carlo simulation study compares the statistical performance of classical estimation techniques with Bayesian estimation using different prior specifications for a two-level SEM with either continuous or ordinal indicators. Using two software programs (Mplus and Stan), differential effects of between- and within-level sample sizes on estimation accuracy were investigated. Moreover, it was tested to which extent inaccurate priors may have detrimental effects on parameter estimates in categorical indicator models. For continuous indicators, Bayesian estimation did not show performance advantages over ML. For categorical indicators, Bayesian estimation outperformed WLSMV solely in case of strongly informative accurate priors. Weakly informative inaccurate priors did not deteriorate performance of the Bayesian approach, while strong informative inaccurate priors led to severely biased estimates even with large sample sizes. With diffuse priors, Stan yielded better results than Mplus in terms of parameter estimates.