Conditions Equivalent to Unit Representations of Ordered Relational Structures

This paper studies several concepts about subgroups of automorphisms of linearly ordered relational structures. In particular, it focuses on conditions that are equivalent to the translations (automorphisms with no fixed points plus the identity) forming a homogeneous, Archimedean ordered group under the asymptotic order. For the automorphisms of an ordered relational structure, these properties are equivalent to the structure having a numerical representation whose scale type lies between, but does not exclude, the ratio and interval types (Alper, 1987; Luce, 1987; Narens, 1981a, 1981b). One result of this paper (Theorem 5) is that for the automorphisms of an ordered relational structure the following necessary conditions for such a representation are also sufficient: the asymptotic order induced on the automorphisms is connected, the structure is homogeneous, the translations are Archimedean, and the dilations (i.e., automorphisms with fixed points) are Archimedean relative to all automorphisms. The last property is equivalent to there being at most one proper, nontrivial convex subgroup. Contrary to hope, these results do not seem to lead to a simpler proof than Alper's for the Dedekind complete case. The paper concludes with an examination of the structure of parallel automorphisms. Copyright 2001 Academic Press.     

Empirical comparisons of bilinear and nonbilinear utility theories

Several bilinear and nonbilinear utility theories are evaluated using individual data from 144 informants. The nonbilinear models are best for 67% of the informants. The nonrational property of duplex decomposition linking joint receipts and mixed gambles of gains and losses is more adequate than the rational link of general segregation for 73% of the informants. The correlations are very high and linear, even in the worst fitting case. The weighting functions are mostly inverse-S-shaped and for 84% of the informants are fit best by the class of functions proposed by D. Prelec. These fits were generally excellent, with a minimum correlation of.81, a maximum of.99, and an average of.97.     

An Application of the Complier Average Causal Effect Analysis to Examine the Effects of a Family Intervention in Reducing Illicit Drug Use among High‐Risk Hispanic Adolescents

The Complier Average Causal Effect (CACE) method has been increasingly used in prevention research to provide more accurate causal intervention effect estimates in the presence of noncompliance. The purpose of this study was to provide an applied demonstration of the CACE analytic approach to evaluate the relative effects of a family‐based prevention intervention, Familias Unidas, in preventing/reducing illicit drug use for those participants who received the intended dosage. This study is a secondary data analysis of a randomized controlled trial designed to evaluate the relative efficacy of Familias Unidas with high‐risk Hispanic youth. A total of 242 high‐risk Hispanic youth aged 12–17 years and their primary caregivers were randomized to either Familias Unidas or Community Practice and assessed at baseline, 6 months and 12 months postbaseline. CACE models were estimated with a finite growth mixture model. Predictors of engagement were included in the CACE model. Findings indicate that, relative to the intent‐to‐treat (ITT) analytic approach, the CACE analytic approach yielded stronger intervention effects among both initially engaged and overall engaged participants. The CACE analytic approach may be particularly helpful for studies involving parent/family‐centered interventions given that participants may not receive the intended dosage. Future studies should consider implementing the CACE analysis in addition to ITT analysis when examining the effects of family‐based prevention programs to determine whether, and the extent to which, the CACE analysis has more power to uncover intervention effects.     

Deconstructing the effect of self-directed study on episodic memory

Self-directed learning is often associated with better long-term memory retention; however, the mechanisms that underlie this advantage remain poorly understood. This series of experiments was designed to “deconstruct” the notion of self-directed learning, in order to better identify the factors most responsible for these improvements to memory. In particular, we isolated the memory advantage that comes from controlling the content of study episodes from the advantage that comes from controlling the timing of those episodes. Across four experiments, self-directed learning significantly enhanced recognition memory, relative to passive observation. However, the advantage for self-directed learning was found to be present even under extremely minimal conditions of volitional control (simply pressing a button when a participant was ready to advance to the next item). Our results suggest that improvements to memory following self-directed encoding may be related to the ability to coordinate stimulus presentation with the learner’s current preparatory or attentional state, and they highlight the need to consider the range of cognitive control processes involved in and influenced by self-directed study.     

Hormonal changes of intimate partner violence perpetrators in response to brief social contact with women

This study investigated whether men with a history of real-life aggressive, dominant behavior show increases in testosterone and cortisol levels after brief social contact with women. Furthermore, we tested the prediction that such changes in hormones would be larger than those observed previously in young male students. Sixty-seven male participants convicted of intimate partner violence (IPV) either had brief social contact with a female confederate (experimental condition) or a male confederate (control condition). We also performed meta-analyses to investigate whether IPV perpetrators' hormonal responses were larger than the typical responses of young male students in prior studies. All statistical analyses were preregistered. Change in testosterone did not differ across experimental conditions, and testosterone in the IPV perpetrators actually declined from baseline in the female confederate condition. Our meta-analysis showed that this testosterone decrease was different from the testosterone increase typically observed in young male students. The cortisol levels of IPV perpetrators did not change in response to contact with women. This result was consistent with our meta-analysis since young male students also did not experience a cortisol change in response to interactions with women. In sum, our findings provide no evidence that male IPV perpetrators exhibit larger hormone increases to brief interactions with women, although it is possible that the men in this sample did not perceive the social contact period as a courtship opportunity. These results suggest that hormone reactivity to social encounters may differ across subject populations and depend on how subjects perceive social situations within laboratory settings.     

Theory and tests of the conjoint commutativity axiom for additive conjoint measurement

The empirical study of the axioms underlying additive conjoint measurement initially focused mostly on the double cancellation axiom. That axiom was shown to exhibit redundant features that made its statistical evaluation a major challenge. The special case of double cancellation where inequalities are replaced by indifferences–the Thomsen condition–turned out in the full axiomatic context to be equivalent to the double cancellation property but without exhibiting the redundancies of double cancellation. However, it too has some undesirable features when it comes to its empirical evaluation, the chief among them being a certain statistical asymmetry in estimates used to evaluate it, namely two interlocked hypotheses and a single conclusion. Nevertheless, thinking we had no choice, we evaluated the Thomsen condition for both loudness and brightness and, in agreement with other lines of research, we found more support for conjoint additivity than not. However, we commented on the difficulties we had encountered in evaluating it. Thus we sought a more symmetric replacement, which as Gigerenzer and Strube (1983) first noted, is found in the conjoint commutativity axiom proposed by Falmagne (1976, who called it the “commutative rule”). It turns out that, in the presence of the usual structural and other necessary assumptions of additive conjoint measurement, we can show that conjoint commutativity is equivalent to the Thomsen condition, a result that seems to have been overlooked in the literature. We subjected this property to empirical evaluation for both loudness and brightness. In contrast to Gigerenzer and Strube (1983), our data show support for the conjoint commutativity in both domains and thus for conjoint additivity.     

Brightness of different hues is a single psychophysical ratio scale of intensity

Recent studies based on testable behavioral axioms have concluded that psychological scales of subjective intensive attributes involving the ears and eyes form ratio scales. These studies have shown that a certain commutativity of proportion property must hold under either successive increases or successive decreases, with all other independent dimensions fixed. However, until recently limited attention has been paid to whether such subjective intensity scales differ when a dimension independent of intensity, such as frequency or wavelength (e.g., pitch in audition, hue in vision) is varied. Using a simple and favorably tested theoretical model for global psychophysics, Luce, Steingrimsson, and Narens (2010) arrived at a necessary and sufficient cross-frequency, commutativity condition for there to exist a common intensity ratio scale. Here we show that brightness--already established to be a ratio-scalable dimension--and hue satisfy the same conditions.     

Predictions about bisymmetry and cross-modal matches from global theories of subjective intensities

The article first summarizes the assumptions of Luce (2004, 2008) for inherently binary (2-D) stimuli (e.g., the ears and eyes) that lead to a "p-additive," order-preserving psychophysical representation. Next, a somewhat parallel theory for unary (1-D) signals is developed for intensity attributes such as linear extent, vibration to finger, and money. The 3rd section studies the property of bisymmetry in these 2 cases. For the 2-D case and the nontrivial p-additive forms, Proposition 3 shows that bisymmetry implies commutativity of the presentations. Bisymmetry has been empirically well sustained, whereas commutativity has been rejected for loudness, brightness, and perceived contrast, thus implying that pure additivity must obtain in the 2-D context. By contrast, bisymmetry and commutativity are automatically satisfied by the p-additive 1-D theory. The 4th section explores the resulting complex of cross-modal predictions. For the additive 1-D case and the 2-D case, the predictions are power functions. For the nonadditive 1-D cases, other relations are predicted (see Table 2). Some parameter estimation issues are taken up in Appendices B and C.     

Memory for time and place contributes to enhanced confidence in memories for emotional events

Emotion strengthens the subjective sense of remembering. However, these confidently remembered emotional memories have not been found be more accurate for some types of contextual details. We investigated whether the subjective sense of recollecting negative stimuli is coupled with enhanced memory accuracy for three specific types of central contextual details using the remember/know paradigm and confidence ratings. Our results indicate that the subjective sense of remembering is indeed coupled with better recollection of spatial location and temporal context, but not higher memory accuracy for colored dots placed in the conceptual center of negative and neutral scenes. These findings show that the enhanced subjective recollective experience for negative stimuli reliably indicates objective recollection for spatial location and temporal context, but not for other types of details, whereas for neutral stimuli, the subjective sense of remembering is coupled with all the types of details assessed. Translating this finding to flashbulb memories, we found that, over time, more participants correctly remembered the location where they learned about the terrorist attacks on 9/11 than any other canonical feature. Likewise, participants' confidence was higher in their memory for location versus other canonical features. These findings indicate that the strong recollective experience of a negative event corresponds to an accurate memory for some kinds of contextual details but not for other kinds. This discrepancy provides further evidence that the subjective sense of remembering negative events is driven by a different mechanism than the subjective sense of remembering neutral events.