Probabilistic choice models are often based on utility concepts which call for assessments by decision makers of available alternatives. These models assume that distinct utilities can be derived from the decision maker's expressed preferences. Such an assumption is generally valid if the decision maker can recognize arbitrarily small utility differences. If the decision maker is indifferent between the alternatives the corresponding utilities are expected to be similar. In this paper, the concept of minimum perceivable difference is introduced into the conventional binary logit model. It is postulated that two alternatives are perceived as different only if the absolute difference in their utilities exceeds a positive constant. For estimating the parameters of the new model a maximum likelihood technique is employed, and an empirical test of the model is conducted using data on travelers' choice of mode for accessing commuter rail service from Lindenwold (New Jersey) to downtown Philadelphia. The model predicts individuals' choices in a holdout sample significantly better than the conventional logit model.

Movement in response to music represents one of the natural social environments in which physical activity occurs. The study of music and movement, including dance, requires a careful, holistic consideration of many features, which may include music, physical activity, motor learning, social engagement, emotion, and creativity. The overarching goal of this manuscript is to examine qualitative characteristics of and individual responses to a music and movement intervention (Creatively Able) for children with Autism Spectrum Disorder (ASD). We provide a description of Creatively Able, illustrating how the program design and physical and social environment were informed by children’s needs and preferences in order to provide an enriched environment in which to promote multiple systems in children with ASD. Using data from two pilot studies with 20 children with ASD, we illustrate how researchers can use observational research methods to measure important aspects of the social environment (e.g., children’s engagement during intervention sessions) as well as engagement of potential underlying behavioral mechanisms (e.g., self-regulation) that might reduce clinical symptoms. We further illustrate how individual responses to intervention (e.g., improvements in behaviors or symptoms) can be studied in physically active interventions. Our pilot study results showed group-level reductions in Stereotyped and Compulsive behaviors of 8% and 4%, respectively; posthoc analysis revealed that there were substantial individual differences in children’s responses to the intervention. This research illustrates robust methods that can be applied to intervention research to improve our understanding of important features of interventions that might help promote development in various domains, including executive functions and self-regulation.

No abstract

For a marketing situation, mathematical models are developed expressing the relation between net revenue and the variables that affect it. These models are extensions of the ones discussed by Mills, and Krishnan and Gupta. Mills assumed that each competitor has only one controllable variable, viz., promotional effort. Krishnan and Gupta obtained equilibrium solutions for two competitors, each having two controllable variables. This paper deals with multicompetitors and discusses four models when the market potential is independent of both price and promotional effort and when it is dependent on either or both of the controllable variables.