Motivation in action: A process model of L2 motivation

As part of a long-term project aimed at designing classroom interventions to motivate language learners, we have searched for a motivation model that could serve as a theoretical basis for the methodological applications. We have found that none of the existing models we considered were entirely adequate for our purpose for three reasons: (1) they did not provide a sufficiently comprehensive and detailed summary of all the relevant motivational influences on classroom behaviour; (2) they tended to focus on how and why people choose certain courses of action, while ignoring or playing down the importance of motivational sources of executing goal-directed behaviour; and (3) they did not do justice to the fact that motivation is not static but dynamically evolving and changing in time, making it necessary for motivation constructs to contain a featured temporal axis. Consequently, partly inspired by Heckhausen and Kuhl's 'Action Control Theory', we have developed a new 'Process Model of L2 Motivation', which is intended both to account for the dynamics of motivational change in time and to synthesise many of the most important motivational conceptualisations to date. In this paper we describe the main components of this model, also listing a number of its limitations which need to be resolved in future research.

Existence and wandering of bumps in a spiking neural network model

We study spatially localized states of a spiking neuronal network populated by a pulse coupled phase oscillator known as the lighthouse model. We show that in the limit of slow synaptic interactions in the continuum limit the dynamics reduce to those of the standard Amari model. For non-slow synaptic connections we are able to go beyond the standard firing rate analysis of localized solutions allowing us to explicitly construct a family of co-existing one-bump solutions, and then track bump width and firing pattern as a function of system parameters. We also present an analysis of the model on a discrete lattice. We show that multiple width bump states can co-exist and uncover a mechanism for bump wandering linked to the speed of synaptic processing. Moreover, beyond a wandering transition point we show that the bump undergoes an effective random walk with a diffusion coefficient that scales exponentially with the rate of synaptic processing and linearly with the lattice spacing.

Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.