Multilevel Reliability Measures of Latent Scores Within an Item Response Theory Framework

Abstract

This paper evaluated multilevel reliability measures in two-level nested designs (e.g., students nested within teachers) within an item response theory framework. A simulation study was implemented to investigate the behavior of the multilevel reliability measures and the uncertainty associated with the measures in various multilevel designs regarding the number of clusters, cluster sizes, and intraclass correlations (ICCs), and in different test lengths, for two parameterizations of multilevel item response models with separate item discriminations or the same item discrimination over levels. Marginal maximum likelihood estimation (MMLE)-multiple imputation and Bayesian analysis were employed to evaluate the accuracy of the multilevel reliability measures and the empirical coverage rates of Monte Carlo (MC) confidence or credible intervals. Considering the accuracy of the multilevel reliability measures and the empirical coverage rate of the intervals, the results lead us to generally recommend MMLE-multiple imputation. In the model with separate item discriminations over levels, marginally acceptable accuracy of the multilevel reliability measures and empirical coverage rate of the MC confidence intervals were found in a limited condition, 200 clusters, 30 cluster size, .2 ICC, and 40 items, in MMLE-multiple imputation. In the model with the same item discrimination over levels, the accuracy of the multilevel reliability measures and the empirical coverage rate of the MC confidence intervals were acceptable in all multilevel designs we considered with 40 items under MMLE-multiple imputation. We discuss these findings and provide guidelines for reporting multilevel reliability measures.     

A rational analysis of the acquisition of multisensory representations

How do people learn multisensory, or amodal, representations, and what consequences do these representations have for perceptual performance? We address this question by performing a rational analysis of the problem of learning multisensory representations. This analysis makes use of a Bayesian nonparametric model that acquires latent multisensory features that optimally explain the unisensory features arising in individual sensory modalities. The model qualitatively accounts for several important aspects of multisensory perception: (a) it integrates information from multiple sensory sources in such a way that it leads to superior performances in, for example, categorization tasks; (b) its performances suggest that multisensory training leads to better learning than unisensory training, even when testing is conducted in unisensory conditions; (c) its multisensory representations are modality invariant; and (d) it predicts ‘‘missing” sensory representations in modalities when the input to those modalities is absent. Our rational analysis indicates that all of these aspects emerge as part of the optimal solution to the problem of learning to represent complex multisensory environments.     

Hierarchical models of simple mechanisms underlying confidence in decision making

Choice confidence is a central measure in psychological decision research, often being reported on a probabilistic scale. Simple mechanisms that describe the psychological processes underlying choice confidence, including those based on error and confirmation biases, have typically received support via fits to data averaged over subjects. While averaged data ease model development, they can also destroy important aspects of the confidence data distribution. In this paper, we develop a hierarchical model of raw confidence judgments using the beta distribution, and we implement two simple confidence mechanisms within it. We use Bayesian methods to fit the hierarchical model to data from a two-alternative confidence experiment, and we use a variety of Bayesian tools to diagnose shortcomings of the simple mechanisms that are overlooked when applied to averaged data. Bugs code for estimating the models is also supplied.     

Synapses,Schizophrenia, and Civilization: What Made Homo Sapient?

Progress in technology has allowed dynamic research on the development of the human brain that has revolutionized concepts. Particularly, the notions of plasticity, neuronal selection, and the effects of afferent stimuli have entered into thinking about brain development. Here I focus on development from the age of four years to early adulthood, during which a 30 percent reduction in some brain synapses occurs that is out of proportion to changes in neuronal numbers. This corresponds temporally with changes in normal child behavior from the loose‐associative, almost schizoid, thinking and art of the four‐year‐old to the more trained, or disciplined, or acculturated—and restrained—personality of the young adult. I propose that the synaptic changes can best be thought of as a winnowing process likely subject to environmental influences. Acquisition of language and the ability to link linguistic cognition to the plastic development of the brain provide a potentially powerful means of explaining the evolutionally explosive development of human cognition and culture. Schizophrenia, a disease that can be envisioned as representing a derangement of synaptic maturation, may provide an entry into the search for genes controlling the processes mediating the unprecedented development of Homo sapiens over the past 40,000 to 70,000 years. The recently completed mapping of the genome of the chimpanzee provides a new frame of reference that may speed the search.     

A Duet for one

This paper considers communication in terms of inference about the behaviour of others (and our own behaviour). It is based on the premise that our sensations are largely generated by other agents like ourselves. This means, we are trying to infer how our sensations are caused by others, while they are trying to infer our behaviour: for example, in the dialogue between two speakers. We suggest that the infinite regress induced by modelling another agent – who is modelling you – can be finessed if you both possess the same model. In other words, the sensations caused by others and oneself are generated by the same process. This leads to a view of communication based upon a narrative that is shared by agents who are exchanging sensory signals. Crucially, this narrative transcends agency – and simply involves intermittently attending to and attenuating sensory input. Attending to sensations enables the shared narrative to predict the sensations generated by another (i.e. to listen), while attenuating sensory input enables one to articulate the narrative (i.e. to speak). This produces a reciprocal exchange of sensory signals that, formally, induces a generalised synchrony between internal (neuronal) brain states generating predictions in both agents. We develop the arguments behind this perspective, using an active (Bayesian) inference framework and offer some simulations (of birdsong) as proof of principle.