Regime-Switching Bivariate Dual Change Score Model

Mixture structural equation model with regime switching (MSEM-RS) provides one possible way of representing over-time heterogeneities in dynamic processes by allowing a system to manifest qualitatively or quantitatively distinct change processes conditional on the latent “regime” the system is in at a particular time point. Unlike standard mixture structural equation models such as growth mixture models, MSEM-RS allows individuals to transition between latent classes over time. This class of models, often referred to as regime-switching models in the time series and econometric applications, can be specified as regime-switching mixture structural equation models when the number of repeated measures involved is not large. We illustrate the empirical utility of such models using one special case—a regime-switching bivariate dual change score model in which two growth processes are allowed to manifest regime-dependent coupling relations with one another. The proposed model is illustrated using a set of longitudinal reading and arithmetic performance data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 study (ECLS-K; U.S. Department of Education, National Center for Education Statistics, 2010).     

Necessity is the mother of invention: avoidance motivation stimulates creativity through cognitive effort

Compared with approach motivation, avoidance motivation has often been related to reduced creativity because it evokes a relatively inflexible processing style. This finding seems inconsistent with the dual pathway to creativity model, which poses that both flexible and persistent processing styles can result in creative output. Reconciling these inconsistencies, the authors hypothesized that avoidance-motivated individuals are not unable to be creative, but they have to compensate for their inflexible processing style by effortful and controlled processing. Results of 5 experiments revealed that when individuals are avoidance motivated, they can be as creative as when they are approach motivated, but only when creativity is functional for goal achievement, motivating them to exert the extra effort (Experiments 1-4). The authors found that approach motivation was associated with cognitive flexibility and avoidance motivation with cognitive persistence (Experiment 1), that creative tasks are perceived to be more difficult by avoidance- than by approach-motivated individuals, and that avoidance-motivated individuals felt more depleted after creative performance (Experiment 2a, 2b, and 3). Finally, creative performance of avoidance-motivated individuals suffered more from a load on working memory (Study 4). The present results suggest that for people focusing on avoiding negative outcomes, creative performance is difficult and depleting, and they only pay these high cognitive costs when creativity helps achieving their goals.     

Understanding choice utterances

When individuals offer choices, they intend them to be mandatory (requiring action) or permissive (not requiring action), and they intend them to be open (allowing the choice of both options) or closed (not allowing the choice of both options). In two studies subjects were presented with sets of syntactically equivalent disjunctive sentences with varying content designed to represent four patterns of permitted choice. The research indicates that individuals distinguish four distinct uses of “or” in deontic contexts, and that individuals more often judge choices as mandatory than permissive. The research also compared responses to questions about choice giver intent and receiver choice. The data indicate that when judging intent, individuals are inclined to understand some choices to be permissive. However, when judging what action they might take as choice receiver, subjects tend to regard action to be mandatory. It appears that although people have some facility in assessing a permission giver's intent, they often apply a more restrictive rule to themselves than is required by the choice giver.     

Discrete dynamic choice: An extension of the choice models of thurstone and luce

The present paper deals with the extension of two well-known static discrete choice theories to the dynamic situation in which individuals make choices at several points in (continuous) time. A dynamic version of Luce's Axiom, “independence from irrelevant alternatives”, is proposed and some of its implications are derived. In the static case Yellott (J. Math. Psych. 1977, 15, 109–146) and others have demonstrated that an independent random utility model generated from the extreme value distribution exp(?e^?ax?b) becomes equivalent to Luce's Axiom. Yellott also introduced an axiom called “invariance under uniform expansions of the choice set”, and he proved that within the class of random utility models with independent identically distributed utilities (apart from a location shift) this axiom is equivalent to Luce's Axiom. These results are extended to the dynamic situation and it is shown that if the utility processes are expressed by so-called extremal processes the corresponding choice model is Markovian. A nonstationary generalization is proposed which is a substantial interest in applications where the parameters of the choice process are influenced by previous choice experience or by time-varying exogenous variables. In particular, it is demonstrated that the nonstationary model is Markovian if and only if the joint choice probabilities at two points in time have a particular form. Thus, the paper provides a rationale for applying a specific class of Markov models as the point of departure when modelling mobility processes that involve individual discrete decisions over time.     

预测视角下双因子模型与高阶模型的模拟比较

双因子模型和高阶因子模型,作为既有全局因子又有局部因子的两个竞争模型,在研究中得到了广泛应用。本文采用Monte Carlo模拟方法,在模型拟合比较的基础上,比较了效标分别为外显变量和内潜变量时,两个模型在各种负荷水平下预测准确度的差异。结果发现,两种模型在拟合效果方面无显著差异;但在预测效度方面,当效标为显变量时,两个模型的结构系数估计值皆为无偏估计;而效标为潜变量时,高阶因子模型表现优于双因子模型:高阶因子模型的结构系数为无偏估计,双因子模型的结构系数估计值则在50%左右的情况下存在偏差。     

Predicting binary choices from probability phrase meanings

The issues of how individuals decide which of two events is more likely and of how they understand probability phrases both involve judging relative likelihoods. In this study, we investigated whether derived scales representing probability phrase meanings could be used within a choice model to predict independently observed binary choices. If they can, this simultaneously provides support for our model and suggests that the phrase meanings are measured meaningfully. The model assumes that, when deciding which of two events is more likely, judges take a single sample from memory regarding each event and respond accordingly. The model predicts choice probabilities by using the scaled meanings of individually selected probability phrases as proxies for confidence distributions associated with sampling from memory. Predictions are sustained for 34 of 41 participants but, nevertheless, are biased slightly low. Sequential sampling models improve the fit. The results have both theoretical and applied implications.     

Automatic and conscious processing in retarded and nonretarded adolescents

Educable mentally retarded and nonretarded adolescents participated in incidental learning tasks that emphasized the utilization of processes that were consciously controlled but not deliberately aimed at memory (Experiment 1). Retarded individuals' performance on a standard recognition test was equivalent to that of nonretarded subjects following phonetic encoding and nonstrategic encoding, but was deficient following semantic encoding. Retarded subjects also demonstrated a lower level of performance on a rhyme recognition task. In Experiment 2, retarded subjects provided a pattern of responding identical to that of nonretarded subjects on a picture-word interference task designed to assess automatic processing. The two groups produced equivalent levels of semantic activation. It was argued that the results of the two experiments indicate deficient semantic processing on the part of retarded individuals relative to that of nonretarded individuals that cannot be accommodated by a structural-deficiency model, a developmental-lag model, or a hypothesis that predicts intelligence-related differences only when the task involves the use of deliberate mnemonic strategies.     

Discrimination nets as psychological models

Simulations of human cognitive processes often employ discrimination nets to model the access of permanent memory. We consider two types of discrimination nets—EPAM and positive-proper-only nets—and argue that they have insufficient psychological validity. Their deficiencies arise from negative properties, insufficient sensitivity to the discriminativeness of properties, extreme sensitivity to missing or incorrect properties, inefficiency in representing multiple knowledge domains, and seriality. We argue that these deficiencies stem from a high degree of test contingency in utilizing property information during acquisition and memory search. Discrimination nets are compared to other models that have less or no test contingency (e.g., PANDEMONIUM) and that thereby avoid the problems of discrimination nets. We propose that understanding test contingency and discovering psychologically valid ways to implement it will be central to understanding and simulating memory indexing in human cognition.     

A simple multivariate probabilistic model for preferential and triadic choices

Multidimensional probabilistic models of behavior following similarity and choice judgements have proven to be useful in representing multidimensional percepts in Euclidean and non-Euclidean spaces. With few exceptions, these models are generally computationally intense because they often require numerical work with multiple integrals. This paper focuses attention on a particularly general triad and preferential choice model previously requiring the numerical evaluation of a 2n-fold integral, wheren is the number of elements in the vectors representing the psychological magnitudes. Transforming this model to an indefinite quadratic form leads to a single integral. The significance of this form to multidimensional scaling and computational efficiency is discussed.The authors would like to thank Jean-Claude Falmagne and Norman Johnson for suggestions and advice concerning quadratic forms.     

Mathematical models and the experimental analysis of behavior

The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make equally accurate predictions for a large body of data. In such cases, it is important to find and investigate situations for which the competing models make different predictions because, unless two models are actually mathematically equivalent, they are based on different assumptions about the psychological processes that underlie an observed behavior. Mathematical models developed in basic behavioral research have been used to predict and control behavior in applied settings, and they have guided research in other areas of psychology. A good mathematical model can provide a common framework for understanding what might otherwise appear to be diverse and unrelated behavioral phenomena. Because psychologists vary in their quantitative skills and in their tolerance for mathematical equations, it is important for those who develop mathematical models of behavior to find ways (such as verbal analogies, pictorial representations, or concrete examples) to communicate the key premises of their models to nonspecialists.     

On Nonequivalence of Several Procedures of Structural Equation Modeling

The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure is correctly specified, the four procedures are asymptotically equivalent. However, this equivalence is often used when models are not correctly specified. This short paper clarifies conditions under which these procedures are not asymptotically equivalent. Analytical results indicate that, when a model is not correct, two factors contribute to the nonequivalence of the different procedures. One is that the estimated covariance matrices by different procedures are different, the other is that they use different scales to measure the distance between the sample covariance matrix and the estimated covariance matrix. The results are illustrated using real as well as simulated data. Implication of the results to model fit indices is also discussed using the comparative fit index as an example. The work described in this paper was supported by a grant from the Research Grants Council of Hong Kong Special Administrative Region (Project No. CUHK 4170/99M) and by NSF grant DMS04-37167.     

The self-attention-induced feedback loop and social facilitation

It has been proposed that self-directed attention leads to the engagement of a cybernetic feedback loop, by which discrepancies between present behavior and a standard of comparison are reduced. This analysis is applied to performance facilitation effects, which are more typically explained in terms of drive theories. Though these two approaches to motivation make similar behavioral predictions in this context, they assume different mediating states. Support is noted for the assumptions that mirror presence and audience presence induce self-focus, and that they lead to comparison with salient behavioral standards. Support for the assumption that these manipulations increase arousal is also reviewed, and is challenged on methodological grounds. The attentional analysis is used to derive predictions regarding changes in physiological state over the course of a typical social facilitation procedure. An experiment is reported which confirmed these predictions. Discussion centers on how to interpret physiological changes in terms that are compatible with control theory, how to account for social impairment phenomena in terms of the present model, and the conceptual relationship between mirror presence and audience presence as experimental manipulations.     

On the Relation Between the Linear Factor Model and the Latent Profile Model

The relationship between linear factor models and latent profile models is addressed within the context of maximum likelihood estimation based on the joint distribution of the manifest variables. Although the two models are well known to imply equivalent covariance decompositions, in general they do not yield equivalent estimates of the unconditional covariances. In particular, a 2-class latent profile model with Gaussian components underestimates the observed covariances but not the variances, when the data are consistent with a unidimensional Gaussian factor model. In explanation of this phenomenon we provide some results relating the unconditional covariances to the goodness of fit of the latent profile model, and to its excess multivariate kurtosis. The analysis also leads to some useful parameter restrictions related to symmetry.     

Job-decision inconsistencies involving social comparison information: the role of dominating alternatives

Previous research on joint versus separate preference reversals has demonstrated that individuals focus on social comparison information when they are evaluating a single option but focus on absolute salary when they are considering more than 1 option. Study 1 demonstrates that social comparison information is important in multiple option scenarios when an option favorable on social comparison dominates an inferior, 3rd alternative. Study 2 examines why dominating alternatives are so attractive by investigating the role that the value-shift, weight-change, and emergent-value models play in explaining the pattern of results obtained in Study 1. Results provide support for the value-shift and emergent-value models and further suggest that these 2 models may be interrelated, with justification (emergent-value model) mediating the relationship between the attractiveness of the attributes (value-shift model) and the attractiveness of the dominating alternative.     

Action Emulation between Canonical Models

In this paper we investigate Kripke models, used to model knowledge or belief in a static situation, and action models, used to model communicative actions that change this knowledge or belief. The appropriate notion for structural equivalence between modal structures such as Kripke models is bisimulation: Kripke models that are bisimilar are modally equivalent. We would like to find a structural relation that can play the same role for the action models that play a prominent role in information updating. Two action models are equivalent if they yield the same results when updating Kripke models. More precisely, two action models are equivalent if it holds for all Kripke models that the result of updating with one action model is bisimilar to the result of updating with the other action model. We propose a new notion of action emulation that characterizes the structural equivalence of the important class of canonical action models. Since every action model has an equivalent canonical action model, this gives a method to decide the equivalence of any pair of action models. We also give a partial result that holds for the class of all action models. Our results extend the work in van Eijck et al. (Synthese 185(1):131–151, 2012).     

Word informativity influences acoustic duration: Effects of contextual predictability on lexical representation

Language-users reduce words in predictable contexts. Previous research indicates that reduction may be stored in lexical representation if a word is often reduced. Because representation influences production regardless of context, production should be biased by how often each word has been reduced in the speaker’s prior experience. This study investigates whether speakers have a context-independent bias to reduce low-informativity words, which are usually predictable and therefore usually reduced. Content word durations were extracted from the Buckeye and Switchboard speech corpora, and analyzed for probabilistic reduction effects using a language model based on spontaneous speech in the Fisher corpus. The analysis supported the hypothesis: low-informativity words have shorter durations, even when the effects of local contextual predictability, frequency, speech rate, and several other variables are controlled for. Additional models that compared word types against only other words of the same segmental length further supported this conclusion. Words that usually appear in predictable contexts are reduced in all contexts, even those in which they are unpredictable. The result supports representational models in which reduction is stored, and where sufficiently frequent reduction biases later production. The finding provides new evidence that probabilistic reduction interacts with lexical representation.     

Heuristic and analytic processes in mental models for conditionals: An integrative developmental theory

This article presents a developmental dual-process theory of the understanding of conditionals that integrates Evans’ heuristic–analytic theory within the revised mental model theory of conditional proposed by Barrouillet, Gauffroy, and Lecas (2008). According to this theory, the interpretation of a conditional sentence is driven by unconscious and implicit heuristic processes that provide individuals with an initial representation that captures its meaning by representing the cases that make it true. This initial model can be enriched with additional models (a process named fleshing out within the mental model theory) through the intervention of conscious and demanding analytic processes. Being optional, these processes construct representations of cases that are only compatible with the conditional, leaving its truth-value indeterminate when they occur. Because heuristic processes are relatively immune to developmental changes, while analytic processes strongly develop with age, the initial model remains stable through development whereas the number of additional models that can be constructed increases steadily. Thus, the dual-process mental model theory predicts in which cases conditionals will be deemed true, indeterminate, or false and how these cases evolve with age. These predictions were verified in children, adolescents and adults who were asked to evaluate the truth value and the probability of several types of conditionals. The results reveal a variety of developmental trajectories in the way different conditionals are interpreted, which can all be accounted for by our revised mental model theory.     

MODELING RELATIONS

In the ordinary way of representing relations, the order of the relata plays a structural role, but in the states themselves such an order often does not seem to be intrinsically present. An alternative way to represent relations makes use of positions for the arguments. This is no problem for the love relation, but for relations like the adjacency relation and cyclic relations, different assignments of objects to the positions can give exactly the same states. This is a puzzling situation. The question is what is the internal structure of relations? Is the use of positions still justified, and if so, what is their ontological status? In this paper mathematical models for relations are developed that provide more insight into the structure of relations “out there” in the real world.