Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients

The method of finding the maximum likelihood estimates of the parameters in a multivariate normal model with some of the component variables observable only in polytomous form is developed. The main stratagem used is a reparameterization which converts the corresponding log likelihood function to an easily handled one. The maximum likelihood estimates are found by a Fletcher-Powell algorithm, and their standard error estimates are obtained from the information matrix. When the dimension of the random vector observable only in polytomous form is large, obtaining the maximum likelihood estimates is computationally rather labor expensive. Therefore, a more efficient method, the partition maximum likelihood method, is proposed. These estimation methods are demonstrated by real and simulated data, and are compared by means of a simulation study.     

Structure of RIASEC scores in China: A structural meta-analysis

A structural meta-analysis was conducted to evaluate the fit of four different representations of the relations among RIASEC types, [13] and [14] circular order model, Gati’s (1991) three-group partition model, Rounds and Tracey’s (1996) alternative three-group partition model, and Liu and Rounds’ (2003) modified octant model, on 29 RIASEC correlation matrices collected from Chinese participants. The randomization test of hypothesized order relations was used to evaluate model fit. The results indicated that Holland’s model had the worst fit and was lower than it is fit in US samples; while Gati’s and Rounds and Tracey’s models had best fit. The fit of the Liu and Rounds’ model lay between the fit of Holland’s model and the other models. There was minimal difference in this ordering of model fit across instrument, age, gender and region. These results are interpreted with respect to differences in Chinese culture relative to the US.     

Selfish strategies develop in social problem situations in chimpanzee (Pan troglodytes) mother–infant pairs

Humans employ various strategies, including selfish and altruistic strategies, depending on the situation. In order to examine whether non-human animals show such flexibility or not, we analyzed chimpanzees’ selfish and cooperative behavior in two types of social problem situations. In this study, we tested chimpanzee mother–infant pairs in two adjacent booths, each equipped with a vending machine. When a token was inserted into a vending machine, the vending machine delivered food rewards to the adjacent booth. In experiment 1, a partition between the two booths was open. In experiment 2, the partition was closed and a mother and her infant were placed in separate booths, so that reciprocal cooperation was essential for them to receive rewards. The participants did not cooperate reciprocally in either experiment. In experiment 1, the chimpanzees developed selfish tactics to get rewards and changed their tactics flexibly according to the partner’s behaviors. In experiment 2, in which they could not receive rewards without cooperation, they stopped altogether inserting tokens. In both cases, the infants stopped cooperating first. These findings support the idea that chimpanzees are primarily competitive rather than cooperative. Chimpanzees’ high social intelligence might be demonstrated in the flexibility of their selfish tactics, but not in the form of reciprocal cooperation at least when food is involved. We suggest that the failure to establish reciprocal cooperation was due to the social relationship between the mother and her infant, which was characterized by infant’s privilege and mother’s tolerance.     

A Latent Class Multidimensional Scaling Model for Two-Way One-Mode Continuous Rating Dissimilarity Data

In this paper, we propose a cluster-MDS model for two-way one-mode continuous rating dissimilarity data. The model aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low-dimensional space. Under the normal distribution assumption, a latent class model is developed in terms of the set of dissimilarities in a maximum likelihood framework. In each iteration, the probability that a dissimilarity belongs to each of the blocks conforming to a partition of the original dissimilarity matrix, and the rest of parameters, are estimated in a simulated annealing based algorithm. A model selection strategy is used to test the number of latent classes and the dimensionality of the problem. Both simulated and classical dissimilarity data are analyzed to illustrate the model.     

Stereo-motion cooperation and the use ofmotion disparity in the visual perception of 3-D structure

When an observer views a moving scene binocularly, both motion parallax and binocular disparity provide depth information. In Experiments lA-1C, we measured sensitivity to surface curvature when these depth cues were available either individually or simultaneously. When the depth cues yielded comparable sensitivity to surface curvature, we found that curvature detection was easier with the cues present simultaneously, rather than individually. For 2 of the 6 subjects, this effect was stronger when the component of frontal translation of the surface was vertical, rather than horizontal. No such anisotropy was found for the 4 other subjects. If a moving object is observed binocularly, the patterns of optic flow are different on the left and right retinae. We have suggested elsewhere (Cornilleau-Pérès & Droulez, in press) that this motion disparity might be used as avisual cue for the perception of a 3-D structure. Our model consisted in deriving binocular disparity from the left and right distributions of vertical velocities, rather than from luminous intensities, as has been done in classical studies on stereoscopic vision. The model led to some predictions concerning the detection of surface curvature from motion disparity in the presence or absence of intensity-based disparity (classically termedbinocular disparity). In a second set of experiments, we attempted to test these predictions, and we failed to validate our theoretical scheme from a physiological point of view.     

A model for realism of confidence judgments: Implications for underconfidence in sensory discrimination

In a recent issue of this journal, Björkman, Juslin, and Winman (1993) presented a model of the calibration of subjective confidence judgments for sensory discrimination which they called “subjective distance theory.” They proposed that there was a robust underconfidence bias in such judgments, that the model predicted such a bias, and that two different models were needed for the calibration of subjective confidence for cognitive judgments and for sensory ones. This paper addresses issues they raised. It points out that they have not presented a new model, but rather a portion of a more general one, the “decision-variable partition model” originally proposed in Ferrell and McGoey (1980). This paper explores properties of the model and shows, contrary to Björkman, Juslin, and Winman’s hypotheses, that the model does not predict under-confidence, that the “hard-easy effect” can be observed with sensory discriminations, and that the model fits not only sensory, but also cognitive judgments.     

Modeling dynamic resource utilization in populations with unique constraints: preadolescents with and without Down syndrome

In this study we used a damped inverted pendulum and spring with an escapement function model to compare the global levels of stiffness and forcing used by 12 preadolescents with Down syndrome (DS) and 12 with typical development (TD). Participants walked overground at their self-selected speed and on a treadmill at speeds slower and faster than overground. Children with DS, who are characterized as hypotonic with reduced capacity for producing muscle force, exhibited significantly higher levels of stiffness and forcing (angular impulse) when walking on the treadmill and higher forcing but not stiffness overground, than children with TD. Both groups adapted to imposed speed increases similarly by increasing their global stiffness and angular impulse. We propose children with DS increased stiffness in order to overcome their hypotonia and joint laxity, thus, optimizing on stability, rather than metabolic efficiency. Higher angular impulse values for children with DS may reflect higher energy cost associated with increasing stiffness and their inherent biomechanical and physiological characteristics that reduce efficiency. We conclude that the inverted pendulum and spring with escapement function model is a useful tool for uncovering solutions to movement problems-solutions that reflect the dynamic resources of the individual and ones that are discovered, rather than prescribed.     

Jeffrey conditioning,rigidity, and the defeasible red jelly bean

Jonathan Weisberg has argued that Jeffrey Conditioning is inherently “anti-holistic” By this he means, inter alia, that JC does not allow us to take proper account of after-the-fact defeaters for our beliefs. His central example concerns the discovery that the lighting in a room is red-tinted and the relationship of that discovery to the belief that a jelly bean in the room is red. Weisberg’s argument that the rigidity required for JC blocks the defeating role of the red-tinted light rests on the strong assumption that all posteriors within the distribution in this example are rigid on a partition over the proposition that the jelly bean is actually red. But individual JC updates of propositions do not require such a broad rigidity assumption. Jeffrey conditionalizers should consider the advantages of a modest project of targeted updating focused on particular propositions rather than seeking to update the entire distribution using one obvious partition. Although Weisberg’s example fails to show JC to be irrelevant or useless, other problems he raises for JC (the commutativity and inputs problems) remain and actually become more pressing when we recognize the important role of background information.     

Geometric and semantic similarity in visual masking

Semantic and geometric or physical similarity were manipulated separately in a backward-masking situation. When the target was a word to be read aloud, formal similarity between the letters of target and mask facilitated target recognition, as did associative similarity. Masking a target word by its own anagram also facilitated whole word report. In contrast, formal similarity was inhibitory rather than facilitatory of report when the target was spelled letter-by-letter, rather than read whole. This was true even for the same target words whose whole report was facilitated by formal similarity. A model to account for this reversal in the broader context of the neural substrate of reading is advanced. It is proposed that letter and word processing are fundamentally different in that letters are recognized by hierarchical feature analysis while words are stored and recognized wholistically by diffuse and redundant networks. Implications of the results for the study of reading are discussed.     

Bayesian estimation of a multilevel IRT model using gibbs sampling

In this article, a two-level regression model is imposed on the ability parameters in an item response theory (IRT) model. The advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error. Another advantage is that, contrary to observed scores, latent scores are test-independent, which offers the possibility of using results from different tests in one analysis where the parameters of the IRT model and the multilevel model can be concurrently estimated. The two-parameter normal ogive model is used for the IRT measurement model. It will be shown that the parameters of the two-parameter normal ogive model and the multilevel model can be estimated in a Bayesian framework using Gibbs sampling. Examples using simulated and real data are given.     

A further analysis of time bisection behavior in children with and without reference memory: the similarity and the partition task

Experiment 1 compared the temporal performance of 5-year-olds, 8-year-olds and adults in a bisection task with and without referent durations (similarity vs. partition). The results showed that temporal sensitivity was lower in the partition than in the similarity condition in children, whereas it was similar in these two conditions in the adults. In addition, the 5-year-olds produced a higher bisection point value in the partition than in the similarity task. Experiment 2, which examined changes in bisection performance over the trial blocks in the partition task, revealed that the 5-year-olds' bisection performance improved over the trial blocks, whereas the performance of the older participants did not. Further analyses revealed a greater variability in the establishment of the duration criterion in young children.     

Letters and words in word identification

Studies by Barron and Henderson (1977) and Johnson (1975) provide evidence that whole words may be the unit of identification in word perception, rather than single letters. Johnson found that words were matched faster than a letter to the first letter in a word. Barron and Henderson found faster matching times for words than for legal non-word items in a letter-matching task. These findings support the interpretation that words are identified before individual letters. If so, a word-frequency effect should be expected. Experiments 1 and 2 tested for word vs. first-letter-in-word differences, as well as for a word-frequency effect in simultaneous and delayed visual matching tasks. In the simultaneous task, first letters in words were matched faster than words. In the delayed task, there was no difference between matching words or matching the first letters in words. With both tasks there was a word-frequency effect for word matches but not for first-letter-in-word matches. In Experiment 3, first-letter matching time was unrelated to word frequency or lexical status, although it did vary with orthographic legality. These results, on the whole, are consistent with a race model in which identifications take place simultaneously at word, letter-cluster, and letter levels, rather than a sequential model in which the whole word is identified before the component letters.     

How framing statistical statements affects subjective veracity: Validation and application of a multinomial model for judgments of truth

Extending the well-established negativity bias in human cognition to truth judgments, it was recently shown that negatively framed statistical statements are more likely to be considered true than formally equivalent statements framed positively. However, the underlying processes responsible for this effect are insufficiently understood. Therefore, a multinomial processing tree model is herein proposed to distinguish between differences in (a) knowledge or (b) response bias that may account for the framing effect. Three model validation experiments supported the psychological interpretability of model parameters. Model application revealed that the framing effect can be considered a bias: Given insufficient knowledge, individuals more likely guessed "true" when faced with a negatively framed statistical statement. The probability of conclusive knowledge, however, remained constant across frames. In summary, this article puts forwards and validates a formal model that can be used more generally to investigate processes underlying truth judgments. Based on this model, it is herein shown that one particular phenomenon - framing effects observed for statistical statements - can be considered a response bias, rather than the upshot of differential knowledge.     

Cross-cultural evidence for the fundamental features of extraversion

Psychologists have not determined the defining characteristics of extraversion. In four studies, the authors tested the hypothesis that extraversion facets are linked by reward sensitivity. According to this hypothesis, only facets that reflect reward sensitivity should load on a higher order extraversion factor. This model was tested against a model in which sociability links the facets. The authors also tested the generalizability of the model in a diverse sample of participants from 39 nations, and they tested the model using widely used extraversion scales. Results of all studies indicate that only facets that reflect reward sensitivity load on a higher order extraversion factor and that this factor correlates strongly with pleasant affect. Although sociability is undoubtedly an important part of extraversion, these results suggest that extraverts' sociability may be a by-product of reward sensitivity, rather than the core feature of the trait.     

Effects of noise similarity and redundancy on the information processed from brief visual displays

When a target letter form is presented tachistoscopicalfy and embedded in a matrix of irrelevant letter forms (noise), correct detections of the target at a given matrix size can be used to estimate indirectly the amount of information processed from the display, according to a model developed by Estes. In three experiments, the physical similarity between noise and target letters and noise-letter redundancy were varied to determine if the detection mechanism was responsive to these variables. It was found that increases in the physical differences between noise and target letters and increases in redundancy facilitated detection. It is argued that these data support a detection model that assumes parallel rather than serial information processing.     

The Hard–Easy Effect in Subjective Probability Calibration

Four different factors have been used to explain the hard–easy effect in subjective probability judgments, in which calibration goes systematically from over- to underconfidence as task difficulty decreases. The factors are biased judgment, lack of suitable adjustment of response criteria (decision variable partition model), biased choice of stimulus material (ecological model), and random error in judgment (error model). Although there is strong evidence for judgmental bias, it seems unlikely to account fully for the systematic character of the effect. We describe the judgment models that emphasize the other three factors and then present two new experiments and a further analysis of the calibration problem. The findings of these experiments and the analysis support the response criteria approach and indicate that the ecological model, and biased choice of stimulus material, is not correct. Since error by itself cannot fully explain observed underconfidence phenomena, we conclude that the most likely explanation of the hard–easy effect is in terms of response criteria. A simulation of the decision variable partition model shows that its behavior closely matches the observed relation between overconfidence and proportion correct for a large sample of experimental results.     

Evidence for a parallel input serial analysis model of word processing

A parallel input serial analysis (PISA) model of word processing was developed and tested. The goal was to expand on the "critical processing duration" hypothesis of Johnson, Allen, and Strand (1989) so that both single-word and multiple-word presentation, letter detection data could be explained. In Experiments 1-3 four different word frequency categories on a single-presentation, letter detection task were used. These three experiments indicated that there was a curvilinear relationship between word frequency and letter detection reaction time (RT). That is, letter detection RTs for medium-high-frequency words were significantly longer than letter detection RTs for very-high-, low-, and very-low-frequency words. These results support the PISA model rather than the Healy, Oliver, and McNamara (1987) version of the unitization model. In Experiments 4-5 multiple-presentation (i.e., two words), letter detection tasks were used. The PISA model could also account for the results from these two experiments, but the unitization model could not.     

Reply to William R. Ferrell’s paper “A model for realism of confidence judgments: Implications for underconfidence in sensory discrimination”

Ferrell’s decision-variable partition model and our subjective distance model belong to the same family of Thurstonial models. The subjective distance model is limited to sensory discrimination with the method of constant stimuli and rooted in such notions as discriminal dispersion and sense distance. Ferrell’s model is intended to be wider in scope and to apply to both cognitive and sensory tasks. Both models need supplementary assumptions to predict calibration phenomena. The point of departure for us is the fact that the model predicts under-confidence under “guessing” and the empirical finding that people are about 100% correct when they report “absolutely certain.” Ferrell makes assumptions about cutoffs on the decision variable. The respondent is assumed to adjust or not adjust cutoffs according to “cues to difficulty.” We disagree with Ferrell’s claim that the hard-easy effect is explained by the respondent’s failure to adjust cutoffs sufficiently when there is a change in level of difficulty, and argue that this amounts to little more than a translation of the hard-easy effect into the lingua of Ferrell’s decision-variable partition model. Our argument is that the hard-easy effect is a consequence of the post hoc division of items according to solution probability. In addition, error variance may contribute to regression effects that enlarge the hard-easy effect. Finally, in contrast to Ferrell’s position, we regard inference (cognitive uncertainty) and discrimination (sensory uncertainty) as different psychological processes. An understanding of calibration in these two areas requires separate models.