Fitting and testing carroll's weighted unfolding model for preferences

A quadratic programming algorithm is presented for fitting Carroll's weighted unfolding model for preferences to known multidimensional scale values. The algorithm can be applied directly to pairwise preferences; it permits nonnegativity constraints on subject weights; and it provides a means of testing various preference model hypotheses. While basically metric, it can be combined with Kruskal's monotone regression to fit ordinal data. Monte Carlo results show that (a) adequacy of true preference recovery depends on the number of data points and the amount of error, and (b) the proportion of data variance accounted for by the model sometimes only approximately reflects true recovery.This study is based on a doctoral dissertation submitted to the University of Illinois at Urbana-Champaign. The author wishes to thank the members of his dissertation committee—Lawrence E. Jones, Chairman, Charles Lewis, Stephen Golding, Ledyard Tucker, and Nancy Wiggins—for their helpful comments.     

Assessing depressive symptoms with the Borg centiMax Scale® in a Swedish sample of patients and students

The Borg centiMax Scale, is a psychophysically composed general intensity ratio scale, which could enable more precise inter- and intraindividual comparisons of the intensity of depressive symptoms. In the present study, the properties of the centiMax scale were examined in 38 patients with clinical depression and 109 students. Additionally, preliminary centiMax cut-off scores for mild, moderate and severe depression were estimated. The psychometric properties of the centiMax were found to be satisfactory regarding internal consistency, convergent, discriminative and predictive validity. Moreover, the centiMax was demonstrated to provide meaningful comparisons of symptom intensity, which makes it possible to evaluate the relative importance of individual symptoms in a profile and make more precise comparisons within and between individuals. With regard to intraindividual comparisons, patients rated , for example, the intensity of feeling “guilt” twice as strong as feelings of “being punished,” and the intensity of “loss of pleasure” almost three times as strong as “being punished.” With regard to interindividual comparisons, patients rated e.g., the intensity of “being punished” as 12 times stronger than controls, and the intensity of “worthlessness” about nine times stronger. In conclusion, the centiMax was shown to be reliable and valid for assessing depressive symptoms. The centiMax with level anchored ratio data, appears to be highly advantageous as it permits rather precise values of symptom intensity for intra- and interindividual comparisons that could be useful in the diagnostic process and in treatment planning.     

Pitch distribution,melodic contour or both? Modeling makam schema with multidimensional scaling and self-organizing maps

Experienced listeners internalize musical tonal knowledge via statistical learning of pitch distributions as a result of exposure to musical environment. Cross-cultural studies of music cognition offer new perspectives to investigate the acquisition of tonal schema. Makam music is a rich musical system characterized by modal structures defined by micro-tonal pitch sets, and melodic progression patterns (aka seyir features). Makam schema is possibly acquired by internalizing the seyir in addition to pitch features. In the current study, we examined whether an ideal model of makam schema is built with multidimensional scaling analysis and with self-organizing maps (SOMs). We were interested in whether statistical information about seyir features, in addition to pitch distributions, would form an acceptable makam schema model. We qualitatively analyzed topographical organizations in the models to understand whether they reflect complex relations between makams. Multidimensional scaling analyses did not produce an acceptable model for makam schema. The SOM trained with pitch distributions provided an adequate model for makam schema. However, the SOM trained with both pitch distributions and seyir features was better in capturing the complex relations between makams. Further behavioral research is necessary to understand whether melodic progression patterns are intrinsic features of the tonal knowledge of the experienced listeners of makam music.     

Checking the Assumptions of Rasch's Model for Speed Tests

Two new tests for a model for the response times on pure speed tests by Rasch (1960) are proposed. The model is based on the assumption that the test response times are approximately gamma distributed, with known index parameters and unknown rate parameters. The rate parameters are decomposed in a subject ability parameter and a test difficulty parameter. By treating the ability as a gamma distributed random variable, maximum marginal likelihood (MML) estimators for the test difficulty parameters and the parameters of the ability distribution are easily derived. Also the model tests proposed here pertain to the framework of MML. Two tests or modification indices are proposed. The first one is focused on the assumption of local stochastic independence, the second one on the assumption of the test characteristic functions. The tests are based on Lagrange multiplier statistics, and can therefore be computed using the parameter estimates under the null model. Therefore, model violations for all items and pairs of items can be assessed as a by-product of one single estimation run. Power studies and applications to real data are included as numerical examples.     

A person-fit index for polytomous rasch models,latent class models,and their mixture generalizations

A normally distributed person-fit index is proposed for detecting aberrant response patterns in latent class models and mixture distribution IRT models for dichotomous and polytomous data.This article extends previous work on the null distribution of person-fit indices for the dichotomous Rasch model to a number of models for categorical data. A comparison of two different approaches to handle the skewness of the person-fit index distribution is included.Major parts of this paper were written while the first author worked at the Institute for Science Education, Kiel, Germany. Any opinions expressed in this paper are those of the authors and not necessarily of Educational Testing Service. The results presented in this paper were improved by valuable comments from J. Rost, K. Yamamoto, N.D. Verhelst, E. Bedrick and two anonymous reviewers.     

Adaptation in Visuomanual Tracking Depends on Intact Proprioception

The role of arm proprioception in motor learning was investigated in experiments in which, by moving the arm, subjects followed the motion of a target displayed on a monitor screen. Adaptive capabilities were tested in visuomanual tracking tasks following alterations in the relationship between the observer's actual arm movement and visual feedback of the arm movement given by a cursor motion on the screen. Tracking performance and adaptive changes, measured in terms of spatiotemporal error, tracking trajectory curvature, and spatial gain, were compared in 7 control subjects (CSs) and in 1 deafferented subject (DS). CSs adapted appropriately to altered visuomanual relationships; those changes were present in trials immediately after restoration of normal scaling. In contrast, although the DS modified his tracking strategy from trial to trial according to the altered conditions, he did not show plastic changes in internal visuomanual scaling. Like the results of prismatic adaptation experiments, the present results suggest that arm proprioception contributes to the plastic changes that follow alterations in the scaling of visuomanual gain.     

Getting the big picture: Development of spatial scaling abilities

Spatial scaling is an integral aspect of many spatial tasks that involve symbol-to-referent correspondences (e.g., map reading, drawing). In this study, we asked 3–6-year-olds and adults to locate objects in a two-dimensional spatial layout using information from a second spatial representation (map). We examined how scaling factor and reference features, such as the shape of the layout or the presence of landmarks, affect performance. Results showed that spatial scaling on this simple task undergoes considerable development, especially between 3 and 5 years of age. Furthermore, the youngest children showed large individual variability and profited from landmark information. Accuracy differed between scaled and un-scaled items, but not between items using different scaling factors (1:2 vs. 1:4), suggesting that participants encoded relative rather than absolute distances.     

Validating the coping scale for Chinese athletes using multidimensional Rasch analysis

Objective

The Coping Scale for Chinese Athletes (CSCA) was developed and validated using classic testing theory in 2004 (Chung, Si, Lee, & Liu, 2004). This study aimed to validate CSCA using multidimensional Rasch analysis with the ConQuest software programme.

Method

The sample in this study comprised 367 athletes from mainland China. A Multidimensional Rating Scale model was applied to investigate the validity of the four-dimension scale. Standard fit statistics (Infit and Outfit MNSQ) and Differential item functioning (DIF) were computed to examine the model-data fit. Test reliability and category functioning were also checked.

Results

The item difficulty and the athletes’ trait level of coping were calibrated along the same latent trait scale. Three items were removed from the scale due to misfit with the Rasch model. No DIF across gender was found for the remaining 21 items. Test reliabilities for the four subscales ranged from 0.66 to 0.76. The results also indicated that the original 5-category rating scale structure did not function well.

Conclusion

The multidimensional Rasch analysis supported that the 21-item CSCA measures four latent traits of coping of Chinese athletes as expected. The results also demonstrated advantages of multidimensional Rasch analysis over unidimensional Rasch analysis as well as traditional approach in examining the quality of multidimensional scale in sport settings.     

Modeling the effect of reward amount on probability discounting

The present study with college students examined the effect of amount on the discounting of probabilistic monetary rewards. A hyperboloid function accurately described the discounting of hypothetical rewards ranging in amount from $20 to $10,000,000. The degree of discounting increased continuously with amount of probabilistic reward. This effect of amount was not due to changes in the rate parameter of the discounting function, but rather was due to increases in the exponent. These results stand in contrast to those observed with the discounting of delayed monetary rewards, in which the degree of discounting decreases with reward amount due to amount-dependent decreases in the rate parameter. Taken together, this pattern of results suggests that delay and probability discounting reflect different underlying mechanisms. That is, the fact that the exponent in the delay discounting function is independent of amount is consistent with a psychophysical scaling interpretation, whereas the finding that the exponent of the probability-discounting function is amount-dependent is inconsistent with such an interpretation. Instead, the present results are consistent with the idea that the probability-discounting function is itself the product of a value function and a weighting function. This idea was first suggested by Kahneman and Tversky (1979), although their prospect theory does not predict amount effects like those observed. The effect of amount on probability discounting was parsimoniously incorporated into our hyperboloid discounting function by assuming that the exponent was proportional to the amount raised to a power. The amount-dependent exponent of the probability-discounting function may be viewed as reflecting the effect of amount on the weighting of the probability with which the reward will be received.