Remarks on the identifiability of thurstonian paired comparison models under multiple judgment

It is well-known that the representations of the Thurstonian models for difference judgment data are not unique. It has been shown that equivalence classes can be formed to provide a more meaningful partition of the covariance structures of the Thurstonian ranking models. In this paper, we examine the equivalence relations between Thurstonian covariance structure models for paired comparison data obtained under multiple judgment and discuss their implications on the general identification constraints and methods to check for parameter identifiability in restricted models.The author is indebted to Ulf Böckenholt and Albert Maydeu-Olivares for their significant comments and suggestions which led to considerable improvement in this article.     

A general model for the analysis of multilevel data

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multiple time series, and variance and covariance component models.We would like to acknowledge the helpful comments of Ruth Silver. We also wish to thank the referees for helping to clarify the paper. This work was partly carried out with research funds provided by the Economic and Social Research Council (U.K.).     

Optimal scaling of paired comparison and rank order data: An alternative to guttman's formulation

A formulation, which is different from Guttman's is presented. The two formulations are both called the optimal scaling approach, and are proven to provide identical scale values. The proposed formulation has at least two advantages over Guttman's. Namely, (i) the former serves to clarify close relations of the optimal scaling approach to those of Slater and the vector model of preferential choice, and (ii) in addition to the stimulus scale values, it provides scores for the subjects, which indicate the degrees of response consistency (transitivity), relative to the optimum solution. The method is assumption-free and capable of multidimensional analysis.This study was partly supported by the National Research Council Grant (No. A4581) to S. Nishisato. The author is indebted to Dr. Bert F. Green, Jr., Mr. Tomoichi Ishizuka, and anonymous reviewers for their valuable comments on an earlier draft.     

Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling

We relate Thurstonian models for paired comparisons data to Thurstonian models for ranking data, which assign zero probabilities to all intransitive patterns. We also propose an intermediate model for paired comparisons data that assigns nonzero probabilities to all transitive patterns and to some but not all intransitive patterns.There is a close correspondence between the multidimensional normal ogive model employed in educational testing and Thurstone's model for paired comparisons data under multiple judgment sampling with minimal identification restrictions. Alike the normal ogive model, Thurstonian models have two formulations, a factor analytic and an IRT formulation. We use the factor analytic formulation to estimate this model from the first and second order marginals of the contingency table using estimators proposed by Muthén. We also propose a statistic to assess the fit of these models to the first and second order marginals of the contingency table. This is important, as a model may reproduce well the estimated thresholds and tetrachoric correlations, yet fail to reproduce the marginals of the contingency table if the assumption of multivariate normality is incorrect.A simulation study is performed to investigate the performance of three alternative limited information estimators which differ in the procedure used in their final stage: unweighted least squares (ULS), diagonally weighted least squares (DWLS), and full weighted least squares (WLS). Both the ULS and DWLS show a good performance with medium size problems and small samples, with a slight better performance of the ULS estimator.This paper is based on the author's doctoral dissertation; Ulf Böckenholt, advisor. The final stages of this research took place while the author was at the Department of Statistics and Econometrics, Universidad Carlos III de Madrid. The author is indebted to Adolfo Hernández for stimulating discussions that helped improve this paper, and to Ulf Böckenholt and the Associate Editor for a number of helpfulsuggestions to a previous draft.     

Stress related changes in immunological and psychological variables induced by the preparation and defense of a PhD-thesis

Abstract

Results are reported from a field study on 47 healthy subjects preparing and defending a PhD-thesis in the Netherlands. Measurements before, about and after thesis defense are used to quantify the temporal effects of this perceived stressor on immunological and psychological variables. Moreover, multivariate analysis of variance for repeated measurements was used to explore a potential causal relationship between changes in immune variables and changes in psychological variables. Significant temporal effects were observed for the immunological variables, percentage CD4 cells (p = 0.037), the proliferative response to pokeweed mitogen (p = 0.040), concanavalin A 10 μg/ml (p = 0.010) and concanavalin A 40 μg/ml (p = 0.005) and the psychological variables, average subjective distress (p = 0.002), highest subjective distress (p = 0.000) and the coping strategy depressive reaction pattern (p= 0.02). No evidence was obtained for a causal relation between the immunological and psychological variables.     

On the use of heterogeneous thresholds ordinal regression models to account for individual differences in response style

This paper proposes a general approach to accounting for individual differences in the extreme response style in statistical models for ordered response categories. This approach uses a hierarchical ordinal regression modeling framework with heterogeneous thresholds structures to account for individual differences in the response style. Markov chain Monte Carlo algorithms for Bayesian inference for models with heterogeneous thresholds structures are discussed in detail. A simulation and two examples based on ordinal probit models are given to illustrate the proposed methodology. The simulation and examples also demonstrate that failing to account for individual differences in the extreme response style can have adverse consequences for statistical inferences.The author is grateful to Ulf Böckenholt, an associate editor, and three anonymous reviewers for helpful comments, and Kristine Kuhn and Kshiti Joshi for providing the data.     

Assessing vocational interests in the Basque Country using paired comparison design

This article proposes the Thurstonian paired comparison model to assess vocational preferences and uses this approach to evaluate the Realistic, Investigative, Artistic, Social, Enterprise, and Conventional (RIASEC) model in the Basque Country (Spain). First, one unrestricted model is estimated in the Structural Equation Modelling framework using one paired comparison design. Secondly, the RIASEC circumplex structure is evaluated upon the estimated latent preferences correlation matrix. The results show good fit between the Thurstonian model and the data, but do not confirm the RIASEC structure in the Basque population.     

On testing the equality of proportions in the paired case with incomplete data

The problem of testing two correlated proportions with incomplete data is considered by means of Monte Carlo simulations studies. A test proposed in this paper, which can be regarded as a generalization of McNemar's test, is recommended in all cases with incomplete data and not too small samples.     

Neuropsychological changes in children with cancer: The treatment of missing data in longitudinal studies

Researchers conducting longitudinal studies with children or adults are inevitably confronted with problems of attrition and missing data. Missing data in longitudinal studies is frequently handled by excluding from analyses those cases for whom data are incomplete. This approach to missing data is not optimal. On the one hand, if data are missing at random, then dropping incomplete cases ignores information collected on those cases that could be used to improve estimates of population parameters (e.g., means, variances, covariances, and growth rates) and improve the power of significance tests of statistical hypotheses. On the other hand, if data are not missing at random, then dropping incomplete cases leads to biased parameter estimates and hypothesis tests that may be internally and externally invalid. This study uses three years of follow-up data from a longitudinal investigation of neuropsychological outcomes of cancer in children to demonstrate the problems presented by missing data in repeated measures designs and some solutions. In evaluating potential biasing effects of attrition, the study extends previous research on neuropsychological outcomes in pediatric cancer by inclusion of patients whose disease had relapsed, and by comparison of surviving and nonsurviving patients. Although the data presented have specific relevance to the study of neuropsychological outcome in pediatric cancer, the problems of missing data and the solutions presented are relevant to a wide variety of diseases and conditions of interest to researchers in child and adult neuropsychology.     

(Non)Issues of Infinite Regress in Modeling Motor Behavior

In the past, infinite regress criticisms that have been raised about models of motor behavior have been reserved for executive-type models (e.g., Beek & Meijer, 1988). On the basis of Gödel's (1930/1986) proof that an algorithm cannot prove its own validity, the authors reason that executive- as well as self-organized-type explanatory models of motor behavior have infinite regress difficulties. The conclusion offered in the present article is that judgments on a model's theoretical importance should be based not on issues of infinite regress but on other relevant characteristics, such as its propensity for falsification (Popper, 1959).     

Recovery of structure in incomplete data by alscal

A Monte Carlo study was carried out in order to investigate the ability of ALSCAL to recover true structure inherent in simulated proximity measures when portions of the data are missing. All sets of simulated proximity measures were based on 30 stimuli and three dimensions, and selection of missing elements was done randomly. Properties of the simulated data varied according to (a) the number of individuals, (b) the level of random error, (c) the proportion of missing data, and (d) whether the same entries or different entries were deleted for each individual. Results showed that very accurate recovery of true distances, stimulus coordinates, and weight vectors could be achieved with as much as 60% missing data as long as sample size was sufficiently large and the level of random error was low.     

Solution Strategies and Achievement in Dutch Complex Arithmetic: Latent Variable Modeling of Change

In the Netherlands, national assessments at the end of primary school (Grade 6) show a decline of achievement on problems of complex or written arithmetic over the last two decades. The present study aims at contributing to an explanation of the large achievement decrease on complex division, by investigating the strategies students used in solving the division problems in the two most recent assessments carried out in 1997 and in 2004. The students’ strategies were classified into four categories. A data set resulted with two types of repeated observations within students: the nominal strategies and the dichotomous achievement scores (correct/incorrect) on the items administered.It is argued that latent variable modeling methodology is appropriate to analyze these data. First, latent class analyses with year of assessment as a covariate were carried out on the multivariate nominal strategy variables. Results showed a shift from application of the traditional long division algorithm in 1997, to the less accurate strategy of stating an answer without writing down any notes or calculations in 2004, especially for boys. Second, explanatory IRT analyses showed that the three main strategies were significantly less accurate in 2004 than they were in 1997.     

An Illustration of Diagnostic Classification Modeling in Student Learning Outcomes Assessment

The assessment of higher-education student learning outcomes is an important component in understanding the strengths and weaknesses of academic and general education programs. This study illustrates the application of diagnostic classification models, a burgeoning set of statistical models, in assessing student learning outcomes. To facilitate understanding and future applications of diagnostic modeling, the log-linear cognitive diagnosis model used in this study is presented in a didactic manner. The model is applied in a context where undergraduate students were assessed along four learning outcomes related to psychosocial research across two time points. Results focus on implications and methods to aid stakeholders’ interpretation of the analyses. Contrasts to traditional measurement models and potential future applications are also discussed.     

Latent change classes in dichotomous data

Changes in dichotomous data caused by treatments can be analyzed by means of the so-called linear logistic model with relaxed assumptions (LLRA). The LLRA does not require observable criteria representing a single underlying latent trait, but it postulates the generalizability of the treatment effects over criteria and subjects. To test this latter crucial assumption, the mixture LLRA was proposed that allows directly unobservable types of subjects to have different treatment effects. As the earlier methods for estimating the parameters of the mixture LLRA have specific drawbacks, a further method based on the conditional maximum likelihood principle will be presented here. In contrast to the earlier conditional methods, it uses all of the dichotomous change data while having fewer parameters. Further, its goodness-of-fit tests become more sensitive to a falsely specified number of change-types even though the treatment effects are biased. For typically occurring small to moderate sample sizes, however, parametric bootstrapping of the distributions of the fit statistics is recommended for performing hypotheses tests. Finally, three applications of the new method to empirical data are described: first, about the effect of the so-called Trager psychophysical integration, second, about the effect of autogenic therapy on patients with psychosomatic symptoms, and, third, about the effect of religious education on the attitude towards sects. The mixture LLRA is implemented in the menu-driven program MIXLLRA which can be obtained from Ivo Ponocny via e-mail (ivo.ponocny@univie.ac.at).     

Estimating latent distributions in recurrent choice data

This paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data. These choice models are derived by specifying elements of the choice process at the individual level. Probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior. Due to the explicit consideration of random effect sources, the choice models are parsimonious and readily interpretable. An easy to implement EM algorithm is presented for parameter estimation. Two applications illustrate the proposed approach.     

Psychological distress in university students: A comparison with general population data

Objective: While the mental health of university students is recognised internationally as an important public health issue, more epidemiological data are needed that allows benchmarking with general population data. Methods: All enrolled students from two large Australian universities were invited to complete a web‐based survey. Anxiety‐mood disorders were assessed using the Kessler 10. A total of 6,479 students participated in the study with sociodemographics generally consistent with the university population. Results: The estimated prevalence for mental health problems was 19.2% with 67.4% reporting subsyndromal symptoms. These rates were significantly higher than the general population. Psychological distress was associated with disability and lower academic achievement. Predictors of distress included: full‐time status, financial stress, being aged between and 18 and 34 years, being female, and in a subsequent undergraduate year of their degree. Conclusions: The extremely high prevalence of mental health problems in university students provides evidence for this being an at‐risk population. Implications: The results highlight the need for universal early interventions to prevent the development of severe mental illness in university students.     

Re-conceptualizing the past: Historical data in vocational interest research

Noteworthy progress has been made in the development of statistical models for evaluating the structure of vocational interests over the past three decades. It is proposed that historically significant interest datasets, when combined with modern structural methods of data analysis, provide an opportunity to re-examine the underlying assumptions of J.L. Holland’s [Holland, J. L. (1959). A theory of vocational choice. Journal of Counseling Psychology, 6, 35–45; Holland, J. L. (1997). Making vocational choices (3rd ed.). Odessa, FL: Psychological Assessment Resources] RIASEC model. To illustrate this potential, data obtained from J. P. Guilford’s study of interest structure were re-analyzed using modern circumplex and hierarchical clustering techniques to evaluate Holland’s and I. Gati’s [Gati, I. (1979). A hierarchical model for the structure of interests. Journal of Vocational Behavior, 15, 90–106; Gati, I. (1991). The structure of vocational interests. Psychological Bulletin, 109, 309–324] interest structures. Obtained results indicate that a circumplex model can be used to effectively represent the structure underlying Guilford’s interest measures. However, hierarchical clustering results suggest that Holland’s RIASEC types may not be the most effective categories for grouping specific interest measures into broader interest areas. The current findings provide support for the continued investigation of alternatives to Holland’s interest categories using modern measures of basic interests.     

Categorization and abstraction abilities in 3-year-old children: a comparison with monkey data

Three-year-old children were tested on three categorization tasks of increasing levels of abstraction (used with adult baboons in an earlier study): the first was a conceptual categorization task (food vs toys), the second a perceptual matching task (same vs different objects), and the third a relational matching task in which the children had to sort pairs according to whether or not the two items belonged to the same or different categories. The children were tested using two different procedures, the first a replication of the procedure used with the baboons (pulling one rope for a category or a relationship between two objects, and another rope for the other category or relationship), the second a task based upon childrens prior experiences with sorting objects (putting in the same box objects belonging to the same category or a pair of objects exemplifying the same relation). The children were able to solve the first task (conceptual categorization) when tested with the sorting into boxes procedure, and the second task (perceptual matching) when tested with both procedures. The children were able to master the third task (relational matching) only when the rules were clearly explained to them, but not when they could only watch sorting examples. In fact, the relational matching task without explanation requires analogy abilities that do not seem to be fully developed at 3 years of age. The discrepancies in performances between children tested with the two procedures, with the task explained or not, and the discrepancies observed between children and baboons are discussed in relation to differences between species and/or problem-solving strategies.