The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features

A method is discussed which extends principal components analysis to the situation where the variables may be measured at a variety of scale levels (nominal, ordinal or interval), and where they may be either continuous or discrete. There are no restrictions on the mix of measurement characteristics and there may be any pattern of missing observations. The method scales the observations on each variable within the restrictions imposed by the variable's measurement characteristics, so that the deviation from the principal components model for a specified number of components is minimized in the least squares sense. An alternating least squares algorithm is discussed. An illustrative example is given.Copies of this paper and of the associated PRINCIPALS program may be obtained by writing to Forrest W. Young, Psychometric Laboratory, Davie Hall 013-A, Chapel Hill, NC 27514.     

A Simple Incomplete Extension of T which is the Union of Two Complete Modal Logics with f.m.p.

I present here a modal extension of T called KTLM which is, by several measures, the simplest modal extension of T yet presented. Its axiom uses only one sentence letter and has a modal depth of 2. Furthermore, KTLM can be realized as the logical union of two logics KM and KTL which each have the finite model property (f.m.p.), and so themselves are complete. Each of these two component logics has independent interest as well.     

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).     

Validation of psychoanalytic theories: Towards a conceptualization of references

The authors discuss criteria for the validation of psychoanalytic theories and develop a heuristic and normative model of the references needed for this. Their core question in this paper is: can psychoanalytic theories be validated exclusively from within psychoanalytic theory (internal validation), or are references to sources of knowledge other than psychoanalysis also necessary (external validation)? They discuss aspects of the classic truth criteria correspondence and coherence, both from the point of view of contemporary psychoanalysis and of contemporary philosophy of science. The authors present arguments for both external and internal validation. Internal validation has to deal with the problems of subjectivity of observations and circularity of reasoning, external validation with the problem of relevance. They recommend a critical attitude towards psychoanalytic theories, which, by carefully scrutinizing weak points and invalidating observations in the theories, reduces the risk of wishful thinking. The authors conclude by sketching a heuristic model of validation. This model combines correspondence and coherence with internal and external validation into a four‐leaf model for references for the process of validating psychoanalytic theories.     

论权利与义务的关系

权利与义务的关系可以归结为两种相关性。一种是一个人的权利与他人的义务的关系:一个人的权利,必然是他人的义务;反之亦然。这是一个人的权利与他人的义务的必然的、客观的、事实如何的关系,亦即所谓“权利与义务的逻辑相关性”。另一种则是基于这种逻辑相关性的“权利义务道德相关性”,亦即一个人的权利应该是对他自己的义务的交换:一个人所享有的权利应该等于他所负有的义务;而他所行使的权利则应该至多等于他所履行的义务。     

A comparison of normative data for the Trail Making Test from several countries: equivalence of norms and considerations for interpretation

The Trail Making Test may not be equivalent across cultures, i.e., differences in the scores across different cultures may not reveal real differences in the ability of the subjects on the construct being measured. In order to assess this hypothesis, normative samples from ten different countries were compared. Age decade subgroups across samples were ranked based on mean time taken to complete each part of the task. Large Z scores differences were found between these samples when comparing the first with the second, and the last in the rank. These differences were significant even when age and education were comparable across samples. Following Van de Vijver & Tanzer (1997), several possible sources of bias were identified. Incomparability of samples and administration differences were the most likely factors accounting for differences. Because of the lack of validity studies in the countries considered, no firm conclusions could be obtained regarding construct bias. Although the TMT may be measuring visual scanning, psychomotor speed and mental flexibility, normative data from different countries and cultures are not equivalent which might lead to serious diagnostic errors.     

From Zero to Sixty: Calibrating Real-Time Responses

Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying covariates to a continuous response variate. Using real-time data obtained from an experiment in psychoacoustics, we showcase new statistical tools that incorporate dynamical elements of an input-output system. We employ functional data analysis (FDA) methods and a simple differential equation to analyze and model the continuous responses. Furthermore, we outline the issues involved in analyzing input-output systems when the exact form of the underlying mathematical model is not known. Finally, we develop a calibration method to facilitate inter-subject and intra-subject comparisons. This work was supported by grants from the National Sciences and Engineering Research Council (NSERC) to J. O. Ramsay and to D. J. Levitin, and by a grant from the Social Sciences and Humanities Research Council (SSHRC) to D. J. Levitin. We would like to thank Bennett Smith for designing and implementing the software used to conduct the pitch tracking experiment. Also, we wish to thank the research assistants in the Levitin Laboratory involved in the data collection: Catherine Chapados, Andrew Schaaf and Carla Himmelman. We would also like to acknowledge Giles Hooker’s work on implementing the generalized profiling software used within this paper.     

The CHIC Model: A Global Model for Coupled Binary Data

Often problems result in the collection of coupled data, which consist of different N-way N-mode data blocks that have one or more modes in common. To reveal the structure underlying such data, an integrated modeling strategy, with a single set of parameters for the common mode(s), that is estimated based on the information in all data blocks, may be most appropriate. Such a strategy implies a global model, consisting of different N-way N-mode submodels, and a global loss function that is a (weighted) sum of the partial loss functions associated with the different submodels. In this paper, such a global model for an integrated analysis of a three-way three-mode binary data array and a two-way two-mode binary data matrix that have one mode in common is presented. A simulated annealing algorithm to estimate the model parameters is described and evaluated in a simulation study. An application of the model to real psychological data is discussed. T. Wilderjans is a Research Assistant of the Fund for Scientific Research—Flanders (Belgium). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/2005/04). We are grateful to Kristof Vansteelandt for providing us with an interesting data set. We also thank three anonymous reviewers for their useful comments.