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.     

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.     

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.     

Disaggregating the Distal,Proximal, and Time-Varying Effects of Parent Alcoholism on Children’s Internalizing Symptoms

We tested whether children show greater internalizing symptoms when their parents are actively abusing alcohol. In an integrative data analysis, we combined observations over ages 2 through 17 from two longitudinal studies of children of alcoholic parents and matched controls recruited from the community. Using a mixed modeling approach, we tested whether children showed elevated mother- and child-reported internalizing symptoms (a) at the same time that parents showed alcohol-related consequences (time-varying effects), (b) if parents showed greater alcohol-related consequences during the study period (proximal effects), and (c) if parents had a lifetime diagnosis of alcoholism that predated the study period (distal effects). No support for time-varying effects was found; proximal effects of mothers' alcohol-related consequences on child-reported internalizing symptoms were found and distal effects of mother and father alcoholism predicted greater internalizing symptoms among children of alcoholic parents. Implications for the time-embedded relations between parent alcoholism and children's internalizing symptoms are discussed.     

The seven virtues of simple type theory

Simple type theory, also known as higher-order logic, is a natural extension of first-order logic which is simple, elegant, highly expressive, and practical. This paper surveys the virtues of simple type theory and attempts to show that simple type theory is an attractive alternative to first-order logic for practical-minded scientists, engineers, and mathematicians. It recommends that simple type theory be incorporated into introductory logic courses offered by mathematics departments and into the undergraduate curricula for computer science and software engineering students.     

不同条件下拟合指数的表现及临界值的选择

在本模拟研究中设计了6种样本容量,6种因子载荷,和4种评分等级,并考察了正态和非正态分布两种情况。采用的错误模型为参数误置（真模型中每个因子各由5个题目来测量,错误模型中则是第一个因子由6个题测量,另两个因子各由4个和5个题来测量,即有一个因子载荷被误置）模型。结果发现（1）样本量、载荷量、评分等级数和分布形态都对GOF的取值确有影响。其中分布形态的影响最大。NNFI、IFI在不同条件下的平均值是最稳定的,其次是CFI、RMSEA和SRMR。它们都算是值得推荐的GOF,尤其是NNFI和IFI。（2）在正态分布中,当样本量≥1000时,根据NNFI、IFI、CFI、RMSEA、SRMR对模型是否拟合做出判断时有很低的两类错误率,在样本量<1000时则不理想。在偏态条件下无论选择哪个GOF两类错误率都很高。（3）采用2指数策略在很多情况下也不能显著降低两类错误率。（4）由于在数据分布非正态,或正态但样本量<1000时是难判断模型是否拟合的。因此我们提出了2界值策略。即为每个GOF确定上下两个界值。低于下界值时可判断模型是不正确的,而高于上界值时则可判断模型是正确的。GOF取值处于上下界值之间时难以判断模型是否拟合,只能说越高拟合的可能性越大。这时就要通过跨样本验证和增加样本量来确定模型是否正确