The choice of constraints in correspondence analysis

A discussion of alternative constraint systems has been lacking in the literature on correspondence analysis and related techniques. This paper reiterates earlier results that an explicit choice of constraints has to be made which can have important effects on the resulting scores. The paper also presents new results on dealing with missing data and probabilistic category assignment.I am most grateful to the following for their helpful comments. Arto Demirjian, Michael Greenacre, Michael Healy, Shizuhiko Nishisato, Roderick Mcdonald, and several anonymous referees.     

Latent trait models and dichotomization of graded responses

This paper discusses thecompatibility of the polychotomous Rasch model with dichotomization of the response continuum. It is argued that in the case of graded responses, the response categories presented to the subject are essentially an arbitrary polychotomization of the response continuum, ranging for example from total rejection or disagreement to total acceptance or agreement of an item or statement. Because of this arbitrariness, the measurement outcome should be independent of the specific polychotomization applied, for example, presenting a specific multicategory response format should not affect the measurement outcome. When such is the case, the original polychotomous model is called compatible with dichotomization.A distinction is made between polychotomization or dichotomization before the fact, that is, in constructing the response format, and polycho- or dichotomization after the fact, for example in dichotomizing existing graded response data.It is shown that, at least in case of dichotomization after-the-fact, the polychotomous Rasch model is not compatible with dichotomization, unless a rather special condition of the model parameters is met. Insofar as it may be argued that dichotomization before the fact is not essentially different from dichotomization after the fact, the value of the unidimensional polychotomous Rasch model is consequently questionable. The impact of our conclusion on related models is also discussed.     

Estimation for structural equation models with missing data

A direct method in handling incomplete data in general covariance structural models is investigated. Asymptotic statistical properties of the generalized least squares method are developed. It is shown that this approach has very close relationships with the maximum likelihood approach. Iterative procedures for obtaining the generalized least squares estimates, the maximum likelihood estimates, as well as their standard error estimates are derived. Computer programs for the confirmatory factor analysis model are implemented. A longitudinal type data set is used as an example to illustrate the results.This research was supported in part by Research Grant DAD1070 from the U.S. Public Health Service. The author is indebted to anonymous reviewers for some very valuable suggestions. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.     

Typical coping patterns: A person-centered approach to coping

Applying the person-oriented approach to coping can provide a unique perspective by revealing typical latent patterns. The study examined typical latent patterns shown by task-, emotion- and avoidance-oriented trait-based coping styles. We performed secondary analyses with Latent Profile Analysis on our former data and three independent datasets containing coping measures with the CISS-48 scale (Endler & Parker, 1994). Gender differences were also studied. Two basic profiles seem universal: the first is characterized by a high level of task-oriented coping, and the second profile is with moderately high scores on all three coping styles. The finding indicates that two fundamental latent coping profiles exist, which suggests a within-subject comparison in practice instead of investigating the absolute value of coping styles. Comparing data before and after 2020, COVID-19 does not seem to affect these profiles. The person-centered approach provides a possibility for the integration of coping-related findings.     

Penalized optimal scaling for ordinal variables with an application to international classification of functioning core sets

Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric, implying linear relationships between the variables at hand; alternatively, non-linear PCA is applied where the obtained quantifications are sometimes hard to interpret. Non-linear PCA for categorical data, also called optimal scoring/scaling, constructs new variables by assigning numerical values to categories such that the proportion of variance in those new variables that is explained by a predefined number of principal components (PCs) is maximized. We propose a penalized version of non-linear PCA for ordinal variables that is a smoothed intermediate between standard PCA on category labels and non-linear PCA as used so far. The new approach is by no means limited to monotonic effects and offers both better interpretability of the non-linear transformation of the category labels and better performance on validation data than unpenalized non-linear PCA and/or standard linear PCA. In particular, an application of penalized optimal scaling to ordinal data as given with the International Classification of Functioning, Disability and Health (ICF) is provided.     

Lifespan normative data (18–89 years) for Raven's Advanced Progressive Matrices Set I

Raven's Advanced Progressive Matrices (APM) Set I is a validated and brief test of fluid intelligence, ideal for use in busy clinical settings. However, there is a dearth of normative data allowing an accurate interpretation of APM scores. To address this, we present normative data from across the adult lifespan (18–89 years) for the APM Set I. Data are presented in five age cohorts (total N = 352), including two older adult cohorts (65–79 years and 80–89 years), which allows age-standardized assessment. We also present data from a validated measure of premorbid intellectual ability, which was absent from previous standardizations of longer forms of the APM. In line with previous findings, a striking age-related decline was noted, beginning relatively early in adulthood and most marked amongst lower-scoring individuals. Older adults did not demonstrate difficulty with specific test items or make an increased proportion of specific errors. Sex was not a significant predictor of performance. The data set is of particular use in the neuropsychological assessment of older adults, given the known susceptibility of fluid intelligence to both the effects of normal ageing and acquired brain injury in older age. The results are discussed in light of theories of neurological ageing.     

Psychometric properties and factor structure of the Fear Questionnaire phobia subscale items in two normative samples

Normative data for the Fear Questionnaire (Marks & Mathews, 1979), a popular self-report instrument measuring phobic concerns, were collected from both a community and a collegiate sample. The covariation and internal consistency of the blood-injury phobia (BI), social phobia (SO), and agoraphobia (AG) subscales were assessed in each sample, and the factor structure of the items from these three subscales was examined. Results indicated that, in general, community subjects reported more phobic concerns than did collegiate subjects, and females reported greater phobic concerns than did males. Results from confirmatory factor analyses suggest that the three factors of BI, SO, and AG did not emerge from either data set. Follow-up exploratory factor analyses did identify the general factors of blood-injury phobia and agoraphobia. Normative data from the present study are compared to those obtained previously, and directions for future research are provided.     

Social networks with two sets of actors

Traditional network research analyzes relational ties within a single group of actors: the models presented in this paper involve relational ties exist beteen two distinct sets of actors. Statistical models for traditional networks in which relations are measured within a group simplify when modeling unidirectional relations measured between groups. The traditional paradigm results in a one-mode socionatrix; the network paradigm considered in this paper results in a two-mode socionatrix; A statistical model is presented, illustrated on a sample data set, and compared to its traditional counterpart. Extensions are discussed, including those that model multivariate relations simultaneously, and those that allow for the inclustion of attributes of the individuals in the group.We thank the Editor and two anonymous reviewers for their helpful comments. We are also grateful to George Barnett for allowing us to analyze his data.     

Data Smoothing: Prediction of Human Behavior, Detection of Behavioral Patterns, and Monitoring Treatment Effectiveness in Single-Subject Behavioral Studies

Data-smoothing can be particularly useful in predicting human behavior, detecting behavioral patterns, and monitoring treatment effectiveness in highly variable single-subject behavioral experiments that cannot be determined by only visual inspection of their graphs. Using an example from the applied behavior analytic literature, the use of moving-average and exponential data-smoothing aided the detection of the unique behavioral patterns of a child with autism across different treatments. Furthermore, the utility of the data-smoothing procedures to monitor and control the effectiveness of an intervention is discussed. The ease of their calculations suggest use of data-smoothing by behavior analysts whenever the effects of particular interventions are questionable.     

A marginalization model for the multidimensional unfolding analysis of ranking data

A marginalization model for the multidimensional unfolding analysis of ranking data is presented. A subject samples one of a number of random points that are multivariate normally distributed. The subject perceives the distances from the point to all the stimulus points fixed in the same multidimensional space. The distances are error perturbed in this perception process. He/she produces a ranking dependent on these error-perturbed distances. The marginal probability of a ranking is obtained according to this ranking model and by integrating out the subject (ideal point) parameters, assuming the above distribution. One advantage of the model is that the individual differences are captured using the posterior probabilities of subject points. Three sets of ranking data are analyzed by the model.