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.     

Aggression as a reinforcer: operant behavior in the mouse-killing rat

Two experiments examined mouse killing as a reinforcer of key pressing by rats that killed mice. In Experiment I, mouse-killing rats performed the key-pressing response when each press was reinforced with presentation of a mouse. Offered a choice between a key that yielded presentation of mice and one that did not, the rats preferred the key that yielded mice. When the contingency was reversed, the rats preferred the other key and continued to kill mice. In Experiment II, mouse-killing rats that did not kill rat pups performed a key-pressing response reinforced with presentation of mice on a variable-interval schedule. In tests for responding reinforced on that schedule with presentation of normal mice, anesthetized mice, dead mice, or rat pups, these rats that killed mice but not rat pups exhibited a decline in response rate when rat pups were the reinforcer. Altering the condition of the mice did not significantly affect performance.     

The development of stimulus control with and without a lighted key

In two experiments, the effect of an illuminated response key on the acquisition of stimulus control by an airflow stimulus was assessed. In the first experiment, pigeons were given nondifferential training with airflow emerging from behind the response key in one of three conditions of illumination: trained to peck a lighted key, trained to peck an unlighted key with a houselight present, trained to peck a key in total darkness. After 10 days of training on a variable-interval schedule of reinforcement, all subjects were given a generalization test on airflow velocity. The gradients for subjects trained in the dark were sharp, while those for subjects trained in lighted conditions were shallow. In the second experiment, the effect of an irrelevant keylight on the acquisition of an airflow velocity discrimination was assessed. Two groups of pigeons were trained to discriminate two airflow velocities. One group was trained with a lighted response key and the other was trained to peck the response key in total darkness. The dark-trained subjects acquired the discrimination more rapidly. The results demonstrate that the acquisition of stimulus control by airflow with either a differential or nondifferential training procedure can be overshadowed by keylight.     

A NOTE ON THE POSSIBLE DETERMINANT OF “SPLIT REPRESENTATION” AS AN ARTISTIC STYLE

L'A. fait L'hypothèse que le dédoublement de la représentation, qui est caractéristique du style graphique de certaines cultures, provient d'une préférence universelle pour ce type de dessin chez les tout jeunes enfants de toutes cultures; mais dans la plupart des cultures, cette préférence serait supprimée parce que, paradoxalement, les dessins doubles ne permettent pas de reconnaître les objets dessinés aussi facilement que les dessins conventionnels qui sont plus proches de la projection rétinienne des objets. Les dessins avec enchaînement ou dédoublement de la représentation seraient conservés chaque fois qu'ils sont appréciés en tant que code utilisé à d'autres fins que L'information sur les objets peints et pour leur valeur esthétique.     

CIRCULAR RELATION BETWEEN UNDERSTANDING AND LOGIC

Procedures for determining logicality presuppose understanding, and procedures for determining understanding presuppose logic. One can escape from this circle only by presupposing logicality, in agreement with common-sense thinking. Understanding can then be studied as an empirical variable. Traditional research has been based on the opposite solution: Logicality is treated as an empirical variable, understanding is implicitly presupposed; hence results are obtained which do not 'make sense'. One cannot understand the illogical.