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.     

An individual difference model for the multidimensional analysis of preference data

A model for the analysis of paired comparison data is presented which combines features of the BTL-model with features of the Unfolding model. The model is metric, mathematically tractable, and has an exact algebraic solution. Since it is multidimensional and allows for individual differences, it is thought to be more realistic for some choice situations than either the Thurstone model or the BTL-model. No claim is made that the present model will be appropriate for all conceivable choice situations. Rather, it is argued that the fact that it is explicitly falsifiable is a point in its favor.This work was supported by a grant of the United States Public Health Service (1 R03 MH19139 01 MSM) and a David Ross (XR) grant of the Purdue Research Foundation (PRF 2132), both of which are gratefully acknowledged. We also owe thanks to Dr. Terry Cooper, whose careful scrutiny of an earlier draft of this paper allowed us to reduce the number of errors from n to n-1.     

Some new results on factor indeterminacy

Some relations between maximum likelihood factor analysis and factor indeterminacy are discussed. Bounds are derived for the minimum average correlation between equivalent sets of correlated factors which depend on the latent roots of the factor intercorrelation matrix . Empirical examples are presented to illustrate some of the theory and indicate the extent to which it can be expected to be relevant in practice.     

Early judgments of semantic and syntactic acceptability by children

Judgments of the acceptability of correct, word order reversed, and semantically anomalous sentences were elicited from 2- and 3-year-old children in a game played with hand puppets. All of the sentences used were simple imperatives and each child was asked to correct those he called wrong. Performance on the judgment task was correlated with each child's mean length of utterance and with his comprehension of reversible active and passive sentences. Only the linguistically most advanced children were able to make a significant number of appropriate judgments and corrections of reversed word order imperatives. Less developed children could appropriately judge and correct semantically anomalous but not incorrect word order imperatives. The importance of semantic as opposed to syntactic factors in children's judgments of the acceptability of sentences is stressed.This research was supported in part by PHS Grant HD-02908 from the National Institute of Child Health and Development. Roger Brown is the principal investigator.     

Air-puff-elicited startle: Habituation over trials and measurement of a hypothetical emotional response

In the first of two experiments, it was demonstrated that an air puff elicited a reliable startle reflex in rats which showed no habituation over 50 trials. In the second study an attempt was made to measure an emotional response by recording startle reactions to the air puff during presentation of a presumed fear-eliciting CS. It was concluded that the air-puff-elicited startle reflex can be employed as an indirect measure of a hypothetical emotional response.     

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.     

Statistical methods for a general theory of all-or-none learning

Greeno and Steiner have shown that a three state Markov Chain with a single absorbing state is equivalent to many of the current formalizations of All-or-None learning theories. Distribution statistics and other summary statistics are derived from the general model. Expressions for the maximum likelihood estimators of its parameters and the sampling variances of the estimates are presented. Likelihood ratio tests for several different null hypotheses are derived. These tests permit one to evaluate the usual null hypotheses in terms of the parameters of a process model.This research was supported in part by a USPHS Predoctoral Research Fellowship, 1-F1-MH-31-289-01, by a grant from the Graduate School of the University of Texas, and by grant HD-02212-01 from the National Institute of Child Health and Human Development to Dr. John Theios.     

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.