A general model for the analysis of multilevel data

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multiple time series, and variance and covariance component models.We would like to acknowledge the helpful comments of Ruth Silver. We also wish to thank the referees for helping to clarify the paper. This work was partly carried out with research funds provided by the Economic and Social Research Council (U.K.).     

Declines in Major League Batting Performance as a Function of Game Pressure: A Drive Theory Analysis1

Zajonc's (1965) drive theory explanation argues that greater arousal tends to impair performance on difficult tasks. The hypothesis that arousal generated by “pressure situations” during major league baseball games would hinder batting performance—a difficult task—was tested by examining such performance during the 1989 season. Six “pressure situations” were identified, some occurring during the late innings of close games and others occurring throughout the game when there were two outs. Two measures of batting performance (batting average and slugging average) were employed. Results indicated broad support for the hypothesis. Reasons for this pattern are discussed, as are possible alternative explanations for these findings.     

Word-finding abilities of three types of aphasic subjects

Word-finding difficulties are often observed among different types of aphasic patients. This investigation analyzed the word-finding abilities of 30 aphasic subjects (10 Broca's, 10 Wernicke's, and 10 anomic). Forty nouns counterbalanced according to word length and frequency of occurrence in English language usage were used as stimuli and presented through four modalities (oral expression, writing, auditory comprehension, and reading comprehension). It was expected that patterns of word finding abilities would help in the classification of the different types of aphasia. In addition, long words and less frequently occurring words in English language usage should prove more difficult in word-finding ability, regardless of modality. The results of this study found long words and less frequent words were more difficult for aphasic subjects. Among the modalities, long words were significantly harder than short words for the writing modality only. It was also found that semantic errors were the most common errors for all types of aphasic subjects. Broca's subjects produced significantly moreno response errors in oral expression; Wernicke's subjects produced significantly more semantic and phonemic errors in reading comprehension; and, Wernicke's subjects produced significantly more unrelated errors in both oral expression and reading comprehension. Clinical implications were also discussed.The present study was based on a doctoral dissertation completed at the City University of New York in partial fulfillment of the requirements of the doctoral degree in Speech and Hearing Sciences by the first author under the direction of the second author. The authors wish to thank Dr. Louis J. Gerstman for his assistance with the statistical analysis of this research and Dr. Robert Goldfarb for all his helpful suggestions and editorial comments.     

Conditioned taste aversions support drug discrimination learning at low dosages of morphine.

The present experiment shows that a conditioned taste aversion procedure can support discrimination learning at dosages of morphine comparable to those required to produce motivational effects. Sprague-Dawley rats were injected with 4.0 mg/kg morphine sulfate prior to a saccharin-lithium chloride pairing, and physiological saline prior to a saccharin-saline pairing. The rats avoided the saccharin solution following the administration of morphine and consumed significantly more saccharin following saline administration after four discrimination cycles. After this initial discrimination the subjects were trained with progressively lower doses of morphine. Discrimination learning was apparent at doses of 2.0, 1.5, 1.0, 0.75 and 0.5 mg/kg. Animals initially trained with 1.0 mg/kg morphine also learned the discrimination but required 10 training cycles. After this initial discrimination the subjects were trained with progressively lower dosages of morphine and showed a discrimination at a dosage of 0.5 mg/kg.     

Low-dimensional chaos maps learning in a model neuropil (olfactory bulb).

Quantification of a chaotic system can be made by calculating the correlation dimension (D2) of the data that the system generates (Packard et al., 1980). The D2 algorithm, however, requires stationarity of the generator, a feature that biological data rarely reflect (Mayer-Kress et al., 1988). So we developed the "point correlation dimension" (PD2), an algorithm that accurately tracks D2 in linked data of different dimensions (Carpeggiani et al., 1991). We now present a mathematical argument that, for stationary data, individual PD2s converge to D2 and we demonstrate that the algorithm rejects contributions made by bursts of noise. Data were obtained from the surface of the olfactory bulb of the conscious rabbit (64 electrodes, 640 Hz each, 1.3 sec epochs) before and after presentation of a novel or habituated odor. D2 could be calculated in only 1 of 10 novel-odor trials, whereas PD2 could be calculated in all. Both algorithms indicated that a novel odor evokes a spatially uniform dimensional increase. The PD2 uniquely exhibited the dimensional decreases that occur during inspiration and the gradients of mean dimension present during the nonstimulated control state. These control gradients remained unchanged without odor experience, but showed spatially specific PD2 increases following odor habituation. It is interpreted that, 1) the PD2 is sensitive, accurate, and appropriate for dimensional assessment of biological data, 2) that during analysis of unfamiliar information a single global process is transiently evoked in the neuropil, and 3) after experience multiple spatially specific processes tonically map the sites of learning.     

Application of chaos theory to biology and medicine

The application of “chaos theory” to the physical and chemical sciences has resolved some long-standing problems, such as how to calculate a turbulent event in fluid dynamics or how to quantify the pathway of a molecule during Brownian motion. Biology and medicine also have unresolved problems, such as how to predict the occurrence of lethal arrhythmias or epileptic seizures. The quantification of a chaotic system, such as the nervous system, can occur by calculating the correlation dimension (D2) of a sample of the data that the system generates. For biological systems, the point correlation dimension (PD2) has an advantage in that it does not presume stationarity of the data, as the D2 algorithm must, and thus can track the transient non-stationarities that occur when the systems changes state. Such non-stationarities arise during normal functioning (e.g., during an event-related potential) or in pathology (e.g., in epilepsy or cardiac arrhythmogenesis). When stochastic analyses, such as the standard deviation or power spectrum, are performed on the same data they often have a reduced sensitivity and specifity compared to the dimensional measures. For example, a reduced standard deviation of heartbeat intervals can predict increased mortality in a group of cardiac subjects, each of which has a reduced standard deviation, but it cannot specify which individuals will or will not manifest lethal arrhythmogenesis; in contrast, the PD2 of the very same data can specify which patients will manifest sudden death. The explanation for the greater sensitivity and specificity of the dimensional measures is that they aredeterministic, and thus are moreaccurate in quantifying the time-series. This accuracy appears to be significant in detecting pathology in biological systems, and thus the use of deterministic measures may lead to breakthroughs in the diagnosis and treatment of some medical disorders.     

Low-dimensional chaos maps learning in a model neuropil (olfactory bulb)

Quantification of a chaotic system can be made by calculating the correlation dimension (D2) of the data that the system generates (Packard et al., 1980). The D2 algorithm, however, requires stationarity of the generator, a feature that biological data rarely reflect (Mayer-Kress et al., 1988). So we developed the “point correlation dimension” (PD2), an algorithm that accurately tracks D2 in linked data of different dimensions (Carpeggiani et al., 1991). We now present a mathematical argument that, for stationary data, individual PD2s converge to D2 and we demonstrate that the algorithm rejects contributions made by bursts of noise. Data were obtained from the surface of the olfactory bulb of the conscious rabbit (64 electrodes, 640 Hz each, 1.3 sec epochs) before and after presentation of a novel or habituated odor. D2 could be calculated in only 1 of 10 novel-odor trials, whereas PD2 could be calculated in all. Both algorithms indicated that a novel odor evokes a spatially uniform dimensional increase. The PD2 uniquely exhibited the dimensional decreases that occur during inspiration and the gradients of mean dimension present during the nonstimulated control state. These control gradients remained unchanged without odor experience, but showed spatially specific PD2 increases following odor habituation. It is interpreted that, 1) the PD2 issensitive, accurate, and appropriate for dimensional assessment of biological data, 2) that during analysis of unfamiliar information a singleglobal process is transiently evoked in the neuropil, and 3) after experience multiplespatially specific processes tonically map the sites of learning. Grant Support: National Institutes of Health, HL 31164 and NS27745     

Spatial frequencies and the cerebral hemispheres: contrast sensitivity, visible persistence, and letter classification

The hypothesis that the two cerebral hemispheres are specialized for processing different visual spatial frequencies was investigated in three experiments. No differences between the left and right visual fields were found for: (1) contrast-sensitivity functions measured binocularly with vertical gratings ranging from 0.5 to 12 cycles per degree (cpd); (2) visible persistence durations for 1- and 10-cpd gratings measured with a stimulus alternation method; and (3) accuracy (d') and reaction times to correctly identify digitally filtered letters as targets (L or H) or nontargets (T or F). One significant difference, however, was found: In Experiment 3, a higher decision criterion (beta) was used when filtered letters were identified in the right visual field than when they were identified in the left. The letters were filtered with annular, 1-octave band-pass filters with center spatial frequencies of 1, 2, 4, 8, and 16 cpd. Combining four center frequencies with three letter sizes (0.5 degrees, 1 degree, and 2 degrees high) made some stimuli equivalent in distal spatial frequency (cycles per object) and some equivalent in proximal spatial frequency (cycles per degree). The effective stimulus in the third experiment seemed to be proximal spatial frequency (cycles per degree) not distal (cycles per object). We conclude that each cerebral hemisphere processes visual spatial frequency information with equal accuracy but that different decision rules are used.     

Counselling issues in the fostering and adoption of children at risk of HIV infection

The heterosexual nature of the HIV epidemic in Lothian is such that a number (50 to date) of babies have been born to women who have HIV. Some have needed social work services such as Children Centre placement, foster parents or adopters. Since this work began in 1986, our understanding of the transmission and manifestation of HIV infection in children has grown. However, it is still not possible until children reach the age of two to be certain whether or not they have been infected, or what the outlook is for them. Even then there are some further areas of uncertainty. We have developed a programme of preparation, training and support which has enabled a number of families to live with this uncertainly in offering placements to children at risk of HIV infection.