Multilevel models in developmental psychological research: Rationales and applications

The armoury of statistical techniques has recently been enhanced with the multilevel model for longitudinal data. The present article explains the multilevel model for longitudinal data to the statistically non-sophisticated reader. It shows how the model relates to the five rationales of longitudinal research, as they were put forward by Baltes and Nesselroade (1979). In addition, it shows how the model matches Wohlwill's methodology of developmental functions. To elucidate the model further, three applications are given. The applications pertain to the development of children's sleeping duration during the first 18 months of life, the effects of early hospitalization on the daily frequency of crying, and the developmental relationship between social and solitary play.     

A tether system for cardiovascular studies with the behaving micropig

A tether system has been developed for continuous monitoring of blood pressure in the micropig. The micropig is a suitable model for blood-pressure research because of the similarity of its cardiovascular system to that of humans and because of its sensitivity to high sodium intake. The system consists of a metal boom, attached via a universal joint to a wall 6 ft above floor level, that extends horizontally to the center of the enclosure. A fluid and electronic swivel affixed to the boom is connected to a flexible, hollow, metal tether that descends to a vest worn by the micropig. The vest contains a pressure transducer to which an indwelling arterial catheter is connected via a stopcock. The transducer cable and an infusion line ascend through the interior of the tether to the swivel. The system remains in equilibrium through a system of pulleys and counterweights. Continuous, 24-h recording shows a diurnal variation characterized by higher heart rate but lower blood pressure during the day than at night. The system has been found to be effective for continuous studies over intervals of a month or more.     

Response-key input via the IBM PC/XT/AT’s parallel printer port

A simple and inexpensive way to connect response keys to the IBM PC/XT/AT’s parallel printer port is presented.     

Shaw’s stored information as a quantitative measure of sequential structure

In this paper, we describe a method to study the sequential structure in interevent times. The technique uses the stored information of an iterative map developed by-Shaw (1984). The stored information is a quantitative measure of the sequential organization or predictability in data. This paper discusses the concept of stored information and provides a FORTRAN routineto compute the stored information of interevent time data. Several synthetic data sets with known sequential structures are examined. Finally, we present some initial results from computing the stored information of experimental interresponse time data.     

GRADER: A computer program that recommends student letter grades

GRADER, a computer program that makes student test and/or course letter grade recommendations to instructors, is described. The program uses an algorithm to combine the content mastery (percentage correct) and peer comparison (“curve”) approaches to set grade cutoffs. In addition to standardizing the procedures with which letter grade cutoffs are made, GRADER may help to reduce instructor grading subjectivity and obviate tendencies toward grade inflation or deflation.     

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.     

The effect of unilateral stellectomy on the regulation of heart rate during behavioral stress

Changes in heart rate were examined during classical aversive conditioning before and after either left (n=10) or right stellectomy (n=8). Heart rate (HR) significantly (p<0.01) increased in response to the conditional stimulus with a further increase noted during the unconditional stimulus. After right stellectomy (RSGx) the aversive stress elicited a significantly (p<0.01) smaller increase in heart rate (peak HR change: control 66.8 +/- 6.0; RSGx 36.1 +/- 6.8 beats/min). In contrast left stellectomy did not significantly alter the heart rate conditional response. Cardioselective beta-adrenergic receptor blockade, metoprolol HCl (BB, 1.0 mg/kg, n=8), significantly (p<0.01) reduced the heart-rate conditional response (peak HR change: control 66.8 +/- 6; BB 25.1 +/- 3.8 beats/min) to the same extent as noted during RSGx. These data suggest that the heart-rate increases elicited by aversive stress are mediated in part by sympathetic nerves that originate or pass through the right stellate ganglion. The residual HR increase noted after RSGx or BB probably results from the withdrawal of cardiac parasympathetic activity.     

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     

The linkage between stimulus frequency and covert peak areas as it relates to monaural localization

Head-related transfer functions for differently centered narrow noise bands were obtained on 6 subjects. Derived from these measurements were covert peak areas (CPAs), defined as the spatial constellation of loudspeakers that generates maximal sound pressure at the entrance of the ear canal for specific bands of frequency. On the basis of previous data, we proposed that different frequency bands served as important spectral cues for monaural localization of sounds from different loci and that location judgments were directed toward the CPAs associated with the different bands. In the first study, the stimuli were bandpass filtered so that they contained only those frequencies whose associated CPAs occupied either the monaural listener’s “upper” or “lower” spatial regions. Loudspeakers, separated by 15°, were stationed in the left hemifield, ranging from 0° to 180° azimuth and ?45° to 60° elevation. Subjects reported the loudspeaker from which the sound appeared to originate. Judgments of the sound’s elevation were in general accord with the CPAs associated with the different frequency segments. In the second study, monaural localization tests were administered in which different 2.0-kHz-wide frequency bands linked with specific CPAs were notch filtered from a 3.5-kHz highpass noise band. For the control condition, the highpass noise was unfiltered. The data demonstrated that filtering a frequency segment linked with specific CPAs resulted in significantly fewer location responses directed toward that particular spatial region. These results demonstrate in greater detail the relation between the directional filtering properties of the pinna and monaural localization of sound.     

Three-space inference from two-space stimulation

Oblique contours sloping at 30° with respect to the horizontal were presented alone, in combination to form chevrons, or with a vertical line to form arrowhead or Y patterns; they were projected onto a screen in the frontal parallel plane and viewed from positions that gave viewing angles of 90° (normal to the screen’s surface), 53°, or 34°. The perceived orientation of the contours, as assessed by a movable arm that the subjects set to be parallel to the obliques, changed monotonically as a function of viewing angle. The change was as great for single obliques as for combinations of obliques within the chevron, arrowhead, and Y patterns. The results of Experiment 1 were extended in Experiment 2, in which obliques at 30° and 50° with respect to the horizontal were presented singly or in combination as chevron patterns. It is argued that the results of both experiments indicate that single two-space oblique lines are immediately interpreted as lying in three-space and that the changes in perceived orientation are a consequence of this perceptual inference.