Design and analysis for three level hierarchical structures with count response

In numerous intervention studies and education field trials, random assignment to treatment occurs in clusters rather than at the level of observation. This departure of random assignment of units may be due to logistics, political feasibility, or ecological validity. Data within the same cluster or grouping are often correlated. Application of traditional regression techniques, which assume independence between observations, to clustered data produce consistent parameter estimates. However such estimators are often inefficient as compared to methods which incorporate the clustered nature of the data into the estimation procedure (Neuhaus 1993).1 Multilevel models, also known as random effects or random components models, can be used to account for the clustering of data by estimating higher level, or group, as well as lower level, or individual variation. Designing a study, in which the unit of observation is nested within higher level groupings, requires the determination of sample sizes at each level. This study investigates the design and analysis of various sampling strategies for a 3-level repeated measures design on the parameter estimates when the outcome variable of interest follows a Poisson distribution. ^ Results study suggest that second order PQL estimation produces the least biased estimates in the 3-level multilevel Poisson model followed by first order PQL and then second and first order MQL. The MQL estimates of both fixed and random parameters are generally satisfactory when the level 2 and level 3 variation is less than 0.10. However, as the higher level error variance increases, the MQL estimates become increasingly biased. If convergence of the estimation algorithm is not obtained by PQL procedure and higher level error variance is large, the estimates may be significantly biased. In this case bias correction techniques such as bootstrapping should be considered as an alternative procedure. For larger sample sizes, those structures with 20 or more units sampled at levels with normally distributed random errors produced more stable estimates with less sampling variance than structures with an increased number of level 1 units. For small sample sizes, sampling fewer units at the level with Poisson variation produces less sampling variation, however this criterion is no longer important when sample sizes are large. ^ 1Neuhaus J (1993). “Estimation efficiency and Tests of Covariate Effects with Clustered Binary Data”. Biometrics , 49, 989–996^

AN ELECTROPHYSIOLOGICAL ANALYSIS OF THE AMYGDALOID AND SUBICULAR PROJECTIONS TO THE VENTROMEDIAL NUCLEUS OF THE HYPOTHALAMUS IN THE RABBIT

Electrophysiological experiments were performed on 96 male New Zealand white rabbits, anesthetized with urethane. Glass electrodes, filled with 2M NaCl, were used for microstimulation of three fiber pathways projecting from "limbic" centers to the ventromedial nucleus of the hypothalamus (VMH). Unitary and field potential recordings were made in the VMH after stimulation.^ Stimulation of the lateral portion of the fimbria, which carries fibers from the ventral subiculum of the hippocampal formation, evokes predominantly an inhibition of neurons medially in the VMH, and excitation of neurons located laterally.^ Stimulation of the dorsal portion of the stria terminalis, which carries fibers from the cortical nucleus of the amygdala, also produces predominantly an inhibition of cells medially and excitation laterally.^ Stimulation of the ventral component of the stria terminalis, which carries fibers from the medial nucleus of the amygdala, evokes excitation of cell medially, with little or no response seen laterally.^ Cells recorded medially in the VMH received convergent inputs from each of the three fiber systems: inhibition from fimbria and dorsal stria stimulation, excitation from ventral stria stimulation.^ The excitatory unitary responses recorded medially to ventral stria stimulation and laterally to fimbria and dorsal stria stimulation were subjected to a series of threshold stimulus intensities. From these tests it was determined that each of these three projections terminates monosynaptically on VMH neurons.^ The evidence for convergence upon single VMH neurons of projections from the amygdala and the hippocampal formation suggests this area of the brain to be important for integration of information from these two limbic centers. The VMH has been implied in a number of behavioral states: eating, reproduction, defense and aggression; it has further been linked to control of the anterior pituitary. These data provide a functional circuit through which the amygdaloid complex and the hippocampal formation can channel information from higher cortical centers into a hypothalamic area capable of coordinating behavioral and hormonal responses. ^