The relationship between the field-shifting phenomenon and representational coherence of place cells in CA1 and CA3 in a cue-altered environment.

Subfields of the hippocampus display differential dynamics in processing a spatial environment, especially when changes are introduced to the environment. Specifically, when familiar cues in the environment are spatially rearranged, place cells in the CA3 subfield tend to rotate with a particular set of cues (e.g., proximal cues), maintaining a coherent spatial representation. Place cells in CA1, in contrast, display discordant behaviors (e.g., rotating with different sets of cues or remapping) in the same condition. In addition, on average, CA3 place cells shift their firing locations (measured by the center of mass, or COM) backward over time when the animal encounters the changed environment for the first time, but not after that first experience. However, CA1 displays an opposite pattern, in which place cells exhibit the backward COM-shift only from the second day of experience, but not on the first day. Here, we examined the relationship between the environment-representing behavior (i.e., rotation vs. remapping) and the COM-shift of place fields in CA1 and CA3. Both in CA1 and CA3, the backward (as well as forward) COM-shift phenomena occurred regardless of the rotating versus remapping of the place cell. The differential, daily time course of the onset/offset of backward COM-shift in the cue-altered environment in CA1 and CA3 (on day 1 in CA1 and from day 2 onward in CA3) stems from different population dynamics between the subfields. The results suggest that heterogeneous, complex plasticity mechanisms underlie the environment-representating behavior (i.e., rotate/remap) and the COM-shifting behavior of the place cell.

Effect of nonnormal random components on level and power in group-randomized trials

The use of group-randomized trials is particularly widespread in the evaluation of health care, educational, and screening strategies. Group-randomized trials represent a subset of a larger class of designs often labeled nested, hierarchical, or multilevel and are characterized by the randomization of intact social units or groups, rather than individuals. The application of random effects models to group-randomized trials requires the specification of fixed and random components of the model. The underlying assumption is usually that these random components are normally distributed. This research is intended to determine if the Type I error rate and power are affected when the assumption of normality for the random component representing the group effect is violated. ^ In this study, simulated data are used to examine the Type I error rate, power, bias and mean squared error of the estimates of the fixed effect and the observed intraclass correlation coefficient (ICC) when the random component representing the group effect possess distributions with non-normal characteristics, such as heavy tails or severe skewness. The simulated data are generated with various characteristics (e.g. number of schools per condition, number of students per school, and several within school ICCs) observed in most small, school-based, group-randomized trials. The analysis is carried out using SAS PROC MIXED, Version 6.12, with random effects specified in a random statement and restricted maximum likelihood (REML) estimation specified. The results from the non-normally distributed data are compared to the results obtained from the analysis of data with similar design characteristics but normally distributed random effects. ^ The results suggest that the violation of the normality assumption for the group component by a skewed or heavy-tailed distribution does not appear to influence the estimation of the fixed effect, Type I error, and power. Negative biases were detected when estimating the sample ICC and dramatically increased in magnitude as the true ICC increased. These biases were not as pronounced when the true ICC was within the range observed in most group-randomized trials (i.e. 0.00 to 0.05). The normally distributed group effect also resulted in bias ICC estimates when the true ICC was greater than 0.05. However, this may be a result of higher correlation within the data. ^

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^