A full-likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability. The binomial and beta-binomial models are shown to occur as special cases correspondingly, respectively, to the choice of degenerate and beta-mixing distributions. For a finite exchangeable binary sequence of random variables, expressions for the joint distribution, moments, and correlations of all orders are derived. Maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster. In an application to developmental toxicology data analysis, the procedure introduced is compared with a beta-binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose.

Turn-taking is a universal and fundamental feature of human vocal communication. Through protoconversation, caregivers play a key role for infants in helping them learn the turn-taking system. Infants produce both speech-like vocalizations (i.e., protophones) and cries from birth. Prior research has shown that caregivers take turns with infant protophones. However, no prior research has investigated the timing of caregiver responses to cries. The present work is the first to systematically investigate different temporal patterns of caregiver responses to protophones and to cries. Results showed that, even in infants' first 3 months of life, caregivers were more likely to take turns with protophones and to overlap with cries. The study provides evidence that caregivers are intuitively aware that protophones and cries are functionally different: protophones are treated as precursors to speech, whereas cries are treated as expressions of distress.

Hormetic effects have been observed at low exposure levels based on the dose-response pattern of data from developmental toxicity studies. This indicates that there might actually be a reduced risk of exhibiting toxic effects at low exposure levels. Hormesis implies the existence of a threshold dose level and there are dose-response models that include parameters that account for the threshold. We propose a function that introduces a parameter to account for hormesis. This function is a subset of the set of all functions that could represent a hormetic dose-response relationship at low exposure levels to toxic agents. We characterize the overall dose-response relationship with a piecewise function that consists of a hormetic u-shape curve at low dose levels and a logistic curve at high dose levels. We apply our model to a data set from an experiment conducted at the National Toxicology Program (NTP). We also use the beta-binomial distribution to model the litter response data. It can be seen by observing the structure of these data that current experimental designs for developmental studies employ a limited number of dose groups. These designs may not be satisfactory when the goal is to illustrate the existence of hormesis. In particular, increasing the number of low-level doses improves the power for detecting hormetic effects. Therefore, we also provide the results of simulations that were done to characterize the power of current designs in detecting hormesis and to demonstrate how this power can be improved upon by altering these designs with the addition of only a few low exposure levels.

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