JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY We propose the use of the mean parameter for regression analysis of a multivariate binary response. We model the association using dependence ratios defined in terms of the mean parameter, the components of which are the joint success probabilities of all orders. This permits flexible modelling of higher-order associations, using maximum likelihood estimation. We reanalyse two data sets, one with variable cluster size and the other a longitudinal data set with constant cluster size.

This paper investigates the relation between shareholders' portfolio concentration and firm performance. Using data on more than 1.3 million unique shareholders, we create an index that measures how concentrated shareholder portfolios are in each firm. We posit that portfolio concentration will affect incentives when shareholders are resource constrained. We find that average shareholder portfolio concentration is positively related to future operational performance and valuation. We also find that portfolio concentration is positively correlated with abnormal stock returns. Our findings suggest that shareholders with concentrated portfolios are more informed and play a governance role through the stock market.

Models for a multivariate binary response are parameterized by univariate marginal probabilities and dependence ratios of all orders. The w-order dependence ratio is the joint success probability of w binary responses divided by the joint success probability assuming independence. This parameterization supports likelihood-based inference for both regression parameters, relating marginal probabilities to explanatory variables, and association model parameters, relating dependence ratios to simple and meaningful mechanisms. Five types of association models are proposed, where responses are (1) independent given a necessary factor for the possibility of a success, (2) independent given a latent binary factor, (3) independent given a latent beta distributed variable, (4) follow a Markov chain, and (5) follow one of two first-order Markov chains depending on the realization of a binary latent factor. These models are illustrated by reanalyzing three data sets, foremost a set of binary time series on auranofin therapy against arthritis. Likelihood-based approaches are contrasted with approaches based on generalized estimating equations. Association models specified by dependence ratios are contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients.

A set of longitudinal binary, partially incomplete, data on obesity among children in the USA is reanalysed. The multivariate Bernoulli distribution is parameterized by the univariate marginal probabilities and dependence ratios of all orders, which together support maximum likelihood inference. The temporal association of obesity is strong and complex but stationary. We ®t a saturated model for the distribution of response patterns and ®nd that non-response is completely at random for boys but that the probability of obesity is consistently higher among girls who provided incomplete records than among girls who provided complete records. We discuss the statistical and substantive features of respectively pattern mixture and selection models for this data set.