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 fit a saturated model for the distribution of response patterns and find that non-response is missing 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.