Raindrop plots: A new way to display collections of likelihoods and distributions

In a variety of settings, it is desirable to display a collection of likelihoods over a common interval. One approach is simply to superimpose the likelihood curves. However, where there are more than a handful of curves, such displays are extremely difficult to decipher. An alternative is simply to display a point estimate with a confidence interval, corresponding to each likelihood. However, these may be inadequate when the likelihood is not approximately normal, as can occur with small sample sizes or nonlinear models. A second dimension is needed to gauge the relative plausibility of different parameter values. We introduce the raindrop plot, a shaded figure over the range of parameter values having log-likelihood greater than some cutoff, with height varying proportional to the difference between the log-likelihood and the cutoff. In the case of a normal likelihood, this produces a reflected parabola so that deviations from normality can be easily detected. An analogue of the raindrop plot can also be used to display estimated random effect distributions, posterior distributions, and predictive distributions.