A major aim of island biogeography has been to describe general patterns of species richness across islands and to identify the processes responsible. Data are often collected across many islands; with larger datasets providing increased statistical power and more accurate parameter estimates. However, there is often structure in observational data, violating an assumption of linear models that each datum is independent. In island biogeography this structure may take the form of an island, archipelago or taxon being represented by multiple data points. We survey recent papers in this field and find that these forms of non-independence are a common feature. Most authors addressed this problem by conducting separate analyses for each archipelago, taxon or combination of the two, but a better tool for dealing with non-independence and structure in data, the mixed model, already exists. We demonstrate the advantages of a mixed model approach by applying it to a well-known dataset that spans 134 observations of single island endemic (SIE) richness across 39 islands, four archipelagos and four taxa. Taking island area and age into account, SIE richness varies substantially more among archipelagos than it does among islands or taxa. We find that SIE richness rises with island age on the Azores and Galapagos, while on the Canaries and Hawaii SIE richness initially rises with age but later declines on older islands. Our analyses demonstrate three advantages to island biogeography of applying a mixed modelling approach: 1) structure in the data is controlled for; 2) the variance among islands, archipelagos and taxa is estimated; 3) all the data can be included in a single model, making it possible to test whether trends are general across all archipelagos and taxa or are idiosyncratic.