In this thesis I consider a number of methodological innovations that allow context and heterogeneity to be statistically modelled when using temporal data in the social sciences. It is argued first that multilevel models are to be preferred to 'fixed effects' (FE) models, because of the formers' ability to explicitly model heterogeneity; the supposed downsides of FE models are easily solvable within the random effects framework, through the explication of 'within' and 'between' individual effects. Second, I consider the age-period-cohort (APC) identification problem, showing that one supposed solution, the Hierarchical APe model, is flawed. An adaption of that multilevel model is suggested, but this requires certain assumptions to be made, such as that there are no period trends. This model can also be extended to incorporate other spatial contexts, and to include within and between effects. These methodological recommendations are illustrated with a number of empirical examples, which bring into question current understandings of substantive debates across the social sciences. I show that the relationship between growth and debt varies greatly between countries, and in general operates in the direction from growth to debt and not vice-versa as suggested by many in the literature. Second, I show that the effect of democracy on globalisation is also somewhat variable, and that the average effect is not statistically significant. Third, I show that mental wellbeing worsens throughout the life course, and does not form a U-shape as previously suggested by others. That all of these findings directly contradict current knowledge in a number of areas shows the importance of the methodological arguments made, and the importance of accounting for and measuring heterogeneity in a realistically complex way.