Empirical studies in software engineering use software repositories as data sources to understand software development. Repository data is either used to answer questions that guide the decision-making in the software development, or to provide tools that help with practical aspects of developers’ everyday work. Studies are classified into the field of Empirical Software Engineering (ESE), and more specifically into Mining Software Repositories (MSR). Studies working with repository data often focus on their results. Results are statements or tools, derived from the data, that help with practical aspects of software development. This thesis focuses on the methods and high order methods used to produce such results. In particular, we focus on incremental methods to scale the processing of repositories, declarative methods to compose a heterogeneous analysis, and high order methods used to reason about threats to methods operating on repositories. We summarize this as technical and methodological improvements. We contribute the improvements to methods and high-order methods in the context of MSR/ESE to produce future empirical results more effectively. We contribute the following improvements. We propose a method to improve the scalability of functions that abstract over repositories with high revision count in a theoretically founded way. We use insights on abstract algebra and program incrementalization to define a core interface of highorder functions that compute scalable static abstractions of a repository with many revisions. We evaluate the scalability of our method by benchmarks, comparing a prototype with available competitors in MSR/ESE. We propose a method to improve the definition of functions that abstract over a repository with a heterogeneous technology stack, by using concepts from declarative logic programming and combining them with ideas on megamodeling and linguistic architecture. We reproduce existing ideas on declarative logic programming with languages close to Datalog, coming from architecture recovery, source code querying, and static program analysis, and transfer them from the analysis of a homogeneous to a heterogeneous technology stack. We provide a prove-of-concept of such method in a case study. We propose a high-order method to improve the disambiguation of threats to methods used in MSR/ESE. We focus on a better disambiguation of threats, operationalizing reasoning about them, and making the implications to a valid data analysis methodology explicit, by using simulations. We encourage researchers to accomplish their work by implementing ‘fake’ simulations of their MSR/ESE scenarios, to operationalize relevant insights about alternative plausible results, negative results, potential threats and the used data analysis methodologies. We prove that such way of simulation based testing contributes to the disambiguation of threats in published MSR/ESE research.