2 Researcher Degrees of Freedom
The choices that generate a multiverse are the researcher degrees of freedom: the many defensible ways to move from raw data to a reported estimate (Simmons et al. 2011). They are seldom recorded, and when they are made after seeing the data, even careful analysts can walk a garden of forking paths toward a preferred result without any deliberate fishing (Gelman and Loken 2013).
2.1 Where the choices live
Most degrees of freedom fall into a few families:
- Model specification. Functional form, link function, interactions, and random-effect structure.
- Covariate and confounder selection. Which variables adjust the target association.
- Transformations. Scaling, logarithms, spline terms, and categorisation cut-points.
- Missing-data handling. Complete cases, single imputation, or multiple imputation.
- Exposure and outcome coding. Thresholds, composites, and event definitions.
- Sample construction. Inclusion criteria, outlier rules, and eligibility windows.
2.2 The combinatorics
Choices multiply. Six independent binary decisions already give two to the sixth power, or sixty-four, analyses. A study that varies a handful of covariates, two coding rules, and a missing-data strategy reaches the thousands. Enumerating that space by hand is impractical, which is why the workflow programs it.
2.3 Principled and arbitrary forks
Forks differ in standing. Some reflect substantive knowledge, such as a covariate that a causal diagram marks as a confounder. Others are arbitrary, such as an outlier cut-off chosen for convenience. A useful multiverse separates the two: it gives weight to specifications a domain expert would accept and treats the arbitrary ones as sensitivity checks rather than competing answers. Chapter 9 returns to this distinction. For now the task is to write the decision space down, which the next chapter does with two functions.