3.23 Models: Assumptions
- Statistical inference → statistical assumptions
- e.g. independence of observations; normality & equal variance of errors; linearity etc.11
- Q: Examples of violations?
- e.g. independence of observations; normality & equal variance of errors; linearity etc.11
- Measurement → measurement assumptions
- e.g. validity & reliability & measurement equivalence (Q: ?)
- Causal inference → “causal inference assumptions” (Stone 1993)
- e.g. selection on observables; parallel trends etc.
- Sometimes assumptions can be tested (their implications), sometimes we simply “make them”
- Data + Assumptions = Conclusions (???)
- Necessity of assumptions for various designs is debated
- We’ll discuss concrete examples!
References
Stone, Richard. 1993. “The Assumptions on Which Causal Inferences Rest.” J. R. Stat. Soc. Series B Stat. Methodol. 55 (2): 455–66.
Assumptions are often related to the data collection process (e.g. assumption that our data represents a simple random sample). Moreover, one can differentiate between model-based assumptions (distributional assumptions, structural assumption, cross-variation assumptions) and design-based assumptions (Wikipedia). Assumptions can be violated, e.g. individuals living in the same household may affecting each other (independence assumption) or individuals with internet my have higher likelihood to end up in a sample (simple random sample) or average of income does not increase linearly with higher levels of education (linearity assumption) etc.↩