Determining dependence among random variables across observations

Abstract

It is common in applied research to analyze data from data generating processes with dependencies among random variables across observations. Such dependencies impact power calculations and standard errors. However, it is also common to mistake the structure of data for the structure of the data generating process and thereby to use inappropriate standard error estimators. The challenge is not merely to distinguish data from data generating processes but also to determine dependence. This paper discusses the problem and provides a four-step guide, with examples, for determining dependence of random variables across observations.

Keywords

• clustered standard errors
• data generating process
• dependent random variables
• hierarchical models
• nested data