Observed heterogeneity is variation in outcome propensities explained by measured covariates, such as age or sex. In logistic regression, subjects with different recorded predictor values may have different success probabilities, even before allowing for their previous outcomes. This is heterogeneity visible through observed predictors.
Unobserved heterogeneity is persistent variation between subjects arising from unmeasured characteristics. A subject-specific latent variable or random intercept can represent it. Subjects with high latent success propensities tend to succeed repeatedly, so their observed outcomes can have positive serial correlation even when outcomes are conditionally independent given that propensity. Apparent persistence therefore need not imply true state dependence.
True state dependence, also called true contagion, means that a previous outcome changes the distribution of a subsequent outcome after controlling both measured covariates and persistent unobserved heterogeneity. For example, an earlier successful week may make later success more likely through habit formation. A lagged-outcome coefficient in an inadequate statistical model can also reflect omitted subject differences, so positive observed persistence alone does not distinguish true state dependence from unobserved heterogeneity.
Articles by others on the same topic
There are currently no matching articles.