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Working Independence versus modeling correlation Longitudinal Example

Working Independence versus modeling correlation Longitudinal Example. Generate data in clusters (i.e., a person) 5 observations per cluster Response is a linear function of time Y it =  0 +  1 t + e it The residuals are first-order autoregressive, AR(1)

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Working Independence versus modeling correlation Longitudinal Example

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  1. Working Independence versus modeling correlationLongitudinal Example Generate data in clusters (i.e., a person) • 5 observations per cluster Response is a linear function of time Yit = 0 + 1t + eit The residuals are first-order autoregressive, AR(1) eit =ei(t-1) + uit(the u’s are independent) corr(ei(t+s) , eit) = s Estimate the slope by • OLS: assumes independent residuals • Maximum likelihood: models the autocorrelation Bio753: Adv. Methods III

  2. Comparisons Compare the following reported Var(1) • That reported by OLS (it’s incorrect) • That reported by a robustly estimated SE for the OLS slope (It’s correct for the OLS slope) • That reported by the MLE model • It’s correct if the MLE model is correct You can use any working correlation model, but need a robust SE to get valid inferences Bio753: Adv. Methods III

  3. Variance of OLS & MLE Estimates of b versus , the first-lag Correlation MLE reported variance OLS reported variance True variance of OLS Bio753: Adv. Methods III

  4. Benefits & Drawbacks of working non-independence Benefits • Efficient estimates • Valid standard errors and sampling distributions • Protection from some missing data processes • The MLM/RE approach allows estimating conditional-level parameters, estimating latent effects and improving estimates Drawbacks • Working non-independence imposes more strict validity requirements on the fixed effects model (the Xs) • Can get valid SEs via working independence with robust standard errors • At a sacrifice in efficiency Bio753: Adv. Methods III

  5. There is no free lunch! Working independence models (coupled with robust SEs!!!) are sturdy, but inefficient Fancy models are potentially efficient, but can be fragile Bio753: Adv. Methods III

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