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I estimated a random slope,random intercept model and have estimates of the fixed-effects $\beta_i$ and the random effects $b_i$. I also have their associated standard errors $SE_{\beta_i}$ and $SE_{b_i}$ and their 95$\%$ estimated confidence intervals, $\mu_{\beta_i} \pm 1.96\cdot SE_{\beta_i}$ and $\mu_{b_i} \pm 1.96\cdot SE_{b_i}$. My question is, is there a way to form an equivalent 95$\%$ confidence interval for the quantity $\beta_i + b_i$? Is this even possible? Thanks!

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    $\begingroup$ Finding a confidence interval for a random effect seems odd. AFAIK, normally one estimates its variance. $\qquad$ $\endgroup$ – Michael Hardy Jul 2 '16 at 18:45
  • $\begingroup$ @MichaelHardy Thanks for the reply! Just to put it in context, I'm trying to compare group level coefficients from the classical linear mixed effects model with an equivalent hierarchical bayesian linear regression model. I thought comparing confidence intervals on the group-level coefficients would be one way to compare the two along with deviance and log-likelihood and predictive error. I suppose this would lead to another question of whether this is appropriate, but that's why I'm trying to get the confidence intervals. Thanks! $\endgroup$ – TSP Jul 2 '16 at 19:09

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