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Grammar mistake
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Haziq Jamil committed Jun 27, 2018
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2 changes: 1 addition & 1 deletion chapters/04/04x-examples.tex
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Expand Up @@ -288,7 +288,7 @@ \subsection{Random effects models}
Then, each of these $f^j$ has a slope and intercept for which we can estimate from the fitted regression lines $\hat f^j(x_{ij})$, $i=1,\dots,n_j$.
This would give us the posterior mean estimates of the random intercepts and slopes.
In order to obtain these intercepts and slopes, we simply run a best fit line through the I-prior estimated \code{conc} values.
Furthermore, as $\sigma_0^2$ and $\sigma_1^2$ represent measures of group variability for the intercepts and slopes respectively, we can also calculate this manually for the 10 intercepts and slopes of the fitted I-prior model.
Furthermore, as $\sigma_0^2$ and $\sigma_1^2$ represent measures of group variability for the intercepts and slopes respectively, we can also calculate these manually for the 10 intercepts and slopes of the fitted I-prior model.
In the same spirit, $\rho_{01} = \sigma_{01} / (\sigma_0 \sigma_1)$, which is the correlation between the random intercept and slope, can also be calculated.

\cref{fig:IGF.plot.beta} illustrates the differences in the estimates for the random coefficients, while \cref{tab:igf} illustrates the differences in the estimates for the covariance matrix.
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2 changes: 1 addition & 1 deletion chapters/R/04x-examples.Rnw
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Expand Up @@ -130,7 +130,7 @@ Denote by $f^j$ the individual linear regression lines for each of the $j=1,\dot
Then, each of these $f^j$ has a slope and intercept for which we can estimate from the fitted regression lines $\hat f^j(x_{ij})$, $i=1,\dots,n_j$.
This would give us the posterior mean estimates of the random intercepts and slopes.
In order to obtain these intercepts and slopes, we simply run a best fit line through the I-prior estimated \code{conc} values.
Furthermore, as $\sigma_0^2$ and $\sigma_1^2$ represent measures of group variability for the intercepts and slopes respectively, we can also calculate this manually for the 10 intercepts and slopes of the fitted I-prior model.
Furthermore, as $\sigma_0^2$ and $\sigma_1^2$ represent measures of group variability for the intercepts and slopes respectively, we can also calculate these manually for the 10 intercepts and slopes of the fitted I-prior model.
In the same spirit, $\rho_{01} = \sigma_{01} / (\sigma_0 \sigma_1)$, which is the correlation between the random intercept and slope, can also be calculated.

\cref{fig:IGF.plot.beta} illustrates the differences in the estimates for the random coefficients, while \cref{tab:igf} illustrates the differences in the estimates for the covariance matrix.
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