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CPS2169 Carmen D. Tekwe et al.
Based on our analyses, none of the fitted models detected statistically
significant associations between SDEE at baseline and BMI at 18 months post
baseline. By ad hoc comparisons of the AIC values obtained under all the
models considered, the AIC value associated with the 50th quantile function
of BMI was the lowest (AIC = -416). The AIC values for the LRM and FLRM were
-396 and -392, respectively, indicating that the use of polynomial splines to
represent SDEE did not necessarily provide a better model fit when the two
conditional mean-regression based methods are compared. However, we note
that the AIC values associated with the quantile regression-based models
varied from -218 to -416. No statistically significant associations were also
observed for the impact of SDEE on the conditional quantile functions of BMI
under all the quantile functions considered. The AIC values obtained for all the
quantile functions except for the 50th were either comparable to the values
obtained under the mean regression-based methods or larger. Based on our
analyses, the use of the CFQRM at the 50th level provided the best model fits
when compared to all the other models considered.

Figure 3. Plot of the estimated functional coefficients and their corresponding 95\% point-wise
bootstrap confidence intervals at the 10th, 25th, 50th, 85th, 95th and 99th quantiles. For each
plot, the solid line indicates the estimated quantile specific functional coefficient, while the
dashed lines represent the upper and lower bounds of the confidence intervals.

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