Page 111 - Contributed Paper Session (CPS) - Volume 4

CPS2135 Sumonkanti Das et al.
denoted by dummy 2009). The year variable is also used quantitatively to
define linear time trends by using its scaled and centered version (denoted as
yr.c). The final time series model has been developed incorporating fixed and
random effects of these covariates along with the sex, ageclass, motive and
mode variables. A summary of the random effect terms included in the
selected model is shown in Table 1. A very brief summary of the model
building process is given below:
1. In the final selected model the following fixed effects components are
included, where the term like ∗ includes both main and
interaction effects:
∗ + ∗ + ( + +
) ∗ (_ + . ) (4)
2. Higher order fixed effect terms are modeled with random effects
terms, which included level break effects, random intercepts, and
random linear time trends. Full covariance among these effects
improved the model. The resulting model term is named “V BR” in
Table 1.
3. Time trend components were added at different levels, starting with
smooth common trends at an overall level. In the end, using time
trends at the two aggregation levels motive × mode and ageclass ×
motive × mode were found to work best. The terms are named
RW2MM and RW2AMM respectively in Table 1. Best results have
been obtained with diagonal variance for RW2MM and a scalar
variance for the more detailed RW2AMM component.
4. To capture effects of the most influential 2009 outliers, random
effects of dummy 2009 have been included at the domain level, and
the resulting model term is named “V 2009”.
5. White noise was added to capture unstructured dependence over all
levels of all factors. The white noise term is named WN in Table 1.
6. Non-normal prior distributions have been tried for most random
effect terms. A Laplace prior distribution for the random effects term
“V BR” and a horseshoe prior for the outlier term “V 2009” were found
to improve the model performance.

The means over the posterior draws are used as trend estimates, whereas
the standard deviations serve as standard error estimates. The trend estimates
based on the selected model, the direct input estimates and the model fitted
values are shown in Figure 1 at overall level. The black lines are series of direct
estimates, the red lines are the model fit based on all model components, and
the green lines are trend series estimates benchmarked to the OViN level
(including white noise). The trend lines, model fit and the direct estimates are
compared at different level of aggregation including the most detailed level

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