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03_methods.qmd
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03_methods.qmd
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# Methodology
```{r setup, file = "R/chapter_start.R", include = FALSE}
library(tidyverse)
library(modelsummary)
```
```{r setup2, include = FALSE}
# Other packages ------
# These are packages that get used in this chapter but aren't part of the default set.
library(kableExtra)
```
To estimate the impact of Utah's IMT program expansion, UHP CAD crash data and UDOT TransSuite lane closures data were integrated, IMT performance measures were calculated for each incident after obtaining all required timestamps, and user impacts were quantified for each incident with qualifying characteristics.
## Crash Dataset Integration
The primary crash data source for this analysis was the UHP CAD database, which includes the timestamps of IMTs and UHP teams for each incident response. UHP provided the research team with a version of the data with confidential information redacted. The crash types included in the CAD data are PDO, PI, and FII. @fig-TIM_Timeline shows the timestamps required to calculate RT, RCT, and ICT. The timestamps needed for calculating performance measures are T~1~, T~4~, T~5~, and T~6~. T~1~ corresponds with the time when the incident was reported. T~2~ was assumed to be equal to T~1~ due to most incidents being reported by UHP officers who patrol for crashes that are then verified by UDOT Traffic Operations Center personnel. T~4~ is the time at which responders arrived at the incident location. T~5~ corresponds with the time when all lanes of traffic were cleared, and T~6~ corresponds with the time when first responders left the site. RT, RCT, and ICT are calculated by taking the difference of T~4~, T~5~, and T~6~ with T~1~, respectively. T~7~ is the time at which the flow of traffic returns approximately to normal flow conditions.
```{r chunk}
#| label: fig-TIM-Timeline
#| fig-cap: TIM timeline (adapted from @conkliin_data_2013).
#| out-width: 100%
knitr::include_graphics("images/TIMtimeline.png")
```
The CAD data were adequate to determine the performance measures of RT and ICT for most incidents but not for RCT, which was obtained from the UDOT TransSuite database. The TransSuite database includes the timestamps of lane closures, which were used for the T~5~ timestamp for each incident in which TransSuite had the data available. An Excel Visual Basic for Applications (VBA) script was used to pair incidents from the CAD dataset and TransSuite dataset within a similar timeframe as potential matches for the same incident, and potential matches were evaluated and verified by the research team based on the locations and details included in both databases for the given incident. The lane closure data for confirmed matches were then integrated into the CAD data using a VBA script.
The total number of incidents contained in the 2018 and 2022 datasets were 1,097 and 1,526, respectively, which were both taken for the months of March through August of the respective years. Of these total incidents, the majority were PDO crashes. PI crashes made up a minor portion and FII crashes made up less than one percent for both years. Nearly all incidents had an ICT value and the majority had an RT value, as shown in @tbl-datatype. However, only 28 percent of incidents in 2018 and 21 percent of incidents in 2022 had an available RCT value due to TranSuite only overlapping with the CAD database for that portion of incidents. This reduced the total number of incidents with all necessary timestamps and performance measures (RT, RCT, and ICT) to 283 and 307 incidents for 2018 and 2022, respectively, leaving only 26 percent and 20 percent of the original number of incidents, respectively.
| Data Type | 2018 Crashes | 2018 Percentage | 2022 Crashes | 2022 Percentage |
|:-------------:|:-------------:|:-------------:|:-------------:|:-------------:|
| Incidents | 1,097 | 100% | 1,526 | 100% |
| ICT | 1,089 | 99% | 1,520 | \>99% |
| RT | 944 | 86% | 1,272 | 83% |
| RCT | 305 | 28% | 319 | 21% |
| ICT, RT, and RCT | 283 | 26% | 307 | 20% |
| Incidents Analyzed for User Impacts | 172 | 16% | 236 | 15% |
: Data Type {#tbl-datatype}
Summary statistics for the performance measures, user impacts, and other pertinent IMT data for years 2018 and 2022 are compared in @tbl-SummaryStats. All performance measures had large standard deviations from the mean due to the wide range of values contained for each parameter in the dataset. For IMT performance measures, the mean of RT decreased from 16.5 minutes in 2018 to 13.8 minutes in 2022, for a difference of 2.7 minutes with a standard error of 1.1 minute. However, IMT RCT and ICT increased by 8.9 minutes and 3.6 minutes, respectively, from 2018 to 2022, showing that IMTs did not necessarily clear all lanes of the roadway or leave the crash site any faster in 2022 than in 2018.
```{r tbl-SummaryStats}
#| label: tbl-SummaryStats
#| tbl-cap: Summary Statistics for IMT Incidents Analyzed
IMTSummaryStats <- read_csv("data/TIM Phase III Data for ETT analysis Final.csv") |>
select(Year, `Crash Type`, RT, RCT, ICT, AV, ETT, EUC, T7T0)
datasummary_balance(
~ Year,
IMTSummaryStats |>
rename(`Response time (RT) [min]` = RT,
`Roadway clearance time (RCT) [min]` = RCT,
`Incident clearance time (ICT) [min]`= ICT,
`Affected volume (AV)[veh]` = AV,
`Excess travel time (ETT)[min]` = ETT,
`Excess user costs (EUC)[$]` = EUC) |>
mutate(
`Crash Type` = case_when(
str_detect(`Crash Type`, "PD") ~ "Property damage",
str_detect(`Crash Type`, "PI") ~ "Injury",
str_detect(`Crash Type`, "Fatal") ~ "Fatal",
)
))
```
For user impacts of crashes responded to by IMTs, AV decreased from an average of 7,826.5 vehicles affected per crash in 2018 to 6,505.8 in 2022, for a difference of -1,320.7 vehicles and a percent difference of 16.9 percent between 2018 and 2022. While ETT and EUC both had standard deviations larger than the means due to the wide range of values included for both parameters, ETT decreased from 845.3 hours of delay per crash in 2018 to 476.5 in 2022; this is a difference of -368.8 between 2022 and 2018 and a percent difference of 43.6 between 2018 and 2022. EUC decreased from \$21,725.50 per crash in 2018 to \$12,537.40 in 2022; this is a difference of -\$9,188.20 and a percent difference of 42.3 between 2018 and 2022. The T~7~-T~0~ parameter, representing the total time for which the speed of traffic is significantly reduced, decreased by about 4.5 minutes between 2018 and 2022.
These initial results for the expansion of the IMT program show that while IMT RCT and ICT showed no significant difference that IMT RT decreased slightly and user impacts decreased significantly. AV decreased by 16.9 percent, and ETT and EUC both decreased by approximately 43 percent between 2018 and 2022.
## User Impacts
User impacts were quantified for all incidents that had a decipherable queue and no secondary incidents whose queue affected that of the primary incident. Incidents were evaluated for user impacts by obtaining UDOT traffic data for roadways at the time and location of the incident as well as for the same location but on normal days when an incident did not occur to establish baseline conditions. The stretch of the roadway where traffic was affected by a crash was then segmented into subroutes between ramps to evaluate the time when the average speed of traffic first decreased significantly below normal (T~0~) and when it returned to within normal (T~7~) to a granularity of 5 minutes. The AV of each subroute was taken as the sum of the volume of vehicles between T~0~ and T~7~ for the incident day, and the AV of the incident was taken to be the maximum AV of all subroutes affected by the crash. The effects of diversion were not included in this analysis.
The ETT of an incident was found by calculating the ETT for each 5-minute increment between T~0~ and T~7~ for the incident and average of normal days. The hours of ETT for each 5-minute increment were found by multiplying the average travel time of the subroute by the volume of vehicles at that location. The ETT of an incident was then calculated by taking the difference between the sum of the ETT for each 5-minute increment between T~0~ and T~7~ for the incident and average of normal days.
EUC is the sum of the cost of ETT for passenger vehicles and trucks. Costs due to the ETT of passengers and trucks are the only factors considered in this analysis. The formula used for EUC in @eq-euc is shown below where the percent trucks (T) was the portion of vehicles over 30 ft in length obtained from UDOT Traffic Data; the average vehicle occupancy (AVO) was taken as 1.14 for the I-15 based on @schultz_ut1503_2015; the individual hourly cost (IHC) and truck hourly cost (THC) were taken as \$17.81 and \$53.69 based on @ellis_value_2017. While the IHC and THC are somewhat outdated for the 2022 data, these values were still used to be consistent with 2018 EUC values to make a valid comparison free of the effects of inflation.
$$EUC = ETT \times ((1-T) \times AVO \times IHC + T \times THC) $$ {#eq-euc}
## Models
This study hypothesizes that the expanded IMT program was the primary cause for the reduction in user impacts as well as IMT RT. The dependent variables considered in this analysis were the natural log of all user impacts ($Ln AV$, $Ln ETT$, and $Ln EUC$), the natural log of RCT ($Ln RCT$) and IMT ICT ($Ln ICT$), and IMT $RT$. Due to the data distribution for all user impacts and most performance measures being right-skewed, or skewed towards large outliers, it was determined that a natural log ($Ln$) transformation would be taken to better fit the user impacts and performance measures data with the exception of $RT$, for which a natural log transformation did not help better describe the data for this variable. The independent variables considered for performance measures were incident characteristics described in this section. The independent variables considered for user impacts were $Ln T_{7}-T_{0}$, performance measures, and incident characteristics.
The first incident characteristics considered in the models for this analysis was the $Year$. The years for which crash data were analyzed were 2018 (reference case) and 2022, explaining the difference in user impacts and IMT performance based on IMT program size before and after the expansion. This was treated as a categorical variable. The $Crash Type$ variable was included due to it accounting for some significant differences in crash data; the crash types included are PDO, PI (reference), and FII. It should be noted that FII crashes had a very small sample size, thus skewing many of the results due to the irregular nature of these crashes and the complications introduced by them to incident response protocol.
The $Time Range$ variable was included; crashes analyzed for user impacts were divided into the following time ranges:
- Morning Off Peak (Morning): 11:45 PM to 5:30 AM
- AM Peak: 5:30 AM to 9:00 AM
- Afternoon Off Peak (Afternoon) (Reference case): 9:00 AM to 3:45 PM
- PM Peak: 3:45 PM to 6:15 PM
- Night Off Peak (Night): 6:15 PM to 11:45 PM
The Number of IMTs ($N.IMTs$) that responded to a crash was included. Note that this is a reactionary variable; IMT protocol was to dispatch one team for crash response for most incidents or two teams for more severe incidents. Additional teams were sent based on crash severity and IMT availability rather than an anticipated number being sent initially. A variable similar in nature to this that was also included in the analysis was the Number of UHPs Teams ($N.UHPs$) that responded to a crash. These parameters were both found to be correlated with IMT performance measures but not as well with user impacts.
The Number of Lanes Closed ($N. Lanes Closed$)at any point during incident response was well correlated with ETT. A similar variable that was quantified to further investigate the effect of IMTs clearing a lane at any given time was the time weighted number of lanes closed ($TWNLC$). This is the time weighted average of the number of lanes closed during incident response, which was initially hypothesized to more precisely determine the user impacts of a crash. This was calculated using the relationship in @eq-twnlc where t~i~ is the number of minutes that each given lane i was closed (0 minutes for lanes that were not closed), N is the number of lanes at the bottleneck of the crash, and t^\*^ is the total time for which any lane of the roadway was closed during an incident. One limitation of this parameter is that not all incidents analyzed for user impacts had all lane closures clearly defined without errors in the data to clearly determine $TWNLC$, therefore only 379 incidents of the 401 total number of incidents analyzed for user impacts (95 percent) could be analyzed for this parameter.
$$ TWNLC = \frac{\sum_{i=1}^{N}t_i}{N \times t^*}$$ {#eq-twnlc}
The Total Number of Lanes at the bottleneck of a crash ($TotalLanes$) was included for user impacts analysis as it was correlated with AV. The dominant independent variable for user impacts was $Ln T_{7}-T_{0}$, or the natural log of the difference between the time when the average speed of traffic during an incident returned to within approximately 20 mph of the average speed at normal conditions (T~7~) and the time when the incident occurred (T~0~). This is effectively the incident duration for which roadway users are impacted. A logarithmic transformation was applied due to the right-skew of the data and to achieve best fit in linear regression.
The model groups analyzed to evaluate the UDOT IMT program expansion are shown in @eq-pmi and @eq-uii. The variable index $i$ denotes being for a single incident, PM is performance measure, TR is time range, CT is crash type, and $X$ is a vector of the other incident characteristics variables not listed above, and $\beta$ are estimated coefficients. While various models were evaluated for each performance measure and user impact, only those with most meaningful results are presented hereafter. $$ {PM}_i = {Year}_i + {TR}_i + {CT}_i + X_i\beta $$ {#eq-pmi}\
$$ {UI}_i = {Year}_i + {TR}_i + {CT}_i + {Ln(T_7 -T_0)}_i\beta + {PM}_i\beta + X_i\beta$$ {#eq-uii}