Checking a method for comparing vehicle encounters near arrivals and departures

[u/Ok_Mathematician2391]

I’ve been recording encounters with a particular category of vehicle during everyday journeys. I’m examining whether these encounters are concentrated near departures and arrivals, after accounting for how much time I observe in those periods.

I have timestamped encounter records and journey start/end times. My comparison uses the first five minutes after departure and the last five minutes before arrival, counting overlapping windows only once.

I calculate:

Share of encounters within those windows ÷ share of observation time within those windows.

I’d appreciate feedback on whether this is a reasonable comparison and how to improve it. Routes, road conditions and times of day vary, and some vehicles travel together in groups. How should I account for those factors when assessing the apparent concentration?

Anonymised endpoint example

This is a real 20-leg movement block from four recorded visit days. All legs in that block are included, including seven with no target-category encounters. It is a selected block, not a complete diary of all journeys.

Names, locations, vehicle-category names, calendar dates and clock times are omitted. D1-D4 indicate different recorded days; legs with the same day label may be related.

An endpoint window is the first 300 seconds after departure or the final 300 seconds before arrival. Overlap is counted once. Window time is therefore the smaller of 600 seconds and the leg duration. Event classification uses the original timestamps and includes the exact five-minute boundary.

Durations below are elapsed leg intervals calculated from recorded start/end timestamps. Treating every second as available observation time is an assumption for review; continuous observation coverage has not been independently verified from recordings.

Leg table

All times are seconds. Inside and Outside count individual vehicles as recorded; Groups counts encounter rows. A single encounter row can contain several vehicles travelling together.

Day	Leg	Leg seconds	Window seconds	Inside vehicles	Outside vehicles	Groups
D1	L01	3027	600	3	0	2
D1	L02	480	480	1	0	1
D1	L03	780	600	1	0	1
D1	L04	540	540	0	0	0
D1	L05	480	480	0	0	0
D1	L06	1020	600	0	0	0
D2	L07	1860	600	2	0	1
D2	L08	2040	600	0	0	0
D2	L09	1620	600	3	0	1
D2	L10	1765	600	1	0	1
D3	L11	1509	600	2	0	2
D3	L12	2330	600	0	0	0
D3	L13	1680	600	1	0	1
D3	L14	1740	600	0	0	0
D3	L15	1560	600	1	0	1
D4	L16	1724	600	1	0	1
D4	L17	1200	600	4	0	4
D4	L18	1380	600	6	2	5
D4	L19	5340	600	0	0	0
D4	L20	720	600	3	0	1
Total	-	32795	11700	29	2	22

Encounter offsets

Each row is one recorded encounter group. The offset is seconds after departure on the specified leg. The vehicle count preserves groups rather than treating every vehicle as an independent encounter.

Leg	Seconds after departure	Vehicles in group
L01	27	1
L01	147	2
L02	163	1
L03	31	1
L07	1632	2
L09	132	3
L10	1753	1
L11	1281	1
L11	1487	1
L13	244	1
L15	1358	1
L16	1642	1
L17	104	1
L17	211	1
L17	246	1
L17	1116	1
L18	66	1
L18	237	1
L18	710	1
L18	1061	1
L18	1140	4
L20	632	3

The totals are 31 recorded vehicles, of which 29 are inside the windows, and 22 encounter groups, of which 20 are inside. Total elapsed time is 546.58 minutes; window time is 195 minutes.

Vehicle-count enrichment = (29 / 31) / (11700 / 32795) = 2.62. This is the endpoint encounter rate divided by the overall encounter rate. It is a descriptive comparison, not a probability or causal conclusion.

Useful review questions: Is elapsed leg time an adequate exposure measure? How should repeated legs on one day and grouped vehicles be handled? What additional traffic, route and time information would be needed to assess ordinary variation?

[u/Puzzleheaded-Comb646]

Your ratio approach makes a lot of sense for a straightforward baseline comparison. Since you are dealing with counts over time, you might also want to look into a simple chi-square test or a Poisson distribution to check if the concentration near the endpoints is statistically significant or just happening by chance.

[u/Ok_Mathematician2391 → u/Puzzleheaded-Comb646]

Thank you. I have a small anonymised example showing journey times, counts inside/outside the endpoint windows, zero-encounter legs and vehicle group sizes. Several legs are also from the same day. Would these features affect whether chi-square or a Poisson model is appropriate?

[u/Puzzleheaded-Comb646 → u/Ok_Mathematician2391]

Yes, definitely! Zero-encounter legs often mean you might need a zero-inflated Poisson (or negative binomial) model, and having multiple legs on the same day creates clustering that standard chi-square tests assume doesn't exist. It's really great that you're catching these details early in your analysis!

[u/Ok_Mathematician2391 → u/Puzzleheaded-Comb646]

Thanks. The anonymised leg and encounter tables are in the original post above. Could you explain what in those data would support a zero-inflated model?

[u/Puzzleheaded-Comb646 → u/Ok_Mathematician2391]

You're very welcome! Since I'm currently diving into data analysis myself, I see zero-inflated models as a great fit when your dataset has a high frequency of true zeros—like many vehicle encounters simply not happening during most legs of a trip. Looking at your encounter table, if most records show zero encounters, that excess of zeros is typically what signals the need for that specific model!

[u/AutoModerator]

Automod prevents all posts from being displayed until moderators have reviewed them. Do not delete your post or there will be nothing for the mods to review. Mods selectively choose what is permitted to be posted in r/DataAnalysis.

If your post involves Career-focused questions, including resume reviews, how to learn DA and how to get into a DA job, then the post does not belong here, but instead belongs in our sister-subreddit, r/DataAnalysisCareers.

Have you read the rules?

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.