Behavioral Validation — Västberg §4.4 Style

HH θ̂ · N=2 workers · R=5 replications/person · 10 total paths · generated 2026-06-24

0 Goodness-of-fit headline

not computed (--skip-null)

McFadden ρ²

—

Adjusted ρ̄²

Free params

Workers

Reps/person

Quantity	Value	Notes
LL(θ̂)	-74.189	At estimated parameters
LL(0)	not computed	Null: estimated params = 0 (ASCs only)
ρ² = 1 − LL(θ̂)/LL(0)	not computed (--skip-null)	McFadden (1974)
ρ̄² = 1 − (LL(θ̂)−K)/LL(0)	—	Adjusted for K=8 free params

The null model sets all estimated parameters to 0 while keeping the fixed HH MNL mode constants (ASC[m], β_time, β_cost). It is not the uniform-path null — it already captures mode-specific travel preferences from the household survey MNL. ρ² measures improvement over this ASC-anchored baseline.

1 Activity timing overlays (Västberg Fig 1)

Proportion of 15-min timesteps in each activity, by hour of day. Blue = observed diary data, Red = simulated under θ̂ (R=5 replications per worker). K-S statistic: two-sample Kolmogorov–Smirnov on the underlying distributions.

2 Trips and tours (Västberg Fig 2)

Distributions of trips per person-day, tours per person-day (home→away→home loops), and trips per tour. Normalized to proportions for comparability across sample sizes.

3 Trip-length distributions by mode (Västberg Fig 3)

CDFs of trip duration (minutes) per transport mode. Observed: from trip_data_higashihiroshima.csv (arrtime − deptime). Simulated: EndTime − StartTime of TRAVEL rows (15-min grid resolution → step-coarseness caveat in §5).

4 Aggregate comparison (Västberg Table 4)

Summary statistics over the matched worker sample (N=2). Δ = Simulated − Observed; green = |Δ| < 3pp, red = |Δ| ≥ 10pp.

Mode shares (% of travel steps)

Mode	Observed	Simulated	Δ
CAR	28.6%	59.1%	+30.5%
TRAIN	—	—	—
BUS	—	—	—
WALK	71.4%	9.1%	-62.3%
BICYCLE	—	—	—

Activity time shares (% of all 15-min steps)

Activity	Observed	Simulated	Δ
HOME	50.0%	56.7%	+6.7%
WORK	46.2%	40.6%	-5.6%
SHOPPING	—	0.2%	—
LEISURE	—	2.5%	—

Activity-travel statistics (per person-day)

Statistic	Observed	Simulated	Δ
Trips / person	2.50	4.40	+1.90
Tours / person	1.00	2.20	+1.20
Trips / tour	2.50	2.00	-0.50
Avg travel time	17.00 min	26.59 min	+9.59 min

5 Caveats and scope

Same-subsample discipline: observed stats are computed on the same worker subset used in estimation (persons filtered to those with WORK in their mandatory sequence, Motorcycle/Taxi excluded).
Null model: LL(0) sets estimated params (δ, α, β, β₁_shop, β₀_shop, β₁_leis, β₀_leis, θ_travel) to zero; fixed HH MNL constants (ASC, β_time, β_cost) are unchanged. This is the standard ρ² for this model family, not the uniform-path null.
15-min step coarseness: simulated trip durations are multiples of 15 min. Observed trip durations from the CSV are exact (minute-level) — slight distributional mismatch at the lower end is expected.
Tour segmentation: observed tours are segmented from trip_data_higashihiroshima.csv using purpose='Home' for return trips. Simulated tours are segmented from TRAVEL/HOME alternation in simulated paths. Imperfect alignment in segment definition may inflate K-S.
Scope: This is in-sample validation — the same workers used for estimation. Out-of-sample validation requires a held-out subsample (future work).