Interaction term screen (α = 1)

Analysis Master 21-07-2026

Could combined or squared terms help the model? Five such terms were tested together, on top of the 7-parameter model with shared weights. An interaction term multiplies two inputs, for example f_distribution × σ. A term with a t-value above about 2 counts as significant.

Term	w	t
f_distance²	+4.588	3.81	significant
σ²	+0.165	2.22	significant
f_distribution × σ	-0.058	-0.15
f_distance × f_directional	+0.150	0.11
f_distribution × share_type	+5.264	5.57	significant, largest

The three significant terms were added to Model 4a: alternative-specific parameters. This gives Model 6, with 16 parameters:

\[V_t = w_{1,t} f_\text{distribution} + w_{2,t} f_\text{distance} + w_{3,t} f_\text{directional} + w_{4,t}\,share_t + w_5\,\sigma + w_6\,f_\text{distance}^2 + w_7\,\sigma^2 + w_8\,(f_\text{distribution}\times share_\text{type})\]

	4a	Model 6 (α = 1)
Accuracy	0.717	0.724
Building / street / open space	0.902 / 0.443 / 0.466	0.876 / 0.497 / 0.524
CV accuracy (grouped)	0.707 ± 0.069	0.711 ± 0.077
Condition number	775	20,695

Model 6 is the first model that improves open space (to 0.524), but building accuracy drops a little. Inside the larger model, σ² stops working (t falls to -0.27). And f_distance² turns out to make up for an α that was not yet tuned: The f_distance² artifact.

The two terms that were not significant are built from inputs that overlap strongly (VIF up to 73). So "not significant" is weak evidence for them.

The same test with the tuned α: Model 6, re-derived at calibrated alpha. Part of Calibration.

Linked from Calibration · MNL model development · Model 4a: alternative-specific parameters · Model progression · The f_distance² artifact · f_distribution