Helendale MARS/GLR/GAM Comparative Analysis

1. Executive Summary

Three independent regression methods were fitted to the same 780-comparable sales dataset to estimate the subject’s market value. All three were run on the raw dollar scale (no log transform) so their fit statistics and value conclusions are directly comparable. The indicated values cluster within 4.22% of one another:

earthUI and glmnetUI agree to within 0.68%; mgcvUI sits highest, about 3.51% above earthUI. Cross-validated accuracy, however, diverges sharply — earthUI generalizes best and mgcvUI shows clear overfitting (see §5).

2. Value Reconciliation & Differences

A coefficient of variation of 2.23% across three structurally different models is tight reconciliation — well inside the spread an appraiser would typically see across approaches.

3. Model Fit — Side by Side

All metrics are on the raw dollar scale. CV R² (out-of-sample, 10-fold) is the honest measure of predictive accuracy; in-sample R² flatters models that overfit.

^†mgcv RMSE/MAE were not stored in the report bundle; deviance-explained (75.25%) is the GAM analogue of R². Note mgcv fit on 781 rows vs 780 for the others — it did not drop the subject row.

4. Model Sections

4.1 earthUI — Multivariate Adaptive Regression Splines (MARS)

4.2 glmnetUI — Elastic-Net Regularized Regression

4.3 mgcvUI — Generalized Additive Model (GAM)

5. Discussion — Why the Differences?

Why the value indications differ

earthUI and glmnetUI agree to 0.68% because both resolve to compact, well-regularized structures dominated by the same main effects (size, location, age, water view). mgcvUI lands 3.51% higher because its richer smooth + interaction surface bends more steeply toward the subject’s particular feature combination — helpful if those bends are real signal, but partly noise here.

Why mgcv’s CV R² is so much lower

This is the headline finding. On identical (raw-$) footing:

earthUI’s gap is essentially zero (0.0116): MARS’s GCV pruning keeps only terms that pay their way. glmnetUI’s gap (0.0828) is modest — ridge/lasso shrinkage. mgcvUI’s gap (0.2275) is large: 16 penalized smooths plus 8 tensor interactions and factor-by-smooths give it enough effective degrees of freedom to chase patterns that don’t replicate on held-out folds. REML smoothing resists this but cannot fully offset that much flexibility on ~781 rows.

Other points of interest

• Consistent value signal. Three different mathematical engines independently land within 4.22% — strong triangulation of the subject’s value.
• Same drivers everywhere. Size (sq_ft_total), location (area/latitude), age, and especially water view dominate all three models.
• Row handling. mgcv fit on 781 rows vs 780 for earth/glmnet (it retained the subject row); a minor inconsistency worth aligning.

6. Caveat — Latent Variables (Condition & Quality)

This analysis does not model property Condition and Quality, which are the two latent variables most likely to carry material unexplained value here. Their absence has two consequences:

• Part of every model’s residual variance — and a share of the ~4.22% spread between the three indications — is almost certainly Condition/Quality differences between the subject and comparables that the models cannot see.
• Because Condition and Quality often correlate with included features (newer/larger/water-view homes tend to be higher quality), the models may be absorbing some of that effect through correlated proxies — flattering in-sample fit while adding out-of-sample noise (a contributor to mgcv’s CV gap).

Incorporating Condition and Quality (e.g. as ordinal factors or factor-by-smooth terms) is the single most promising avenue to tighten all three models and their reconciliation.