PhD_thesis/integrated_model_comparison.txt at main · SamueleBumbaca/PhD_thesis · GitHub

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=== INTEGRATED MODEL COMPARISON SUMMARY ===
Date: 2025-08-03 17:40:24

Comparison of RCBD vs SpATS Spatial Model
Dataset: 54 observations, 3 treatments, 3 blocks
RCBD Model: Linear Mixed Model with random block effects
SpATS Model: Spatial spline model with PSANOVA smoothing

OVERALL MODEL PERFORMANCE (Mean Absolute Errors):
=================================================

Model                Treatment_Error      Environmental_Error
-----                ---------------      ------------------
RCBD_Model           0.2075               1.1237
SpATS_Spatial        0.0506               1.0937


ESTIMATED vs TRUE TREATMENT EFFECTS:
====================================

Treatment    True_Effect  RCBD_Estimate   SpATS_Estimate  RCBD_Error   SpATS_Error
---------    -----------  -------------   --------------  ----------   -----------
Control      0.000        0.000           0.000           0.000        0.000
Test         1.000        0.894           1.024           0.106        0.024
Reference    0.500        1.016           0.627           0.516        0.127


BLOCK EFFECTS vs SPATIAL MODELING:
===================================

RCBD Block Effects:
(Random Effects from Mixed Model)
Block 1: +0.2675 t/ha
Block 2: -0.1327 t/ha
Block 3: -0.1348 t/ha

SpATS Spatial Modeling:
- Uses PSANOVA splines to model continuous spatial variation
- Spatial effect range: 11.635 to 13.660 t/ha


MODEL ASSUMPTION TESTS:
=======================

RCBD Model:
-----------
(Linear Mixed Model with random block effects)
Normality (Shapiro-Wilk): W = 0.9111, p-value = 0.0007
Interpretation: Non-normal residuals (p ≤ 0.05)
Homoscedasticity (Bartlett): K-squared = 0.4842, p-value = 0.7850
Interpretation: Homoscedastic residuals (p > 0.05)

SpATS Model:
------------
Normality (Shapiro-Wilk): W = 0.9567, p-value = 0.0489
Interpretation: Non-normal residuals (p ≤ 0.05)
Homoscedasticity (Bartlett): K-squared = 4.1230, p-value = 0.1273
Interpretation: Homoscedastic residuals (p > 0.05)
Spatial Autocorrelation (Moran's I): I = -0.1890, p-value = 0.9720
Interpretation: No significant spatial autocorrelation (p > 0.05)


MODEL COMPARISON INTERPRETATION:
================================

Treatment Effect Estimation: SpATS performs better (lower error)
Environmental Effect Estimation: SpATS performs better (lower error)

Key Differences:
- RCBD: Captures environmental variation through discrete block effects
- SpATS: Models continuous spatial variation using smooth splines
- Mixed Model: Accounts for pseudoreplication with random effects (if convergent)
- Spatial Model: Explicitly models spatial correlation structure