=== URBAN LICHENOMETRY: ANALYSIS LOG ===

--- MODEL SELECTION RESULTS ---
       Model      AIC      BIC Delta_BIC Schwarz_Weight
      Linear 4853.097 4871.090 136.17882   2.681145e-30
 Square Root 4754.370 4772.363  37.45223   7.354065e-09
  Asymptotic 4724.954 4747.445  12.53412   1.894200e-03
    Logistic 4740.349 4762.841  27.92980   8.596007e-07
    Gompertz 4712.419 4734.911   0.00000   9.981049e-01

Note: Gompertz model selected based on lowest AIC/BIC.

--- BIOLOGICAL GROWTH SUMMARY ---
Age at maximum growth:   7.83  ±  0.2 years
Maximum growth rate:     3.37  ±  0.08 mm/year
Size at maximum growth:  22.72  ±  0.49 mm

--- COVARIATE SELECTION: ENVIRONMENTAL FACTORS ---

1. Comparison of shade models (BIC):
                    df      BIC
Shade (interaction)  5 4208.368
Shade (direct)       5 4211.978
Base (age only)      4 4214.123
Shade (both)         6 4214.830

 Comparison to base model (ANOVA):
                    Model df      AIC      BIC    logLik   Test  L.Ratio p-value
Base (age only)         1  4 4196.185 4214.123 -2094.092                        
Shade (interaction)     2  5 4185.944 4208.368 -2087.972 1 vs 2 12.24024   5e-04

RESULT: Shade Interaction model fits the best (lowest BIC): shade cover negatively impact on growth rate.
and interaction effect is significant (ANOVA).

2. Comparison of sidewalk surface area models (BIC):
                       df      BIC
Base (age only)         4 4214.123
Log Area (interaction)  5 4215.994
Log Area (direct)       5 4216.270
Log Area (both)         6 4222.243

 Comparison to base model (ANOVA):
                  Model df      AIC      BIC    logLik   Test  L.Ratio p-value
Base (age only)       1  4 4196.185 4214.123 -2094.092                        
Log Area (direct)     2  5 4193.847 4216.270 -2091.923 1 vs 2 4.337764  0.0373

RESULT: Including surface area does not improve the model (higher BIC),
but effect is significant (ANOVA).

3. Comparison of city models (BIC):
                   df      BIC
City (both)         8 4139.275
City (interaction)  6 4141.281
City (direct)       6 4180.889
Base (age only)     4 4214.123

 Comparison to base model (ANOVA):
                Model df      AIC      BIC    logLik   Test  L.Ratio p-value
Base (age only)     1  4 4196.185 4214.123 -2094.092                        
City (both)         2  8 4103.398 4139.275 -2043.699 1 vs 2 100.7867  <.0001

RESULT: Including city significantly improves the model (Lower BIC)
and effect is significant (ANOVA).

4. City Interaction Test (BIC):
                                  df      BIC
Shade (interaction) + City (both)  9 4136.361
City (both)                        8 4139.275
Shade (interaction)                5 4208.368
Base (age only)                    4 4214.123

 Comparison to base models (ANOVA):
                                  Model df      AIC      BIC    logLik   Test  L.Ratio p-value
Shade (interaction)                   1  5 4185.944 4208.368 -2087.972                        
Shade (interaction) + City (both)     2  9 4095.999 4136.361 -2039.000 1 vs 2 97.94523  <.0001
                                  Model df      AIC      BIC    logLik   Test  L.Ratio p-value
City (both)                           1  8 4103.398 4139.275 -2043.699                        
Shade (interaction) + City (both)     2  9 4095.999 4136.361 -2039.000 1 vs 2 9.398809  0.0022

RESULT: Including both city and shade significantly improves the model (Lower BIC)
and effects are significant (ANOVA).

5. Post-hoc Comparisons (slopes by city):
 contrast           estimate     SE  df t.ratio p.value
 Arnhem - Nijmegen     0.422 0.0636 600   6.640 <0.0001
 Arnhem - Woerden     -0.056 0.0625 592  -0.897  0.6426
 Nijmegen - Woerden   -0.478 0.0684 634  -6.997 <0.0001

Degrees-of-freedom method: satterthwaite 
P value adjustment: tukey method for comparing a family of 3 estimates 

--- FINAL CONCLUSION ---
Nijmegen has a significantly lower growth rate compared to Arnhem and Woerden,
even when accounting for higher shade cover.

=== REPRODUCIBILITY METADATA (Session Info) ===
R version 4.4.3 (2025-02-28 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows 11 x64 (build 26200)

Matrix products: default


locale:
[1] LC_COLLATE=English_Netherlands.utf8  LC_CTYPE=English_Netherlands.utf8    LC_MONETARY=English_Netherlands.utf8
[4] LC_NUMERIC=C                         LC_TIME=English_Netherlands.utf8    

time zone: Europe/Amsterdam
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] emmeans_2.0.1    nlme_3.1-167     MASS_7.3-65      minpack.lm_1.2-4 ggplot2_4.0.1    dplyr_1.1.4      extrafont_0.20  

loaded via a namespace (and not attached):
 [1] gtable_0.3.6        compiler_4.4.3      crayon_1.5.3        tidyselect_1.2.1    scales_1.4.0        lattice_0.22-6     
 [7] coda_0.19-4.1       R6_2.6.1            labeling_0.4.3      generics_0.1.3      tibble_3.2.1        pillar_1.10.1      
[13] RColorBrewer_1.1-3  rlang_1.1.4         Rttf2pt1_1.3.14     S7_0.2.1            estimability_1.5.1  cli_3.6.3          
[19] withr_3.0.2         magrittr_2.0.3      grid_4.4.3          rstudioapi_0.17.1   mvtnorm_1.3-3       lifecycle_1.0.4    
[25] vctrs_0.6.5         glue_1.8.0          farver_2.1.2        numDeriv_2016.8-1.1 extrafontdb_1.1     tools_4.4.3        
[31] pkgconfig_2.0.3    
