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  1. lowest_AIC <- mixed_model(yield ~ stock,
  2.                     random = ~  1 | groups,
  3.                     data = trees,
  4.                     family = hurdle.lognormal(), n_phis = 1,
  5.                     zi_fixed = ~ stock
  6. )
  7.  
  8. > AIC(lowest_AIC)
  9. [1] 2784.14
  10. > mean(residuals(lowest_AIC)^2)
  11. [1] 0.1474714
  12. > summary(lowest_AIC)
  13.  
  14. Call:
  15. mixed_model(fixed = yield ~ stock, random = ~1 | groups, data = trees,
  16.     family = hurdle.lognormal(), zi_fixed = ~stock, n_phis = 1)
  17.  
  18. Data Descriptives:
  19. Number of Observations: 20583
  20. Number of Groups: 2
  21.  
  22. Model:
  23.  family: hurdle log-normal
  24.  link: identity
  25.  
  26. Fit statistics:
  27.   log.Lik     AIC      BIC
  28.  -1386.07 2784.14 2776.299
  29.  
  30. Random effects covariance matrix:
  31.               StdDev
  32. (Intercept) 1.396311
  33.  
  34. Fixed effects:
  35.             Estimate Std.Err  z-value p-value
  36. (Intercept)   0.0004  0.0061   0.0731 0.94177
  37. stock        -0.0907  0.0062 -14.7410 < 1e-04
  38.  
  39. Zero-part coefficients:
  40.             Estimate Std.Err  z-value p-value
  41. (Intercept)  -2.4295  0.0257 -94.3862 < 1e-04
  42. stock         0.1934  0.0238   8.1089 < 1e-04
  43.  
  44. log(residual std. dev.):
  45.   Estimate Std.Err
  46.    -0.1746  0.0051
  47.  
  48. Integration:
  49. method: adaptive Gauss-Hermite quadrature rule
  50. quadrature points: 11
  51.  
  52. Optimization:
  53. method: EM
  54. converged: TRUE
  55.      
  56. best <- mixed_model(yield ~ stock + slope + precipitation + n_trees + soil_depth + rocks  + position,
  57.                     random = ~  1 | groups,
  58.                     data = trees,
  59.                     family = hurdle.lognormal(), n_phis = 1,
  60.                     zi_fixed = ~ stock + slope + precipitation + rocks + position,
  61.                     zi_random = ~  1 | groups
  62.  
  63. )
  64.  
  65. > AIC(best)
  66. [1] 2839.902
  67. > mean(residuals(best)^2)
  68. [1] 0.1890385
  69. > summary(best)
  70.  
  71. Call:
  72. mixed_model(fixed = yield ~ stock + slope + precipitation + n_trees +
  73.     soil_depth + rocks + position, random = ~1 | groups, data = trees,
  74.     family = hurdle.lognormal(), zi_fixed = ~stock + slope +
  75.         precipitation + rocks + position, zi_random = ~1 | groups,
  76.     n_phis = 1)
  77.  
  78. Data Descriptives:
  79. Number of Observations: 20528
  80. Number of Groups: 2
  81.  
  82. Model:
  83.  family: hurdle log-normal
  84.  link: identity
  85.  
  86. Fit statistics:
  87.    log.Lik      AIC      BIC
  88.  -1387.951 2839.902 2798.083
  89.  
  90. Random effects covariance matrix:
  91.                 StdDev    Corr
  92. (Intercept)     1.4117        
  93. zi_(Intercept)  0.1331  0.0477
  94.  
  95. Fixed effects:
  96.                            Estimate Std.Err  z-value p-value
  97. (Intercept)                  0.4576  0.0176  25.9341 < 1e-04
  98. stock                       -0.0644  0.0059 -10.8639 < 1e-04
  99. slope                       -0.0593  0.0059 -10.1307 < 1e-04
  100. precipitation               -0.0858  0.0061 -14.1035 < 1e-04
  101. n_trees                     -0.0630  0.0060 -10.5368 < 1e-04
  102. soil_depth                   0.0590  0.0061   9.7462 < 1e-04
  103. rocks2                      -0.0847  0.0155  -5.4514 < 1e-04
  104. rocks3                      -0.0942  0.0178  -5.2897 < 1e-04
  105. rocks4                      -0.1437  0.0184  -7.8039 < 1e-04
  106. rocks5                      -0.1933  0.0258  -7.5044 < 1e-04
  107. rocks6                      -0.4962  0.0574  -8.6376 < 1e-04
  108. position-0.561514296868636  -0.2333  0.0180 -12.9644 < 1e-04
  109. position0.381120787744946   -0.4953  0.0193 -25.6413 < 1e-04
  110. position1.32375587235853    -0.8913  0.0234 -38.0653 < 1e-04
  111. position2.26639095697211    -1.0993  0.0276 -39.8970 < 1e-04
  112.  
  113. Zero-part coefficients:
  114.                            Estimate Std.Err  z-value  p-value
  115. (Intercept)                 -3.5587  0.1180 -30.1541  < 1e-04
  116. stock                        0.1724  0.0255   6.7729  < 1e-04
  117. slope                        0.2517  0.0272   9.2508  < 1e-04
  118. precipitation               -0.1457  0.0296  -4.9197  < 1e-04
  119. rocks2                       0.3587  0.0719   4.9900  < 1e-04
  120. rocks3                       0.3497  0.0823   4.2506  < 1e-04
  121. rocks4                       0.3951  0.0845   4.6742  < 1e-04
  122. rocks5                       0.5387  0.1110   4.8507  < 1e-04
  123. rocks6                       0.5434  0.2539   2.1404 0.032319
  124. position-0.561514296868636   0.3085  0.1215   2.5384 0.011136
  125. position0.381120787744946    0.8707  0.1219   7.1406  < 1e-04
  126. position1.32375587235853     1.5953  0.1251  12.7515  < 1e-04
  127. position2.26639095697211     2.0707  0.1270  16.3061  < 1e-04
  128.  
  129. log(residual std. dev.):
  130.   Estimate Std.Err
  131.    -0.2856  0.0052
  132.  
  133. Integration:
  134. method: adaptive Gauss-Hermite quadrature rule
  135. quadrature points: 11
  136.  
  137. Optimization:
  138. method: hybrid EM and quasi-Newton
  139. converged: TRUE
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