[R] Stepwise logistic discrimination - II

Peter Ho peter at esb.ucp.pt
Tue Jan 4 12:36:34 CET 2000

```I apologise for writing again about the problem with using stepAIC +
multinom, but I think the reason why I had it in the first place is
perhaps there may be a bug in either stepAIC or multinom.
Just to repeat the problem, I have 126 variables and 99 cases. I don't
know if the large number of variables could be the problem. Of couse the
reason for doing a stepwise method is to reduce this number. Anyway,
after getting the error message : " arguments imply differing number of
rows: 1, 126", I decided to run the same procedure with just 21
variables. The results are in setp20.txt. This removed 3 variables. This
seemed to indicate that there was no problem with using  stepAIC +
multinom. I then repeated the procedure for the 126 variables by
replacing the "~" by the full list of variables "F25 +F26
+........+F150". StepAIC removed the first 2 variables then produced the
same error message as before. See setp126.txt

Is this a bug? Is there a maximum number of variables which stepAIC can
handle?

Peter
--------------------
Peter Ho
Escola Superior de Biotecnologia
Rua Dr. António Bernardino de Almeida
4200 Porto
Tel: ++351-22-5580043

-------------- next part --------------
> nose20s.mu <- multinom(Spoilage ~ FRAG25 + FRAG26 + FRAG27 + FRAG28 + FRAG29 + FRAG30 + FRAG31 + FRAG32 + FRAG33 + FRAG34 + FRAG35 + FRAG36 + FRAG37 + FRAG38 + FRAG39 + FRAG40 + FRAG41 + FRAG42 + FRAG43 + FRAG44 + FRAG45 , nose126s)
# weights:  92 (66 variable)
> nose20s.mu
Call:
multinom(formula = Spoilage ~ FRAG25 + FRAG26 + FRAG27 + FRAG28 +
FRAG29 + FRAG30 + FRAG31 + FRAG32 + FRAG33 + FRAG34 + FRAG35 +
FRAG36 + FRAG37 + FRAG38 + FRAG39 + FRAG40 + FRAG41 + FRAG42 +
FRAG43 + FRAG44 + FRAG45, data = nose126s)

Coefficients:
(Intercept)        FRAG25       FRAG26        FRAG27        FRAG28
week2 -5.875869e-09 -0.0002762473 0.0002939013 -5.006443e-05 -1.974740e-07
week3  1.746245e-08 -0.0001898158 0.0001851999  4.408521e-05  1.891675e-07
week4 -1.537005e-09 -0.0000875455 0.0003595600 -9.254731e-05  4.324163e-07
FRAG29        FRAG30        FRAG31        FRAG32       FRAG33
week2 -1.490694e-07  2.315180e-06  9.758291e-05  3.165469e-07 3.952147e-06
week3  3.518809e-07 -2.465738e-06  5.035361e-05 -2.422289e-07 2.018635e-06
week4 -1.465070e-06 -5.844817e-06 -2.273580e-05 -4.492861e-07 8.629373e-07
FRAG34        FRAG35        FRAG36        FRAG37        FRAG38
week2 -1.292201e-05 -1.299600e-04  0.0002157680 -1.403039e-06  1.563939e-04
week3  1.370027e-06 -8.570172e-05  0.0001604013  5.836834e-05 -6.640826e-05
week4  1.036472e-04 -1.074593e-05 -0.0001013518  1.537383e-04 -1.583539e-04
FRAG39        FRAG40        FRAG41       FRAG42        FRAG43
week2 -0.0000797642 -2.390592e-06 -7.689589e-07 1.890469e-05 -1.097805e-05
week3 -0.0001937116 -1.416947e-06 -1.447538e-05 3.001617e-05 -1.331443e-05
week4  0.0000098747 -6.936876e-06 -3.986990e-05 4.132049e-05  5.652583e-06
FRAG44        FRAG45
week2 1.293299e-06 -2.333693e-05
week3 7.904613e-07 -1.528914e-05
week4 4.329840e-07  2.801562e-06

Residual Deviance: 144.7702
AIC: 276.7702
> nose20s.step <- stepAIC(nose20s.mu)
Start:  AIC= 276.77
Spoilage ~ FRAG25 + FRAG26 + FRAG27 + FRAG28 + FRAG29 + FRAG30 +
FRAG31 + FRAG32 + FRAG33 + FRAG34 + FRAG35 + FRAG36 + FRAG37 +
FRAG38 + FRAG39 + FRAG40 + FRAG41 + FRAG42 + FRAG43 + FRAG44 +
FRAG45

# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
# weights:  88 (63 variable)
Df    AIC
- FRAG41  3 270.37
- FRAG29  3 272.89
- FRAG27  3 273.41
- FRAG40  3 273.74
- FRAG34  3 273.79
- FRAG30  3 273.85
- FRAG37  3 274.16
- FRAG42  3 274.49
- FRAG25  3 274.98
- FRAG36  3 275.17
- FRAG35  3 275.49
- FRAG43  3 275.54
- FRAG28  3 275.69
<none>      276.77
- FRAG38  3 277.19
- FRAG32  3 277.37
- FRAG31  3 278.68
- FRAG39  3 278.83
- FRAG26  3 281.75
- FRAG45  3 282.08
- FRAG44  3 283.98
- FRAG33  3 287.36
# weights:  88 (63 variable)

Step:  AIC= 270.37
Spoilage ~ FRAG25 + FRAG26 + FRAG27 + FRAG28 + FRAG29 + FRAG30 +
FRAG31 + FRAG32 + FRAG33 + FRAG34 + FRAG35 + FRAG36 + FRAG37 +
FRAG38 + FRAG39 + FRAG40 + FRAG42 + FRAG43 + FRAG44 + FRAG45

# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
# weights:  84 (60 variable)
Df    AIC
- FRAG29  3 263.70
- FRAG40  3 264.94
- FRAG31  3 266.53
- FRAG30  3 266.88
- FRAG34  3 267.49
- FRAG27  3 267.55
- FRAG37  3 267.68
- FRAG28  3 267.79
- FRAG42  3 268.13
- FRAG43  3 268.25
- FRAG25  3 269.08
- FRAG36  3 269.61
- FRAG35  3 269.73
- FRAG32  3 270.23
<none>      270.37
- FRAG38  3 270.46
- FRAG39  3 271.21
- FRAG26  3 274.42
- FRAG45  3 275.81
- FRAG44  3 277.14
- FRAG33  3 283.03
# weights:  84 (60 variable)

Step:  AIC= 263.7
Spoilage ~ FRAG25 + FRAG26 + FRAG27 + FRAG28 + FRAG30 + FRAG31 +
FRAG32 + FRAG33 + FRAG34 + FRAG35 + FRAG36 + FRAG37 + FRAG38 +
FRAG39 + FRAG40 + FRAG42 + FRAG43 + FRAG44 + FRAG45

# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
# weights:  80 (57 variable)
Df    AIC
- FRAG38  3 257.68
- FRAG42  3 259.54
- FRAG37  3 261.83
- FRAG35  3 263.24
- FRAG34  3 263.48
- FRAG25  3 263.51
<none>      263.70
- FRAG36  3 263.76
- FRAG27  3 264.27
- FRAG40  3 264.63
- FRAG43  3 265.36
- FRAG31  3 266.72
- FRAG39  3 267.79
- FRAG32  3 267.95
- FRAG30  3 267.98
- FRAG44  3 269.59
- FRAG26  3 269.89
- FRAG28  3 271.38
- FRAG45  3 272.77
- FRAG33  3 280.81
# weights:  80 (57 variable)

Step:  AIC= 257.68
Spoilage ~ FRAG25 + FRAG26 + FRAG27 + FRAG28 + FRAG30 + FRAG31 +
FRAG32 + FRAG33 + FRAG34 + FRAG35 + FRAG36 + FRAG37 + FRAG39 +
FRAG40 + FRAG42 + FRAG43 + FRAG44 + FRAG45

# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
# weights:  76 (54 variable)
Df    AIC
<none>      257.68
- FRAG36  3 258.67
- FRAG30  3 258.82
- FRAG25  3 262.90
- FRAG42  3 263.05
- FRAG35  3 264.37
- FRAG43  3 264.63
- FRAG32  3 264.89
- FRAG37  3 265.36
- FRAG27  3 266.09
- FRAG34  3 266.36
- FRAG40  3 266.79
- FRAG31  3 267.27
- FRAG28  3 267.89
- FRAG44  3 270.42
- FRAG26  3 270.91
- FRAG45  3 272.28
- FRAG39  3 275.62
- FRAG33  3 284.95
> nose20s.step
Call:
multinom(formula = Spoilage ~ FRAG25 + FRAG26 + FRAG27 + FRAG28 +
FRAG30 + FRAG31 + FRAG32 + FRAG33 + FRAG34 + FRAG35 + FRAG36 +
FRAG37 + FRAG39 + FRAG40 + FRAG42 + FRAG43 + FRAG44 + FRAG45,
data = nose126s)

Coefficients:
(Intercept)        FRAG25       FRAG26        FRAG27        FRAG28
week2  -1.5157947 -0.0002194994 0.0002842470 -2.466799e-05 -1.014998e-07
week3  19.3060768 -0.0001738133 0.0001989165  2.272838e-05  2.140365e-07
week4  -0.3392685 -0.0017064852 0.0037632213 -1.446068e-03 -3.162564e-07
FRAG30       FRAG31        FRAG32       FRAG33        FRAG34
week2  2.245144e-06 6.619727e-05  2.247694e-07 4.091580e-06 -2.227733e-05
week3 -1.331929e-06 4.628403e-05 -4.878292e-07 2.714806e-06  8.011659e-07
week4 -7.890984e-05 9.337661e-04  2.642356e-07 1.236701e-05  4.871116e-04
FRAG35        FRAG36       FRAG37        FRAG39        FRAG40
week2 -1.007672e-04  0.0001646577 2.661853e-05 -7.502071e-05 -1.614241e-06
week3 -9.105109e-05  0.0001238630 6.857822e-05 -1.982485e-04 -9.625837e-07
week4 -7.025223e-04 -0.0019407329 1.566509e-03 -4.168799e-04 -3.021176e-05
FRAG42        FRAG43       FRAG44        FRAG45
week2 1.782480e-05 -8.935123e-06 9.910160e-07 -1.808292e-05
week3 2.735904e-05 -1.151881e-05 7.413345e-07 -1.532306e-05
week4 4.880167e-04 -7.139705e-05 1.360150e-05 -2.548684e-04

Residual Deviance: 143.6754
AIC: 257.6754
-------------- next part --------------
> nose126s2.mu <- multinom(Spoilage ~ F25 + F26 + F27 + F28 + F29 + F30 + F31+ F32 + F33 + F34 + F35+ F36 + F37 + F38 + F39+ F40 + F41 + F42 +F43 + F44 + F45 + F46 + F47 + F48 + F49 + F50 + F51 + F52 + F53 + F54 + F55 + F56 + F57 + F58 + F59 + F60 + F61 + F62 + F63 + F64 + F65 + F66 + F67 + F68 + F69 + F70 + F71 + F72 + F73 + F74 + F75 + F76 + F77 + F78 + F79 + F80 + F81 + F82 + F83 + F84 + F85 + F86 + F87 + F88 + F89 + F90 + F91 + F92 + F93 + F94 + F95 + F96 + F97 + F98 + F99 + F100 + F101 + F102 + F103 + F104 + F105 + F106 + F107 + F108 + F109 + F110 + F111 + F112 + F113 + F114 + F115 + F116 + F117 + F118 + F119 + F120 + F121 + F122 + F123 + F124 + F125 + F126 + F127 + F128 + F129 + F130 + F131 + F132 + F133 + F134 + F135 + F136 + F137 + F138 + F139 + F140 + F141 + F142 + F143 + F144 + F145 + F146 + F147 + F148 + F149 + F150
+ , data = nose126s2)
# weights:  512 (381 variable)
> nose126s2.mu
Call:
multinom(formula = Spoilage ~ F25 + F26 + F27 + F28 + F29 + F30 +
F31 + F32 + F33 + F34 + F35 + F36 + F37 + F38 + F39 + F40 +
F41 + F42 + F43 + F44 + F45 + F46 + F47 + F48 + F49 + F50 +
F51 + F52 + F53 + F54 + F55 + F56 + F57 + F58 + F59 + F60 +
F61 + F62 + F63 + F64 + F65 + F66 + F67 + F68 + F69 + F70 +
F71 + F72 + F73 + F74 + F75 + F76 + F77 + F78 + F79 + F80 +
F81 + F82 + F83 + F84 + F85 + F86 + F87 + F88 + F89 + F90 +
F91 + F92 + F93 + F94 + F95 + F96 + F97 + F98 + F99 + F100 +
F101 + F102 + F103 + F104 + F105 + F106 + F107 + F108 + F109 +
F110 + F111 + F112 + F113 + F114 + F115 + F116 + F117 + F118 +
F119 + F120 + F121 + F122 + F123 + F124 + F125 + F126 + F127 +
F128 + F129 + F130 + F131 + F132 + F133 + F134 + F135 + F136 +
F137 + F138 + F139 + F140 + F141 + F142 + F143 + F144 + F145 +
F146 + F147 + F148 + F149 + F150, data = nose126s2)

Coefficients:
(Intercept)           F25           F26          F27           F28
week2  1.219487e-09 -3.195595e-04  4.748949e-05 4.900736e-05 -8.570984e-08
week3 -1.660521e-09 -1.669241e-05 -1.557546e-04 1.422205e-04  1.666224e-06
week4 -3.602248e-10  6.105686e-06  2.218175e-04 6.301120e-06  1.859483e-07
F29           F30          F31           F32          F33
week2 1.710885e-06 -9.045937e-07 8.003105e-05  2.222240e-07 4.309332e-07
week3 1.289507e-06  5.626157e-06 7.382627e-05 -1.914310e-06 8.075129e-07
week4 2.701291e-07  2.040672e-06 8.257451e-05  6.487177e-08 1.220925e-06
F34           F35           F36          F37          F38
week2 -6.946838e-05 -1.036917e-04  0.0001346780 9.765023e-05 0.0001347326
week3 -1.407161e-04 -6.302338e-05  0.0000803148 1.562163e-04 0.0001995156
week4 -2.800638e-06 -3.653815e-05 -0.0001079454 1.269093e-04 0.0001865822
F39           F40          F41           F42           F43
week2  5.939505e-05  1.994993e-07 3.684524e-07  1.351041e-05 -1.951654e-05
week3  1.253717e-04  7.369284e-06 6.813911e-05 -5.965207e-05  8.492853e-06
week4 -1.422959e-05 -3.035808e-06 7.185366e-06  3.684513e-06 -3.036853e-06
F44           F45           F46           F47           F48
week2 8.864302e-07 -2.645466e-05  5.704703e-05 -9.009798e-05  2.884689e-05
week3 1.510644e-06 -3.532714e-05  7.309184e-05  1.310930e-04  2.479969e-04
week4 8.686075e-07 -1.896736e-05 -3.718972e-05  3.357612e-05 -8.155125e-05
F49           F50           F51           F52           F53
week2 0.0001385802 -0.0004309755 -1.680142e-04 -1.362987e-04  1.969091e-04
week3 0.0001613050 -0.0004092794 -3.227822e-04  3.662302e-05 -2.208027e-04
week4 0.0001668033 -0.0002275217 -2.391445e-05 -1.015035e-04 -2.805235e-05
F54           F55           F56           F57           F58
week2 0.0003869048 -4.882195e-05 -0.0001465853 -7.775261e-05  1.201297e-04
week3 0.0004646550  9.679303e-05 -0.0004167201  3.546621e-05 -2.678546e-05
week4 0.0001645254 -1.586859e-05 -0.0001048692  9.515473e-05  3.275785e-05
F59           F60           F61          F62           F63
week2 -1.062365e-04 -1.441587e-04  1.746909e-04 2.770054e-04 -2.091082e-04
week3 -3.214771e-05 -4.001424e-04  2.314351e-05 4.745612e-05 -1.437427e-04
week4 -2.439799e-05 -4.225132e-05 -8.295949e-05 8.353129e-05 -3.177624e-05
F64           F65           F66           F67          F68
week2 -2.811005e-05 -0.0002071163 -3.251519e-05  6.643846e-05 0.0001247540
week3 -1.472040e-04  0.0000729866  3.436884e-04 -2.141885e-04 0.0001807832
week4  9.373653e-05 -0.0001121832 -1.372773e-06 -1.445839e-04 0.0001170291
F69           F70          F71          F72           F73
week2 -7.655736e-05 -0.0001213041 0.0003393180 9.103568e-05  1.335855e-05
week3  4.108082e-04 -0.0005591488 0.0001612363 8.649987e-05  3.386516e-06
week4 -3.781369e-05 -0.0002429615 0.0000732286 7.743961e-06 -5.235559e-06
F74           F75          F76           F77           F78
week2 -1.489640e-05 -6.629044e-05 9.112797e-05 -1.468495e-04 -1.163437e-04
week3 -1.330108e-04 -9.652093e-05 2.581334e-04  6.659711e-06 -3.879176e-04
week4  9.679911e-05  1.254652e-06 6.564406e-05  1.026719e-04 -5.271073e-05
F79           F80           F81          F82           F83
week2 -3.332732e-05 -0.0001736478  1.267276e-04 8.745587e-05  1.082721e-04
week3 -3.486963e-04 -0.0004537347  3.756661e-04 8.703546e-06 -3.513668e-05
week4  7.367455e-05 -0.0000673614 -2.290305e-05 2.131521e-04  7.431593e-06
F84           F85           F86          F87           F88
week2 -1.790248e-05 -9.843397e-05 -2.360408e-05 3.892072e-04 -0.0001394700
week3 -2.039337e-04 -4.262150e-04  2.859180e-04 5.887645e-04  0.0003035760
week4 -3.319747e-04 -5.678564e-05  1.756806e-04 5.909675e-05  0.0001728799
F89           F90           F91           F92          F93
week2 -1.087832e-04  9.825400e-05 -8.795629e-05  8.208226e-07 8.443821e-05
week3 -2.966860e-05 -2.180570e-04  8.121998e-05 -3.033707e-04 4.113564e-05
week4  5.669098e-05  2.352611e-05  1.240733e-04 -1.817354e-05 3.050886e-05
F94           F95           F96           F97           F98
week2 -1.480021e-04 -0.0003813541  9.544601e-05  7.794559e-05  1.424058e-05
week3  2.200224e-04 -0.0002113889 -3.247726e-04  2.352040e-04  2.943059e-04
week4 -4.962679e-05 -0.0001025270 -7.479078e-05 -5.539545e-05 -3.965151e-05
F99          F100         F101          F102          F103
week2  1.118326e-04 -4.596317e-05 0.0003021668 -3.353995e-04  4.018968e-06
week3 -7.145675e-05 -3.418465e-04 0.0001317142 -3.912184e-05 -8.535487e-05
week4  1.477765e-04 -9.313495e-05 0.0001375701 -1.195548e-04  4.737395e-05
F104          F105          F106          F107         F108
week2  4.780841e-06  2.018494e-05 -5.748224e-05  4.053847e-04 9.594164e-05
week3 -3.984163e-05 -1.804153e-04 -3.193939e-04 -6.470191e-05 1.072822e-04
week4 -1.237422e-04 -5.280561e-07 -9.524986e-05  3.384964e-05 7.893730e-05
F109          F110          F111          F112          F113
week2 -1.511568e-04 -1.138763e-04  6.152346e-05  0.0001636572 -1.529929e-05
week3 -5.743415e-05  3.705444e-04  5.051566e-05  0.0001233737 -3.204458e-04
week4 -1.519348e-04  2.992059e-05 -2.037970e-05 -0.0001748865  6.096422e-05
F114         F115         F116          F117          F118
week2 -0.0004850277 5.368748e-05 0.0002063432 -0.0001378167 -6.175149e-05
week3 -0.0004078296 2.145279e-04 0.0003707961 -0.0004237074 -4.618330e-05
week4 -0.0001534238 7.073613e-05 0.0000475460 -0.0001967731 -1.482364e-04
F119          F120          F121          F122         F123
week2 -5.695025e-05 -4.366846e-05  1.601291e-04 -2.511383e-05 0.0001466871
week3  2.767698e-04  8.503119e-05  3.332916e-05 -8.513142e-05 0.0003851340
week4 -9.814509e-05  3.783492e-05 -8.465943e-05  3.327701e-05 0.0000954519
F124          F125          F126          F127         F128
week2  1.922263e-04 -1.454775e-04 -1.454383e-04  2.255451e-04 6.723274e-05
week3 -6.532567e-05  5.348111e-05 -2.057253e-04  4.687788e-04 9.922645e-05
week4  9.244874e-05  3.209590e-05 -3.067741e-05 -3.846402e-05 7.667765e-05
F129          F130          F131          F132         F133
week2 0.0002331977 -0.0003061774  1.179456e-04 -2.249172e-05 3.924194e-05
week3 0.0006633887 -0.0002366577 -2.364009e-05  1.234181e-05 7.908068e-05
week4 0.0001358766 -0.0001467059  6.824760e-05  1.349611e-04 4.838422e-05
F134          F135         F136          F137          F138
week2 -0.0001202145  1.869369e-04 0.0001476740 -1.766882e-05 -2.012973e-06
week3  0.0000895994 -4.322409e-04 0.0002233970 -3.691256e-04 -7.679695e-05
week4  0.0000615005 -2.045526e-06 0.0001425135 -1.045794e-04 -1.366160e-04
F139          F140          F141          F142         F143
week2 6.063255e-05 -1.957020e-04  1.673815e-04 -1.483463e-04 1.256884e-04
week3 4.655877e-04  4.239508e-05  4.956891e-06 -5.923583e-05 1.864335e-04
week4 3.273633e-05 -2.237530e-05 -9.117080e-06 -1.795420e-04 9.587126e-05
F144          F145          F146          F147         F148
week2 -0.0000979091 -1.490324e-04 -1.437660e-04 -3.893712e-06 4.606350e-05
week3  0.0002832077 -3.100981e-04 -1.878327e-04  1.254730e-04 4.905824e-06
week4  0.0001436083 -6.791397e-05  1.252013e-05  2.165160e-05 2.446709e-05
F149          F150
week2 -0.0001381260 -2.165186e-05
week3 -0.0001115298 -1.141151e-04
week4 -0.0001030075  1.792253e-05

Residual Deviance: 19.53574
AIC: 613.5357
> nose126s2.step <- stepAIC(nose126s2.mu)
Start:  AIC= 613.54
Spoilage ~ F25 + F26 + F27 + F28 + F29 + F30 + F31 + F32 + F33 +
F34 + F35 + F36 + F37 + F38 + F39 + F40 + F41 + F42 + F43 +
F44 + F45 + F46 + F47 + F48 + F49 + F50 + F51 + F52 + F53 +
F54 + F55 + F56 + F57 + F58 + F59 + F60 + F61 + F62 + F63 +
F64 + F65 + F66 + F67 + F68 + F69 + F70 + F71 + F72 + F73 +
F74 + F75 + F76 + F77 + F78 + F79 + F80 + F81 + F82 + F83 +
F84 + F85 + F86 + F87 + F88 + F89 + F90 + F91 + F92 + F93 +
F94 + F95 + F96 + F97 + F98 + F99 + F100 + F101 + F102 +
F103 + F104 + F105 + F106 + F107 + F108 + F109 + F110 + F111 +
F112 + F113 + F114 + F115 + F116 + F117 + F118 + F119 + F120 +
F121 + F122 + F123 + F124 + F125 + F126 + F127 + F128 + F129 +
F130 + F131 + F132 + F133 + F134 + F135 + F136 + F137 + F138 +
F139 + F140 + F141 + F142 + F143 + F144 + F145 + F146 + F147 +
F148 + F149 + F150

# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)
# weights:  508 (378 variable)

Step:  AIC= 613.31
Spoilage ~ F26 + F27 + F28 + F29 + F30 + F31 + F32 + F33 + F34 +
F35 + F36 + F37 + F38 + F39 + F40 + F41 + F42 + F43 + F44 +
F45 + F46 + F47 + F48 + F49 + F50 + F51 + F52 + F53 + F54 +
F55 + F56 + F57 + F58 + F59 + F60 + F61 + F62 + F63 + F64 +
F65 + F66 + F67 + F68 + F69 + F70 + F71 + F72 + F73 + F74 +
F75 + F76 + F77 + F78 + F79 + F80 + F81 + F82 + F83 + F84 +
F85 + F86 + F87 + F88 + F89 + F90 + F91 + F92 + F93 + F94 +
F95 + F96 + F97 + F98 + F99 + F100 + F101 + F102 + F103 +
F104 + F105 + F106 + F107 + F108 + F109 + F110 + F111 + F112 +
F113 + F114 + F115 + F116 + F117 + F118 + F119 + F120 + F121 +
F122 + F123 + F124 + F125 + F126 + F127 + F128 + F129 + F130 +
F131 + F132 + F133 + F134 + F135 + F136 + F137 + F138 + F139 +
F140 + F141 + F142 + F143 + F144 + F145 + F146 + F147 + F148 +
F149 + F150

# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)
# weights:  504 (375 variable)

Step:  AIC= 613.77
Spoilage ~ F27 + F28 + F29 + F30 + F31 + F32 + F33 + F34 + F35 +
F36 + F37 + F38 + F39 + F40 + F41 + F42 + F43 + F44 + F45 +
F46 + F47 + F48 + F49 + F50 + F51 + F52 + F53 + F54 + F55 +
F56 + F57 + F58 + F59 + F60 + F61 + F62 + F63 + F64 + F65 +
F66 + F67 + F68 + F69 + F70 + F71 + F72 + F73 + F74 + F75 +
F76 + F77 + F78 + F79 + F80 + F81 + F82 + F83 + F84 + F85 +
F86 + F87 + F88 + F89 + F90 + F91 + F92 + F93 + F94 + F95 +
F96 + F97 + F98 + F99 + F100 + F101 + F102 + F103 + F104 +
F105 + F106 + F107 + F108 + F109 + F110 + F111 + F112 + F113 +
F114 + F115 + F116 + F117 + F118 + F119 + F120 + F121 + F122 +
F123 + F124 + F125 + F126 + F127 + F128 + F129 + F130 + F131 +
F132 + F133 + F134 + F135 + F136 + F137 + F138 + F139 + F140 +
F141 + F142 + F143 + F144 + F145 + F146 + F147 + F148 + F149 +
F150

Error: arguments imply differing number of rows: 1, 126
```