Which model would you choose?

#1
Dear readers,

I am struggeling with the model selection (ICs are very different and many insignificant models). Which model would you choose, and can you give a reason why you would choose this model? And what would an alternative? I would highly appreciate your input!!

Model F>P ---R2 ---MSE ----AIC -- BIC
1 -----0.691 0.0001 530 103953 103987
2 -----0.051 0.0003 143 86260 86297
3 -----0.024 0.0006 66.784 75953 75974
4 -----0.028 0.0007 36.651 67844 67864
5 -----0.000 0.0014 0.0837 -14351 -14331
6 -----0.000 0.0015 0.0491 -21543 -21522
7 -----0.462 0.0002 955 111898 111925
8 -----0.367 0.0003 603 105706 105734
9 -----0.073 0.0005 122.48 84149 84169
10 ----0.000 0.0009 0.680 13965 13985
11 ----0.000 0.0010 0.099 -12027 -12000
12 ----0.000 0.0010 0.084 -14361 -14334
13 ----0.282 0.0002 23000 123859 123880
14 ----0.444 0.0006 12000 114756 114777
15 ----0.200 0.0006 421.244 100843 100863
16 ----0.000 0.0008 0.284 2163 2184
17 ----0.000 0.0005 0.1737 -4476 -4448
18 ----0.000 0.0005 0.1554 -5982 -5955
 
#2
It may be worth conduct a chi-square difference test, as some of the models with similar fit may be so similar, that none are significantly better than an another.