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I am struggling 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?

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
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  • $\begingroup$ Were each of these models fit to the same data? $\endgroup$ – generic_user Aug 12 '15 at 11:48
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    $\begingroup$ I'm struggling to see why you're struggling: the AIC & BIC are lowest for the same model, which also has the highest $R^2$. See Is there any reason to prefer the AIC or BIC over the other? for explanation of the differences between the two criteria, & also Algorithms for automatic model selection for discussion of the perils of this type of approach. $\endgroup$ – Scortchi Aug 12 '15 at 11:48
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    $\begingroup$ Is any of these models worthwhile? $R^2$ at 0.0015 or below looks pretty terrible. $\endgroup$ – Richard Hardy Aug 12 '15 at 11:51
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    $\begingroup$ I agree with Richard Hardy, none of the model seems to explain the data well. I would suggest to use some graphical check e.g. plot the data v.s. the best model with its estimated parameters (if possible) to get insight if the model is indeed bad, whether there is problem with fitting assumptions or if there is a mistake somewhere, instead of only trusting the numbers. $\endgroup$ – MarkoJ Aug 12 '15 at 16:15

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