All parameters need not be statistically significant. The ones that are not significant can (and should) be dropped and the model should be retrained with the remaining parameters. The new model's AIC should be compared with the previous model's AIC to see if there is an improvement in the goodness-of-fit. If the goodness-of-fit of the new model (with fewer parameters) is better than that of the previous model, it is better to go with the new model with fewer parameters. See my article on AIC for how to use it to compare the goodness-of-fit of 'nested' models.

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