I'm running LMM models and could I ask if I can just report the model after comparing random intercept with random intercept and slope model without excluding nonsignificant factor?
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On the contrary, it is necessary to include all the insignificant predictors to get the parameter estimates and inferences "right". This has been discussed at length on this site. There are many issues but to mention one briefly, discarding "insignificant" variables greatly biases standard errors towards zero.