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  1. During doing analysis in R, when I want to know 1) whether there is an effect of B

and 2) whether there is an effect of C, why do I have to compare these two models (Model1 ,Model2)

Model 1 <- A ~ B + C + D + (1 | individual) + B:C + B:D + C:D + B:C:D

Model 2 <- A ~ B + C + D + (1 | individual) + B:C + B:D + C:D

  1. And I did AIC and BIC test, if the Model 2 is better one, what is important information?

Can I so analyze that Model2 is better one, cause 3-way interaction has no effect?

  1. And I got information of each models in console: values of Scaled residuals, Random effects, Fixed effects of each factor and their interactions and Correlation of fixed effects of each factor and their interactions Are they not important for analyzing?
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During doing analysis in R, when I want to know 1) whether there is an effect of B and 2) whether there is an effect of C

That's OK, provided that B and C are unrelated. But if there is a causal link between them (direct or indirect) then you will need to fit a different model to assess the impact of each variable. It is also necessary to consider the causal links with all the variables. The main point here is that you have to avoid conditioning on a mediator or a collider. See here for more details:
How do DAGs help to reduce bias in causal inference?

why do I have to compare these two models (Model1 ,Model2)

Well, you have fitted two model and if you want to make some inferences about your data, then I don't see any way to avoid some kind of comparison.

And I did AIC and BIC test, if the Model 2 is better one, what is important information?

The usual criteria is that you choose the model with the lowest AIC or BIC.

And I got information of each models in console: values of Scaled residuals, Random effects, Fixed effects of each factor and their interactions and Correlation of fixed effects of each factor and their interactions Are they not important for analyzing?

The most important information is the estimates of the regression coefficients for the fixed effects (main effects and interactions). The information you listed is mostly for checking diagnostics (eg no correlations between fixed or random effects of close to +/-1), no variance component (random effects) close to zero, and perhaps an assessment of normality of the residuals.

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  • $\begingroup$ Thanks a lot!! 1. As mentioned, AIC and BIC Test told me model2 is better one but through anova the difference is not significant nonetheless I took the model2. Then what I can report: I had fitted two model but through AIC, BIC Tests I decided to take the model2 but the difference is not significant -> Is it enough for model comparison or? $\endgroup$
    – Taede17
    Commented Jul 18, 2021 at 14:50
  • $\begingroup$ 2. Then the information I have listed over is not important for analyzing? The model 2 is mixed linear model, you mean, then do I have to do Regression analysis with this model2 for the questions 1) whether there is an effect of B and 2) whether there is an effect of C so that I can get regression coefficients? (I have already done analysis for the questions with contrast comparison but I'd love to do more analysis if I can!) $\endgroup$
    – Taede17
    Commented Jul 18, 2021 at 14:54
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    $\begingroup$ You're welcome :) Don't worry too much about p-values and statistical significance. If the underlying theory suggests that a 3-way interaction in plausible, then choose model 1. I have mentioned what you can consider for analysis in the last paragraph of my answer. $\endgroup$ Commented Jul 18, 2021 at 16:16
  • $\begingroup$ hi actually I got a information from my supervisor that I can use lme4 also linear mixed model for model comparison but a ohter recommend easily ANOVA cuz it is also regression analyse and show the effect of each fator and interaction. Can I take ANOVA for 2 model comparison? $\endgroup$
    – Taede17
    Commented Sep 1, 2021 at 14:21

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