mixed linear models comparison

Question

When I get 2 mixed linear Models for a comparison between them

For example, (B, C, D are factors)

Mdoel 1 <- lmer(A ~ B * C * D + (1|individual), data = Data_1) in script Outcome in console: A ~ B * C * D + (1 | individual)

Model 2 <- update(Model 1, . ~ . - B : C : D) in script Outcome in console : A ~ B + C + D + (1 | individual) + B:C + B:D + C:D

1. Also, B,C,D are for fixed effects and (1|individual) is for a random effect

What is the difference between A ~ B + C + D + (1|individual) and A ~ BCD + (1|individual)?

2. By Model 2 what do mean ". ~ ." and "- B : C : D" both in Script?

2-2. A ~ B + C + D + (1 | individual) + B:C + B:D + C:D What does mean " B:C + B:D + C:D "?

Answer 1

What is the difference between A ~ B + C + D + (1|individual) and A ~ BCD + (1|individual)?

I think you mean B * C * D, not BCD. BCD would represent a variable called BCD, wheras B * C * D means "fit fixed effects for B, C and D, and all the interactions between them" (that is, the three 2-way interactions plus the 3 way interaction). So the difference betwwen A ~ B + C + D and A ~ B * C * D is that in the former we fit fixed effects for the each of the variables while in the latter we also fit all the interactions.

By Model2 what do mean ". ~ ." and "- B : C : D" both in Script?

You are telling the software to update model 1 by removing the 3-way interaction B:C:D(because you used the minus symbol -), so that model 2 contains only the 2-way interactions (and the main effects)

What does mean "B:C + B:D + C:D"?

B:C + B:D + C:D tells the software to fit the three 2-way interactions between the variables. Note that

~ B * C * D

is exactly the same as:

~ B + C + D + B:C + B:D + C:D