interaction term in multilevel analysis using lmer() function-CodePudding

level 1 variable:

income - continuous

level 2 variable:

state's general whether: three leveled categorical variable: hot/moderate/cool

         used effect coded, and generate two variables because it has three levels.
        (weather_ef1, weather_ef2)  


enrolled in university - binary : yes/no  ( effect coded. yes = -1, no =1)

DV: math score

grouping variable: household

model 1: (fixed slope)

Dv is predicted by income, enrollment, and the interaction between enrollment and income. in this case,

lmer(y~ 1   income   enrollment  income*enrollment  (1|householdID), data=data)
lmer(y~ 1   income   enrollment  income:enrollment  (1|householdID), data=data)

: is it for interaction? or * is it for interaction?

further, do I have to do factor(enrollment)? or is it okay because it is already effect coded?

model 2: (fixed slope)

DV is predicted by income, weather, and interaction between income and weather

lmer( y ~ 1   income    weather_ef1   weather_ef2   weather_ef1*income
   weather_ef2*income  (1|houshold_id), data) 

lmer ( y ~ l   income   weather_ef1  weather_ef2   weather_ef1:income 
  weather_ef2:income    (1|houshold_id), data)

Still confusing * is right or: is right.

I think the effect code variables are already effect coded, so I don't have to do use the factor(weather_ef1) things.

CodePudding user response：

From the documentation (use ?formula):

The * operator denotes factor crossing: a*b interpreted as a b a:b.

In other words a*b add the main effects of a and b and their interaction. So in your model in you use income*enrollment this is the same as income enrollment income:enrollment. The two versions you described for each model should give identical results. You could just have used:

lmer(y~ 1   income*enrollment  (1|householdID), data=data)

which also describes the same model.

If your variables are effect coded then you don't need to use factor but be careful about the interpretation of the effects.