Dears,

I have a model like the following in the first level:

Y = b_0 + b_1*X1

And in the second level, I have a variable X2 which effect only makes sense
on b_1, not directly on the mean of Y, through b_0. I have two questions.

First, is it correct to model it like the following:

b_0 = j_00 + u0
b_1 = j_10 + j_11*X2 + u1

So:
Y = j_00 + u0 + j_10*X1 + j_11*X2*X1 + u1*X1

Or should I also cross-level X2 on the b_0 of level 1 anyway, in spite of
the what I am theoretically trying to model?

Second, would it be correct to specify such equation with lmer() like the
following:

lmrob( Y ~ X1+ X1:X2 + (1 | level2 ) + ( 0 + X1 | level2), data=my.data)

Thanks!

R.

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