Random slope with cross-level interaction

Hi Yashree,
The interpretation of the interaction term do change whether you include
the main effect of not.
Usually having only the interaction term in the model requires a specific
hypothesis. Thus, the lower level terms (i.e., the main effects) are almost
always included.
The lmer function automatically includes the lower level terms even if you
just include an interaction term.
For example, if you setup your model as follow, the main effects of
fertilizer and wheatlanduse will be still taken into account.
Production = seed + fertilizer : wheatlanduse + (1 + fertilizer |
Household)

Thanks,
Sala

*************
Salahadin (Sala) Lotfi

PhD Candidate of Cognitive Psychology & Neuroscience

University of Wisconsin-Milwaukee

Anxiety Disorders Laboratory

President, Association of Clinical and Cognitive Neuroscience, UWM

Hi,

I have the following model:

Production = seed + fertilizer + fertilizer : wheatlanduse + (1 +
fertilizer | Household)

As the formula indicates, the household level is specified as the random
intercept. Fertilizer is specified as random slope , and has also been
specified as a fixed effect.

I am interested in cross-level interaction between fertilizer and the
wheatlanduse variable. So, I have inserted "fertilizer : wheatlanduse".

My question is: Do I have to include "wheatlanduse" as a main effect in the
formula as well? Or is it acceptable to only have it as a part of the
interaction term?

Thank you,

Regards,
Yashree

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