How to build a correct LME model through the 3dLMEr program

AFNI Message Board
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Hi, Dear AFNI team!

A reviewer raised some questions about an LME model implemented in our article using the 3dLMEr program. But we are confused by their questions, how can I answer their questions? Hope the AFNI team can give us some suggestions. The original text of the question raised by the reviewer is as follows:

In the section Group-level Analysis, it reads “We use LMM to detect the diagnostic effect and its influence of age and gender while allowing site-varying effects. LMM describes the relationship between a response variable (i.e., VMHC) and independent variables (here, diagnosis and covariates of age, sex, education, and head motion), with coefficients that can vary with respect to the site. We utilized 3dLMEr in AFNI (https://afni.nimh.nih.gov/) to test the model (LMM-1): y ∼1 + Diagnosis Age Sex + Education + motion + (1| Site), which yields Z and P values for the fixed effect of Diagnosis, Diagnosis×Age, Diagnosis×Sex, and Diagnosis×Age×Sex.” No individual fixed effect of diagnosis is included in the specified LMM-1 model but it yields z and p-values for the fixed effects? Two-way interactions are not specified in the model?

Thanks

KeKe

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No individual fixed effect of diagnosis is included in the specified LMM-1 model but it yields z and p-values for the fixed effects?
Two-way interactions are not specified in the model?

The R notation for the model formulation

Diagnosis Age Sex

is equivalent to

Diagnosis + Age + Sex + Diagnosis:Age + Diagnosis:Sex + Age:Sex + Diagnosis:Age:Sex

In other words, all the main effects, two-way and three-way interactions among the three variables (Diagnosis, Age, and Sex) are included in the model.