# Zero weights in multiple membership models

In the multilevel vignette, there is a discussion of multiple membership weights in Example 4.

For students who went to a single school during the study period, the data is organized as follows:

``````data_mm[101:106, ]
s1 s2 w1  w2 y
101  2  2 0.5 0.5 27.247851
102  9  9 0.5 0.5 24.041427
103  4  4 0.5 0.5 12.575001
104  2  2 0.5 0.5 21.203644
105  4  4 0.5 0.5 12.856166
106  4  4 0.5 0.5 9.740174
``````

In other words, this could be read as student 101 spending 50% of the time in School 1 and the other 50% of the time in School 2.

However, would the model give equivalent estimates if the weights were 1 and 0, respectively. Accordingly:

``````data_mm[101:106, ]
s1 s2 w1 w2 y
101  2  2  1  0 27.247851
102  9  9  1  0 24.041427
103  4  4  1  0 12.575001
104  2  2  1  0 21.203644
105  4  4  1  0 12.856166
106  4  4  1  0 9.740174
``````

In my experience, that is a more natural way of organizing the data. But that depends on whether the structures would result in equivalent inferences in BRMS. Thanks again.

• Operating System: Mac OS
• brms Version: 2.7
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EDIT: I understand your question now. You were referring to students who just attend a single school. In that case, indeed the weights donâ€™t matter (as long as they sum to 1).

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Right. Thanks, Paul. In keeping with the school study, some students switch schools but I was wondering if I could organize the data like the above example (with zero weights) in some columns for students who didnâ€™t switch schools.

Am I understanding correctly that every â€śsâ€ť column needs an ID even if its corresponding weight is zero? In other words, brm() wouldnâ€™t work well if there were NA values (or zeroes) in the s2 column for students that didnâ€™t switch, is that right?

Right, sorry I misunderstood you initial question (please see my EDIT above). And you are also right that brms wonâ€™t work well with NAs both in the ID and in the weights columns.