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I am dealing with the following data frame:

GroupID Month Year   Concession_10Yr  Action  Historical_Action_5Yr
XY1       12   1984     1                0                 0
...

Here GroupID is a unique identifier for an organization. Then we have data every ear and month on whether the organization took "action", whether there was a "concession" (think "treatment") to this organization over the past 10 years and then whether the organization took action over the last 5 years.

What I'm trying to do is model the probability of an organization taking action. Clearly I can't do a simple linear regression as the organizations would be correlated with one another as some organizations are more likely to take action then others.

As such, I was thinking of a non-linear mixed effects model, something like:

lmer(Action ~ GroupID + Historical_Action_5Yr + Concession_10Yr +
     1/GroupID/Concession_10Yr + 1/GroupID/Historical_Action_5Yr, 
     family = binomial(link = logit)

However, I am not sure that I have the nesting correct. Also, this doesn't account for time directly...

Any guidance would be much appreciated!

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According to this paper about the package, the (1 | g1/g2) (or the equivalent (1 | g1)+(1 | g1:g2)) notation means:

Intercept varying among g1 and g2 within g1

Thus your model consists of the following parts:

  • A fixed effect for GroupID
  • A fixed effect for Historical_Action_5Yr
  • A fixed effect for Concession_10Yr
  • An intercept varying for GroupID and an intercept for Concession_10Yr withing GroupID, noted as (1 | GroupID/Concession_10Yr)
  • An intercept for GroupID and an intercept for Historical_Action_5Yr within GroupID, noted as (1 | GroupID/Historical_Action_5Yr). Since there is already an intercept varying for GroupID you could also use (1 | GroupID:Historical_Action_5Yr) to compute the intercept for all combinations of GroupID and Historical_Action_5Yr.

In short:

lmer(Action ~ GroupID + Historical_Action_5Yr + Concession_10Yr + (1 |GroupID/Concession_10Yr) + (1 | GroupID:Historical_Action_5Yr), family = binomial(link =logit)
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  • $\begingroup$ Hi Pieter: That's the thing, I'm not quite sure I need all combinations of GroupID & Historical_Action_5YR -- I'm looking for some help on how the model should be? $\endgroup$ – user1357015 Jan 7 '17 at 20:34
  • $\begingroup$ There no such thing as a correct answer on that. You should think about what you think the relations are like. The data could also guide you to an answer. Start by learning a simple model and check the coefficients and error distribution. If the latter it is normally distributed and the spread is small enough, you're done :) If not, include additional variable (interactions) and check if they make sense (correct direction?) and if they add something. $\endgroup$ – Pieter Jan 7 '17 at 22:30

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