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We did a study with a course participants where we have one outcome variable and several metrics calculated for each message they posted on a discussion forum. Basically, the data are structure in the following way:

student | outcome (grade) | timestamp     | discussion_metric1 | discussion_metric2 | ...
stud1   | 4               |1402409844779  | 0.34               | 1.2                |...
stud1   | 4               |time2          | 1.34               | 0.85               |...
stud1   | 4               |time3          | 0.7                | 1.25               |...
stud1   | 4               |time4          | 0.8                | 3.4                |...
stud2   | 3.7             |time5          | 0.8                | 2.2                |...
stud2   | 3.7             |time6          | 1.34               | 1.9                |...

In this example, stud1 has posted 4 messages (different time of course), and for each message we have values for metrics 1 and 2. On the other hand, stud2 posted two message, and for both of them outcome (grade) is the single value for the course. Not that every discussion is graded, but there is only one grade for the course.

I was thinking that predicting learning outcome with metrics 1 and 2 as fixed effects would make sense. But, not sure whether student could (should) be considered as a random effect? On the other hand, how can I include time in the model? Regarding the time, I could also cluster those times into weeks (week1 to week10) if that would make more sense...

Any suggestion would be much appreciated.

Srecko
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  • How many observations per student do you have? I ask because you should also [take it into consideration](http://stats.stackexchange.com/questions/128872/linear-mixed-model-number-of-observations-per-group/128882#128882). – Tim Dec 12 '14 at 18:54
  • That depends on how many messages they posted. In total we have around 7000 observations, but per student it varies from 1 to 30... some of them where quite active, while some of them were not... – Srecko Dec 12 '14 at 19:18
  • I forgot to mention that those data were collected within a single course. That is why I'm also concerned whether student as a random effect make sense – Srecko Dec 12 '14 at 19:19

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