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I have created an outcome variable which ranges from 0 to 1.

This variable represents students' average grade, across different courses s/he has passed at the university; with 0 being the sufficiency and 1 being the max obtainable grade. Basically, this outcome variable is a percentage which has been constructed from two different scales of grades:

  1. Scale one, with U = fail, G = good (worse grade), VG = very good (best grade). I have transformed it in this way: G = 0 and VG = 1
  2. Scale two, with U = fail, then 1 (worse grade) - 2 - 3 - 4 - 5 (best grade). I have transformed it in this way: 1 = 0, 2 = 0.25, 3 = 0.5, 4 = 0.75, 5 = 1.

In both the scales U is accounted for as a missing value, since failing an exam does not have any repercussions on your average grade.

For some courses, a student's exam may be graded based on the first scale and, for other courses, the grade will be based on the second scale (it depends on the teacher and on the field of the course, whether it is either a soft or hard science).

What model should I use to regress this outcome variable?

I was thinking that a tobit model would suits well my study, the alternative is a linear probability model.

What is your advice?

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    $\begingroup$ I wouldn't recommend either approach. I'd recommend generalized linear models with logit link, binomial family and robust standard errors. The binomial is qualitatively right here. See stata-journal.com/sjpdf.html?articlenum=st0147 for an introduction. Quasilikeihood is a keyword here. Several posts in this forum address the same question. $\endgroup$ – Nick Cox Jan 8 '16 at 11:12
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    $\begingroup$ Quasi-likelihood seems the more common spelling. Also consider beta regression. $\endgroup$ – Nick Cox Jan 8 '16 at 11:20

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