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semicontinuous variables: what likelihoods are available?

Aurelie Cosandey Godin <GodinA at ...> writes:


[snip]
Can you say any more about exactly what a semicontinuous response variable
is?  Poking around (e.g <http://lpsolve.sourceforge.net/4.0/semi-cont.htm>)
doesn't make it entirely clear: are these data that are

truncated, i.e. values <= a lower threshold are absent from the data set;
censored, i.e. values <= a lower threshold are recorded as 
   "less than threshold"?
positive, i.e. values <0 don't even exist?
are the data non-negative (i.e. >=0) or are they positive (>0)?

  The simplest of these cases is positive data, which you
can model fairly easily by log transformation (i.e. assume
a lognormal distribution), or with slightly more difficulty
using a Gamma distribution ...  if you have censored or truncated
data, or data that include zeros, it gets a little harder ...