Description Usage Arguments Details Value Note Author(s) Examples
Transform a vector of n real-valued variables in (-Inf,Inf) [or (0,1)] to a vector of n+1 variables in (0,1) that sum to 1, or vice versa.
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q |
Unconstrained/transformed values:
vector of n numeric values in (-Inf,Inf) [if |
p |
Vector of n+1 numeric values in (0,1) that sum to 1 |
transf |
(character) "full": use arctan transform to transform (-Inf,Inf) to (0,1) or vice versa; "part": don't; "none"; no transform |
Essentially, this is a
transformation from an unconstrained set of variables to a bounded,
constrained set of variables. If contin is TRUE, an arctan
transformation (v <-> atan(v)/pi+0.5
) is used to transform
(-Inf,Inf) to (0,1) or vice versa. In either case, the correlated
set of variables (which sum to 1) is transformed to an unconstrained
set by taking each variable to be a remainder: x[1]=x[1]
,
x[2]=x[2]/(1-x[1])
, and so forth.
Vector of transformed values.
This transformation is designed to deal with the problems of
bounded optimization and constraints. It actually behaves quite badly
because small values are transformed to large negative values, messing
up the uniform scaling of the parameters. Now that the bounded
optimization of optim
has improved, contin="full"
may not
be a good idea. It's not clear whether the other transformation
(remainders) is better or worse than just optimizing on the first
(n-1) components and assuming that the last frequency equals one minus
the sum of the rest.
Ben Bolker
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