transformations | R Documentation |
Some useful parameter transformations.
logit(p)
expit(x)
log_barycentric(X)
inv_log_barycentric(Y)
p |
numeric; a quantity in [0,1]. |
x |
numeric; the log odds ratio. |
X |
numeric; a vector containing the quantities to be transformed according to the log-barycentric transformation. |
Y |
numeric; a vector containing the log fractions. |
Parameter transformations can be used in many cases to recast constrained optimization problems as unconstrained problems.
Although there are no limits to the transformations one can implement using the parameter_trans
facilty, pomp provides a few ready-built functions to implement some very commonly useful ones.
The logit transformation takes a probability p
to its log odds, \log\frac{p}{1-p}
.
It maps the unit interval [0,1]
into the extended real line [-\infty,\infty]
.
The inverse of the logit transformation is the expit transformation.
The log-barycentric transformation takes a vector X_i
, i=1,\dots,n
, to a vector Y_i
, where
Y_i = \log\frac{X_i}{\sum_j X_j}.
If X
is an n
-vector, it takes every simplex defined by \sum_i X_i = c
, c
constant, to n-dimensional Euclidean space R^n
.
The inverse of the log-barycentric transformation is implemented as inv_log_barycentric
.
Note that it is not a true inverse, in the sense that it takes R^n
to the unit simplex, \sum_i X_i = 1
.
Thus,
log_barycentric(inv_log_barycentric(Y)) == Y,
but
inv_log_barycentric(log_barycentric(X)) == X
only if sum(X) == 1
.
More on implementing POMP models:
Csnippet
,
accumulator variables
,
basic components
,
betabinomial
,
covariates
,
distributions
,
dmeasure specification
,
dprocess specification
,
emeasure specification
,
parameter transformations
,
pomp-package
,
pomp
,
prior specification
,
rinit specification
,
rmeasure specification
,
rprocess specification
,
skeleton specification
,
userdata
,
vmeasure specification
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