contr.isotonic
is used in creating the design matrix
for categorical covariates with a specified order under a
particular parameterisation. For Poisson and negative binomial models, this
occurs if a categorical covariate is defined as monotonic;
for binomial models, each parameterisation defines a
permutation of the levels that must be monotonically
increasing.
For overparameterised binomial models, the design matrix for
categorical covariates must include isotonic-style dummy
covariates for every possible permutation of the levels. This
is the function of contr.opisotonic
.
In the order specified by perm
, the coefficient
associated with each level is the sum of increments between
the preceding levels. That is, the first level is defined
as \(0\), the second as \(0 + d_2\), the third as \(0 + d_2 + d_3\), and
so on. In fitting the model, these increments are
constrained to be non-negative.
Note that these are not `contrasts' as defined in the
theory for linear models; rather this is used to define the
contrasts
attribute of each variable so that
model.matrix
produces the desired design
matrix.