Driver and model definition for a mixture of partially linear models with monotone shape constraints.
To implement: call flexmix() from the flexmix package with mono_reg() as the model argument. E.g.,
the following call to flexmix() produces a model with 6 components, each of which is a partial linear model regressing Y on all other
variables of df and with no intercept. The mon_inc_index argument to mono_reg() instructs the function to estimate a non-parametric,
monotone-increasing, aka isotonic, function on the second independent variable in df.
mod <- flexmix(Y ~ .-1, data = df, k = 6, model = mono_reg(mon_inc_index = 2))flexmix also allows the construction of multiple mixture models within a single object. The following call to stepFlexmix() builds 25 mixture models; for each of
k equal to 1 through 5 components, nrep calls for the construction of 5 models. Now each model contains 2 monotone components -- a monotone-increasing,
or isotonic, relationship between Y and the 2nd independent variable of df, and a monotone-decreasing, or antitonic, relationship between Y and
the 3rd independent variable of df.
m2 <- stepFlexmix(Y ~ .-1, data = df, model = mono_reg(mon_inc_index = 2, mon_dec_index = 3), k = 1:5, nrep = 5)For further discussion of the use of the flexmix package, see the guides here and here, or the following blog.
The indexing arguments passed to mono_reg() are indices of the design matrix constructed by the formula passed to flexmix, so they change
based on the design matrix. For example, without an intercept, mono_inc_index = 2 refers to the 2nd independent variable of the data frame; when
an intercept is included, mono_inc_index = 2 refers to the 1st independent variable of the data frame.