Build the design and the penalty matrix for models involving penalised splines based on a formula and a data set

Build the design and the penalty matrix for models involving penalised splines based on a formula and a data set

Usage

modmat(formula, data, knots = NULL)

make_matrices(formula, data, knots = NULL)

Arguments

formula

formula as used in mgcv. Formulas can be right-side only, or contain a response variable, which is just extracted for naming.

Can also be a list of formulas, which are then processed separately. In that case, both a named list of right-side only formulas or a list of formulas with response variables can be provided.

data

data frame containing all the variables on the right side of the formula(s)

knots

optional list containing user specified knot values for each covariate to be used for basis construction. For most bases the user simply supplies the knots to be used, which must match up with the k value supplied (note that the number of knots is not always just k). See mgcv documentation for more details.

If formula is a list, this needs to be a named (based on the response variables) list over such lists.

Value

a list of class LaMa_matrices containing:

Z

design matrix (or list of such matrices if formula is a list))

S

list of penalty matrices (with names based on the response terms of the formulas as well as the smooth terms and covariates). For tensorproduct smooths, corresponding entries are themselves lists, containing the \(d\) marginal penalty matrices if \(d\) is the dimension of the tensor product)

pardim

list of parameter dimensions (fixed and penalised separately) for each formula, for ease of setting up initial parameters

coef

list of coefficient vectors filled with zeros of the correct length for each formula, for ease of setting up initial parameters

sp0

named vector of initial penalty strengths, with one entry per penalty matrix and names matching S (a smooth with several penalties, e.g. a tensor product, contributes one entry each, named <smooth>.<margin>).

These are initial.sp's guesses times 100, capped at 1e6: the inner optimisation is better behaved when it starts constrained, and the outer iteration relaxes the penalty from there.

It can be passed straight to penalty or penalty2 when each smooth appears once. When a smooth is replicated, e.g. one spline per state, use rep_sp, as a single rep() over sp0 is only correct for some models.

formula

the formula(s) as supplied, in the same nesting as Z

data

the data frame used for the model(s)

gam

unfitted mgcv::gam object used for construction of Z and S (or list of such objects if formula is a list). Its X element is not kept, as it is returned as Z

gam0

fitted mgcv::gam which is used internally to create prediction design matrices (or list of such objects if formula is a list)

knots

knot list used in the basis construction (or named list over such lists if formula is a list)

Details

make_matrices() is the former name of modmat() and still works.

See also

predict.LaMa_matrices for prediction design matrix construction based on the model matrices object created by this function.

Examples

data = data.frame(x = runif(100), 
                  y = runif(100),
                  g = factor(rep(1:10, each = 10)))

# unvariate thin plate regression spline
modmat = modmat(~ s(x), data)
# univariate P-spline
modmat = modmat(~ s(x, bs = "ps"), data)
# adding random intercept
modmat = modmat(~ s(g, bs = "re") + s(x, bs = "ps"), data)
# tensorproduct of x and y
modmat = modmat(~ s(x) + s(y) + ti(x,y), data)
# multiple formulas at once
modmat = modmat(list(mu ~ s(x) + y, sigma ~ s(g, bs = "re")), data = data)