# Formulae for BAMLSS This function creates an extended BAMLSS `formula`. In combination with a `bamlss.family` object, each parameter of the response distribution is linked to a single formula. If no formula is supplied for a parameter, a simple intercept only model is created. Moreover, the function identifies hierarchical structures, see the examples. This function is useful for creating complex `model.frame`s for (hierarchical) multi-parameter models and is used by function `bamlss.frame`. ```r bamlss.formula(formula, family = NULL, specials = NULL, env = NULL, ...) ``` ## Arguments - `formula`: A simple `formula`, or a `list` of simple formulae, or an extended `Formula`. For formula lists or extended `Formula`e, each single formula represents one model for the respective parameter as specified in the `family` object. - `family`: A `bamlss.family` object. - `specials`: A character vector specifying special functions to be used within formulae, see `terms.object`. - `env`: The environment that should be assigned to the formula. - ``...``: Arguments passed to the `family`. ## Returns A named list of class `"bamlss.formula"`. Each list entry specifies a model, e.g., for one parameter of a provided `bamlss.family` object. Each entry (parameter model) then holds: - **formula**: A simple `formula`. - **fake.formula**: A formula with all function calls being dropped, e.g., the formula `y ~ s(x1) + s(x2)` is represented in the `fake.formula` entry as `y ~ x1 + x2`. The `fake.formula` is useful for creating model frames. ## See Also `bamlss`, `bamlss.frame`, `bamlss.family` ## Examples ```r ## Simple formula without family object. f <- bamlss.formula(y ~ x1 + s(x2)) print(f) print(str(f)) ## Complex formula with list of formulae. f <- list( y1 ~ x1 + s(x2), y2 ~ x3 + te(lon, lat), u ~ x4 + x1 ) f <- bamlss.formula(f) print(f) print(names(f)) ## Same formula but using extended formulae ## of package Formula. f <- y1|y2|u ~ x1 + s(x2)|x3 + te(lon,lat)|x4 + x1 f <- bamlss.formula(f) print(f) print(names(f)) ## Using a bamlss family object, e.g., gaussian_bamlss(). ## The family has two parameters, mu and sigma, for ## each parameter one formula is returned. If no ## formula is specified an intercept only model is ## generated for the respective parameter. f <- bamlss.formula(y ~ x1 + s(x2), family = gaussian_bamlss) ## Note, same as: f <- bamlss.formula(y ~ x1 + s(x2), family = "gaussian") print(f) ## Specify model for parameter sigma, too f <- list( y ~ x1 + s(x2), sigma ~ x2 + te(lon, lat) ) f <- bamlss.formula(f, family = "gaussian") print(f) ## With complex hierarchical structures, ## each parameter is another list of formulae, ## indicated by the h1,...,hk, names. f <- list( y ~ x1 + s(x2) + id1, sigma ~ x2 + te(lon, lat) + id2, id1 ~ s(x3) + x4 + s(id3), id3 ~ x5 + s(x5, x6), id2 ~ x7 ) f <- bamlss.formula(f, family = "gaussian") print(f) ```

bamlss.formula function