Similar to the well-known
model.frame() function that is used, e.g., by the linear model fitting function
lm(), or for generalized linear models
bamlss.frame() function extracts a “model frame” for fitting distributional regression models. Internally, the function parses model formulae, one for each parameter of the distribution, using the Formula package infrastructures (Zeileis and Croissant 2010) in combination with
model.matrix() processing for linear effects and
smooth.construct() processing of the mgcv package to setup design and penalty matrices for unspecified smooth function estimation (???), see also, e.g., the documentation of function
The most important arguments are
formula can be a classical model formulae, e.g., as used by the
lm() function, or an extended bamlss formula including smooth term specifications like
te(), that is internally parsed by function
bamlss.formula(). Note that the bamlss package uses special
family objects, that can be passed either as a character without the
"_bamlss" extension of the bamlss family name (see the manual
?bamlss.family for a list of available families and the corresponding vignette BAMLSS Families), or the family function itself. In addition, all families of the gamlss (???) and gamlss.dist (Stasinopoulos and Rigby 2019) package are supported.
The returned object, a named list of class
"bamlss.frame", can be employed with all model fitting engines. The most important elements used for estimation are:
x: A named list, the elements correspond to the parameters that are specified within the
familyobject. For each distribution parameter, the list contains all design and penalty matrices needed for modeling (see the upcoming example).
y: The response data.
family: The processed .
To better understand the structure of the
"bamlss.frame" object a print method is provided. For illustration, we simulate data
and set up a
"bamlss.frame" object for a Gaussian distributional regression model including smooth terms. First, a model formula is needed
Afterwards the model frame can be computed with
To keep the overview, there is also an implemented print method for
## 'bamlss.frame' structure: ## ..$ call ## ..$ model.frame ## ..$ formula ## ..$ family ## ..$ terms ## ..$ x ## .. ..$ mu ## .. .. ..$ formula ## .. .. ..$ fake.formula ## .. .. ..$ terms ## .. .. ..$ model.matrix ## .. .. ..$ smooth.construct ## .. ..$ sigma ## .. .. ..$ formula ## .. .. ..$ fake.formula ## .. .. ..$ terms ## .. .. ..$ model.matrix ## .. .. ..$ smooth.construct ## ..$ y ## .. ..$ num ## ..$ delete
For writing a new estimation engine, the user can directly work with the
model.matrix elements, for linear effects, and the
smooth.construct list, for smooth effects respectively. The
smooth.construct is a named list which is compiled using the
smoothCon() function of the mgcv package using the generic
smooth.construct() method for setting up smooth terms.
##  "s(x2)" "s(x3)" "te(lon,lat)"
In this example, the list contains three smooth term objects for parameter
Stasinopoulos, Mikis, and Robert Rigby. 2019. Gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape. https://CRAN.R-project.org/package=gamlss.dist.
Umlauf, Nikolaus, Nadja Klein, Achim Zeileis, and Thorsten Simon. 2021. bamlss: Bayesian Additive Models for Location Scale and Shape (and Beyond). https://CRAN.R-project.org/package=bamlss.
Zeileis, Achim, and Yves Croissant. 2010. “Extended Model Formulas in R: Multiple Parts and Multiple Responses.” Journal of Statistical Software 34 (1): 1–13. https://doi.org/10.18637/jss.v034.i01.