bamlss  R Documentation 
This is the main model fitting function of the package. Function bamlss()
is a wrapper function that parses the data
and the model formula
, or
extended bamlss.formula
, as well as the bamlss.family
into a bamlss.frame
. The bamlss.frame
then holds all model
matrices and information that is needed for setting up estimation engines.
The model matrices are based on mgcv
infrastructures, i.e.,
smooth terms are constructed using smooth.construct
and
smoothCon
. Therefore, all mgcv
model term constructors like
s
, te
, t2
and ti
can be used. Identifiability conditions are imposed using function gam.side
.
After the bamlss.frame
is set up function bamlss()
applies optimizer
and/or sampling functions. These functions can also be provided by the user. See the details
below on how to create new engines to be used with function bamlss()
.
Finally, the estimated parameters and/or samples are used to create model output results like summary statistics or effect plots. The computation of results may also be controlled by the user.
bamlss(formula, family = "gaussian", data = NULL, start = NULL, knots = NULL, weights = NULL, subset = NULL, offset = NULL, na.action = na.omit, contrasts = NULL, reference = NULL, transform = NULL, optimizer = NULL, sampler = NULL, samplestats = NULL, results = NULL, cores = NULL, sleep = NULL, combine = TRUE, model = TRUE, x = TRUE, light = FALSE, ...)
formula 
A formula or extended formula, i.e., the 
family 
A 
data 
A 
start 
A named numeric vector containing starting values to be send to the 
knots 
An optional list containing user specified knots, see the documentation of
function 
weights 
Prior weights on the data. 
subset 
An optional vector specifying a subset of observations to be used in the fitting process. 
offset 
Can be used to supply model offsets for use in fitting. 
na.action 
A function which indicates what should happen when the data
contain 
contrasts 
An optional list. See the 
reference 
A 
transform 
A transformer function that is applied on the 
optimizer 
An optimizer function that returns, e.g., posterior mode estimates
of the parameters as a named numeric vector. The default optimizer function is

sampler 
A sampler function that returns a matrix of samples, the columns represent the
parameters, the rows the iterations. The returned matrix must be coerced to an object of
class 
samplestats 
A function computing statistics from samples, per default function

results 
A function computing results from the parameters and/or samples, e.g., for
creating effect plots, see function 
cores 
An integer specifying the number of cores that should be used for the sampler
function. This is based on function 
sleep 
Time the system should sleep before the next core is started. 
combine 
If samples are computed on multiple cores, should the samples be combined into
one 
model 
If set to 
x 
If set to 
light 
Should the returned object be lighter, i.e., if 
... 
Arguments passed to the 
The main idea of this function is to provide infrastructures that make it relatively easy to create estimation engines for new problems, or write interfaces to existing software packages.
The steps that are performed within the function are:
First, the function parses the data
, the formula
or the extended
bamlss.formula
as well as the bamlss.family
into a model frame
like object, the bamlss.frame
. This object holds all necessary model matrices
and information that is needed for subsequent model fitting engines. Per default,
all package mgcv
smooth term constructor functions like
s
, te
, t2
and
ti
can be used (see also function smooth.construct
),
however, even special user defined constructors can be included, see the manual of
bamlss.frame
.
In a second step, the bamlss.frame
can be transformed, e.g., if a mixed
model representation of smooth terms is needed, see function randomize
.
Then an optimizer function is started, e.g., a function that finds posterior mode estimates of the parameters. A convention for model fitting engines is that such functions should have the following arguments:
optimizer(x, y, family, start, weights, offset, ...)
Internally, function bamlss()
will send the x
object that holds all
model matrices, the response y
object, the family
object, start
ing
values for the parameters, possible weights
and offset
s of the created
bamlss.frame
to the
optimizer function (see the manual of bamlss.frame
for more details on the
x
, y
and other objects). The job of the optimizer is to return a named numeric
vector of optimum parameters. The names of the parameters should be such that they can be
uniquely mapped to the corresponding model matrices in x
. See function
parameters
for more details on parameter names. The default optimizer function
is bfit
. The optimizer can return more information than only the optimum
parameters. It is possible to return a list, the convention here is that an element named
"parameters"
then holds the named vector of estimated parameters. Possible other return
values could be fitted values, the Hessian matrix, information criteria or information
about convergence of the algorithm, etc. Note that the parameters are simply added to the
bamlss.frame
in an (list) entry named parameters
.
After the optimization step, a sampler
function is started. The arguments of such
sampler functions are the same as for the optimizer
functions
sampler(x, y, family, start, weights, offset, ...)
Sampler functions must return a matrix of samples, each row represents one iteration and the matrix
can be coerced to mcmc
objects. The function may return a list of samples,
e.g., if multiple chains are returned each list entry then holds one sample matrix of
one chain. The column names of the sample matrix should be the same as the names of estimated
parameters. For a possible naming convention see function parameters
, which
ensures unique mapping of samples with the model matrices in the x
object of the
bamlss.frame
. The samples are added to the bamlss.frame
in an (list) entry named samples
.
Next, the samplestats
function is applied. This function can compute any quantity
from the samples and the x
object, the arguments of such functions are
samplestats(samples, x, y, family, ...)
where argument samples
are the samples returned from the sampler
function,
and x
, y
and family
are the same objects as passed to the optimizer
and or sampler functions. For example, the default function in bamlss()
for this task
is also called samplestats
and returns the mean of the loglikelihood and the
logposterior computed of all samples, as well as the DIC.
The last step is to compute more complex information about the model using the
results
function. The arguments of such results
functions are
results(bamlss.frame, ...)
here, the full bamlss.frame
including possible parameters
and
samples
is passed to the function within bamlss()
. The default function
for this task is results.bamlss.default
which returns an object of class
"bamlss.results"
for which generic plotting functions are and a summary
function is provided. Hence, the user can control the output of the model, the plotting
and summary statistics, too.
Note that function transform()
, optimizer()
, sampler()
, samplestats()
and results()
can be provided from the bamlss.family
object, e.g.,
if a bamlss.family
object has an element named "optimizer"
, which
represents a valid optimizer function such as bfit
, exactly this optimizer
function will be used as a default when using the family.
An object of class "bamlss"
. The object is in principle only a slight extension
of a bamlss.frame
, i.e., if an optimizer
is applied it will hold the
estimated parameters in an additional element named "parameters"
. If a sampler function
is applied it will additionally hold the samples in an element named "samples"
.
The same mechanism is used for results
function.
If the optimizer
function computes additional output next to the parameters, this will
be saved in an element named "model.stats"
. If a samplestats
function is applied,
the output will also be saved in the "model.stats"
element.
Additionally, all functions that are called are saved as attribute "functions"
in the
returned object.
Nikolaus Umlauf, Nadja Klein, Achim Zeileis.
Umlauf N, Klein N, Zeileis A (2019). BAMLSS: Bayesian Additive Models for Location, Scale and Shape (and Beyond). Journal of Computational and Graphical Statistics, 27(3), 612–627. doi: 10.1080/10618600.2017.1407325
Umlauf N, Klein N, Simon T, Zeileis A (2021). bamlss: A Lego Toolbox for Flexible Bayesian Regression (and Beyond). Journal of Statistical Software, 100(4), 1–53. doi: 10.18637/jss.v100.i04
bamlss.frame
, family.bamlss
, bamlss.formula
,
randomize
, bamlss.engine.setup
,
opt_bfit
, sam_GMCMC
, continue
,
coef.bamlss
, parameters
, predict.bamlss
,
plot.bamlss
## Not run: ## Simulated data example. d < GAMart() f < num ~ s(x1) + s(x2) + s(x3) + te(lon, lat) b < bamlss(f, data = d) summary(b) plot(b) plot(b, which = 3:4) plot(b, which = "samples") ## Use of optimizer and sampler functions: ## * first run optimizer, b1 < bamlss(f, data = d, optimizer = opt_bfit, sampler = FALSE) print(b1) summary(b1) ## * afterwards, start sampler with staring values, b2 < bamlss(f, data = d, start = coef(b1), optimizer = FALSE, sampler = sam_GMCMC) print(b2) summary(b2) ## Continue sampling. b3 < continue(b2, n.iter = 12000, burnin = 0, thin = 10) plot(b3, which = "samples") plot(b3, which = "maxacf") plot(b3, which = "maxacf", burnin = 500, thin = 4) ## End(Not run)
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