DirichReg {DirichletReg} | R Documentation |
Fitting a Dirichlet Regression
Description
This function allows for fitting Dirichlet regression models using two different parametrizations.
Usage
DirichReg(formula, data, model = c("common", "alternative"),
subset, sub.comp, base, weights, control, verbosity = 0)
Arguments
formula |
the model formula (for different specifications see “Details”) |
data |
a |
model |
specifies whether the |
subset |
estimates the model for a subset of the data |
sub.comp |
analyze a subcomposition by selecting specific components (see “Details”) |
base |
redefine the base variable |
weights |
frequency weights |
control |
a list containing control parameters used for the optimization |
verbosity |
prints information about the function's progress, see Details |
Details
Formula Specification and Models
formula
determines the used predictors.
The responses must be prepared by DR_data
and can be optionally stored in the object containing all covariates which is then specified as the argument data
.
(Although “on-the-fly” processing of DR_data
in a formula works, it is only intended for testing purposes and may be removed at any time – use at your own risk.)
There are two different parametrization (controlled by the argument model
, see below):
the “common” param. that models each
\alpha
by an (possibly individual) set of predictors, andthe “alternative” param. that models expected values (
\mu
; as in multinomial logistic regression) and precision parameters (\phi
) with two sets of predictors.
As the two models offer different modeling strategies, the specification of their formulae differ:
Formulae for the “Common” Model
The simplest possible model here is to include only an intercept for all components.
If DV
is the ‘dependent variable’ (i.e., compositional data) with three components, we can request this null-model by DV ~ 1
.
We always have at least two dependent variables, so simple formulae as the one given above will be expanded to DV ~ 1 | 1 | 1
, because DV
hast three components.
Likewise, it is possible to specify a common set of predictors for all components, as in DV ~ p1 * p2
, where p1
and p2
are predictors.
If the covariates of the components shall differ, one has to set up a complete formula for each subcomposition, using |
as separators between the components, for example, DV ~ p1 | p1 + p2 | p1 * p2
will lead to a model where the first response in DV
will be modeled using p1
, the second will be predicted by p1 + p2
and the third by p1 * p2
.
Note that if you use the latter approach, the predictors have to be stated
explicitly for all response variables.
Formulae for the “Alternative” Model
The simplest possible model here is to include an intercept for all components (except the base) and an intercept for precision. This can be achieved by DV ~ 1
, which is expanded to DV ~ 1 | 1
. The part modeling the ‘mean’ (first element on the right-hand side) is mandatory, if no specification for precision is included, an intercept will be added. Note that you need to set model = "alternative"
to use this parametrization!
The alternative parametrization consists of two parts: modeled expected values (\mu
) and their ‘precision’ (\phi
).
As in multinomial logistic regression, one response variable is omitted (by default the first, but this can be changed by the base
argument in DR_data
or DirichReg
) and for the rest a set of predictors is used with a multinomial logit-link.
For precisions, a different set of predictors can be set up using a log-link.
DV ~ p1 * p2 | p1 + p2
will set up a model where the expected values are predicted by p1 * p2
and precision are modeled using p1 + p2
.
Data Preparation
The data
argument accepts a data.frame
that must include the dependent variable as a named element (see examples how to do this).
Changing the Base Component and Analyzing Subcompositions
The base-component (i.e., omitted component) is initially set during the stage of data preparation DR_data
, but can easily be changed using the argument base
which takes integer values from 1 to the maximum number of components.
If a data set contains a large number of components, of which only a few are relevant, the latter can be ‘sorted out’ and the irrelevant (i.e., not selected) components will be aggregated into a single variable (row sums) that automatically becomes the base category for the model, unless specified otherwise by base
. The positioning of variables will necessarily change: the aggregated variable takes the first column and the others are appended in their order of selection.
Subsets and Weights
Using subset
, the model can be fitted only to a part of the data, for more information about this functionality, see subset
.
Note that, unlike in glm
, weights
are not treated as prior weights, but as frequency weights!
Optimization and Verbosity
Using the control
argument, the settings passed to the optimizers can be altered.
This argument takes a named list.
To supply user-defined starting values, use control = list(sv=c(...))
and supply a vector containing initial values for all parameters.
Optimizer-specific options include the number of iterations (iterlim = 1000
) and convergence criteria for the BFGS- and NR-optimization ((tol1 = 1e-5
) and (tol2 = 1e-10
)).
Verbosity takes integer values from 0
to 4
.
0
, no information is printed (default).
1
prints information about 3 stages (preparation, starting values, estimation).
2
prints little information about optimization (verbosity
values greater than one are passed to print.default = verbosity - 1
of maxBFGS
and maxNR
).
3
prints more information about optimization.
4
prints all information about optimization.
Value
call |
[ |
parametrization |
[ |
varnames |
[ |
n.vars |
[ |
dims |
[ |
Y |
[ |
X |
[ |
Z |
[ |
sub.comp |
[ |
base |
[ |
weights |
[ |
orig.resp |
[ |
data |
[ |
d |
[ |
formula |
[ |
mf_formula |
[ |
npar |
[ |
coefficients |
[ |
coefnames |
[ |
fitted.values |
[ |
logLik |
[ |
vcov |
[ |
hessian |
[ |
se |
[ |
optimization |
[ |
Author(s)
Marco J. Maier
Examples
ALake <- ArcticLake
ALake$Y <- DR_data(ALake[,1:3])
# fit a quadratic Dirichlet regression models ("common")
res1 <- DirichReg(Y ~ depth + I(depth^2), ALake)
# fit a Dirichlet regression with quadratic predictor for the mean and
# a linear predictor for precision ("alternative")
res2 <- DirichReg(Y ~ depth + I(depth^2) | depth, ALake, model="alternative")
# test both models
anova(res1, res2)
res1
summary(res2)