Creates an object containing the parameters of a Dirichlet distribution. This is used for constructing the prior or storing the information of the posterior.
Value
Returns an object of class "inz_ddir".
An object of class "inz_ddir" is a list which contains the following:
- alpha
a vector or a matrix of the shape parameters \(\alpha\).
- k
the number of categories.
If the function is used to construct the prior, the likelihood is stored
as an attribute.
Details
The shape parameter: \(\alpha_i > 0\); each corresponding to a level/group in the categorical variable
\(k ≥ 2\)
The Dirichlet distribution is the conjugate prior for (but is not limited to) the Multinomial likelihood.
If the data is grouped, alpha should be a matrix with one row per group.
Otherwise, alpha should be a vector.
For prior use only:
If no alpha values are provided, the default value of \(\alpha_i = 1\),
will be used for the prior (e.g. Dirichlet(1,1,1,1) for a k=4 level categorical
variable).
Examples
# Constructing the prior with the likelihood (default prior is used)
if (FALSE) { # \dontrun{
lik <- inz_lmulti(surf_data, Qualification)
inz_ddir(likelihood = lik)
# Using a subjective prior (prior belief that degree and school qualifications are more common)
inz_ddir(likelihood = lik, alpha = c(10, 2, 10, 2))
} # }
# Grouped data example
if (FALSE) { # \dontrun{
grouped_lik <- inz_lmulti(surf_data, Qualification, Ethnicity)
inz_ddir(likelihood = grouped_lik)
} # }
# Example of inz_ddir usage in the calculate_posterior function
posterior <- inz_ddir(alpha = c(29,40,67,68), k = 4)