vcov.clv.fitted

Returns the variance-covariance matrix of the parameters of the fitted model object.
The variance-covariance matrix is derived from the Hessian that results from the optimization procedure.
First, the Moore-Penrose generalized inverse of the Hessian is used to obtain an estimate of the
variance-covariance matrix.
Next, because some parameters may be transformed for the purpose of restricting their value during
the log-likelihood estimation, the variance estimates are adapted to
be comparable to the reported coefficient estimates.
If the result is not positive definite, <a href="/link/Matrix%3A%3AnearPD?package=CLVTools&version=0.11.2" data-mini-rdoc="CLVTools::Matrix::nearPD">Matrix::nearPD</a> is used
with standard settings to find the nearest positive definite matrix.
If multiple estimation methods were used, the Hessian of the last method is used.

A set of state-of-the-art probabilistic modeling approaches to derive estimates of individual customer lifetime values (CLV).
Commonly, probabilistic approaches focus on modelling 3 processes, i.e. individuals' attrition, transaction, and spending process.
Latent customer attrition models, which are also known as "buy-'til-you-die models", model the attrition as well as the transaction process.
They are used to make inferences and predictions about transactional patterns of individual customers such as their future purchase behavior.
Moreover, these models have also been used to predict individuals’ long-term engagement in activities such as playing an online game or
posting to a social media platform. The spending process is usually modelled by a separate probabilistic model. Combining these results yields in
lifetime values estimates for individual customers.
This package includes fast and accurate implementations of various probabilistic models for non-contractual settings
(e.g., grocery purchases or hotel visits). All implementations support time-invariant covariates, which can be used to control for e.g.,
socio-demographics. If such an extension has been proposed in literature, we further provide the possibility to control for time-varying
covariates to control for e.g., seasonal patterns.
Currently, the package includes the following latent attrition models to model individuals' attrition and transaction process:
[1] Pareto/NBD model (Pareto/Negative-Binomial-Distribution),
[2] the Extended Pareto/NBD model (Pareto/Negative-Binomial-Distribution with time-varying covariates),
[3] the BG/NBD model (Beta-Gamma/Negative-Binomial-Distribution) and the
[4] GGom/NBD (Gamma-Gompertz/Negative-Binomial-Distribution).
Further, we provide an implementation of the Gamma/Gamma model to model the spending process of individuals.

Patrick Bachmann

CLVTools

Tools for Customer Lifetime Value Estimation

Niels Kuebler

Markus Meierer

Jeffrey Naef

E. Shin Oblander

Patrik Schilter

vcov.clv.fitted function

<dl><dt>object</dt>
<dd>a fitted clv model object</dd>
<dt>...</dt>
<dd>Ignored</dd></dl>

Arguments

Returns the variance-covariance matrix of the parameters of the fitted model object.
The variance-covariance matrix is derived from the Hessian that results from the optimization procedure.
First, the Moore-Penrose generalized inverse of the Hessian is used to obtain an estimate of the
variance-covariance matrix.
Next, because some parameters may be transformed for the purpose of restricting their value during
the log-likelihood estimation, the variance estimates are adapted to
be comparable to the reported coefficient estimates.
If the result is not positive definite, <a href='https://rdrr.io/pkg/Matrix/man/nearPD.html'>Matrix::nearPD</a> is used
with standard settings to find the nearest positive definite matrix.
If multiple estimation methods were used, the Hessian of the last method is used.

Calculate Variance-Covariance Matrix for CLV Models fitted with Maximum Likelihood Estimation — vcov.clv.fitted

<dl>

<dt>object</dt>
<dd>a fitted clv model object</dd>


<dt>...</dt>
<dd>Ignored</dd>

</dl>

vcov.clv.fitted: Calculate Variance-Covariance Matrix for CLV Models fitted with Maximum Likelihood Estimation

Description

Usage

Value

Arguments

See Also