Dirichlet regression in Excel tutorial

Dataset for Dirichlet regression

The dataset used here to illustrate this Dirichlet regression is the ArticLake dataset which comes from the DirichletReg R package. It contains the proportions of the composition of a lake floor (soil, slit, clay) as well as the depth of the lake for every measurement taken.
The goal of this tutorial is to explain the composition of the lake floor by its depth.

Setting up a Dirichlet regression in XLSTAT with XLSTAT-R

• Open XLSTAT.

• Go to XLSTAT-R / dirichlet / Dirichlet regression (DirichReg). The Dirichlet Regression dialog box will appear.

• In the General tab, select the Y variables. These are the columns containing the proportions to be explained.

• Select the Explanatory variables. In our case, we only have one and it is the column containing the depth of the lake.

• Select the Model.

• Check the Variable labels since the names of our columns are specified.

• In the Options tab, you can choose a level of interactions between explanatory variables.

Interpreting the results of a Dirichlet regression

First, the Goodness of fit coefficients or the model are displayed. They contain the number of observations, the degrees of freedom, the value taken by the Log-likelihood along with two statistical indicators: the AIC and the BIC.

Then, the regression coefficients for each proportion are displayed, as well as their significance.

Two plots are available:
The ternary plot enables us to visualize the proportions for each observation on a same plane.

The scatterplot enables us to visualize each proportion depending on depth. For example, we may suggest that the proportion of sand decreases as depth increases and that the proportions of slit and clay increase.