Think about data.

Data is just text, but this text has meaning.

One can have data with numbers, letters, or even logical values.

The way we manage the data is what envolves skills.

There are several approaches to how to manage data, which tools to use, and what can be done.

In some fields, like forestry, data corresponds to forest-derived measurements.

The most common is the measurement of the "diameter at breast height" (also known as dbh or by IUFRO standards, \(d\)) for all trees in a measurement area (generally a plot), and a subset of heights (\(h\)) within the same measurement unit.

With statistics, a regression model can be use in order to estimate the values of \(h\) for the trees that were not measured at start.

A basic model, has the following form:

\begin{equation} h_{i} = \beta_{0} + \beta_{1} \frac{1}{d_{i}} + \varepsilon_{i} \end{equation}

Where:

• \(h_{i}\) is the height of the i-th tree in the plot.
• \(d_{i}\) is the dbh of the i-th tree in the plot.

Then, one can accounts for the different species in the plot. This leads to fit the model for each subset of species, obtaining different values for the parameters in each case. Or, a new version of the model can be established, where the species has an effect in the values obtained, but just one model is fitted:

\begin{equation} h_{ij} = \beta_{0} + \beta_{1} \frac{1}{d_{ij}} + \varepsilon_{ij} \end{equation}

Where:

• \(h_{ij}\) is the height of the i-th tree of the j-th species in the plot.
• \(d_{ij}\) is the dbh of the i-th tree of the j-th species in the plot.

That means that a mixed effect has to be added to some of the parameters, moving our model from a simple linear regression model to a mixed effects model.