*2.3. Case Study*

The case study was based in southwestern France (Figure 3). Maize has high economic and cultural value in southwestern France but requires more water in summer than many other field crops. Maize farms in this region use an average of 54,000 m<sup>3</sup> of water per year. Most of the maize-growing area is irrigated (i.e., 90%, for farms specialized in field crops). The increase in droughts in summer leads to a greater need for irrigation of maize, making these farms economically dependent on irrigation in six out of ten years on average [30].

**Figure 3.** Location of the Tarn, Gers and Haute-Garonne departments in the Midi-Pyrénées sub-region of the Occitanie region of France.

> To recruit participants for the survey, the regional Chamber of Agriculture gave us contact information for 69 farmers who grew irrigated maize (waxy, popcorn, grain or seed). We contacted them and 35 farmers responded positively. Their farms were located in the administrative departments of the Tarn (nine farms), the Gers (14 farms) and the

Haute-Garonne (11 farms) (Figure 3). Interviews were conducted in April, May, September and October 2019. Each interview lasted 1–4 h.

#### *2.4. Data Processing and Analysis*

The data (quantitative and qualitative) collected in the surveys were entered in a Microsoft Excel® file (35 rows (farmers) × 184 columns (variables)) for further analysis. Before analyzing the data, we cleaned the data in several steps (Figure 4). Step 5 consisted of sorting the 44 variables into the eight groups of observable and non-observable factors: farmers' characteristics, farm characteristics, agronomic practices, irrigation practices, risk preferences, reactivity, assistance and deliberation. When variables in a group remained correlated (R<sup>2</sup> > 0.4 for quantitative variables and *p*-value < 0.05 for qualitative variables), we selected no more than three variables with the greatest influence on the date of first irrigation. Keeping a few variables in each group allowed us to represent each group fairly, and this final step left one response variable (the date of first irrigation) and 24 explanatory variables.

**Figure 4.** The data cleaning and selection procedure. d1i: date of first irrigation.

Two statistical models were then used to model the influence of these explanatory variables on the date of first irrigation: linear regression and a regression tree (Table 2). The linear regression was performed using stepwise selection (forward and backward). We selected and tested several combinations of the 24 variables to find the best set of explanatory variables. Since linear regression models consider variables additively, without considering non-additive effects, combined effects or interactions, we built a regression tree [31].). Regression trees thus consider local interactions among variables.

Statistical analyses were performed using R software ([32]. We used a classification approach (*ClustOfVar* package ([33]) and the *FAMD* function (of the *FactoMineR* package) to compare all variables and identify redundant information.


**Table 2.** Characteristics of the two statistical models: linear regression and regression tree.
