*3.2. The Use of External Capital and the Features of a Farm—A Model Approach*

Based on the adopted research assumptions, first, a logistic regression model was constructed, in which eight explanatory variables were included (Table 1). Then, using the backward elimination method, successive predictors were eliminated and the assessment of change in the value of criteria adopted for the model quality assessment was made. Finally, two independent variables related to the farmer's education level were eliminated from the initial model: EDU and EDU\_EC, whose impact on the probability of using external capital by the farm, as a source of financial energy, was not statistically significant. Six variables remained in the final model (Table 3), the matrix of case classification is presented in Table 4.


**Table 3.** Results of estimation of model parameters—final model.

Source: Own study.

**Table 4.** Matrix of case classification.


Source: Own study.

The estimated model of the probability of financing agricultural activity with external capital is as follows:

Prob(DEB = 1) = Λ(0.012AREA − 0.037AGE + 0.766GEND\_Male + 0.568SUC − 0.678SPEC + 1.221PROD\_VALUE − 0.553)

where: Λ(*x*) = *<sup>e</sup><sup>x</sup>* <sup>1</sup>+*e<sup>x</sup>* logistic distribution function.

Based on the model, 73% of cases were correctly classified (Count R<sup>2</sup> = 0.73). The quality of the constructed model was assessed on the basis of Cox-Snell R<sup>2</sup> (0.228), Nagelkerke R<sup>2</sup> (0.310) and the ROC curve (Figure 1).

**Figure 1.** ROC curve for the model of the tendency to indebtedness of farms in Central Pomerania. Source: Own study.

The area under the ROC curve (AUC) is 0.785, which indicates a good quality of the constructed model (AUC > 0.5). The *LR*-statistic value is 89.87 (*p* < 0.001), the critical value of this statistic for 6 degrees of freedom is 16.81.

The results of the study show that the following characteristics of the farmer had a statistically significant positive impact on the probability of using external capital as a form of improving financial energy by farms in Central Pomerania: gender (**GEND\_Male**) and having a successor who would take over running the farm in the future (**SUC**), as well as the following characteristics of a farm: farm area in ha (**AREA**) and annual production value (**PROD\_VALUE**). On the other hand, the farmer's age (**AGE**) and farm specialization targeting one type of crop or animal production (**SPEC**) had a statistically significant negative impact on the tested probability. The direction of the impact of the variables: **AGE**, **GEND**, **EDU**, **EDU\_EC**, **SUC** and **PROD\_VALUE** and **AREA** turned out to be consistent with the assumed one, thus confirming the research results presented so far in the literature (e.g., [50,55,57,58,64,72,74]). In the case of the **SPEC** variable, the results of our research showed a different than assumed impact of production specialization on the use of external capital in order to improve the financial energy of the farm.

In accordance with the established methodology of the study, in the next stage of the analysis, the key features of the farmer and the farm that affect the propensity to use external capital were identified. For this purpose, classification and regression tree analysis (CRT) was used. The results of the classification of the researched farms in Central Pomerania according to the criterion of using external capital to increase financial energy based on classification and regression trees (CRT) and the importance of independent variables included in the analysis are presented in Figures 2 and 3.

**Figure 2.** Classification and regression tree (CRT). Source: Own study.

**Figure 3.** Importance of independent variables. Note: Scale 0–1; 0—variable is no important; 1—variable is very important. Source: Own study.

The decision rules are designed in the root (ID 1), branch (IDs: 1, 2, 5, 6 and 9) and leaves (IDs: 3, 4, 7, 8, 10 and 11) views. The tree consists of five shared nodes and six terminal nodes. The certainty of the forecast is 74.7%.

The first split of the studied population was made on the basis of the **PROD\_VALUE** variable. On the basis of this criterion, the surveyed group was divided into two groups: farms with an annual production value of more than PLN 100,000 (ID 2) and those with an annual production value of up to PLN 100,000 (ID 3). It was found that in the case of entities with a lower annual production value, the vast majority (80%) did not use external capital as a form of increasing financial energy. On the other hand, among farms characterized by a higher production value (ID 2), 58% used outside capital. The key variable differentiating the studied population in node 2 (ID 2) was the farm area (**AREA**). As a result of the classification, two groups were obtained: users of farms with an area of up to 36.37 ha (ID 4)—among them 35% were willing to use outside capital, and users of farms with an area exceeding 36.37 ha (ID 5), of which 66% used outside capital. The split of entities in node 5 (ID 5) was made based on the variable **AGE**. As a result of the classification, two groups were obtained: farmers aged up to 63.5 years (ID 6) and 69% of them were characterized by a tendency to indebtedness, and farmers aged over 63.5 years (ID 7), among whom only 14% used external capital. Subsequently, farms from node 6 (ID 6) were divided based on the **SPEC** variable. Among the entities diversifying production (ID 8), 86% used external capital to finance their activities. On the other hand, among specialized farms, 61% were characterized by the use of external capital in order to improve their financial energy (ID 9). Then, the entities from node 9 (ID 9) were further classified using the **AREA** variable and two groups were obtained: users of farms with an area of up to 165.06 ha inclusive (ID 10) and users of farms with an area exceeding 165.06 ha (ID 11). It was found that specialized units were more willing to use outside capital when they used a farm with an area greater than 165 ha (92% of entities in node 11 were characterized by financing agricultural activities with outside capital).
