**2. Materials and Methods**

The study uses primary data obtained in the course of a survey conducted in the second quarter of 2020 among farms covered by the European Farm Accountancy Data Network (FADN). The spatial scope of the study covered the area of Central Pomerania (Poland). 361 farms participated in the study, which constitutes 88% of all entities covered by FADN agricultural accounting in the analyzed area. After substantive verification, the results concerning 348 entities were accepted for analysis. The survey was carried out by advisers from Agricultural Advisory Centers through personal contact with the farmer and supplementary telephone contact (Paper & Pen Personal Interview—PAPI and Computer Assisted Telephone Interview—CATI methods). The data obtained concern 2019 (some questions also related to the period from 2004—i.e., from the moment of Poland's accession to the European Union). A total of 69 questions were included in the questionnaire, divided into three main sections: (A) General information about the household, (B) Information about the financial management of the household, (C) Information about the farm.

The logistic regression model and the classification-regression tree analysis (CRT) were used to identify the features of farms in Central Pomerania which use external capital to improve the financial energy of their agricultural holdings. Based on the results of the logistic regression model, the factors influencing the probability of using external capital by a farm were determined. Then, the classification and regression trees (CRT) analysis was applied, which allowed for the identification of key features of a farmer and a farm affecting the propensity to finance agricultural activity with external capital.

The first method used, logistic regression, allows to study the influence of many independent variables *x*1, ... ,*xk* (which can be both qualitative and quantitative) on the dependent variable *Y*, which is dichotomous (zero-one variable) [75,76]. In this study it was assumed that the dependent variable *Y* is the use of external capital to finance agricultural activity. This variable, due to its dichotomous nature, takes the value 1 in the case when the researched farm used external capital (130 cases), otherwise the variable takes the value 0 (218 cases).

The probability that an agricultural holding will use outside capital to finance agricultural activity (*Y* = 1) was determined using the following function [77,78]:

$$Prob(Yi = 1) = \frac{e^{a\_0 + a\_1x\_1 + \dots + a\_kx\_k}}{1 + e^{a\_0 + a\_1x\_1 + \dots + a\_kx\_k}} \tag{1}$$

where: *Prob*(*Yi* = 1)—the probability that the dependent variable for an entity with characteristic *i* will take the value 1; *α*0, *α*1, ... , *αk*—model parameters; *x*1, ... ,*xk*—independent variables.

The selection of independent variables for the logistic regression model was made using the backward elimination method. The model parameters were estimated using the maximum likelihood (ML) method [79]. The significance of the obtained model was verified using the Likelihood Ratio (LR) [79]. The significance of individual model parameters was verified on the basis of z<sup>2</sup> Wald Test [80]. The Akaike Information Criterion (AIC) was analyzed as the criterion of the model's optimality [81]. Cox-Snell R2, Nagelkerke R2 and Count R<sup>2</sup> statistics were used to assess the fit of the model to the observed data [79,82]. Goodness of model fit was also assessed using the AUC—Area Under Curve index, calculated on the basis of the Receiver Operating Characteristic (ROC) [77]. The Odds Ratio was used to interpret the obtained results of the logistics model [83]. Statistical analyzes were performed using the Statistica 13.3 software.

The second of the methods used in the study, the analysis of classification and regression trees, is used to determine whether objects belong to classes on the basis of measurements of one or more explanatory variables, determining their impact on the qualitative dependent variable *Y* [84]. Decision trees are a graphic form of presenting possible decisions and their consequences [85]. The analysis of classification-regression trees consists in the sequential partitioning of the *L*-dimensional space of *X<sup>L</sup>* variables into subspaces *Rk* (segments), until the dependent variable *Y* reaches the minimum level of differentiation in each of them, which is measured by the appropriate loss function (more on this topic: [86–88]). This partitioning is displayed in a tree structure which is called a decision tree, with the root node at the top of the tree [89]. In the study, the dependent variable was the use of external capital by a farm to finance agricultural activity. As in the case of logistic regression, this variable can take two values: *Y =* 1—when the researched farm used external capital to increase their financial energy (130 farms), and *Y* = 0 otherwise (218 farms). The assessment of the degree of differentiation of the subspace *Rk* was based on the Gini index [86,90]. In order to obtain a simplified form of a classification and regression tree and to identify the key features influencing the use of external capital by farms, the recursive splitting was stopped before achieving segment homogeneity, for this purpose the FACT—Fast Algorithm for Classification Trees rule was applied for a given object fraction [91]. Cross-validation was used in the classification and regression trees (CRT) analysis [89,92]. Statistical analyses were performed using the Statistica 13.3 software (C&RT algorithm).

The explanatory variables used both in the logistic regression model and in the classification and regression tree analysis were selected on the basis of the literature studies. Eight independent variables relating to the socio-economic characteristics of the farmer and the characteristics of the farm were used to assess the probability tested. Their characteristics and their hypothetical impact—established on the basis of the research results presented in the literature—on the inclination of the researched farms in Central Pomerania to finance agricultural activities with external capital are presented in Table 1.


**Table 1.** Set of potential variables adopted for the study.


**Table 1.** *Cont.*

Source: Own study based on: [50,53,55,57–59,63–65,69–72,74,93,94].
