#### Abstract

This paper focuses on the scale efficiency of dried fruit economic forestry production in Shandong Province. Based on the analysis of the basic characteristics of the production of economic forest products by the sample farmers, the main factors influencing the production of economic forest products by the sample farmers were further analyzed using the optimal scale regression method. Factor analysis is a statistical method that uses a few factors to describe the association between many indicators or factors, reflecting most of the information of the original data with fewer factors. It provides some suggestions for farmers’ production activities and government decision making.

#### 1. Introduction

Optimal scale regression quantifies the different values of the categorical variables, thus converting them into numerical forms for statistical analysis. Based on a questionnaire survey on the production and management of economic forest products such as chestnut, walnut, jujube, and ginkgo, the variables are specifically defined as (1) La, labour input for economic forest management; (2) Cap, capital input for economic forest management; (3) Area, area of economic forest management; (4) Frac, degree of forest land fineness (how many pieces); (5) Age, age of operator; (6) Edu, operator’s education level (1 = elementary school; 2 = junior high school; 3 = high school; 4 = college; 5 = university and above); (7) Cad, whether the operator is a village cadre (1 = yes; 2 = no); (8) Tra, whether the operator has received technical training (1 = yes; 2 = no); (9) Co, whether the operator is a member of a professional cooperative (1 = yes; 2 = no); (10) Inc, household income (1 = very rich; 2 = relatively rich; 3 = upper middle class; 4 = lower middle class; 5 = relatively poor); (11) Site, standing conditions of economic forestry operations; (12) Outp, total economic forestry output (yield) (2017); and (13) Pri, selling price of economic forestry products (unit price in 2017, yuan/catty). A total of 510 questionnaires were distributed to survey the production and operation of economic forest products such as chestnut, walnut, jujube, and ginkgo, and 502 valid questionnaires were distributed to different economic forest product production areas, including 212 jujube, 118 chestnut, 116 walnut, and 56 ginkgo and other economic forests [1–3]. Factor analysis was used to determine the weight values of each indicator, and optimal scale regression analysis was used to determine the importance of factors affecting the production of economic forest products by farmers. The analysis was carried out.

#### 2. Optimal Scale Regressions of Economic Forest Product Production by Sample Farmers

##### 2.1. Correlation Analysis of Factors Influencing the Production of Economic Forest Products by Farm Households

The research data are mostly categorical variables and the accuracy is poor if linear regression analysis is used. In the survey on the sample farmers of chestnut, walnut, jujube, and gingko economic forest product production, most of the 13 variables (question items) involved were categorical variables; therefore, the linear correlation coefficient could not accurately determine the relationship between different variables; here, the correlation coefficient between different variables calculated mainly using the correlation coefficient formula in the scale regression is shown in Table 1 [4].

From the calculation results in Table 1 and Table 2, it can be seen that the total production of economic forest products produced by farmers has the largest correlation coefficient of 0.229 with capital input (Cap), followed by the area of economic forest operation (Area) with a correlation coefficient of 0.191. The third is the operator's education level (Edu), with a correlation coefficient of 0.186. The fourth is the farm household income (Inc) with a correlation coefficient. In terms of the magnitude of the eigenvalues of the scale regression correlation coefficients, among these influencing factors, labour input in economic forest management (La) with an eigenvalue of 2.184 is the most important factor in economic forest management, followed by capital input (Cap) with an eigenvalue of 1.803 and area of economic forest management (Area) with an eigenvalue of 1.530. The third, fourth, and fifth are, respectively, the degree of fine fragmentation of forest land (Frac), operator’s age (Age), and operator’s education (Edu) with eigenvalue magnitudes of 1.157, 1.090, and 1.000. Therefore, both from the correlation analysis of the scale regression and from the ranking of the eigenvalue magnitudes of the scale regression, the area of economic forest management (Area), operator’s education (Edu), etc. all have a greater impact on the production of economic forest products by farm households [5–9].

In addition, the two-dimensional plot of the influence of important factors for the correlation analysis of the factors affecting the production of economic forest products by farmers is shown in Figure 1. The table of loading coefficients before and after rotation of the scaled regression of important influencing factors is shown in Table 3.

It can also be seen from Table 2 that in dimension 1 and dimension 2, both before and after rotation, labour input (La), operator’s education level (Edu), area of economic forest operation (Area), degree of fine fragmentation of forest land (Frac), operator’s age (Age), and capital input (Cap) have important effects on the total production of economic forest products produced by farm households. Therefore, to improve the efficiency of economic forest product production by farmers in Shandong Province, it is necessary to strengthen the management of these factors [10–13].

##### 2.2. The Importance of Factors Influencing the Production of Economic Forest Products by Farm Households

Further optimal scale regression analysis was conducted on the importance of the factors influencing the production of economic forest products by farmers. The multivariate correlation coefficient *R* of the optimal scale regression equation calculated with the grouped production of total production of economic forest products by farmers as the dependent variable and other influencing factors as independent variables was 0.576 and *R*^{2} = 0.332. The ANOVA table for the optimal scale regression equation is shown in Table 4.

As can be seen from Table 4, the significant level of F-value of the optimal scale regression ANOVA Sig. is less than 0.01, indicating that the regression equation presents a level of significance.

Table 5 shows the analysis of the correlation coefficients for the optimal scale regression, and the final equation, based on the beta coefficients in standardized coefficients, is

According to the importance coefficients (Importance) of the optimal scale regression in Table 5, it can be judged that the influencing factor capital input (Cap) has the highest importance in the equation, followed by the area of the farmer’s economic forest operation (Area), the operator’s education level (Edu), etc. Therefore, the optimal scale regression can further determine that the capital input (Cap) of economic forestry operations, the area of economic forestry operations of farmers (Area), and the education level of operators (Edu) are the main influencing factors affecting the production efficiency of economic forestry products of dried fruits of farmers in Shandong Province [14].

#### 3. Factor Analysis of Factors Affecting the Productivity of Economic Forest Products of a Sample of Farmers

##### 3.1. Mathematical Model

###### 3.1.1. Characteristics of Factor Analysis

The number of dependent variables is less than the number of original indicator variables, serving to classify the original indicators and reduce the computational effort.

Factor analysis does not reduce the original variables; it reorganizes and constructs them based on information from the original variables, reflecting the vast majority of the original information.

There is no linear relationship between the dependent variables, which is more convenient for variable analysis.

Factor variables that synthesize and reflect information on the original variables can be renamed and are explanatory.

The mathematical model for factor analysis iswhere *x*_{1}, *x*_{2}, ⋯, *x*_{p} represent the *P* original variables, which are standardized variables with mean zero and standard deviation 1, and *F*_{1}, *F*_{2}, ⋯, *F*_{N} is an m-factor variable, with *m* less than *P*, expressed in matrix form aswhere *F* is the factor variable or common factor, A is the factor loading matrix, is the factor loading, which is the loading of the *i*-th original variable on the *j*-th factor variable, and is the special factor.

##### 3.2. Factor Analysis of Factors Influencing the Productivity of Economic Forest Products of Farm Households

Based on the definition of variables from the previous optimal scale regressions for the analysis of influences on the production of economic forest products such as chestnuts, walnuts, dates, and gingko by farmers, further factor analysis of different influences was carried out using the statistical software SPSS 21.0 to find the influences on the paths to increase the production of different economic forest products [15].

To ensure that the selected objectives are credible and valid, the KMO test and Bartlett’s sphericity test were applied to the selected objectives. The KMO test analyzes whether there is a biased correlation between the variables, and in general, when the KMO value is below 0.5, then factor analysis is not appropriate. The calculated value of KMO for this study is 0.609 (Table 6), which is greater than the standard required by 0.5 and therefore suitable for factor analysis.

The total variance explanation table for the 13 variables calculated for the study is shown in Table 7, and the gravel plot for the six factors extracted is shown in Figure 2.

Therefore, the calculation results from Table 7 show that after extracting the 5 factors, the cumulative variance contribution of the 5 factors after rotation is 71.779%, and the variance contribution of the first to the sixth factor is 22.888%, 17.494%, 12.187%, 10.718%, and 8.491%, respectively. These five factors were able to provide a good description of the information of the original 13 variables. It can also be seen from Figure 2 that the variation tends to smooth out after the 5th eigenvalue; therefore, the selection of 5 factors is appropriate. The further rotated results of the factor loading matrix calculated using the method of extreme variance are shown in Table 8.

The results in Table 8 show that the first factor, after rotation, basically reflects “training or not,” “membership in cooperative or not,” “household income,” “cadre or not,” etc. The second factor basically reflects “capital input,” “area of operation,” “total production,” etc. The third factor reflects “labour input,” “age,” etc. The fourth factor reflects “household income,” “land conditions,” etc. The fifth factor reflects “labour input,” “capital input,” etc. The sixth factor reflects “fragmentation,” “labour input,” etc. Thus, these factors reflect specific paths and methods to improve the efficiency of economic forest products of farmers. The scatter plot of the calculated output factor loadings is shown in Figure 3.

Finally, the calculated factor score matrix is shown in Table 9.

Thus, based on the factor score matrix in Table 9, the factor equation for the pathway to improve the efficiency of the farmers’ forest products was obtained as

Accordingly, it can be seen from the above factor equation that in the first factor *F*_{1} whether to train (Tra) and whether to join a cooperative (Co) play a relatively large role. This also suggests that training of producers and membership of cooperatives should be strengthened as factors influencing the efficiency of production of economic forestry products by farmers. In the second factor *F*_{2}, area and capital input play a greater role. In the third factor *F*_{3}, labour input (La) plays a greater role. In the fourth factor *F*_{4}, Inc and Site play a greater role. In the fifth factor *F*_{5}, labour input (La) and capital input (Cap) play a greater role.

In the sixth factor *F*_{6}, land fragmentation (Frac) plays a greater role. Therefore, in order to improve the production efficiency of economic forestry products of farmers, these factors should be taken into account in order to find ways to improve the production efficiency of different economic forestry products.

#### 4. Conclusions

This paper analyzes the data of the sampled farmers mainly using optimal scale regression analysis and factor analysis and analyzes the important factors and major factors affecting farmers' economic forestry production. This study mainly analyzes the micro-level farmers’ survey data, details the method and questionnaire design and content of the sample farmers’ survey, analyzes the data obtained based on the questionnaire survey in terms of the basic situation of the sample farmers, the degree of farmers’ participation in economic forest products production technology, the participation of farmers’ professional cooperatives, and the basic characteristics of the production of economic forest products of the sample farmers, and conducts statistical tests on the indicators of farmers’ total input cost, average annual income, and net profit after fruiting for walnut, jujube, chestnut, ginkgo, and other dried fruit economic forest products. The analysis was also conducted on the total input costs, average annual returns, and net profit after fruiting of walnut, jujube, chestnut, ginkgo, and other dried fruit economic forest products. The analysis mainly focuses on the application of economic forestry production technology, economic forestry management methods, land characteristics of economic forestry plantations, market costs of economic forestry products and the costs and benefits of different types of economic forestry plantations, etc. to lay the foundation for the later empirical analysis.

In addition, this study also analyzed the importance of the factors affecting the production of economic forest products by using the optimal scale regression analysis and found that the capital input (Cap), the area of economic forest management (Area), and the education level (Edu) of the operator have an important role in affecting the production of economic forest products by farmers. This paper also analyses the factors influencing the production efficiency of economic forestry products of farmers and finds that “Training or not (Tra),” “membership of cooperatives (Co),” “area of operation (Area),” “capital input (Cap),” “labour input (La),” “household income (Inc),” “site conditions (Site),” and “land fragmentation (Frac)” are all important factors influencing the production efficiency of economic forestry products of farmers and that these factors should be taken into account when looking for ways to improve the production efficiency of economic forestry products of farmers. “Site” and “Frac” are important factors that affect the production efficiency of economic forest products of farmers.

#### Data Availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

(1) Project title: The system for the preparation and implementation of the 14th Five-Year Plan for natural resources, No. 121102000000190014. (2) Project title: A study of statistical norms for the valuation of natural resource assets and the preparation of liability statements under the SEEA framework, No. 2017LD03.