# Sample Farmers Analysis of Factors Influencing Production of Economic Forest Products

Authors: Dong Meng; Tianke Liu; Ying Zhang
Journal: Mathematical Problems in Engineering
 (2022)

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## 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.


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## Body

## 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 Table1 [4].Table 1
Correlation coefficients of factors influencing the production of economic forest products by farm households.
Influencing factorsLabour inputsCapital inputsBusiness areaFinesseAgeEducation levelIs it a cadresLabour inputs1.0000.2370.2440.0240.3280.048−0.194Capital inputs0.2371.0000.297−0.016−0.0780.258−0.211Business area0.2440.2971.0000.0150.1750.071−0.151Finesse0.024−0.0160.0151.000−0.0010.0070.025Age0.328−0.0780.175−0.0011.000−0.346−0.081Education level0.0480.2580.0710.007−0.3461.000−0.040Is it a cadres−0.194−0.211−0.1510.025−0.081−0.0401.000Training or not−0.0420.013−0.0370.0410.114−0.3840.115Whether to join a cooperative−0.0210.019−0.1050.0090.055−0.3430.088Household income−0.118−0.058−0.1210.018−0.084−0.0150.208Site conditions0.0620.1120.0380.024−0.0420.1160.014Unit price0.045−0.009−0.047−0.0040.091−0.008−0.142Total production0.0930.2290.191−0.005−0.0270.1860.023Dimension1234567Eigenvalue2.1841.8031.5301.1571.0901.0000.889Missing values were imputed with variable mode.From the calculation results in Table1 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].Table 2
Correlation coefficients of factors influencing the production of economic forest products by farm households.
Influencing factorsTraining or notWhether to join a cooperativeHousehold incomeSite conditionsUnit priceTotal productionLabour inputs−0.042−0.021−0.1180.0620.0450.093Capital inputs0.0130.019−0.0580.112−0.0090.229Business area−0.037−0.105−0.1210.038−0.0470.191Finesse0.0410.0090.0180.024−0.004−0.005Age0.1140.055−0.084−0.0420.091−0.027Education level−0.384−0.343−0.0150.116−0.0080.186Is it a cadres0.1150.0880.2080.014-0.1420.023Training or not1.0000.6130.141−0.0770.046−0.031Whether to join a cooperative0.6131.0000.144−0.0710.044−0.056Household income0.1410.1441.0000.335−0.0140.118Site conditions−0.077−0.0710.3351.0000.0010.073Unit price0.0460.044−0.0140.0011.000−0.031Total production-0.031−0.0560.1180.073−0.0311.000Dimension8910111213Eigenvalue0.7490.7020.5610.5140.4460.374Missing values were imputed with variable mode.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 Figure1. The table of loading coefficients before and after rotation of the scaled regression of important influencing factors is shown in Table 3.Figure 1
Two-dimensional diagram of the impact of important factors.Table 3
Loading coefficients before and after rotation for the scale regression of important influences.
Influencing factorsComponent loading dimensionRotated component loading dimension1212Labour inputs0.3180.6170.1510.678Capital inputs0.4440.396−0.0880.588Business area0.4230.503−0.0040.657Finesse−0.0490.0190.050−0.017Age−0.1310.6240.5000.395Education level0.672−0.386−0.7630.133Is it a cadres−0.341−0.3760.021−0.507Training or not−0.6760.3930.770−0.131Whether to join a cooperative−0.6690.3520.739−0.158Household income−0.328−0.1910.130−0.357Site conditions0.2760.096−0.1510.250Unit price−0.0310.1720.1330.112Total production0.3360.136-0.1710.320Variable Principal Normalization. a. Rotation Method: Varimax with Kaiser Normalization. The Rotation failed to converge in 3 iterations (convergence = 0.000).It can also be seen from Table2 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 coefficientR 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 R2 = 0.332. The ANOVA table for the optimal scale regression equation is shown in Table 4.Table 4
Optimal scale regression analysis.
VarianceSum of squaresdfMean squaredFSig.Return161.505179.50013.7020.000Residuals324.4954680.693Total486.000485Dependent variable: total production grouping; predictors: labour input, capital input, area of operation subdivided, education, age, whether cadre, whether training, whether joining cooperative, household income, standing conditions, and unit price.As can be seen from Table4, 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.Table5 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(1)Outpg=0.130La+0.292Cap+0.246Area+0.023Frac+0.201Edu+0.034Age+0.179Cad+0.151Tra+0.028Co+0.120Inc−0.153Site−0.03Pri.Table 5
Correlation coefficients for optimal scale regression.
Influencing factorsStandardizedCoefficientsdfFSig.BetaErrorLabour inputs0.1300.05625.2770.005Capital inputs0.2920.062122.5380.000Business area0.2460.054120.6770.000Finesse0.0230.03010.5770.448Age0.2010.046219.3610.000Education level0.0340.04110.7090.400Is it a cadres0.1790.040119.8430.000Training or not0.1510.05816.7960.009Whether to join a cooperative0.0280.03410.6590.417Household income0.1200.03939.4940.000Site conditions−0.1530.045211.7290.000Unit price−0.0300.01513.9960.046Dependent variable: total production grouping.According to the importance coefficients (Importance) of the optimal scale regression in Table5, 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].


## 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 Table1 [4].Table 1
Correlation coefficients of factors influencing the production of economic forest products by farm households.
Influencing factorsLabour inputsCapital inputsBusiness areaFinesseAgeEducation levelIs it a cadresLabour inputs1.0000.2370.2440.0240.3280.048−0.194Capital inputs0.2371.0000.297−0.016−0.0780.258−0.211Business area0.2440.2971.0000.0150.1750.071−0.151Finesse0.024−0.0160.0151.000−0.0010.0070.025Age0.328−0.0780.175−0.0011.000−0.346−0.081Education level0.0480.2580.0710.007−0.3461.000−0.040Is it a cadres−0.194−0.211−0.1510.025−0.081−0.0401.000Training or not−0.0420.013−0.0370.0410.114−0.3840.115Whether to join a cooperative−0.0210.019−0.1050.0090.055−0.3430.088Household income−0.118−0.058−0.1210.018−0.084−0.0150.208Site conditions0.0620.1120.0380.024−0.0420.1160.014Unit price0.045−0.009−0.047−0.0040.091−0.008−0.142Total production0.0930.2290.191−0.005−0.0270.1860.023Dimension1234567Eigenvalue2.1841.8031.5301.1571.0901.0000.889Missing values were imputed with variable mode.From the calculation results in Table1 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].Table 2
Correlation coefficients of factors influencing the production of economic forest products by farm households.
Influencing factorsTraining or notWhether to join a cooperativeHousehold incomeSite conditionsUnit priceTotal productionLabour inputs−0.042−0.021−0.1180.0620.0450.093Capital inputs0.0130.019−0.0580.112−0.0090.229Business area−0.037−0.105−0.1210.038−0.0470.191Finesse0.0410.0090.0180.024−0.004−0.005Age0.1140.055−0.084−0.0420.091−0.027Education level−0.384−0.343−0.0150.116−0.0080.186Is it a cadres0.1150.0880.2080.014-0.1420.023Training or not1.0000.6130.141−0.0770.046−0.031Whether to join a cooperative0.6131.0000.144−0.0710.044−0.056Household income0.1410.1441.0000.335−0.0140.118Site conditions−0.077−0.0710.3351.0000.0010.073Unit price0.0460.044−0.0140.0011.000−0.031Total production-0.031−0.0560.1180.073−0.0311.000Dimension8910111213Eigenvalue0.7490.7020.5610.5140.4460.374Missing values were imputed with variable mode.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 Figure1. The table of loading coefficients before and after rotation of the scaled regression of important influencing factors is shown in Table 3.Figure 1
Two-dimensional diagram of the impact of important factors.Table 3
Loading coefficients before and after rotation for the scale regression of important influences.
Influencing factorsComponent loading dimensionRotated component loading dimension1212Labour inputs0.3180.6170.1510.678Capital inputs0.4440.396−0.0880.588Business area0.4230.503−0.0040.657Finesse−0.0490.0190.050−0.017Age−0.1310.6240.5000.395Education level0.672−0.386−0.7630.133Is it a cadres−0.341−0.3760.021−0.507Training or not−0.6760.3930.770−0.131Whether to join a cooperative−0.6690.3520.739−0.158Household income−0.328−0.1910.130−0.357Site conditions0.2760.096−0.1510.250Unit price−0.0310.1720.1330.112Total production0.3360.136-0.1710.320Variable Principal Normalization. a. Rotation Method: Varimax with Kaiser Normalization. The Rotation failed to converge in 3 iterations (convergence = 0.000).It can also be seen from Table2 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 coefficientR 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 R2 = 0.332. The ANOVA table for the optimal scale regression equation is shown in Table 4.Table 4
Optimal scale regression analysis.
VarianceSum of squaresdfMean squaredFSig.Return161.505179.50013.7020.000Residuals324.4954680.693Total486.000485Dependent variable: total production grouping; predictors: labour input, capital input, area of operation subdivided, education, age, whether cadre, whether training, whether joining cooperative, household income, standing conditions, and unit price.As can be seen from Table4, 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.Table5 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(1)Outpg=0.130La+0.292Cap+0.246Area+0.023Frac+0.201Edu+0.034Age+0.179Cad+0.151Tra+0.028Co+0.120Inc−0.153Site−0.03Pri.Table 5
Correlation coefficients for optimal scale regression.
Influencing factorsStandardizedCoefficientsdfFSig.BetaErrorLabour inputs0.1300.05625.2770.005Capital inputs0.2920.062122.5380.000Business area0.2460.054120.6770.000Finesse0.0230.03010.5770.448Age0.2010.046219.3610.000Education level0.0340.04110.7090.400Is it a cadres0.1790.040119.8430.000Training or not0.1510.05816.7960.009Whether to join a cooperative0.0280.03410.6590.417Household income0.1200.03939.4940.000Site conditions−0.1530.045211.7290.000Unit price−0.0300.01513.9960.046Dependent variable: total production grouping.According to the importance coefficients (Importance) of the optimal scale regression in Table5, 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 is(2)x1=a11F1+a12F2+⋯+a1mFm+a1ε1x2=a21F1+a22F2+⋯+a2mFm+a2ε2⋯⋯xp=ap1F1+ap2F2+⋯+apmFm+apεp,where x1, x2, ⋯, xp represent the P original variables, which are standardized variables with mean zero and standard deviation 1, and F1, F2, ⋯, Fn is an m-factor variable, with m less than P, expressed in matrix form as(3)X=AF+aε,where F is the factor variable or common factor, A is the factor loading matrix, aij is the factor loading, which is the loading of the i-th original variable on the j-th factor variable, and ε 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 (Table6), which is greater than the standard required by 0.5 and therefore suitable for factor analysis.Table 6
Significant coefficients for optimal scale regression.
Influencing factorsCorrelationsImportanceToleranceZero orderPartialPartAfter transformationBefore transformationLabour inputs0.2290.1430.1180.0890.8260.788Capital inputs0.3900.3010.2580.3430.7810.762Business area0.3420.2660.2250.2530.8410.839Finesse0.0200.0280.0230.0010.9950.994Age0.1890.1950.1620.1140.6510.645Education level−0.0040.0360.0290.0000.7390.717Is it a cadres0.1030.2010.1680.0550.8850.870Training or not0.1340.1370.1130.0610.5620.554Whether to join a cooperative0.0630.0260.0210.0050.5700.575Household income0.1070.1330.1100.0390.8370.801Site conditions−0.074−0.171-0.1420.0340.8530.843Unit price-−0.058−0.035-0.0290.0050.9480.959Dependent variable: total production grouping.The total variance explanation table for the 13 variables calculated for the study is shown in Table7, and the gravel plot for the six factors extracted is shown in Figure 2.Table 7
KMO and Bartlett's test results.
FactorInitial eigenvalueSum of squares of extracted loadsRotation squared and load capacityTotalPercentage varianceCumulative percentageTotalPercentage varianceCumulative percentageTotalPercentage varianceCumulative percentage12.97522.88822.8882.97522.88822.8882.77921.37721.37722.27417.49440.3822.27417.49440.3822.02815.59736.97431.58412.18752.5691.58412.18752.5691.62912.53449.50841.39310.71863.2871.39310.71863.2871.612.30661.81551.1048.49171.7791.1048.49171.7791.2959.96471.77960.7986.13877.91770.7325.63383.54980.5394.14987.69890.4443.41691.114100.3752.88794.001110.3272.51696.517120.2531.94498.461130.21.539100The extraction method is principal component analysis.Figure 2
Gravel map.Therefore, the calculation results from Table7 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.Table 8
Results after rotation of the factor loading matrix.
Factor composition123456Zla: labour input-0.0970.3740.6610.0060.1360.105Zcap: capital input0.0540.789-0.072-0.0130.1780.014Zarea: operating area-0.0470.7220.116-0.0730.032-0.032Zfrac: fine fragmentation0.029-0.0300.019-0.008-0.0200.991Zage: age0.110-0.1160.866-0.0330.024-0.041Zedu: education level-0.5440.395-0.4130.0930.0710.075Zcad: is an officer0.125-0.224-0.1230.228-0.6430.037Ztra: training or not0.8820.0390.0390.021-0.0170.018Zco: to join a cooperative or not0.8680.000-0.0500.0300.0270.035Zinc: household income0.188-0.080-0.1220.798-0.139-0.026Zsite: site conditions-0.1550.1320.0710.7890.0920.017Zoutp: total production-0.0440.5430.0170.202-0.269-0.028Zpri: unit price0.082-0.1170.0100.1390.7920.008Extraction method: principal component analysis; rotation method: variance maximization.The results in Table8 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.Figure 3
Composition diagram for rotation space.Finally, the calculated factor score matrix is shown in Table9.Table 9
Factor score matrix.
Factor compositionZla: labour input−0.0690.1700.4690.0470.0220.096Zcap: capital input0.1160.445−0.104−0.0340.1050.008Zarea: operating area0.0370.4040.057−0.071−0.043−0.039Zfrac: fine fragmentation0.0002-0.0220.005−0.006−0.0120.985Zage: age−0.021-0.0850.6300.037−0.058−0.049Zedu: education level−0.2240.178−0.2750.0460.0650.082Zcad: is an officer0.030−0.074−0.0130.119−0.5090.035Ztra: training or not0.4770.106−0.043−0.0110.0070.008Zco: to join a cooperative or not0.4740.081−0.110−0.0050.0570.025Zinc: household income0.077−0.045−0.0340.567-0.040-0.027Zsite: site conditions−0.0980.0200.1040.5910.1150.017Zoutp: total production0.0130.3170.0390.111−0.262−0.034Zpri: unit price0.053−0.123−0.0670.1620.7080.012Extraction method: principal component analysis; rotation method: variance maximization.Thus, based on the factor score matrix in Table9, the factor equation for the pathway to improve the efficiency of the farmers’ forest products was obtained as(4)F1=−0.069La+0.116Cap+0.037Area+0.0002Frac−0.021Age−0.224Edu+0.03Cad+0.477Tra+0.474Co+0.077Inc−0.098Site+0.013Outp+0.053Pri,F2=0.17La+0.445Cap+0.404Area−0.022Frac−0.085Age+0.178Edu−0.074Cad+0.106Tra+0.081Co−0.045Inc+0.02Site+0.3170utp−0.123Pri,F3=0.469La−0.104Cap+0.057Area+0.005Frac+0.63Age−0.275Edu−0.013Cad−0.043Tra−0.11Co−0.034Inc+0.104Site+0.0390utp−0.067Pri,F4=0.047La−0.034Cap−0.071Area−0.006Frac+0.037Age+0.046Edu+0.119Cad−0.011Tra−0.005Co+0.567Inc+0.591Site+0.1110utp+0.162Pri,F5=0.022La+0.105Cap−0.043Area−0.012Frac−0.058Age+0.065Edu−0.509Cad+0.007Tra+0.057Co−0.04Inc+0.115Site−0.262Outp+0.708Pri,F6=0.096La+0.008Cap−0.039Area+0.985Frac−0.049Age+0.082Edu+0.035Cad+0.008Tra+0.025Co−0.027Inc+0.017Site−0.034Outp+0.012Pri.Accordingly, it can be seen from the above factor equation that in the first factorF1 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 F2, area and capital input play a greater role. In the third factor F3, labour input (La) plays a greater role. In the fourth factor F4, Inc and Site play a greater role. In the fifth factor F5, labour input (La) and capital input (Cap) play a greater role.In the sixth factorF6, 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.


## 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 is(2)x1=a11F1+a12F2+⋯+a1mFm+a1ε1x2=a21F1+a22F2+⋯+a2mFm+a2ε2⋯⋯xp=ap1F1+ap2F2+⋯+apmFm+apεp,where x1, x2, ⋯, xp represent the P original variables, which are standardized variables with mean zero and standard deviation 1, and F1, F2, ⋯, Fn is an m-factor variable, with m less than P, expressed in matrix form as(3)X=AF+aε,where F is the factor variable or common factor, A is the factor loading matrix, aij is the factor loading, which is the loading of the i-th original variable on the j-th factor variable, and ε is the special factor.


## 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 is(2)x1=a11F1+a12F2+⋯+a1mFm+a1ε1x2=a21F1+a22F2+⋯+a2mFm+a2ε2⋯⋯xp=ap1F1+ap2F2+⋯+apmFm+apεp,where x1, x2, ⋯, xp represent the P original variables, which are standardized variables with mean zero and standard deviation 1, and F1, F2, ⋯, Fn is an m-factor variable, with m less than P, expressed in matrix form as(3)X=AF+aε,where F is the factor variable or common factor, A is the factor loading matrix, aij is the factor loading, which is the loading of the i-th original variable on the j-th factor variable, and ε 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 (Table6), which is greater than the standard required by 0.5 and therefore suitable for factor analysis.Table 6
Significant coefficients for optimal scale regression.
Influencing factorsCorrelationsImportanceToleranceZero orderPartialPartAfter transformationBefore transformationLabour inputs0.2290.1430.1180.0890.8260.788Capital inputs0.3900.3010.2580.3430.7810.762Business area0.3420.2660.2250.2530.8410.839Finesse0.0200.0280.0230.0010.9950.994Age0.1890.1950.1620.1140.6510.645Education level−0.0040.0360.0290.0000.7390.717Is it a cadres0.1030.2010.1680.0550.8850.870Training or not0.1340.1370.1130.0610.5620.554Whether to join a cooperative0.0630.0260.0210.0050.5700.575Household income0.1070.1330.1100.0390.8370.801Site conditions−0.074−0.171-0.1420.0340.8530.843Unit price-−0.058−0.035-0.0290.0050.9480.959Dependent variable: total production grouping.The total variance explanation table for the 13 variables calculated for the study is shown in Table7, and the gravel plot for the six factors extracted is shown in Figure 2.Table 7
KMO and Bartlett's test results.
FactorInitial eigenvalueSum of squares of extracted loadsRotation squared and load capacityTotalPercentage varianceCumulative percentageTotalPercentage varianceCumulative percentageTotalPercentage varianceCumulative percentage12.97522.88822.8882.97522.88822.8882.77921.37721.37722.27417.49440.3822.27417.49440.3822.02815.59736.97431.58412.18752.5691.58412.18752.5691.62912.53449.50841.39310.71863.2871.39310.71863.2871.612.30661.81551.1048.49171.7791.1048.49171.7791.2959.96471.77960.7986.13877.91770.7325.63383.54980.5394.14987.69890.4443.41691.114100.3752.88794.001110.3272.51696.517120.2531.94498.461130.21.539100The extraction method is principal component analysis.Figure 2
Gravel map.Therefore, the calculation results from Table7 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.Table 8
Results after rotation of the factor loading matrix.
Factor composition123456Zla: labour input-0.0970.3740.6610.0060.1360.105Zcap: capital input0.0540.789-0.072-0.0130.1780.014Zarea: operating area-0.0470.7220.116-0.0730.032-0.032Zfrac: fine fragmentation0.029-0.0300.019-0.008-0.0200.991Zage: age0.110-0.1160.866-0.0330.024-0.041Zedu: education level-0.5440.395-0.4130.0930.0710.075Zcad: is an officer0.125-0.224-0.1230.228-0.6430.037Ztra: training or not0.8820.0390.0390.021-0.0170.018Zco: to join a cooperative or not0.8680.000-0.0500.0300.0270.035Zinc: household income0.188-0.080-0.1220.798-0.139-0.026Zsite: site conditions-0.1550.1320.0710.7890.0920.017Zoutp: total production-0.0440.5430.0170.202-0.269-0.028Zpri: unit price0.082-0.1170.0100.1390.7920.008Extraction method: principal component analysis; rotation method: variance maximization.The results in Table8 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.Figure 3
Composition diagram for rotation space.Finally, the calculated factor score matrix is shown in Table9.Table 9
Factor score matrix.
Factor compositionZla: labour input−0.0690.1700.4690.0470.0220.096Zcap: capital input0.1160.445−0.104−0.0340.1050.008Zarea: operating area0.0370.4040.057−0.071−0.043−0.039Zfrac: fine fragmentation0.0002-0.0220.005−0.006−0.0120.985Zage: age−0.021-0.0850.6300.037−0.058−0.049Zedu: education level−0.2240.178−0.2750.0460.0650.082Zcad: is an officer0.030−0.074−0.0130.119−0.5090.035Ztra: training or not0.4770.106−0.043−0.0110.0070.008Zco: to join a cooperative or not0.4740.081−0.110−0.0050.0570.025Zinc: household income0.077−0.045−0.0340.567-0.040-0.027Zsite: site conditions−0.0980.0200.1040.5910.1150.017Zoutp: total production0.0130.3170.0390.111−0.262−0.034Zpri: unit price0.053−0.123−0.0670.1620.7080.012Extraction method: principal component analysis; rotation method: variance maximization.Thus, based on the factor score matrix in Table9, the factor equation for the pathway to improve the efficiency of the farmers’ forest products was obtained as(4)F1=−0.069La+0.116Cap+0.037Area+0.0002Frac−0.021Age−0.224Edu+0.03Cad+0.477Tra+0.474Co+0.077Inc−0.098Site+0.013Outp+0.053Pri,F2=0.17La+0.445Cap+0.404Area−0.022Frac−0.085Age+0.178Edu−0.074Cad+0.106Tra+0.081Co−0.045Inc+0.02Site+0.3170utp−0.123Pri,F3=0.469La−0.104Cap+0.057Area+0.005Frac+0.63Age−0.275Edu−0.013Cad−0.043Tra−0.11Co−0.034Inc+0.104Site+0.0390utp−0.067Pri,F4=0.047La−0.034Cap−0.071Area−0.006Frac+0.037Age+0.046Edu+0.119Cad−0.011Tra−0.005Co+0.567Inc+0.591Site+0.1110utp+0.162Pri,F5=0.022La+0.105Cap−0.043Area−0.012Frac−0.058Age+0.065Edu−0.509Cad+0.007Tra+0.057Co−0.04Inc+0.115Site−0.262Outp+0.708Pri,F6=0.096La+0.008Cap−0.039Area+0.985Frac−0.049Age+0.082Edu+0.035Cad+0.008Tra+0.025Co−0.027Inc+0.017Site−0.034Outp+0.012Pri.Accordingly, it can be seen from the above factor equation that in the first factorF1 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 F2, area and capital input play a greater role. In the third factor F3, labour input (La) plays a greater role. In the fourth factor F4, Inc and Site play a greater role. In the fifth factor F5, labour input (La) and capital input (Cap) play a greater role.In the sixth factorF6, 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.



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*Source: 5138968-2022-06-02.xml*