Mathematical and Statistical Strategies for Evaluating the Efficiency of Educational Resource Allocation in Tertiary Education
21 mar 2025
O artykule
Data publikacji: 21 mar 2025
Otrzymano: 16 lis 2024
Przyjęty: 24 lut 2025
DOI: https://doi.org/10.2478/amns-2025-0617
Słowa kluczowe
© 2025 Danqiong Wang, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Evaluation of resource allocation efficiency of higher education
| Decision unit(DMU) | Integrated efficiency(TE) | Pure technical efficiency(PTE) | Scale efficiency(SE) | Scale compensation |
|---|---|---|---|---|
| 1 | 0.999 | 1.000 | 0.999 | irs |
| 2 | 0.934 | 0.944 | 0.989 | irs |
| 3 | 1.000 | 1.000 | 1.000 | - |
| 4 | 0.901 | 0.901 | 1.000 | - |
| 5 | 0.852 | 0.868 | 0.982 | irs |
| 6 | 0.945 | 0.955 | 0.990 | irs |
| 7 | 0.968 | 0.977 | 0.991 | irs |
| 8 | 0.874 | 0.891 | 0.981 | irs |
| 9 | 1.000 | 1.000 | 1.000 | - |
| 10 | 0.999 | 0.999 | 1.000 | - |
| 11 | 1.000 | 1.000 | 1.000 | - |
| 12 | 0.933 | 0.951 | 0.981 | irs |
| 13 | 0.887 | 0.902 | 0.983 | irs |
| 14 | 1.000 | 1.000 | 1.000 | - |
| 15 | 0.941 | 1.000 | 0.941 | irs |
| 16 | 1.000 | 1.000 | 1.000 | - |
| 17 | 0.983 | 1.000 | 0.983 | drs |
| 18 | 0.978 | 0.98 | 0.998 | drs |
| 19 | 1.000 | 1.000 | 1.000 | - |
| 20 | 1.000 | 1.000 | 1.000 | - |
| 21 | 0.872 | 0.999 | 0.873 | irs |
| 22 | 0.941 | 0.951 | 0.989 | drs |
| 23 | 1.000 | 1.000 | 1.000 | - |
| 24 | 0.893 | 0.913 | 0.978 | irs |
| 25 | 0.932 | 0.958 | 0.973 | irs |
| 26 | 0.889 | 1.000 | 0.889 | drs |
| 27 | 0.911 | 0.913 | 0.998 | irs |
| 28 | 0.965 | 0.976 | 0.989 | irs |
| 29 | 0.891 | 1.000 | 0.891 | irs |
| 30 | 0.931 | 1.000 | 0.931 | drs |
| 31 | 0.981 | 0.991 | 0.990 | irs |
| 32 | 0.999 | 1.000 | 0.999 | irs |
| 33 | 0.902 | 0.924 | 0.976 | drs |
| 34 | 0.959 | 1.000 | 0.959 | irs |
| 35 | 0.999 | 1.000 | 0.999 | irs |
| 36 | 0.836 | 0.859 | 0.973 | irs |
| 37 | 0.999 | 1.000 | 0.999 | drs |
| 38 | 1.000 | 1.000 | 1.000 | - |
| 39 | 0.881 | 0.901 | 0.978 | irs |
| 40 | 0.999 | 1.000 | 1.000 | - |
| 41 | 1.000 | 0.999 | 1.000 | - |
| 42 | 1.000 | 1.000 | 1.000 | - |
| 43 | 1.000 | 1.000 | 1.000 | - |
| 44 | 0.992 | 1.000 | 0.992 | irs |
| 45 | 0.928 | 0.945 | 0.982 | irs |
| 46 | 0.88 | 1.000 | 0.880 | irs |
| 47 | 0.999 | 1.000 | 0.999 | irs |
| 48 | 0.999 | 1.000 | 0.999 | irs |
| 49 | 1.000 | 1.000 | 1.000 | - |
| 50 | 1.000 | 1.000 | 1.000 | - |
| 51 | 1.000 | 1.000 | 1.000 | - |
| 52 | 0.829 | 1.000 | 0.829 | irs |
| 53 | 0.981 | 0.998 | 0.983 | irs |
| 54 | 1.000 | 1.000 | 1.000 | - |
| 55 | 0.932 | 0.935 | 0.997 | irs |
| 56 | 0.957 | 0.961 | 0.996 | irs |
| 57 | 0.858 | 1.000 | 0.858 | irs |
| 58 | 0.983 | 0.991 | 0.992 | irs |
| 59 | 0.924 | 0.931 | 0.992 | irs |
| 60 | 1.000 | 1.000 | 1.000 | - |
| Mean | 0.954 | 0.975 | 0.978 |
Education resource allocation efficiency evaluation index system
| Input output | Symbol | Concrete meaning |
|---|---|---|
| University resource input | A1 | Special teacher number (person) |
| A2 | Number of teachers in senior professional technical positions | |
| A3 | Number of courses in the teaching program | |
| A4 | The school occupies the land product (10,000 square meters) | |
| A5 | Library library | |
| A6 | Education cost income (10,000 yuan) | |
| A7 | Teaching research instrument equipment value (10,000 yuan) | |
| Functional output of universities | A8 | Number of graduates |
| A9 | Monthly income (yuan) | |
| A10 | Professional relevance(%) | |
| A11 | Technical turnover (10,000 yuan) | |
| A12 | Vertical scientific funding (10,000 yuan) | |
| A13 | Horizontal technical service to amount (10,000 yuan) | |
| A14 | Non-education training program number (item) | |
| A15 | Non-education training fund to amount (10,000 yuan) |
College input factor matrix and rotating composition matrix
| Factor | Component matrix | Rotational composition matrix | ||||
|---|---|---|---|---|---|---|
| I-F1 | I-F2 | I-F3 | I-F1 | I-F2 | I-F3 | |
| Eigenvalue | 4.028 | 1.548 | 0.885 | 3.048 | 1.897 | 1.516 |
| Contribution (%) | 57.53 | 22.06 | 12.72 | 43.58 | 27.04 | 21.69 |
| Cumulative contribution (%) | 57.53 | 79.59 | 92.31 | 43.58 | 70.62 | 92.31 |
| A1 | 0.747 | -0.212 | 0.459 | 0.243 | 0.321 | 0.842 |
| A2 | 0.346 | 0.517 | 0.759 | 0.222 | 0.364 | 0.877 |
| A3 | 0.843 | -0.418 | -0.189 | 0.896 | 0.35 | 0.017 |
| A4 | 0.882 | -0.33 | 0.121 | 0.881 | 0.188 | 0.306 |
| A5 | 0.922 | -0.092 | 0.175 | 0.75 | 0.289 | 0.481 |
| A6 | 0.904 | 0.265 | -0.124 | 0.49 | 0.761 | 0.369 |
| A7 | 0.802 | 0.405 | -0.402 | 0.301 | 0.888 | 0.305 |
University output factor matrix and rotating composition matrix
| Factor | Component matrix | Rotational composition matrix | ||||
|---|---|---|---|---|---|---|
| O-F1 | O-F2 | O-F3 | O-F1 | O-F2 | O-F3 | |
| Eigenvalue | 4.635 | 1.795 | 1.062 | 3.017 | 2.506 | 1.967 |
| Contribution (%) | 57.92 | 22.45 | 13.24 | 37.72 | 31.32 | 24.57 |
| Cumulative contribution (%) | 57.92 | 80.37 | 93.61 | 37.72 | 69.04 | 93.61 |
| A8 | 0.871 | 0.292 | -0.385 | 0.963 | 0.255 | 0.062 |
| A9 | 0.874 | 0.276 | -0.376 | 0.952 | 0.261 | 0.079 |
| A10 | 0.837 | -0.468 | -0.169 | 0.991 | 0.165 | 0.07 |
| A11 | 0.776 | 0.005 | 0.422 | 0.314 | 0.82 | 0.105 |
| A12 | 0.761 | -0.092 | 0.581 | 0.176 | 0.936 | 0.153 |
| A13 | 0.866 | 0.04 | 0.336 | 0.441 | 0.811 | 0.117 |
| A14 | 0.366 | 0.897 | -0.204 | 0.052 | 0.096 | 0.983 |
| A15 | 0.223 | -0.269 | 0.874 | 0.022 | 0.369 | 0.877 |
Tobit regression
| Variable | Coefficient | Standard deviation | Z-statistic | P value |
|---|---|---|---|---|
| Economic development level | -3.97E-06 | 3.37E-06 | -1.174725 | 0.2406 |
| Total population | 0.000312 | 6.25E-05 | 4.979456 | 0.0000 |
| Compulsory school occupies land product | 5.31E-06 | 7.36E-06 | 0.720106 | 0.4714 |
| Fixed assets | 0.000218 | 8.91E-05 | 2.423568 | 0.0156 |
| Senior professional title and above special teachers | 0.001709 | 0.003298 | 0.518021 | 0.6052 |
| Bachelor degree or above | -0.440256 | 0.151689 | -2.901954 | 0.0038 |
| Constant term | -1.223569 | 0.526481 | -2.332891 | 0.0198 |