Selecting the best target function to predict crop yields using their water use through regression analysis
Determination of the most effective regression model for forecasting the production of corn for grain, soybeans and winter wheat. Rationale for the effectiveness of using the cubic regression function for yield estimation in agricultural research.
| Рубрика | Сельское, лесное хозяйство и землепользование |
| Вид | статья |
| Язык | английский |
| Дата добавления | 19.03.2024 |
| Размер файла | 29,4 K |
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Institute of climate-smart agriculture of NAAS
Selecting the best target function to predict crop yields using their water use through regression analysis
Lykhovyd Pavlo Volodymyrovych,
candidate of agricultural sciences, postdoc student, senior researcher of the department of irrigated agriculture and decarbonization of agroecosystems
Vozhehova Raisa Anatoliivna,
doctor of agricultural sciences, professor, director
Zaiets Serhii Oleksandrovych,
doctor of agricultural sciences, head of the department of climate-oriented agricultural technologies
Piliarska Olena Oleksandrivna,
candidate of agricultural sciences, head of the department of marketing and international activities
Abstract
corn grain wheat agricultural
Current agricultural research is relevant to crop yield prediction. While there are many mathematical methods for predicting agricultural yields, regression analysis is still one of the more popular ones. The effectiveness of the prediction model is crucial, and it is greatly influenced by the selection of the target function. The purpose of this study is to determine the most effective regression model for predicting the production of grain corn, soybeans, and winter wheat. Data on actual crop yields and water use were gathered within 1970-2020 at the Institute of Climate-Smart Agriculture's test plots in the Kherson region of Ukraine. The best subsets regression technique was used to evaluate 145 data pairs to identify the model that provided the greatest fitting quality and prediction accuracy. Microsoft Excel and BioStat were used to conduct all the calculations. The best accuracy is recorded for the hyperbolic (reverse) function in soybeans, quadratic and hyperbolic functions in winter wheat, and cubic function in grain corn. To sum up the study's findings, it is advised that cubic regression function should be employed to estimate crop yields in agricultural studies.
Key words: agricultural modeling, fitting quality, function, grain corn, prediction accuracy, soybeans, winter wheat.
Main part
Introduction. An essential area of current agricultural science is crop modeling. Modern systems of decision support have a strong integration of current crop modeling, which includes areas like yield prediction, phenological modeling, growth and development simulation, natural resource use simulation, modeling and forecasting of environmental impacts, agrotechnological modeling, etc. [1]. An essential area of current agricultural science is crop modeling. Modern systems of decision support have a strong integration of current crop modeling, which includes areas like yield prediction, phenological modeling, growth and development simulation, natural resource use simulation, modeling and forecasting of environmental impacts, agrotechnological modeling, etc. [2]. Also, individual crop producers rely on yield estimates in their daily operations to make intelligent agricultural decisions during the cultivation process to achieve the highest yields while minimizing losses in crop productivity. [2,3]. As a result, it is hard to overestimate the significance of accurate yield estimates in current agriculture.
Several methodological approaches are currently being used to solve the issue of agricultural yield modeling and prediction. Current predictive models can generally be divided into deterministic and stochastic types [4]. While stochastic models may manage disorganized datasets and the data with some degree of uncertainty, deterministic models are based on a specific initial input dataset that must be properly organized and structured. Deterministic models, which can be further classified into statistical, mechanistic, and functional ones, are the most common type of mathematical models used in agriculture. Stochastic models are of little practical utility. Both functional and mechanistic models are frequently intricate and based on actual calculations relating to the well-known effects of agrotechnology or environment on crops. The equation of Penman-Monteith for the reference evapotranspiration assessment is one of the most well-known and widely used agricultural functional models, and it is employed in decision support systems [5, 6].
Statistical models are still in high demand and remain crucial despite being relatively primitive. These models are based on the examination of field experiment findings using a variety of statistical processing techniques. The first statistical models were rather straightforward and had mediocre to poor accuracy. But, when new, better methods for mathematical statistics emerge, agricultural statistical models get more complex and precise [4].
Regression models are the statistical model type that are used in agriculture the most. They use several regression analysis methodologies, starting with the most basic one represented by linear pairwise regression and ending with the complicated multiple fuzzy regression functions, depending on the experimental work's scope, dataset size, number of inputs, and modeling goals [7]. Regression models are sometimes criticized for not being the best option for agricultural modeling considering the development of deep learning data processing, but this claim is debatable because many predictions of the yields of crops are still successfully made using regression techniques, especially non-linear ones [8, 9]. Nonetheless, it is emphasized that the quality and accuracy of regression modeling greatly depend on the intelligent selection of the target function, and recent research have claimed and demonstrated significant differences between various regression models [10, 11]. Besides, it also depends on choosing proper model inputs [12]. For instance, if we were to estimate agricultural yields in the South of Ukraine, where there is a high danger of drought and an increase in aridity, one of the key variables influencing crop yields would be the availability of water [13]. Therefore, it is reasonable to consider this factor as the major input.
The main objective of this study is to determine which popular regression analysis techniques, currently employed in agricultural yield modeling, are best for predicting the yield of important crops grown in the South of Ukraine by the amounts of water they use. Such models are crucial for the region's sustainable crop production because it falls under a category of agriculture that is very dangerous due to a persistent shortage of natural water supply [14].
Materials and methods. The basis for the study were retrospective yielding data for the crops of winter wheat, grain corn and soybeans, recorded at the irrigated and non-irrigated land-plots of the Institute of Climate-Smart Agriculture within 1970-2020. The initial dataset for winter wheat included 45 «yield - water use» pairs (for the period 1971-2016); for grain corn - 47 «yield - water use» pairs (for the period 1970-2016); for soybeans - 53 «yield - water use» pairs (for the period 1981-2020). The direct harvesting of the crops and subsequent recalculation of the yield to the standard moisture (14% for grain of winter wheat and corn, 12% for soybeans), provided the yielding data for the field experiments. The common methodology, described in the paper, was used to determine the studied crops' water use [15], by the Eq. (1):
WU = ER + SM + IR(1)
where:
WU is water use, m3/ha; ER - effective rainfall (rainfall more than 50 m3/ha); SM - soil moisture (only moisture, taken up by the crops), m3/ha; IR - irrigation rate, m3/ha.
Utilizing a rain gauge, effective rainfall was measured under field conditions. Recalculating effective rainfall from millimeters to m3/ha required multiplication of the first figure by 10. The difference between the moisture at the time of sowing and harvesting was used to determine the soil moisture that was consumed by the crops. The gravimetric approach was used to gauge the soil moisture [16].
Using the best subsets regression analysis method and the BioStat v. 7 software, the yields of the crops were mathematically modeled in accordance with the values of their water use [9, 17, 18]. The approach included nine regression target functions, which are presented in the Table 1.
Table 1. Regression functions, utilized to predict the crops' yields
|
Function type |
Equation |
|
|
Linear |
Y=ax+b |
|
|
Quadratic |
Y=ax2+bx+c |
|
|
Cubic |
Y=ax3+bx2+cx+d |
|
|
Stepwise (Power) |
Y=axb |
|
|
Exponential-1 |
Y=aebx |
|
|
Hyperbolic (Reverse) |
Y=a+b/x |
|
|
Logarithmic |
Y=a+bln(x) |
|
|
Exponential-2 |
Y=abx |
|
|
Sigmoid |
Y=ea+b/x |
The value of the Pearson's correlation coefficient (R; the greater, the better) was used to assess how well various regression models fit data, while the accuracy was determined by the values of the mean absolute percentage error (MAPE; the less, the better), the maximum absolute error (MAE; the less, the better), and the magnitude of the absolute errors. (A; the less, the better) [19, 20].
Through the calculation of the total score for each examined model, the ultimate judgment on the model quality was made. For each examined regression function, the best values of the statistical indices were added to determine the total points «for,» with 1 point being assigned to each index. The model with the greatest R and the lowest MAPE should be chosen if the models have equal total scores.
Results. Following the statistical analysis of the crop yielding data, a total of 27 mathematical models for the yield prediction based on the crop water use were created. (Table 2). The statistical indices for the models, which were chosen to assess the accuracy and quality of their fitting, are shown in Table 3. The best overall score, shown in the corresponding graph of Table 3, is used to determine the optimal regression function.
Table 2. Regression models, utilized to predict the crops' yield
|
Function type |
Equations of the regression models |
|||
|
Grain corn |
Winter wheat |
Soybeans |
||
|
Linear |
Y=1.1392x10-4x+3.4934 |
Y=6.4135-1.7234x10-4x |
Y=0.2058+0.0006x |
|
|
Quadratic |
Y=6.4029x10 - 8x2+7.4585x10-4x -11.74 |
Y=3.2958+1.3053x10-3x -1.5903x10-7x2 |
Y=0.1813x10-7x2 +0.0019x-1.8718 |
|
|
Cubic |
Y=3.0951x10- 11x3+4.0807x10-7x2 +1.6047x10-3x+26.492 |
Y=12.927+1.3394x10-2x -3.0184x10 - 6x2+2.1646x10-10x3 |
Y=0.3277x10-11x3 -5.3722x10-3x2+0.0031 - 2.9201 |
|
|
Stepwise (Power) |
Y=1.9388x10-3x072189 |
Y=1.6 1 9x-0.12658 |
Y=4.55 1 8x10-7x1.5859 |
|
|
Exponential- 1 |
Y=4.3889e0.0001433x |
Y=6 5592e-0.000034952x |
Y=0.345ea0005x |
|
|
Hyperbolic (Reverse) |
Y=14.86-27646/x |
Y=5.6093+815.47/x |
Y=4.1027-5102.03/x |
|
|
Logarithmic |
Y=39.592+5.7366ln(x) |
Y=9.2518-0.4104ln(x) |
Y=13.6679+1.9734ln(x) |
|
|
Exponential- 2 |
Y=4.3889x1.0001x |
Y=6.5592x0.99997x |
Y=0.345x1.0005x |
|
|
Sigmoid |
Y=g2.91 - 3482.7/x |
Y=e1.6352 - 366.81/x |
Y=g2.0212 - 4249.6163/x |
The examination of the models revealed that soybeans had the best overall quality of the models (both in terms of fitting quality and prediction accuracy), and winter wheat had the worst. This finding may be explained by the input dataset's higher homogeneity for soybeans (where the crop varieties varied less and all crops were irrigated) and winter wheat's highest variability (many different varieties, cultivation in the irrigated and non-irrigated conditions).
Table 3. Regression statistics for the models, utilized to predict the crops' yield
|
Crop |
Statistics |
Function type |
|||||||||
|
Linear |
Quadratic |
Cubic |
Power |
Exp-1 |
Reverse |
Logarithmic |
Exp-2 |
Sigmoid |
|||
|
Grain corn |
R |
0.40 |
0.46 |
0.47 |
0.40 |
0.38 |
0.43 |
0.42 |
0.39 |
0.42 |
|
|
MAPE |
15.59% |
15.32% |
14.92% |
15.80% |
15.94% |
15.44% |
15.47% |
24.32% |
15.68% |
||
|
MAE |
4.62 |
4.33 |
4.42 |
4.80 |
4.86 |
4.49 |
4.56 |
6.42 |
4.73 |
||
|
A |
4.56 |
4.26 |
4.42 |
4.78 |
4.84 |
4.45 |
4.55 |
6.38 |
4.70 |
||
|
Winter wheat |
R |
0.08 |
0.14 |
0.22 |
0.05 |
0.08 |
0.03 |
0.06 |
0.02 |
0.03 |
|
|
MAPE |
21.11% |
20.54% |
20.59% |
90.38% |
21.26% |
20.54% |
20.66% |
20.67% |
26.57% |
||
|
MAE |
3.52 |
3.81 |
3.59 |
8.40 |
3.48 |
3.75 |
3.73 |
3.87 |
4.29 |
||
|
A |
3.45 |
3.80 |
3.53 |
6.93 |
3.44 |
3.70 |
3.66 |
3.86 |
4.26 |
||
|
Soybeans |
R |
0.79 |
0.87 |
0.87 |
0.74 |
0.63 |
0.87 |
0.85 |
0.63 |
0.83 |
|
|
MAPE |
16.44% |
12.28% |
13.12% |
20.41% |
37.82% |
12.27% |
13.66% |
37.78% |
15.19% |
||
|
MAE |
0.92 |
1.00 |
1.14 |
1.60 |
4.15 |
0.98 |
0.89 |
4.14 |
0.85 |
||
|
A |
0.87 |
1.00 |
1.12 |
1.56 |
4.06 |
0.97 |
0.88 |
4.06 |
0.82 |
||
|
Total pts. «for» |
0 |
4 |
4 |
0 |
2 |
2 |
0 |
0 |
2 |
Additionally, there are differences in the optimal way to respond to regression functions. Soybeans and grain corn often respond well to polynomial functions (quadratic and cubic), but winter wheat responds best to exponential-1 and reverse functions.
When comparing the final scores for each model, we discovered that cubic and quadratic functions both received an equal score of «4» points. We propose that cubic function should be the first option for agricultural modeling because it will perform better if we ignore less significant indices of the greatest absolute error and the amplitude of the absolute errors. We advise against using linear, power (stepwise), logarithmic, and exponential-2 functions in crop modeling unless there are compelling reasons to do so. Of course, there are limitations to this study, and the notion also holds true for models created using medium-sized datasets (45-55 input pairs) as those used in this work.
Discussion. Crop yield forecasting is an important and difficult task for modern agricultural research. As soon as crop yield prediction's relevance was acknowledged, scientists all over the world began looking for suitable mathematical techniques to use for the aforementioned purpose [21]. Regression analysis was the first statistical technique to be used for crop yield prediction [22].
Beginning with a straightforward linear function, the regression approach gained importance over time and complicated the mathematical functions that were being used. Regression analysis over time evolved into a dominant method for predicting crop yield from a variety of inputs (climate models, field experiment results, remote sensing data, etc.), involving a wide range of computation techniques and target functions, including polynomial functions, multiple and multivariate regression, stepwise, logistic regression, etc. [23, 24, 25, 26]. Fuzzy regression and interaction regression models, for example, which have been shown to be quite
trustworthy and accurate in carrying out the task of yield analysis, are two further innovative regression approaches that are still being developed and introduced [27, 28]. Now that yielding data analysis has become critically important, researchers should shift their attention to figuring out the optimum statistical methodology for yield prediction in terms of fitting quality and prediction accuracy [29, 30].
Studies specifically focused on the above-mentioned issue are scarce. The study [31] compares various regression models for agricultural production prediction based on rainfall revenue, which is like what we did. Another study [32] compared the effectiveness of Lasso and traditional polynomial regression methods for predicting crop production. Gonzalez-Sanchez et al. [33] conducted a thorough study of cutting-edge widely used approaches for agricultural yield prediction, including multiple linear regression and stepwise linear regression. Our study only adds to the previously mentioned studies' insights into the art of selecting the best modeling approach in terms of a pure intra-comparison of regression analysis techniques. Although the findings of each study vary considerably, the underlying principle remains the same: the better the regression function that is used, the more accurate predictions of crop yields will be.
A few things should be stated regarding more modern mathematical techniques for analyzing crop yields that use artificial neural networks, which are becoming more and more popular among scientists. Convolutional neural networks, long-short term memory, and deep neural networks are in high demand and are becoming more significant in a variety of models for predicting agricultural yields [34, 35]. These mathematical methods frequently seem to be a little more accurate than traditional ones, such as regression analysis, especially when dealing with large datasets [36, 37, 38]. The latter strategy is not entirely obscured by artificial neural networks, though.
For projecting precision agricultural yields, deep learning algorithms are integrated with multiple regression analysis in a variety of ways. This method has been used with success in various studies [21, 39]. Due to the so-called «black box nature» of the latter, it is extremely difficult to understand how a specific neural network has arrived at its modeling results. Such connected models address this problem by providing a clear equation of yield prediction. Additionally, overfitting is occasionally a problem with artificial neural networks, whereas with regression analysis, the researcher retains authority over it [40]. Regression analysis has so retained its value even now when it is tightly linked with cutting-edge data analytic techniques. Additionally, just as when utilizing regression analysis as a stand-alone data analysis tool, it is crucial to pick the appropriate function to work well with deep learning methods. We will investigate this matter further in the future.
Conclusions. Regression analysis is frequently used in agricultural sciences, despite being considered an outdated technique. The accuracy of the target function selection, in addition to the model's inputs' quality and quantity, is crucial to yield modeling's success. After examining the regression statistics of the models for predicting the yield of the three crops under study, it is determined that a cubic function is the best choice for medium-sized pair datasets. Avoid employing the functions linear, power (stepwise), logarithmic, and exponential-2 regression since they are very unlikely to produce accurate predictions and fitting solutions.
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