Evaluation of non-linear growth models for wheat yield prediction under Bihar conditions

Introduction

Today's major challenge to the scientific community in the states is to increase the wheat productivity not only to provide adequate food to its ever-increasing population but also to create surplus for export to stimulate its overall growth. Forecasting technique is an important element of research in agriculture and allied sectors. It helps the policy makers, agricultural scientists, farmers, govt. agencies to plan their operations for future. However, Reliable and timely forecasts of crop production before the harvest is a challenging problem, hence achieving greater accuracy in forecasting is a topical interest. Such forecasts are needed by the Government, agro-based industries, traders and agriculturists. The Government needs them for use as a basis for its policy decisions in regard to procurement price, distributions like DBT, buffer-stocking, import-export, price fixation, MSP and marketing of agricultural commodities while agro-based industries, traders and the agriculturists need them for properly planning their operations. In India forecasting of crops before harvesting or by next years are being done by the Directorate of Economics and Statistics, Ministry of Agriculture, New Delhi. Other govt. agencies like state govt. institutions, research institutions also predict the crop production. However, these forecasts are subjective in nature since these are based on eye-estimates and personal judgment of agricultural officials and the final crop production estimates through based on objective of crop -cutting experiments are limited utility as these become available quite later after the harvest. Hence, there is a need for developing an objective methodology for pre-harvest crop forecasting. This involves a suitable forecast models using a suitable forecasting techniques which has certain merits over the traditional forecasts methods. These merits include the objectivity of forecasts and its ability to provide a maximum accurate measures of the degree of its prediction which a traditional forecast method cannot provide. Another-merit of prediction through forecasting model is their ability to reflect the impact of cultural practices. Such changes, however, despite slightly affecting the coefficients of parameters in the forecast model do not affect the models responsiveness to these changes.

Thus, the present study has its important significant impact for wheat production, planning for development and growth in future. As per above discussion it is clear that in Indian agriculture as well as in the state of Bihar also, year-to-year fluctuations in output and variations in productivity across space have remained issues of significant concern for researchers as well as policy makers.

Methodology

An attempt will be made to study the non-linear growth pattern of wheat yield in Bihar and below mentioned three agro-climatic zones. For this purpose the three agro-climatic zones comprising of the following districts have been considered.

Zone-1 (13 districts)

There are 13 districts in z-1 namely-Saran, Siwan, Gopalganj, East-Champaran, West-Champaran, Muzaffarpur, Sitamarhi, Shiwhar, Vaishali, Darbhanga, Madhubani, Samastipur and Begusarai.

Zone-2 (8 districts)

It comprises 8 districts: Saharsa, supaul, Madhepura, Purnia, Kishanganj, Araria, Katihar & Khagaria.

Zone-3 (17 districts)

Z-3 having 17 districts are Patna, Nalanda, Arwal, Bhojpur, Buxar, Bhabhua, Rohtas Gaya, Jahanabad, Nawada, Aurangabad, Munger, Sheikhpura, Lakhisarai, Jamui, Bhagalpur and Banka.

Source of data

The study was based on secondary data on productivity of wheat yield in three agro-climatic zones of Bihar and also for whole Bihar. Time series wheat data were collected from Directorate of Economics and Evaluation Department Govt. of Bihar, Patna.

Various non-linear growth models Monomolecular growth model

This model describes the progress of a growth situation in which it is believed that the rate of growth at particular time t is directly proportional to the amount of growth yet to be achieved. It denotes the productivity of wheat yields at time t and c be the ceiling value i.e. the maximum achievable value of y in the long run (when t) The solution of equation is

The curve has an S-shaped between the growth value c/(1+a) and c.

Gompertz Model

For Gompertz model. However, this curve is an S-shaped one like the logistic, it is not symmetrical about its point of inflection.

Compound growth model.

If y t denotes the observation (Wheat yield) at time t and r is the compound growth rate, model employed for estimating r is based on equation

The usual practice is to assume a multiplicative error-term exp (∈) in equation so that the model may be linearized by means of logarithmic transformation, following equation ln (y t ) = A + B t + e

Criteria for selection of model

The appropriateness of the model was judged by (i)

The value of the estimates in terms of their signs and magnitudes. (ii)

Analysis of residuals for randomness as well as for normality assumption, and (iii)

The value of co-efficient of determination (R 2 ). In addition, the following statistics were also used for model section:

/n

The smaller the value of MAE, the better is the model.

(c) Root mean squared Error of (RMSE) RMSE is defined as

The smaller the value of RMSE, the better is the model.

Result & Discussion

The good suitable non-linear model is selected through different eight statistics i.e. R

Conclusion

The present study is based on non-linear growth model such as Monomolecular, Logistic, Gompertz and compound Growth model. The utility of these models is that the provide insight into the under lying mechanism.

In the present study four non-linear models namely Monomolecular, Logistic, Gompertz and Compound for the wheat productivity under various climatic zones I, II, III and complete Bihar has been developed and the result obtained through statistical software. The value has been obtained using the data collected and the method described Draper and Smith (1981) [15] . The four models have been compared considering R 2 , R 2 7 , R 2 8 , RSS, MAPE, MAE, MSE, RMSE. On the basis of these statistics, monomolecular model has been found to be most appropriate suitable for describing the wheat productivity data after comparison among all the models and their fulfillment of assumption has been studied.

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