CROP YIELD FORECAST MODEL USING ORDINAL LOGISTIC REGRESSION VANDITA KUMARI

Transcription

1 मस चक ल ट क सम यण क उपय ग स फसल क उप क प न म न ह त म डल CROP YIELD FORECAST MODEL USING ORDINAL LOGISTIC REGRESSION By VANDITA KUMARI Master of Science in AGRICULTURAL STATISTICS Indian Agricultural Statistics Research Institute Indian Agricultural Research Institute New Delhi

2 मस चक ल ट क सम यण क उपय ग स फसल क उप क प न म न ह त म डल CROP YIELD FORECAST MODEL USING ORDINAL LOGISTIC REGRESSION by VANDITA KUMARI Thesis submitted to the Faculty of Post-Graduate School, Indian Agricultural Research Institute, New Delhi, in partial fulfillment of the requirements for the degree of Master of Science in AGRICULTURAL STATISTICS Indian Agricultural Statistics Research Institute Indian Agricultural Research Institute New Delhi Approved By: Chairman: Dr. Ranjana Agrawal Co-Chairman: Dr. Prajneshu Members: Mr. Amrender Kumar Dr. (Mrs.) Rajni Jain

3 Dedicated to My family

4 INDIAN AGRICULTURAL STATISTICS RESEARCH INSTITUTE (I.C.A.R.) Library Avenue, New Delhi Dr. Ranjana Agrawal Principal Scientist I. A. S. R. I., Library Avenue, Pusa, New Delhi CERTIFICATE This is to certify that the work incorporated in the thesis entitled Crop Yield Forecast Model Using Ordinal Logistic Regression submitted in partial fulfillment of the requirement for the degree of Master of Science in Agricultural Statistics of the Post- Graduate School, Indian Agricultural Research Institute, New Delhi, is a record of bonafide research carried out by Ms. Vandita Kumari under my guidance and supervision and no part of this dissertation has been submitted for any other degree or diploma. All assistance and help received during the course of this investigation has been duly acknowledged. Date: New Delhi-12 (Ranjana Agrawal) Chairman Advisory Committee

5 ACKNOWLEDGEMENT I thank almighty for carrying me when I could not walk and helping me safe under his company of love, care and endless blessings without which this tedious and wearisome task could not be accompanied. At the outset of this epistle, I consider myself fortunate and greatly privileged to have worked under the supervision and guidance of Dr. Ranjana Agarwal, chairperson of my advisory committee. Words are inadequate to express my sincere and deepest feelings of gratitude originating from the innermost core of my heart for her benevolent guidance, meticulous supervision, whole hearted encouragement, critical appreciation in execution of my work and for all the trust she had in my ability primarily responsible for the present accomplishment. I am highly grateful to Dr. Prajneshu, Co-chairman of my Advisory Committee. He has been a source of strength and support throughout my study period at IASRI. With reverence, I would like to thank him for many valuable comments, which helped to shape this work. With stupendous ecstasy and profundity of complacency, I pronounce utmost of gratitude to Mr. Amrender Kumar, member of my advisory committee. He has been a source of strength and support throughout my study period at IASRI. Besides his relentless efforts, sagacious guidance and faultless planning, I am grateful to him for his salutary advice, kind co-operation and congenial discussion on an array of topics. I am extremely thankful to Dr. (Mrs.) Rajni Jain, for her useful suggestions during this investigation and for her encouragement throughout the investigation. I am highly grateful to Dr. V.K. Bhatia, Director, IASRI for providing all facilities throughout the study. My inexplicable gratitude goes to Dr. Rajender Parsad, Head of Division (Design of Experiment) and Professor (Agricultural Statistics), I.A.S.R.I., for his valuable suggestions and punctilious criticism. His critical comments and suggestions were helpful to improve my research work.

6 I extend my thanks to the Dean and Director, IARI, New Delhi and staff of PG school for their helpful attitude and cooperation, throughout the period of study. I take this opportunity to appreciate the help rendered by the staff of TAC, Division of Forecasting & Econometrics and CAS Lab. Special thanks are also due to Sondhi ji, Sanjeev ji, Thakur ji, Ashwni ji and Vijaya ji. Special thanks are also due to my classmates Manju, Anindita, Prakash, Raju, Ranganath, Sumit, Pratyush, Chiranjit who helped me immensely during the whole degree programme. I am thankful to all my seniors for their co-operation and special thanks to Ankur sir, Vishal sir, Kaustav sir, Arpan sir, Sandip sir, Upendra, Mrinmoy and Kanchan. It was always cheerful to have loving and joyous company of all my profound juniors specially Achal and Chiranjib during the whole course of degree programme. I highly acknowledge my Varsha friends specially Trisha, Sukanya, Sonalika, Shweta and Rajani for providing the warm company, encouragement, active help during the degree programme. Where the emotions are involved, words cease to mean. My vocabulary fails to accentuate my profound reverence and sincere regards to my Mummy, Papa and my sister Monika for their ceaseless inspiration, moral and spiritual support, profound love and unending encouragement, guiding me to achieve success at every step in life. The innocent love and support of my loving friend Chanda cannot be appreciated in mere words. How can I forget the ultimate help and inspiration I always got from my Father who is always be the torch bearer in the darkest path of life and always be the role model for me and guiding me to achieve great success at every step in life. Last but not least, I am thankful to IASRI, for the financial assistance provided to me in the form of Junior Research Fellowship during the tenure of my study. I apologize for the faux pass of the person who have extended the help in a way or other and deserved such thanks. Date: IASRI, New Delhi (Vandita Kumari)

7 CONTENTS Chapter Title Page No. 1 Introduction Introduction Motivation and Objectives Organisation of Thesis Background Review on weather based crop forecasting Review on use of Ordinal Logistic Regression in Agriculture Review on use of Discriminant Function Analysis in Agriculture Review on comparison of Logistic regression and Discriminant analysis General research methodology Description of Area and Crop Covered Data description Crop season Methodology Used for the Study Methodology for Objective Methodology for Objective Research Papers Use of ordinal Logistic Regression in Crop yield forecast 28-36

8 4.1.1 Introduction Materials and Methods Results and Discussion Conclusion Ordinal logistic regression model and discriminant function analysis in crop forecasting- a comparative study Introduction Materials and Methods Results and Discussion Conclusion 45 5 General Discussion 46 6 Summary and Conclusion Abstract in English 49 Abstract in Hindi 50 References APPENDIX i-v vi-viii

9 CHAPTER-1 INTRODUCTION 1.1 Introduction Reliable and timely forecasts provide important and useful input for proper, foresighted and informed planning, more so, in agriculture which is full of uncertainties. Agriculture now-adays has become highly input and cost intensive. Without judicious use of fertilizers and plant protection measures, agriculture no longer remains as profitable as before. Under the changed scenario today, forecasting of various aspects relating to agriculture are becoming essential. The official pre-harvest forecasts (advance estimates) of yield/production for major cereals and commercial crops are issued by the Directorate of Economics and Statistics, Ministry of Agriculture, New Delhi. These forecasts are, however, of a subjective nature since these are based on the judgment of agricultural officials. The final estimates, though based on objective crop-cutting experiments, are of limited utility as these become available quite later after the crop harvest. In view of this, there is a need for developing an objective methodology for pre-harvest forecasting. This involves building up suitable forecast models where its use as a forecasting technique has certain merits over the traditional subjective forecasting method. These merits include the objectivity of forecast and its ability to provide a measure of the degree of its prediction which a traditional forecast method cannot provide. Another merit of forecasts through such techniques is their ability to reflect the impact on the components of yield over time due to changes in crop varieties, cultural practices or the crop inputs. For this purpose of developing objective methodology of pre-harvest forecast of the crop yield, models based on the regression approach are favoured by the researchers. At the research level, various organizations in India and abroad are engaged in developing methodology for pre-harvest forecast of crop yields using various approaches. The main factors affecting crop yield are agricultural inputs and weather. Use of these factors forms one approach for crop yield forecast. The other approach uses plant vigour measured through plant characters. It can be assumed that plant characters are integrated effects of all the factors affecting yield. Yet another approach is measurement of crop vigour through remotely sensed data. The methods included weather and growth indices based regression models, discriminant function approach, water balance technique, complex polynomials using GMDH (Group Method of Data

10 Introduction 2 Handling) technique, Markov chain approach, Bayesian approach, within year growth models, ANN approach, non-linear models, etc. 1.2 Motivation and Objectives Crop yield is mostly affected by technological change and weather variability. It can be assumed that the technological factors will increase yield smoothly through time and, therefore, year or other parameters of time can be used to study the overall effect of technology on crop yield. Weather variability both within and between seasons is the second and uncontrollable source of variability in yields. Therefore, models based on trend and weather variables can be used for forecasting crop yields. Weather variables affect the crop differently during different stages of development. Thus extent of weather influence on crop yield depends not only on the magnitude of weather variables but also on the distribution pattern of weather over the crop season which, as such, calls for the necessity of dividing the whole crop season into finer intervals and studying relationships in these intervals. However, doing so will increase number of variables in the model and in turn a large number of parameters will have to be evaluated from the data. This will require a long series of data for precise estimation of model parameters which may not be available in practice. Thus, a technique based on relatively smaller number of manageable parameters and at the same time taking care of entire weather distribution may solve the problem. Ordinal logistic regression model and Discriminant function analysis are two approaches which are used for classification of data into various groups and are used for qualitative forecasting. Discriminant analysis is a multivariate technique concerned with separating distinct sets of objects (or sets of observations) and allocating new objects (or observations) to the previously defined groups. Ordinal logistic model is method to describe the effects of some explanatory variables on a categorical response variable especially when the response variable has an ordinal nature. It is used for prediction of the probability of occurrence of an event by fitting data to a logit function. As an example, a plant pathologist is interested in differentiating between the plants that have had a particular disease and those that have not yet had disease. The plant pathologist then wants to determine whether the probability of a particular disease can be predicted by using tillage practices, soil texture, date of sowing, weather variables, etc. as predictors or independent variables. Discriminant analysis could be used for addressing this problem. However, because the independent variables are often mixture of categorical and continuous variables, the multivariate normality assumption will not hold. In such cases logistic regression can be used as it does not make any assumption to the distribution of independent variables. That is, logistic regression is

11 Introduction 3 normally recommended when the independent variables do not satisfy the multivariate normality assumption. The performance of the two methods for classification has been studied by Press and Wilson (1978), O Gorman and Woolson (1991), Johnson et al. (1996), Pohar et al. (2004), Zibaei and Bakhshoodeh (2008). It was observed that Linear Discriminant Analysis is a more appropriate method when the explanatory variables are normally distributed. In the case of categorized variables, linear discriminant analysis remains preferable and fails only when the number of categories is really small (two or three). But whenever the assumptions of linear discriminant analysis are not met, the use of linear discriminant analysis is not justified, while logistic regression gives good results. Discriminant function has already been used for quantitative forecasting of crop yields but ordinal logistic method has not been used for this purpose. In weather based crop forecast studies, sample size is seldom more than thirty and as such categories are not more than three. Further, some of the weather variables do not follow normal distribution. Therefore, use of logistic regression is worth exploring for forecasting crop yield. Therefore, the present investigation has been taken up to carry out detailed study on qualitative and quantitative forecasting of wheat in Kanpur district of Uttar Pradesh by using ordinal logistic regression based on weather data. Also the performance of this approach vis-à-vis discriminant function analysis has been studied. Objectives Accordingly, the objectives of the present study are framed as follows: 1. To develop forecast model by taking probabilities obtained from ordinal logistic regression as explanatory variables. 2. To compare the performance of ordinal logistic regression model and discriminant function analysis in crop forecasting. 1.3 Organisation of Thesis The thesis has been divided into six chapters followed by bibliography.

12 Introduction 4 The thesis begins with Chapter 1 containing the introduction to the forecasting and motivation along with the objectives of the study. Chapter 2 contains the background material where the review of relevant literature has been undertaken. Chapter 3 describes general research methodology followed in the investigation wherein the detailed procedure has been discussed. Chapter 4 contains two research papers entitled Use of ordinal logistic regression in crop yield forecast and Ordinal logistic regression model and discriminant function analysis in crop forecasting- a comparative study that have been written out of work done under the dissertation study. Chapter 5 contains the general discussion about the results obtained followed by Chapter 6 that contains summary of the salient findings of the study.

13 CHAPTER-2 BACKGROUND 2.1 Review on weather based crop forecasting Weather based approach for forecasting crop yield utilizes variables like maximum and minimum temperature, maximum and minimum relative humidity, precipitation, sunshine hour, etc. Weather affects the crop yield differently during different stages of its development. Thus, extent of weather influence on the crop yield depends not only on the magnitude of the weather variables but also on the distribution pattern of the weather variables throughout the crop season which calls for necessity of dividing the whole crop season into finer intervals and studying crop weather relationships in these intervals. This will increase the number of variables in the model and in turn a large number of model parameters will have to be evaluated from the data. This will require a long series of data, for precise estimation of the parameters, which may not be available in many situations. Thus, a technique based on relatively smaller number of manageable variables and at the same time taking care of entire weather distribution may solve the problem. Pioneering work in this context has been done by Fisher (1924) and Hendricks & Scholl (1943). Fisher studied the effect of rainfall on the wheat yield. He assumed that the effect of change in weather variable in successive weeks would not be an abrupt or erratic change but an orderly one that follows some mathematical law. He assumed that these effects are composed of the terms of a polynomial function of time. Further, the value of weather variable in w th week, X w was also expressed in terms of orthogonal function of time. Substituting these in usual regression equation Y = A 0 + A 1 X 1 + A 2 X A n X n + (Here Y denoted yield, X w rainfall in w th week, w = 1, 2,..., n and the error) and utilizing the properties of orthogonal and normalized functions, he obtained Y = A 0 + a a a a k k + where A 0,a 0,a 1,a 2,...,a k are parameters to be determined and i (i=1, k) are distribution constants of X w and is the error. Fisher has suggested to use k = 5 for most of the practical situations. In fitting this equation for k = 5, the number of model parameters to be evaluated will remain 7, no matter how finely growing season is divided. This model was used by Fisher for studying the influence of rainfall on the yield of wheat.

14 Background 6 Hendricks and Scholl (1943) have modified Fisher s technique. They divided the crop season into n weekly intervals and assumed that second-degree polynomial in the week number should be sufficiently flexible to express the relationship. Mathematically, it can be expressed as A w = a 0 + a 1 w + a 2 w 2 (w = 1, 2,, n) Substituting the expression for A w in regression equation, the model was obtained as Y = A 0 + a 0 w X w + a 1 w w X w + a 2 w w²x w + In this model number of parameters to be determined reduces to 4, irrespective of n. This model was extended for two weather variables to study joint effects. Further, since the data for such studies extended over a long period of years, an additional variate T representing the year was included to make allowance for time trend. Another important contribution in this field is by Baier (1977). He had classified the crop-weather models in three basic types viz. crop growth simulation model, crop-weather analysis model and empirical statistical models. Crop growth simulation model is a tool which mimics the response of the crop to its surrounding atmosphere and inputs. In this approach, basic plant processes - production and distribution of dry matter and water relations are modeled and then the entire response of the plant to environmental condition is simulated. In India, scientists at Water Technology Centre, Indian Agricultural Research Institute, New Delhi and International Crop Research Institute for Semi-Arid Tropics (ICRISAT), Hyderabad are working on this approach. Few studies on selected crops and selected locations have been carried out. Using actual weather up to the time of forecast and assuming normal thereafter, forecasts can be obtained. However, this type of models requires a large and detailed data base which limits the utility of this approach on operational basis. This approach is also being attempted in Forecasting Agricultural output using Space Agrometerology and Land based observations (FASAL) programme funded by Department of Agriculture and Co-operation (DAC), Ministry of Agriculture. Crop-weather analysis models are expressed as the product of two or more factors, each representing the (simplified) functional relationship between a particular plant response (e.g. yield) and the variations in selected variables at different plant developmental phases. Conventional statistical procedures are used in such models to evaluate the coefficients relating crop responses to climatological or derived agrometeorological data. Bair (1973) and Robertson (1974) have utilized these models. The Joint Agricultural Weather Information Centre employs

15 Background 7 the crop weather analysis models that simulate accumulated crop responses to selected agrometeorological variables as a function of crop phenology. Observed weather data and derived agrometeorological variables are used as input data. The most commonly used models in crop forecasting are Empirical Statistical models. In this approach, one or several variables (representing weather or climate, soil characteristics, time trend etc.) are related to crop responses such as yield. The weighting coefficients in these equations are by necessity obtained in an empirical manner using standard statistical procedures, such as multivariate regression analysis. Several Empirical Statistical models have been developed all over the world. The independent variables included weather variables, agrometeorological variables, soil characteristics or some suitably derived indices of these variables, Water Requirement Satisfaction Index (WRSI), Thermal Interception Rate Index (TIR), Growing Degree Days (GDD) are some agro-climatic indices used in the models. Southern Oscillation Index (SOI) has also been used with other weather variables to forecast crop yield. To account for the technological changes, year variable or some suitable function of time was used in the models. Some workers have used two time trends. Moving averages of yield were also used to depict the technological changes. Frere and Popov (1979) used the method which utilizes actual rainfall and climatological information for the calculation of water requirement of crops and in turn crop water balance. The method is based on a cumulative water balance established over the whole growing season for the given crop and for successive periods of 10 days or a week. The water balance is difference between precipitation received by the crop and the water lost by the crop and the soil. Based on water surplus and deficit they have calculated index. Initially the index is taken to be 100 and is modified in successive decades/weeks depending on the water surplus or deficits. This index has been shown to be directly related to yield and can give a very satisfactory and early qualitative estimation of yields in rainfed crops. It may be possible to derive quantitative estimates of yields also but these estimates will have to be based on the potential yield of crops which will depend on local environmental conditions and will vary from place to place. The method is intended mainly for utilization in developing countries, where in rainfed agriculture the main constraint is generally inadequate availability of water to the crop. In India, major organizations involved in developing methodology for forecasting crop yield based on weather variables are India Meteorological Department (IMD), Pune and Indian Agricultural Statistics Research Institute (I.A.S.R.I.), New Delhi. IMD has developed empirical statistical models using correlation and regression technique to forecast rice and wheat yields on operational basis. The methodology involves identification of significant correlation coefficients

16 Background 8 between yield and meteorological variables during successive overlapping periods of 7-60 days of crop growing season. By analyzing the correlation coefficients for statistical and meteorological significance, the critical periods are identified. Using these variables in critical periods along with year, regression models using stepwise technique are developed for meteorological subdivisions where these crops are grown on a large scale. Based on these models, preliminary forecasts for kharif rice for 26 meteorological sub-divisions consisting of 15 states and the country as a whole are issued in August which are revised in September and October and final forecast is issued in November/December. For wheat, preliminary forecasts are issued for 16 meteorological sub-divisions in January which are updated in subsequent months and the final forecast is issued in March/April. By and large, the performance has been found to be satisfactory except in a few isolated cases. Whenever, large and persistent deviations between the actual reported yield and the forecast by any model are observed, the model is modified using the latest yield and weather data and by introducing new suitable predictors like Yield Moisture Index, Generalized Monsoon Index, moisture stress, aridity anomaly index, etc. (Sarwade, 1988; Sarkar, 2002). At I.A.S.R.I., several models based on weather indices, discriminant function analysis and water balance techniques were attempted at district level. The model suggested by Hendricks and Scholl has been modified (Agrawal et al. 1980; 1983; Jain et al. 1980) by expressing effects of changes in weather variables on yield in the w th week as second degree polynomial in respective correlation coefficients between yield and weather variables. This is expected to explain the relationship in a better way as it gives appropriate weightage to different periods. Under this assumption, the models were developed for studying the effects of weather variables on yield using complete crop season data whereas forecast models utilized partial crop season data. These models were found to be better than the one suggested by Hendricks and Scholl. These models were further modified (Agrawal et al. 1986) by expressing the effects of changes in weather variables on yield in w th week as a linear function of respective correlation coefficients between yield and weather variables. As year effect on yield was found to be significant, its effect was removed from yield while calculating correlation coefficients of yield with weather variables to be used as weights. Effects of second degree terms of weather variables were also studied. The results indicated that (i) the models using correlation coefficients based on yield adjusted for year effect were better than the ones using simple correlation coefficients, (ii) inclusion of quadratic terms of weather variables and also the second power of correlation coefficients did not improve the model. This suggested that the following model can be used to study effects of weather on yield and its forecast:

17 Background 9 Y =A 0+ a0z 0+ a1z 1+ ct+ where n j j w w w=1 Z = r X ; j = 0, 1 Here Y is yield; r w is correlation coefficient of the weather variable in w th week (X w ) with yield (adjusted for year effect) and is error term. The models were further extended for studying joint effects. The forecast model has been developed using partial crop season data considering all weather variables simultaneously. The model was of the form p 1 p 1 Y=A + a Z + a Z + ct+ 0 ij ij ii'j ii'j i=1 j=0 i¹i'=1 j=0 where m Z = r X ij w =1 j iw iw ii' j m Z = r X X w =1 j ii'w iw i'w r iw /r ii'w is correlation coefficient of Y with i th weather variable/product of i th and i' th weather variable in w th week, m is week of forecast and p is number of weather variables used. In this model, for each weather variable two indices have been developed, one as simple total of values of weather variable in different weeks and the other one as weighted total, weights being correlation coefficients between detrended yield and weather variable in respective weeks. The first index represents the total amount of weather variable received by the crop during the period under consideration while the other one takes care of distribution of weather variable with reference to its importance in different weeks in relation to crop yield. On similar lines, composite indices were computed with products of weather variables (taken two at a time) for joint effects. These models were used to forecast yield of rice and wheat in different situations, viz. (i) rainfed area having deficient rainfall (rice), (ii) rainfed area having adequate rainfall (rice) and (iii) irrigated area (wheat). The results revealed that reliable forecasts can be obtained using this approach when the crops are weeks old i.e. around two and half months before harvest. This approach was also used to develop forecast model for sugarcane (Mehta et al. 2000).

18 Background 10 At district level, model based on time series data on weather variables has also been developed using the technique of discriminant function analysis (Rai and Chandrahas, 2000). A long series of 25 years has been classified into three groups congenial, normal and adverse with respect to crop yields. Using weather data of these groups, linear/quadratic discriminant functions were fitted. These functions have been used to find weather scores for each year at different phases of crop growth and were used as regressors along with the year variable in the forecast model. The study has been carried out for rice in Raipur district. The study showed that forecast of rice crop can be made about two months before crop harvest. The methodology was further modified using weekly weather data. Various strategies were proposed to solve the problem of number of variables more than number of observations. The study was carried out to forecast wheat yield in Kanpur district (Aditya 2008). In another approach based on water balance technique, models for rainfed crops using weighted stress indices have been developed for rice Raipur, Sorghum Delhi & Pharbani and Maize Delhi. In this approach, water deficit/surplus has been worked out at different phases of crop growth and using suitable weights, accumulated weighted stress index has been developed for each year which was used as regressor in the forecast model. This technique provided forecast six weeks before harvest for sorghum, four weeks before harvest for maize and five weeks before harvest for rice (Saksena et al. 2001). These studies, carried out at district level, revealed data requirement of about years for reliable forecasts. Such a long series may not be available for most of the locations. Therefore, weather indices based model development was attempted at agro climatic zone level. The models were developed by pooling the data of various districts within the zone so that a long series could be obtained in a relatively shorter period. Models were developed for wheat in Vindhya Plateau zone and for rice in then Chattisgarh Plain & Bastar Plateau zone taken together (as a portion of Bastar district falls under Chattisgarh Plain zone whereas remaining under Bastar Plateau zone and yield figures are available at district level only). Agricultural inputs, previous year s yield and moving averages of yield were taken as the variables taking care of variation between districts within the zone. Year was included to take care of technological changes. Different strategies for pooling district level data for the zone were adopted. Results revealed that reliable forecasts can be obtained using this methodology at 12 weeks after sowing i.e. about 2 months before harvest at zone level also. The data requirement reduced to years as against 25 years (approx.) for district level models. The study also revealed that forecast model will be appropriate to forecast the yield of a zone even if data for some districts within the zone are not available at model development stage or at forecasting stage (Agrawal et al. 2001). This approach was further studied in detail for various districts and

19 Background 11 agro climatic zones of Uttar Pradesh for one major kharif crop (rice), one major rabi crop (wheat), one long duration crop (sugarcane) and one vegetable (potato) so as to come out with a suitable methodology for forecasting crop yields at state level. The results of this study indicated that reliable forecasts for rice and wheat can be obtained when crop is 11 weeks old i.e. two and half months before harvest, reliable forecasts for sugarcane can be obtained in middle of September using data of 14 fortnights (starting from March first fortnight) whereas for potato reliable forecast can be obtained about four weeks before harvest (Agrawal et al. 2005; Mehta et al. 2010). This approach is also being attempted in Forecasting Agricultural output using Space Agrometerology and Land based observations (FASAL) programme funded by Department of Agriculture and Co-operation (DAC), Ministry of Agriculture. Complex Polynomial through Group Method of Data Handling (GMDH) technique has also been attempted for forecasting of potato yield in Uttar Pradesh (Mehta, et al. 2010). Weather indices (unweighted and weighted) were used as explanatory variables. The performance of this model was found to be better than indices based regression approach for Bareilly district and north eastern zone. For remaining districts and zones the performance was worse or at par with the indices based regression approach. Chandrahas et al. (2010) developed forecast models for different districts and agro-climatic zones of U.P. state using weekly weather variables data for rice and wheat crops and fortnightly data for sugarcane crop. Regressors (based on weather variables) were developed using discriminant function, principal component and weather indices based statistical approaches. Using these regressors, models were developed at different points of time during crop season taking partial crop season data upto the time of forecast. Result of the study indicated that both discriminant function approach and weather indices based approach are good for forecasting. It also showed that yield forecasts of rice and wheat crops can be obtained about two and a half months before harvest and forecast for sugarcane can be obtained in the middle of September month. Kumar et al. (2010) developed neural network model using detrended crop yield of rice, wheat, sugarcane for central plain zone, eastern plain zone, Bundelkhand zone of Uttar Pradesh as response variable and weather indices as input variables. It was concluded that neural network model possesses considerable potential as an alternative to regression models for forecasting agricultural system.

20 Background Review on use of Ordinal Logistic Regression in Agriculture Ordinal logistic regression has widely been used in the field of agriculture for forewarning of pests and diseases, mostly qualitatively. Some of the studies conducted using logistic regression analysis related to the agriculture are discussed hereunder: Turechek et al. (1998) developed logistic regression for the incidence of pecan scab disease using cultivar, temperature, leaf wetness duration and leaf age. They showed that the probability of a leaf becoming infected decreased with increasing leaf age & temperature and increased with increasing leaf wetness. Wolf et al. (2002) developed logistic regression model for classifying presence and absence of Fusarium head blight in wheat by using information about duration and range of various weather parameters collected at 50 locations representing three different U.S. wheat production regions. They developed a disease prediction model with the aim to estimate the probability (i.e. risk) of an undesirable event occurring at a given location and time. Models suitable for disease forewarning system were identified on the basis of prediction accuracy, sensitivity and specificity. The prediction accuracy of developed logistic regression models ranged from 62 to 85%. Fabre et al. (2003) used logistic regression for classifying yield losses in cereals caused by Barley yellow dwarf virus based on population dynamics of aphis Rhopalosiphum padi at various locations in the northern half of France. Regression coefficients were estimated using binary logistic regression model with maximum likelihood method. With the help of estimated value of the parameters they calculated misclassification rate and found that the model was good enough to correctly classify the yield losses in cereals. Agrawal et al. (2004) used ordinal logistic model for development of weather based forewarning system for important pests and diseases for Sugarcane, mustard & cotton. There was good agreement between the forecasts and observed cases. Mila et al. (2004) used logistic regression to estimate the probability of soyabean sclerotinia stem rot prevalence in north central region of United States using tillage practice, soil texture and weather variables (monthly air temperature and monthly precipitation from April to August) as input variables. They developed two models: one using spring (April) weather condition other using summer (July and August) weather condition as input variables and found that both the models had high classificatory power (78.5 and 77.8% respectively).

21 Background 13 Misra et al. (2004) developed logistic regression models for forewarning powdery mildew disease in mango based on weather variables viz. maximum temperature and relative humidity during in Kakori and Malihabad mango belt (Lucknow) of Uttar Pradesh. Results were validated using data of subsequent years. Henderson et al. (2007) used logistic regression analysis for forecasting late blight in potato crop of southern Idaho. Binary logistic regression model and ordinal logistic regression (scale 0 to 4) model were developed to determine if disease severity could be estimated using variables found to be correlated with occurrence of blight. Binary logistic regression could predict the occurrence of late blight due to high sensitivity (accurate in correctly classifying outbreak years) of 75% however ordinal logistic regression model had lower sensitivity and was unable to predict disease severity. Spencer and O Hara (2007) developed a multiple logistic regression model to assess the relationship between certain stem attributes and probability of number of stems developing Phytopthora ramorum symptoms in redwood Tanoak trees in California and Oregon. The stem variables considered were height, crown class, foliar condition and presence of insects, fungal infection and disease symptoms. Lohse et al. (2008) used method of ordinal logistic model for forecasting relative impacts of land use on anadromous fish habitat to guide conservation planning. Bhowmik (2009) studied logistic regression modelling for classification in agriculture using data pertaining to agricultural ergonomics. Kim et al. (2009) employed the method of ordinal logistic model to identify environmental factors associated with mating flights. The weather variables such as temperature, relative humidity, wind speed, barometric pressure and rainfall were significant factors that influenced fire ant mating flights. 2.3 Review on use of Discriminant Function Analysis in Agriculture Discriminant analysis is a multivariate technique concerned with separating distinct sets of objects (or sets of observations) and allocating new objects (or observations) to the previously defined groups. As a classificatory procedure, it is often employed in order to investigate observed differences when causal relationships are not well understood. Some of the studies

22 Background 14 conducted using discriminant function analysis related to the agriculture for modeling/forecasting purposes are discussed hereunder: Carter et al. (1997) described the methodology of forecasting rainfall over Puertorico with the help of discriminant function analysis and factor analysis. Connor (1999) developed quadratic discriminant function model to forecast the number of salmon fish that would survive in a dam to help managers to effectively time the release of reservoir water to mitigate the problem of reduction in survival. He also developed a multiple regression model using discriminant scores to predict the time during which survivors would pass the dam. Wu and Wilhite (2004) developed the agricultural drought risk discriminant model for corn and soybeans on the basis of weather variables and it improved agricultural drought assessment as compared to the other earlier methods. Gang et al. (2006) forecasted wheat stripe rust by discriminant function analysis based on the occurrence data of the disease and the climate data collected. Aditya, Kaustav (2008) used discriminant function for forecasting of crop yield (wheat). He proposed various strategies for solving the problem of number of variables more than number of data points. Workneh et al. (2008) identified weather variables (temperature and rainfall) as predictors in discriminant analysis that correctly classified all the cases into bunt positive and negative fields, at central Texas. 2.4 Review on comparison of Logistic regression and Discriminant analysis Following researchers compared logistic regression and discriminant analysis for classification: Press and Wilson (1978) carried out two empirical studies of nonnormal classification problems, compared the two methods, and found that logistic regression with MLE outperformed classical linear discriminant analysis in both the cases, but not by large amount. Logistic regression is preferable to discriminant analysis in cases for which variables do not have multivariate normal distributions. However, for normal distribution, logistic regression was found to be less efficient than discriminant function.

23 Background 15 O Gorman and Woolson (1991) compared stepwise variable selection procedure in discriminant analysis with stepwise procedure using logistic regression. In most situations there was little difference between stepwise logistic regression and discriminant analysis in the probability of selecting the related variables. Johnson et al. (1996) described the relationships between weather and outbreaks of potato late blight in the semiarid environment of south-central Washington with linear discriminant and logistic regression analyses and forecasted late-blight outbreaks. The response variable was a year with or without a late blight. They found that logistic regression model performed better than discriminant analysis. Pohar et al. (2004) studied the performance of the logistic regression and discriminant function analysis for classification by simulations. Discriminant function analysis came to be more appropriate when normal distribution of covariates was satisfied. Also, the results of two methods were close when the sample size was large. Zibaei and Bakhshoodeh (2008) compared logistic regression and discriminant analysis for investigating determinants of sprinkler irrigation technology discontinuance in Iran and found that accuracy of classification was better for logistic regression.

24 CHAPTER-3 GENERAL RESEARCH METHODOLOGY 3.1 Description of Area and Crop Covered The study has been conducted for Kanpur district of Uttar Pradesh, India which is situated between 26 o 03' N latitude and 80 o 04' E longitude. It lies in the central plain zone of Uttar Pradesh. It is liberally sourced by the Ganges and Yamuna Rivers and their tributaries. Soils are deep alluvial, medium to medium heavy textured but are easily ploughable. The favorable climate, soil and the availability of ample irrigation facilities make growing of rice and wheat a natural choice for the area. Wheat crop is generally cultivated during the Rabi season because during this period it provides a better environment for the cultivation of the wheat crop. 3.2 Data description Yield data Time series data on yield of wheat crop for Kanpur district of Uttar Pradesh for 39 years ( to ) have been obtained from Directorate of Economics and Statistics, Ministry of Agriculture, New Delhi. Data prior to 1971 has not been taken as in the backdrop of the food crisis that gripped India in the 1960s and 1970s (and few years earlier to that too) the Government of India initiated the Green Revolution program which brought major technological changes Weather data Weekly weather data ( to ) on the weather variables of Kanpur district of Uttar Pradesh have been obtained from Central Research Institute for Dry-Land Agriculture (C.R.I.D.A.), Hyderabad. The data have been taken up to the first 16 weeks of the crop cultivation which included 40 th standard meteorological week (SMW) to 52 nd SMW of a year and 1 st SMW to 3 rd SMW of the next year. The data on five weather variables viz. maximum temperature, minimum temperature, morning relative humidity (Rh1), evening relative humidity (Rh2) and Rainfall have been used in the study. 3.3 Crop season Wheat is generally sown towards the end of October when average daily temperature falls around o C. Sowing of wheat when temperature is high results in poor germination,

25 General Research Methodology 17 reduced tillering and early onset of flowering and thereby exposing the floral parts to the cold damage. The different crop growth phases are discussed below. Pre-Sowing and Germination Phase The pre-sowing phase of the crop is important because in this phase the land is prepared for the cultivation. If the weather condition is adverse during the pre-sowing phase the sowing of the crop is generally delayed. After sowing of the crop there comes the germination phase. Germination generally takes 6-7 days or near about one week after the sowing. Here in the germination phase at appropriate temperature the embryo begins to push both the coleorhiza and coleoptile. Then the seed coat ruptures and the coleoptile turns upwards and the coleorhiza thrusts downwards. Then the leaves come outwards and the roots become forming below the ground. Crown Root Development Phase The crown root initiation occurs in wheat in days after sowing or near about in 3 weeks from germination. The crown root consists of several nodes whereas each node consists of several coronal roots. The crown roots along with branches are principal supply roots of the plant. During this phase plant requires a huge amount of moisture so irrigation is required during this phase. Tillering Phase This phase starts just after the crown root initiation phase and lasts up to days after sowing or near about 2-3 weeks after crown root initiation phase. A bud primordium lies in the leaf axil at each crown node. This bud primordium develops into tillers. Jointing and Reproductive Phase Jointing phase is the peak plant growth stage, starts just after the tillering phase or days after sowing. This is the peak vegetative stage of the crop. In this phase the vegetative growth of the crop is completed and the crop then goes to the reproductive phase. The reproductive phase lasts days after sowing or near about 4-5 weeks after the jointing phase. 3.4 Methodology Used for the Study Data from to have been utilized for model fitting and subsequent three years ( to ) were used for the validation of the model. To start with, linear regression has been fitted between yield (dependent variable) and year (independent variable) using data from to The equation thus obtained was utilised for getting residuals

26 General Research Methodology 18 (detrended yield). These residuals were then used for the group formation. Crop years have been grouped into two (residuals with negative value have been taken as zero representing bad year and that with positive values have been taken as one representing good year) and three groups (residuals have been arranged into ascending order and were divided into three equal groups namely adverse(0), normal(1) and congenial(2)). For modeling of crop yield using weather variables in two/three groups, probabilities/scores were obtained by ordinal logistic regression/discriminant function analysis. These probabilities/scores along with year were used as regressors for development of forecast model. For validation of model, forecasts of subsequent years were obtained and RMSE and MAPE of the forecasts were calculated. Performance of the models was compared on the basis of Adj R 2, PRESS, number of misclassifications and RMSE & MAPE of forecasts. In this study, five variables for 16 weeks were considered which makes number of explanatory variables 80 in logistic/discriminant function analysis. Thus, number of variables becomes more than the number of data points. To solve this problem following strategy has been used. At first week (here 40 th SMW is taken as first week), the weather variables corresponding to the pre-defined groups have been used to compute probabilities/scores by stepwise ordinal logistic regression/discriminant function analysis. At the second week (41 st SMW), the weather variables of this week along with probabilities/scores computed at the first week have been used to compute probabilities/scores using stepwise logistic regression/discriminant function analysis. These steps have been repeated in third week as well and so on upto last week. Forecast models were fitted at different weeks starting from 52 nd SMW using stepwise regression procedure, taking probabilities/scores at week of forecast along with year as regressors Methodology for Objective-1 Under this objective, for different groups (good & bad in case of two groups and adverse, normal & congenial for three groups) probabilities were obtained using ordinal logistic regression. Then, forecast model has been developed using these probabilities along with year as explanatory variables at different weeks starting from 52 nd SMW. Using these models forecasts of subsequent years were obtained Ordinal logistic regression in case of two groups The linear relationship between dependent variable Y and independent variable x is written as: Y= + x+

27 General Research Methodology 19 where is the intercept and is the regression coefficient, ~ N (0, 2 ) Let P 1 denotes the probability that Y=1 for given x, the model for the probability would be: P 1 =P(Y=1 x) = P (Y=1) thus, P (Y=0) = 1- P 1. Under the assumption that E ( ) = 0, it follows that E (Y x) = + x = P 1 If Y can take two values then is also dichotomous, then = 1- P 1 when Y =1 = - P 1 when Y= 0 Because the error is dichotomous (discrete) so normality assumption is violated. Moreover, variance of is not constant, but depends on x through its influence on P 1 i.e. V ( ) = P 1 (1- P 1 ) The logistic regression function is written as: exp( + x) 1 P 1= = 1+exp( + x) 1 exp ( + x) (3.1) For this model odds of making response are: P 1 =exp( + x) 1-P 1 P1 Taking log on both the sides we get g(x)=log = + (x). This transformation is called as 1-P logit transformation. 1