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Open Access
Fitting linear mixed effects models for unbalanced longitudinal data
(CCSHAU, Hisar, 2020-08) Ravita; Verma, Urmil
The classical linear regression model is an important statistical tool but its use is limited because of its standard assumptions. Regression models using time series data occur quite oftenly and the assumption of uncorrelated or independent errors is often not appropriate. Moreover, many time series having complex structure calls for the addition of fixed and random effects accounting for the observational design. Such effects are straightforward to add in a mixed model environment (accommodating unbalanced data). The fixed-effects parameters can be either qualitative (as in the traditional analysis of variance) or quantitative (as in standard linear regression). BLUP is a standard method for estimating random effects of a mixed model. The mixed procedure uses the REML method, also known as residual maximum likelihood. It is here that the Gaussian assumptions are exploited. One such class is varying coefficient models, where the response variable is allowed to depend linearly on some regressors, with coefficients as smooth functions of some other predictor variables, called the effect modifiers. Varying coefficient models, where the effect modifier variable is calendar time, leads to time-varying coefficient models. The statistical modelling approaches viz., multiple linear regression and linear mixed effects were applied to develop mustard yield forecasts models on agro-climatic zone basis in Haryana. The mustard yield data for the period 1980-81 to 2016-17 of Hisar, Bhiwani, Sirsa, Mahendragarh and Gurugram, 1989-90 to 2016-17 of Rewari and 1997-98 to 2016-17 of Jhajjar and Fatehabad districts alongwith fortnightly weather data were used for the purpose. The zonal yield forecast models have been developed on the basis of time-trend and weather data from 1980-81 to 2009-10 while the data from 2010-11 to 2016-17 were used for validity checking of the developed models. Trend yield/time variable was included to take care of variation between districts within zone as the weather data are not available for all the districts, though the zonal model utilized the same weather information in adjoining districts under the zone. The linear mixed effects models with time both as fixed and random effects and weather as random effects with covariance structures; VC, AR(1) and Toeplitz have been fitted. The post-sample predictive performance(s) of alternative LMMs and regression based weather-yield models were observed in terms of percent relative deviations from real-time yield(s) and root mean square error(s), and that differed markedly among the alternative models. LMMs with weather as random effect(s) consistently showed the superiority over regression based weather-yield models in capturing lower percent relative deviations. The LMMs with weather as random effects performed well with lower error metrics as compared to the alternative mixed effects/regression models in most of the post-sample time regimes. Sevensteps ahead (i.e. 2010-11 to 2016-17) predicted values favour the use of LMMs. A critical in-depth of the results indicates the preference of using varying coefficients models in comparison to conventional, i.e., constant/fixed coefficients models developed under this empirical study. The linear mixed effects models with Toeplitz type structure substantially improved the predictive accuracy and produced what can be considered as satisfactory district-level mustard yield prediction in Haryana.
Open Access
Time series intervention modeling and simulation for mustard yield forecasting in Haryana
(CCSHAU,HiSAR, 2020-10) Ajay Kumar; Verma, Urmil
Modeling and Simulation is a discipline for developing a level of understanding of the interaction of the parts of a system, and of the system as a whole. A model is a simplified representation of a system at some particular point in time or space intended to promote understanding of the real system. Simulation permits the evaluation of operating performance prior to the implementation of a system. The study compares the efficacy of time series Intervention models and simulation in quantifying the pre-harvest mustard yield in Hisar, Bhiwani, Sirsa, Fatehabad, Mahendragarh, Rewari, Jhajjar and Gurugram districts of Haryana. The objective of this study was to assess the forecast accuracy of the contending models for district-level mustard yield forecasts in Haryana. The fortnightly weather data on rainfall, minimum temperature and maximum temperature over the crop growth period (September-October to February-March) have been utilized from 1980-81 to 2010-11 for the models‟ building. The weather-yield data from 2011-12 to 2015-16 have been used to check the post-sample validity of the fitted models for mustard yield forecasts in comparison to those obtained from State Department of Agriculture crop yield(s) estimates. The statistical modeling approaches viz., multiple linear regression, ARIMA, regression with ARIMA errors (RegARIMA) and ARIMA-Intervention were applied for the purpose. First of all, weather-yield models based on multiple linear regression were developed to relate mustard yield to fortnightly weather input alongwith linear time-trend yield/crop condition term as an indicator variable.Alternatively, ARIMA, RegARIMA, and ARIMA-Intervention models were fitted as per targeted objectives. Additionally, Student‟s t-copula in SAS is applied as a simulation tool and compared the output to the time series forecasts. The forecasts are compared to determine if there is either a consistent or significant difference between the two output. The forecast performance(s) of the alternative models were observed in terms of percent relative deviations of mustard yield forecasts from observed yield(s) and root mean square error(s). RegARIMA models performed well with lower error metrics as compared to the alternative models in most of the time regimes. Five-steps ahead forecast figures i.e. 2011-12 to 2015-16 favour the use of RegARIMA models to obtain pre-harvest mustard yield forecasts in the districts under study. The forecasts generated by RegARIMA are remarkably close to the forecasts obtained through the simulation process. Empirical evidence from this study confirms that the RegARIMA model can produce reliable forecasts and would therefore provide a more robust approach of forecasting with limited data sets.using the developed forecast models, the district-level mustard yield estimates could be computed successfully well in advance of the actual harvest. On the other hand, the State Department of Agriculture crop yield estimates are obtained quite late after the actual crop harvest.
Open Access
State Space Modelling with Weather as Exogenous Input for Sugarcane Yield Prediction in Haryana
(CCSHAU, Hisar, 2020-05) Hooda, Ekta; Verma, Urmil
Parameter constancy is a fundamental issue for empirical models to be useful for forecasting, analyzing or testing any theory. This work addresses the concept of parameter constancy and the implications of predictive failure. Predictive failure is uniquely a post-sample problem. Unlike classical regression analysis, the state space models are time varying parameters models as they allow for known changes in the structure of the system over time and provide a flexible class of dynamic and structural time series models. The study has been performed in two parts i.e. the development of state space models in two forms (the state space and unobserved component approach), and the state space models with weather as an exogenous input for sugarcane yield prediction in Ambala, Karnal, Kurukshetra, Panipat and Yamunanagar districts of Haryana. The time series sugarcane yield data for the period 1966-67 to 2009-10 of Ambala and Karnal districts, 1972-73 to 2009-10 of Kurukshetra and 1970-71 to 2009-10 of Panipat and Yamunanagar districts were used for the development of different models. The validity of fitted models have been checked for the subsequent years i.e., 2010-11 to 2016-17, not included in the development of the yield forecast models. The selection of autoregressive orders, i.e., five, three, two, four and five looked reasonable for Ambala, Karnal, Kurukshetra, Panipat and Yamunanagar districts respectively helped in determining the amount of past information to be used in the canonical correlation analysis and further leading to the selection of state vector. Information from the canonical correlation and preliminary autoregression analyses were used to form preliminary estimate of the parameters of state space models and that provided the sugarcane yield estimates using Kalman filtering technique. The UCMs with level, trend and irregular components were fitted to study the trend of sugarcane yield. For all the five districts, the irregular component was found to be highly significant while both level and trend component variances were observed non-significant. Lastly, the state space models with weather as exogenous input using different types of growth trends viz., polynomial splines; PS(1), PS(2) and PS(3) were developed. The weather variables used for each district were selected on the basis of stepwise regression method and PS(2) with weather input was selected as the best suited model for all districts. The post-sample sugarcane yield estimates were obtained on the basis of fitted SS, UCM and SSM with exogenous input. The predictive performance(s) of the contending models were observed in terms of percent relative deviations and RMSEs of sugarcane yield forecasts in relation to observed yield(s). The SSMs with weather input consistently showed the superiority over SS and UCM models in capturing lower percent relative deviations. Thus, it is inferred that the state space models may be effectively used pertaining to Indian agriculture data, as it takes into account the time dependency of the underlying parameters which may further enhance the predictive accuracy of time-series models with parameter constancy.
Open Access
Variable selection for classification and discrimination of Indian Mustard (Brassica juncea) genotypes for yield and oil content
(CCSHAU, Hisar, 2019-07-10) Godara, Poonam; Hooda, BK
The present study deals with the problem of variable selection for classification and discrimination of Indian Mustard (Brassica juncea) genotypes for yield and oil content. The study used secondary data on 310 Indian mustard genotypes obtained from Oilseeds section of the department of Genetics and Plant Breeding, CCS HAU, Hisar. The experiment was conducted during rabi season of 2015-16. Five variable selection methods (Univariate Two-Sample t-test, Rao´s F test for Additional Information, STEPDISC Procedure (backward and forward) using Wilk´s Lambda criterion and Random Forests Algorithm) for classification and discrimination were compared using Monte Carlo simulation. Performance of the methods was assessed in terms of leave one out cross validation error for classification. Comparing the performance of various methods affecting seed yield for samples of equal sizes in scheme I, Rao's F test, Wilkˊs lambda (Backward) and Wilkˊs lambda (Forward) were found better than others. In scheme II, the most suitable methods affecting oil content with least leave one out cross validation error rate were Wilkˊs lambda (Backward) and Wilkˊs lambda (Forward). Based on results of the scheme I and II, Wilk´s Lambda (backward and forward) were found most suitable method for classification affecting the seed yield and oil content significantly. In scheme I using leave one out cross validation error rate four important variables for discrimination affecting the seed yield per plants were secondary branches, primary branches, days to maturity and siliqua number on main shoot with least error of rate of 21.72 per cent. The important variables for discrimination which significantly affected the oil content were siliqua length, Secondary branches, primary branches and days to maturity with least error rate of 33.90 per cent. Secondary branches, siliqua number on main shoot, seeds per siliqua and 1000 seed weight were found to be important variables in scheme III with least error rate of 27.68 per cent. Three characters which discriminate the groups having low seed yield and high seed yield were 1000 seed weight, siliqua length and seeds per siliqua, while siliqua length 1000 seed weight and primary branches were found the most discriminating variables affecting oil content. Using the correlation between variables and discriminant score, the most important variables affecting the seed yield were secondary branches, primary branches and days to maturity. The three most important variables discriminating between oil content were siliqua length, secondary branches and seeds per siliqua. Most important variables discriminating between low seed yield with low oil content and high seed yield with high oil content groups were secondary branches, primary branches and siliqua number of main shoot. The variable, number of secondary branches have been found to be the most important for classification and discrimination of Indian mustard genotypes for seed yield and oil content.
Open Access
Prediction of monthly onion arrivals and prices in major Indian markets using Support vector machine and ANN models
(CCSHAU, 2019) Bharti, Deepa; Hooda, B.K.
In the present study, growth rates in area, production, productivity and export of onion in India and world have been studied during 1980-2016. Support Vector Machine (SVM) and Artificial Neural Network (ANN) models were also developed and compared for monthly arrivals and prices of onion in major Indian Markets for the period 1990 to 2016. Study revealed a significant increase in area, production, productivity and export of onion in India during the period 1980-2016 with compound growth rates of 5.13, 6.72, 1.47and 7.62 per cent per annum. While significant increase with compound growth rates 3.54, 4.21 and 0.18 per cent per annum was also observed in area, production and productivity at the world level for the period 1980 to 2016. SVM was found to be the better predictor for onion arrivals in Delhi, Kolkata and Bengaluru markets. While, ANN performed better for the Mumbai and Jaipur market. Also for onion prices of selected market, SVM models were better predictors in three markets prices, while ANN models were fitted on two markets. In Kolkata, Bengaluru and Mumbai markets prices, lower value of RMSE and MAPE were found using SVM model than ANN model. For the Jaipur and Delhi market, least value of RMSE and MAPE were found for ANN model. Hence SVM models outperformed ANN models.
Open Access
Prediction of wheat yield using Artificial Neural Network and Fuzzy time series models in Eastern agro climatic zone of Haryana
(CCSHAU, 2019) Sindhu, Abhishek; Hooda, B.K.
This study deals with the prediction of wheat yield using Artificial Neural Network and Fuzzy time series models in Eastern agro climatic zone of Haryana. It also includes the algorithms for the model development and computations. ANN and fuzzy time series models for wheat yield prediction in Eastern agro climatic zone of Haryana have been developed using meteorological parameters. The predicted yield obtained by the fuzzy time series model have been compared with that of the Artificial neural network model along with the actual wheat yield, and the results are found encouraging. Best fitted architecture for Artificial Neural network was selected based on goodness of fit statistic criterion for wheat yield prediction and is used for prediction of wheat yield in Eastern agro climatic zone of Haryana using meteorological parameters. We found that Logsig transfer function was the best fitted neural network with five neurons in a single hidden layer. The values of R2, MSE, RMSE and MARD criterion were used to compare the performance of ANN and Fuzzy time series models. These criterions indicates that ANN model is slightly better than the fuzzy time series model for prediction of wheat yield in Eastern agro climatic zone of Haryana.
Open Access
Non-linear growth models for area, production and productivity of important foodgrains in Haryana
(CCSHAU, 2019) Sanju; Hooda, B.K.
The persent study was carried out with the objective to develop non-linear growth models for acreage, production and productivity of total foodgrains in Haryana. Season wise and crop wise best non-linear models for describing growth in area, production and productivity of foodgrains were also considered. We discussed different non-linear growth model and also determined the initial value for each parameter. Three different non-linear growth models viz. Logistic, Gompertz and Monomolecular was used for area, production and productivity of important foodgrains(Rice and Wheat) in Haryana for the period 1966 to 2015. The parameters were estimated using Levenberg - Marquardt’s iterative method of non-linear regression. Best model was selected based on goodness of fit statistics such R2, RMSE and MAE. The best model was used for forcasting of area, production and productivity of foodgrains for the period 2016 to 2020. We found that Logistic model was the best fitted growth model for area, production and productivity of total (kharif+rabi) foodgrains. We also observed that Logistic model is the best fitted growth model for area, production and productivity of kharif and rabi foodgrains in Haryana. Finally we concluded that none of the tried models was found suitable to fit for foodgrains area in Haryana. Logistic model was found suitable to fit for production as well as productivity of foodgrains grown in Haryana followed by Gompertz model.
Open Access
Pre harvest forecast models of rice yield based on weather variables for Eastern agro-climatic zone of Haryana using Discriminant function analysis
(CCSHAU, 2019) Nain, Gurmeet; Bhardwaj, Nitin
The present investigation entitled “Pre harvest forecast models of rice yield based on weather variables for Eastern agro-climatic zone of Haryana using Discriminant function analysis” consists of five chapters including summary and conclusion. The purpose of the study is to develop statistical models for studying the relationship between weather variables and crop yield and to develop different forecast models based on discriminant function analysis. Time series data on rice yield and weekly data from 22nd Standard Meteorological Week (SMW) to 41th SMW of on five weather variables viz., minimum temperature, maximum temperature, relative humidity, wind velocity and sun shine hour covering the period from 1996-1997 to 2016-2017 have been utilized for development of pre-harvest forecast model and the remaining two-year 2016-17 and 2017-18 yield data was used to validate the models. Statistical methodology using multiple regression and discriminant functions for developing pre-harvest forecast models has been described. The Model-1 is based on weather indices and rests are based on discriminant functions. The model 9 is proposed one. These models can be used to get the reliable forecast of rice yield about one and half months prior to the harvest. In all, nine models have been developed to study the relationship between crop yield and weather variables. The model-3(R2 =85.8%, Adjust R2=83.1%, PED =1.15 & 1.04 for 2016-17 & 2017-18 respectively) has been found to be the best for studying the relationship between crop yield and weather variables. Model 6 & Model 9 also exposes chances for better forecast. Therefore, these models also can be recommended for pre-harvest forecast of the rice yield in practice.
Open Access
Impact of Agricultural Price Policy on Oilseed and Pulse crop in Haryana
(CCSHAU, 2019) Sandeep Kumar; Luhach, Ved Prakash
The present study was carried out with the objectives to analyse the trend in area, production and productivity, the seasonal variation in price and arrival, gap between FHP (Farm Harvest Prices) and MSP (Minimum Support Prices) and identify the constraints in production and marketing of rapeseed & mustard and chickpea. The study was based on primary as well as secondary data. Bhiwani and Mahendragarh districts were purposively selected based on the highest area under rapeseed & mustard and chickpea from Haryana, respectively. Two blocks namely Tosham and Kairu from Bhiwani district, Kanina and Mahendragarh from Mahendragarh district selected purposively. Further two villages of each selected block were selected randomly. From each village, 10 farmers were selected randomly and finally, 80 farmers of eight villages were interviewed to excerpt all desired information. The outcomes of study revealed an increasing trend in the area, production and productivity of rapeseed and mustard at the national level with CGRs values of 0.05, 1.89 and 1.67 per cent, respectively. Whereas, in Haryana, the trend in area indicated decreasing trend -0.31per cent, while production and productivity illustrated increasing trend with CGRs values of 2.00 and 3.87 per cent, respectively. In the study shown an increasing trend in the area, production and productivity of chickpea at the national level with CGRs values of 1.71, 2.84 and 1.11 per cent, respectively. Whereas, in Haryana, the trend in area and production indicated decreasing trend -8.29 per cent and -7.79 per cent while productivity illustrated increasing trend with CGR values of 0.46 per cent, respectively. Seasonal analysis resulted that the rapeseed & mustard and chickpea arrivals in the selected markets were higher in the months of March to June (Peak period) and lower in the months of February to October to February (Lean period). The inverse relationship was found between price and arrivals of rapeseed & mustard and chickpea in the selected markets. Gap between FHP and MSP resulted that in mostly cases FHP is higher than MSP because higher demand than supplies does not allow the market prices to fall below MSP. In recent year, market prices ruled higher than MSP. The major problems faced by the farmer in the production, marketing of rapeseed & mustard and chickpea in Bhiwani district were inadequate irrigation facilities 74.17 per cent followed by lack of adoption of plant protection measures 70.00 per cent and marketing constraints were wide fluctuation in prices 72.50 per cent followed by remunerative prices 61.67 per cent. In Mahendragarh district major production constraint of rapeseed & mustard and chickpea were inadequate knowledge of recommended packages and practices 61.67 per cent followed by big inadequate irrigation facilities 58.33 per cent, lack of adoption of plant protection measures 55.83 per cent and marketing constraints were was remunerative prices 62.50per cent followed by wide fluctuation in prices 60.00 per cent, large number of intermediaries in marketing process 56.67per cent.

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