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M. Sc. Dissertations

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Now showing 1 - 9 of 17
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    ThesisItemOpen Access
    Incomplete block designs for diallel and partial diallel crosses- A critical review
    (CCSHAU, 2016) Bishnoi, Rekha; Aneja, D.R.
    The objective of present investigation is to give an exhaustive review of work done on incomplete block designs for diallel and partial diallel crosses. Confounded diallel crosses for Methods I and III of Griffing (1956) given by Agarwal (1974, 75) are useful when the experimenter is interested in the estimation of all components i.e. g.c.a, s.c.a, maternal and maternal interaction effects of diallel crosses. The loss of information of different effects and interactions has also been given. N-ary designs using triangular PBIB designs given by Divecha and Ghosh (1994) for estimation of g.c.a, s.c.a, reciprocal effects for all four complete diallel crosses can be used. Efficiency of these designs is a matter of investigation. Optimal complete diallel crosses using Nested (Gupta and Kageyama, 1994) & PBIB designs (Dey and Midha, 1996) and efficient designs for complete diallel crosses through Latin square designs (Sharma et al., 2011) & balanced lattice designs (Sharma, 2005) have been also described in the present manuscript. These designs are efficient/optimal for g.c.a effects only. Catalogue of all such designs for number of inbred lines upto 20 have been also given which will be useful for the experimenter in the selection of appropriate blocked diallel cross design as per his requirement. Optimal complete diallel crosses designs given by Chai and Mukherjee (1999) are optimal for both g.c.a as well as s.c.a comparisons. Method of constructing Incomplete Block Designs for Partial Diallel Crosses using n-ary designs given by Agarwal & Das (1990) and Divecha & Ghosh (1997) have been illustrated through examples also. In these methods, two designs have to be considered; one for construction and another for evaluation of Partial Diallel Crosses. When the list of all such BIB and PBIB designs is not available, Mating Environment designs using circular designs (Sharma, 1998) are useful because these are available for any combination of number of treatments and block sizes. Catalogues of such designs have been provided in in tabular form. Construction method of optimal partial diallel crosses by Mukerjee (1997) & Das et al. (1998) available in literature have been also described.
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    ThesisItemOpen Access
    Ridge regression estimator for milk production in cattle
    (CCSHAU, 2006) Sharma, Yogesh; Grover, Deepak
    The prediction of life time production of an animal on farm may be helpful to decide, whether particular animal should cull or not on the basis of performance of first lactation only. The present investigation has been conducted to find out an appropriate estimation procedure to estimate the regression coefficients of life time production multiple linear regression model of Hariana breed of cattle. To find out an appropriate estimation procedure, life time production multiple linear regression model of Hariana breed of cattle has been studied in detail. Normal probability plot and histogram used to check the normality assumption of model. Plots of standardized residuals against each regressor were utilized to detect the outlier cases in this study. Presence of influential observations was detected with the help of three different measures. Each influential observation and their different combinations excluded from the model one by one to check the considerable change in mean square error value, coefficient of determination value, in sign and significance of regression coefficients. Presence of multicollinearity in independent variables was diagnosed with the help of examination of correlation matrix, variance inflation factors, eigenvalues inspection and condition indices. The result revealed that problem of multicollinearity was serious in the study. In this investigation two estimation procedures, i.e., ordinary least squares and ridge regression technique were compared. Criterion of mean square error, sign and significance of regression coefficients were used to compare the performance of each estimator. The value of ridge constant (K)was estimated by three different methods and accordingly the optimum value of ridge constant (K) was found. The ridge regression estimator by using optimum value of ridge constant was found better as compared to ordinary least squares estimator in terms of mean square error criterion.
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    ThesisItemOpen Access
    Principal variables selection in multivariate analysis
    (CCSHAU, 2007) Deepti Singh; Hooda, B.K.
    Practical as well as theoretical considerations compel the researchers dealing with huge data sets to select principal variables or to discard the redundant variables. Selection or discarding of variables simplifies the analysis and also makes the interpretations of the results easier. In the present study, we discussed and critically reviewed various variable selection and variable discarding procedures. In particular we emphasized on determining the subset of principal variables which provided maximum information using the concept of Principal Component Analysis and that preserved the group structure of the data using Procrustes Analysis. We also made use of generalized dependence and multivariate association based on Canonical Correlation Analysis for selection of principal variables. Comparative study of various variables selection procedures was made using three similarity measures viz., RV- Coefficient, Jolliffe similarity and percentage of variation explained. Empirical comparison was made using both covariance as well as correlation matrix as input. Various variable selection procedures have been applied on mustard data obtained from the department of plant breeding, CCSHAU, Hisar for selection of principal variables
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    ThesisItemOpen Access
    An empirical study of gca and sca effects for wheat crop using Griffing (1956) model
    (CCSHAU, 2007) Malik, Nisha; Hasija, R.C.
    An abstract of the thesis submitted to CCS HAU, Hisar in partial fulfillment of requirement for the degree of Master of Science in Statistics. The development of new varieties by the plant breeders has helped in bringing about Green Revolution in our country. One of the most common breeding methods is hybridization. Mating designs, in general, provide a very simple and convenient method of generating crosses in one or two generations.In the present study critical review of the mating designs has been done and secondary diallel data on nine varieties of wheat namely (WG II, Pewee’s, Buck Buck, Tanager, Junco’s, Harrier, Moncho’s S-308, Bb-Kal) has been analyzed using Griffing (1956) model for all the four methods for two years 1982, 1983 by taking two characters grain yield and tiller/plants.
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    ThesisItemOpen Access
    Robust estimation for multiple linear regression
    (CCSHAU, 2008) Shekhar, Shashi; Grover, Deepak
    The search for better method of estimation is everlasting. Assumptions of ordinary least squares provided numerous opportunities of study when its assumptions are violated in multiple linear regression. The present study is related to the violation of normality assumption. Any process which can give relatively better estimates even after the assumption is violated is a robust estimation process. Modified maximum likelihood method is one such tool which is applied in the present study. Normality assumption of errors is checked with the help of Q-Q plot. Plots of standardized residuals against each independent variable were utilized to detect the outlier cases. Deviation from normal plot gives deviation of each point from normal distribution. Exclusion of outliers caused considerable changes in the values of R2, adjusted R2 and standard error of estimates. We considered a distribution which is in reasonable proximity of error distribution and estimated the unknown parameter of the distribution. The distribution of errors which violate normality assumption can broadly be divided into two parts i.e. symmetric and skewed. Modified maximum likelihood estimates are calculated for a series of value of unknown parameter and the value having maximum value of logarithm of likelihood function is selected as the most plausible value. In present study, two estimation procedures i.e. MMLE and OLS were compared in terms of standard error of estimates. MMLE was found to have lesser standard errors than OLS even when normality assumption was violated and outliers were present. With the help of datasets it is concluded that MML estimates are robust.
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    ThesisItemOpen Access
    A study on two-sex population model with varying growth rates
    (CCSHAU, 2008) Vinita; Batra, S.D.
    The model of Lewis and Leslie (1945, 1948) has been extensively used for the study of population growth in various fields. However, complex growth structures require the use of more general models. The model of Kapur (1979) allows harvesting in the system, is an initial step to move in this direction. However, the need is being felt to develop more general models considering the effect of variable growth rates along with harvesting on the reproductive structure of living organisms. In the present work, a two-sex age-dependent population growth model is proposed where birth, death and harvest rates of viii males and females are the functions of three population groups viz. pre-reproductive, more-reproductive and less-reproductive. A population growth model has been developed with different birth, death, harvesting and migration rates of three age groups of males and females. The model is useful for projection of cattle population in different age groups. Emotions for growth, extinction and stability of the population have also been derived. The model has been applied on the crossbred cattle population by taking 11 years data (1995-2005) collected from Department of Animal breeding, CCS HAU, Hisar. The projected population of males and females in three age groups have also been found after testing the validity of model. A uniform harvesting rate have also been derived for stable population structure observed and projected population structure for males and females of three age groups with given harvesting rate as well as uniform harvesting rate have also been shown graphically.
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    ThesisItemOpen Access
    Statistical analysis of fertility through simultaneous equation model in Haryana
    (CCSHAU, 2008) Sharma, Richa; Kapoor, Kiran
    In today’s scenario to know the fertility pattern is very important as the population is rising rapidly. It is important to use appropriate statistical techniques for their estimation. Single-equation model of fertility behaviour are subject to specification error and often fail to capture the dynamic properties of the model. But the variable considered have two–way causation, thus Simultaneous Equation Model should be used. An attempt has been made by postulating the four equations simultaneous equation model for explaining the fertility pattern in Haryana. This model consists of Fertility Equation, Female Participation Equation, Income Equation and Education equation. Identification was done for examining the efficient method of estimation. All four equations were found to be over–identified. After identification two–stage least squares method of estimation was used for the estimation of regression coefficients. Estimates were compared for OLS as well as for 2SLS in terms of regression coefficient estimates, standard error of estimates, coefficient of multiple determination (R2) and Durbin–Watson test statistic value. Residual analysis was also performed to find out outliers and for establishing the presence of autocorrelation. There was no outlier while indication found for the presence of outliers. By Durbin–Watson statistic it was found that there was no autocorrelation between the successive terms of the residuals of four different endogenous variables. The data of Haryana State for 42 years was splitted into three parts viz. 1966-2007, 1966-1986 and 1987-2007 for examining the time patterns in fertility. Then estimates obtained through OLS method has been compared for three different time periods and also the estimates obtained through 2SLS method has been compared for three different time periods. Then the comparison was made between the estimates obtained through OLS and 2SLS for different time periods. It has been found that infant mortality rate, female literacy rate, female work participation rate has statistically high significant effect on fertility. On comparison, it was found that 2SLS method gives consistent and efficient estimates of regression coefficients as compared to OLS method.
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    ThesisItemOpen Access
    A study on simplified principal component analysis
    (CCSHAU, 2008) Kamlesh; Hooda, B.K.
    Principal component analysis though deduces dimensionality of the data, it suffers from the draw back that the each component is a linear combination of all the original variables and one has to interpret the result in terms of all the original variables. In the present study various techniques for obtaining simplified components have been described and critically reviewed. Best linear predictor (BLP) and corrected sum of variances (CSV) criterion have also been presented for determining the optimality of simple components with respect to the PCA which is considered the optimal solution. Simplified principal components simulated and real data sets were obtained through varimax rotation and as well as using simple component analysis algorithm proposed by Rousson and Gasser (2004) worked out compared with the ordinary principal components both in term of simplicity and optimality.
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    ThesisItemOpen Access
    Principal component analysis in modelling lactation milk yield in Hariana cows
    (CCSHAU, 2009) Deepak Singh; Saxena, K.K.
    A total of 244 first lactation records of Hariana cows maintained in the Department of Animal Breeding, C.C.S.H.A.U., Hisar over a period of 14 years (1989 to 2003) were analyzed. The first lactation traits used for multiple linear regression and principal component regression model were: first lactation milk yield (FLMY), age at first calving (AFC), first peak yield (FPY), first lactation length (FLL), first dry period (FDP), first service period (FSP) and first calving interval (FCI). The phenotypic correlations among explanatory variables were significant at 5 % level of significance. It gave an indication of multicollinearity. Using stepwise regression technique the maximum value of coefficient of determination was obtained as 0.648. The multicollinearity among different explanatory variables made it very difficult to identify the contribution of each explanatory variable. There were non-significant regression coefficients giving an indication of loosing information on some of important explanatory variables. Therefore principal component regression model was fitted. The phenotypic correlations among the traits were used to derive principal component scores and correlation coefficients of these variables with the original variables (component loadings) were analyzed. The first, second, third and fourth principal components (PC’s) explained 45.24, 25.70, 15.33 and 11.68 of total variation in the data. The first four PC’s explained 97.94 % of variance cumulatively. The correlations of first PC with AFC, FPY and FLL were positive ranging from 0.13 to 0.34, while it’s correlations with FDP, FSP and FCI were very high and negative ranging from -0.91 to -0.93. The correlations of second PC were positive with all the variables (ranging from 0.30 to 0.88) except FDP (-0.27). The third PC was positively correlated with all the variables except FPY (-0.47) while the fourth PC was positively correlated with AFC (0.33), FPY (0.58) and FDP (0.24) and negatively with FLL (-0.44), FSP (-0.03) and FCI (-0.01). The first PC can be interpreted as reproduction and production component, the second and fourth PC as production component and the third PC as maturity component. The number of meaningful PC’s were retained on the basis of Kaiser’s, Scree plot, Proportion of variance accounted for (only those PC’s are retained which account for at least 10 % of variation of data), Cumulative percent of variance accounted for (only those PC’s are retained which account for 85% to 90% of variation of data cumulatively) and Jollife (1972) criterions. When we regressed the retained PC’s on FLMY, PC’s retained on basis of “cumulative percent of variance accounted for” criterion gave best results. When we compare the stepwise regression results with the principal component regression model (when FLMY regressed on first three PC’s) we found that there is no significant change in R2 but in the principal component regression model there is contribution of each and every variable. So principal component regression model increases the accuracy and validity of the model.