The Second order kronecker model for simplex-centroid design was fitted where data was for feed supplements blend using a mixture of soya beans, maize jam, cotton seed and fish meal guided by design points in the simplex-centroid design and the respose was the yield of milk in litres. The main objective was to fit a Kronecker model in the simplex-centroid design to formulate optimum dairy meal concentrates. Use the data to fit the second order kronecker model for four components simplex-centroid design. From the Kronecker regression function, coefficient matrix was derived from selected parameter subsystem of interest, moment matrix was then obtained. Information matrix and improved information matrix were derived. The collected data was fitted in the derived Kronecker model and the estimates of the parameters as well as overall model performance were numerically obtained. ANOVA was run to incorporate the constant term. From the analysis it was found that Kronecker model provided a good fit. Therefore the results support that the feed supplement had significant effect to milk productivity. For optimal production the research recommend that more than one ingredients need to be blend. Blends with soya beans and fish meal in two, three and four ingredients were statistically significant and therefore recommended for optimal milk production. From the ANOVA it was found that other factors not included in this study affect milk productivity and therefore the research recommends further studies be done to investigate those other factors such as the breeds, feeding practices and also effect of supplement to other dairy products.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 6, Issue 5) |
| DOI | 10.11648/j.ajtas.20170605.13 |
| Page(s) | 236-247 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Kronecker Model, Simplex-Centroid, Coefficient Matrix, Information Matrix
| [1] | J. A. Cornell. (2002). Experiments with Mixtures, Third Edition. John Wiley, New York. |
| [2] | J. Wegner & T. Stanton. (2006). Formulating ratios with Pearson square. http/www.ext.colostateedu.Pubs/livestock/01618.html |
| [3] | R. Rossi. (2004). Least cost formulation software: An introduction section: feature articles, Aqua feeds: formulation and beyond 3: 3-5. |
| [4] | R. G. Muriungi, J. K. Koske & J. M. Mutiso. (2017). Applying the Polynomial Model in Simplex- Centroid design to formulate the Optimum Dairy Feed. International Journal of Sciences: Basic and Applied Science. ISSN 2307-4531. PP. 101-117. |
| [5] | R. H. Myres, D. C. Montgomery, & C. M. Anderson. (2009), Response Surface Methodology, Wiley and sons, Hoboken New Jersey |
| [6] | G. W. Dean, D. L. Bath, & S. Olayada, (1969). Computer program for maximizing income above feed cost from dairy cattle. American science association journal |
| [7] | S. Chakeredza, F. K. Akinnifesi, C. O. Ajayi, G. Sileshi, S. Mngomba, & F. Gondwe. (2008), A simple method of formulating least-cost diets for smallholder dairy production in Sub-Saharan Africa. African journal of Biotechnology Vol 7 (16), pp 2925-2933 |
| [8] | D. Mahmut, S. T. Omer, A. Tugba, & G. Meryem. (2013) Optimization of Gum Combination in Prebiotic Instant Hot Chocolate Beverage Model System in terms of Rheological Aspect: Mixture Design Approach. Journal of Food and Bioprocess Technology Vol 6 pp 783-794 |
| [9] | L. C. Okpala, & E. C. Okoli. (2013) Optimization of Composite Biscuits Flour by Mixture Response Surface Methodology. Food Science and Technology International 19(4). |
| [10] | L. Shuanzhe, & N. Heinz. (1995) A V-optimal design for Scheffe polynomial model. Statistics and Probability Letters 23, pg 253-258 |
| [11] | J. K. Koske, J. K. Kinyanjui, J. M. Mutiso, & M. R. Cherutich. (2009), Designs with optimal values in the second degree Kronecker non-maximal model mixture experiments. American Journal of Mathematics and Mathematical Sciences vol 1 no. 2 pp 155-160. |
| [12] | D. W. Gaylor & H. C. Sweeny. (1965). Design for Optimal Prediction in Simple Linear Regression. Journal of the American Statistical Association. Vol 60, 1965 no. 309 pp 205-216. |
| [13] | R. L. J. Coetzer, & W. W. Focke. (2010). Optimal designs for estimating the parameters in weighted power-mean mixture models. |
| [14] | N. R. Draper, & F. Pukelsheim. (1999). Kiefer ordering of simplex designs for first- and second-degree mixture models. Journal of statistical planning and inference, 79, 325-348 |
| [15] | N. R. Draper, B. Heiligers, & P. Pukelsheim. (1998). Kiefer ordering of simplex designs for second-degree mixture models with four or more ingredients. Annals of statistics vol 28 no. 2 pg 578-590 |
| [16] | F. Pukelsheim. (1993). Optimal Design of Experiments, John Wiley & sons, Inc., New York. |
APA Style
Robert Muriungi Gitunga, Joseph Kipsigei Koske, Johnstonne Mutiso Muindi. (2017). Using the Second Order Kronecker Model in Simplex –Centroid Design in Formulating Optimum Dairy Feed. American Journal of Theoretical and Applied Statistics, 6(5), 236-247. https://doi.org/10.11648/j.ajtas.20170605.13
ACS Style
Robert Muriungi Gitunga; Joseph Kipsigei Koske; Johnstonne Mutiso Muindi. Using the Second Order Kronecker Model in Simplex –Centroid Design in Formulating Optimum Dairy Feed. Am. J. Theor. Appl. Stat. 2017, 6(5), 236-247. doi: 10.11648/j.ajtas.20170605.13
AMA Style
Robert Muriungi Gitunga, Joseph Kipsigei Koske, Johnstonne Mutiso Muindi. Using the Second Order Kronecker Model in Simplex –Centroid Design in Formulating Optimum Dairy Feed. Am J Theor Appl Stat. 2017;6(5):236-247. doi: 10.11648/j.ajtas.20170605.13
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Download@article{10.11648/j.ajtas.20170605.13,
author = {Robert Muriungi Gitunga and Joseph Kipsigei Koske and Johnstonne Mutiso Muindi},
title = {Using the Second Order Kronecker Model in Simplex –Centroid Design in Formulating Optimum Dairy Feed},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {6},
number = {5},
pages = {236-247},
doi = {10.11648/j.ajtas.20170605.13},
url = {https://doi.org/10.11648/j.ajtas.20170605.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170605.13},
abstract = {The Second order kronecker model for simplex-centroid design was fitted where data was for feed supplements blend using a mixture of soya beans, maize jam, cotton seed and fish meal guided by design points in the simplex-centroid design and the respose was the yield of milk in litres. The main objective was to fit a Kronecker model in the simplex-centroid design to formulate optimum dairy meal concentrates. Use the data to fit the second order kronecker model for four components simplex-centroid design. From the Kronecker regression function, coefficient matrix was derived from selected parameter subsystem of interest, moment matrix was then obtained. Information matrix and improved information matrix were derived. The collected data was fitted in the derived Kronecker model and the estimates of the parameters as well as overall model performance were numerically obtained. ANOVA was run to incorporate the constant term. From the analysis it was found that Kronecker model provided a good fit. Therefore the results support that the feed supplement had significant effect to milk productivity. For optimal production the research recommend that more than one ingredients need to be blend. Blends with soya beans and fish meal in two, three and four ingredients were statistically significant and therefore recommended for optimal milk production. From the ANOVA it was found that other factors not included in this study affect milk productivity and therefore the research recommends further studies be done to investigate those other factors such as the breeds, feeding practices and also effect of supplement to other dairy products.},
year = {2017}
}
TY - JOUR T1 - Using the Second Order Kronecker Model in Simplex –Centroid Design in Formulating Optimum Dairy Feed AU - Robert Muriungi Gitunga AU - Joseph Kipsigei Koske AU - Johnstonne Mutiso Muindi Y1 - 2017/09/08 PY - 2017 N1 - https://doi.org/10.11648/j.ajtas.20170605.13 DO - 10.11648/j.ajtas.20170605.13 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 236 EP - 247 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20170605.13 AB - The Second order kronecker model for simplex-centroid design was fitted where data was for feed supplements blend using a mixture of soya beans, maize jam, cotton seed and fish meal guided by design points in the simplex-centroid design and the respose was the yield of milk in litres. The main objective was to fit a Kronecker model in the simplex-centroid design to formulate optimum dairy meal concentrates. Use the data to fit the second order kronecker model for four components simplex-centroid design. From the Kronecker regression function, coefficient matrix was derived from selected parameter subsystem of interest, moment matrix was then obtained. Information matrix and improved information matrix were derived. The collected data was fitted in the derived Kronecker model and the estimates of the parameters as well as overall model performance were numerically obtained. ANOVA was run to incorporate the constant term. From the analysis it was found that Kronecker model provided a good fit. Therefore the results support that the feed supplement had significant effect to milk productivity. For optimal production the research recommend that more than one ingredients need to be blend. Blends with soya beans and fish meal in two, three and four ingredients were statistically significant and therefore recommended for optimal milk production. From the ANOVA it was found that other factors not included in this study affect milk productivity and therefore the research recommends further studies be done to investigate those other factors such as the breeds, feeding practices and also effect of supplement to other dairy products. VL - 6 IS - 5 ER -
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