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Modeling & Statistical Information

Topical Reviews

L.M. Pla. 2007.0. Livestock Sci.. 106.0:107-119 

This paper is a survey of the different sow models described in literature, which made use of different mathematical methodologies, and were intended for sow herd management. 
 

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A. Dumas; J. Dijkstra; J. France. 2008.0. J. Agr. Sci.. 146.0:123-142 

The current review aims to ascertain the ontogeny of current concepts, underline the connection between ideas and people and pay tribute to those pioneers who have contributed significantly to modeling in animal nutrition. 
 

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R.L. Baldwin and R.D. Sainz. 1995.0. Ann. Rev. Nut.. 15.0:191-211 

We first present a brief discussion of early and current models (feeding systems) used to estimate animal energy and protein requirements and to predict performance based on feed composition and intake. We then touch on some limitations inherent in these systems. Next, we propose that dynamic (i.e. time-variant) models and mechanistic models (i.e. equations based on knowledge of physiological functions) are superior to earlier systems for both practical and research applications. Finally, we describe a number of applied and research models of animal growth and lactation to illustrate how biological concepts may be represented in equation form. 
 

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Modeling Books

R.L. Baldwin. 1995.0. 

This book fills the gap in the available literature on modelling farm animal systems. This monograph has a broad and comprehensive coverage of ruminant systems and features the application of models in animal biology. It will be of great value to animal scientists, agricultural scientists, modelers and animal physiologists. 
 

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J. H. M. Thornley; J. France. 2007.0. 

Bringing together the disciplines of agriculture, animal science, plant science and ecology, this book explores how mathematics can be used to understand and explain agricultural processes. It starts by providing a review of the mathematical models currently available to agriculturalists, and the philosophy behind, and objectives of, modeling. The book then applies these techniques to real-life problems faced by people managing crops and animals, including the influence of digestion on growth rates and levels of photosynthesis on crop yield. 
 

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J. France; E. Kebreab. 

Mathematical modeling is increasingly applicable to the practical sciences. Here, mathematical approaches are applied to the study of mechanisms of digestion and metabolism in primary animal species. Farmed animals - ruminants, pigs, poultry and fish, are comprehensively covered, as well as sections on companion animals. Common themes between species, such as energy and amino acid metabolism, are explored with a worldwide approach. Leading researchers from around the world have contributed to France and Kebreab's volume to provide an integrated approach to mathematical modelling in animal nutrition. 
 

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J. A. Jacquez. 1985.0. 

Deals with basic linear and nonlinear systems and graph theory, distribution of tracer-labeled materials, connectivity and identifiability.

K. Godfrey. 1983.0.

L. Edelstein-Keshet. 1988.0. 

Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. Connections are made between diverse biological examples linked by common mathematical themes, exploring a variety of discrete and continuous ordinary and partial differential equation models. Although great advances have taken place in many of the topics covered, the simple lessons contained in Mathematical Models in Biology are still important and informative. Shortly after the first publication, the genomics revolution turned Mathematical Biology into a prominent area of interdisciplinary research. In this new millennium, biologists have discovered that mathematics is not only useful, but indispensable! As a result, there has been much resurgent interest in, and a huge expansion of, the fields collectively called Mathematical Biology. This book serves as a basic introduction to concepts in deterministic biological modelling 
 

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J. Dijkstra; J. M. Forbes; J. France. 2005.0. 

The first edition of this book, published in 1993, was well received as providing a comprehensive review of the digestion and metabolism of ruminant animals. Since its publication, much new research has been conducted in the subject and knowledge has increased. This is incorporated in this second edition through the addition of five completely new chapters. These cover: the gas production technique in feed evaluation, calorimetry, the relationship between pasture characteristics and animal performance, feed processing and the integration of data in feed evaluation systems. Other chapters have been fully expanded and updated as appropriate and Dr. Dijkstra has also been enrolled as the lead editor. This book brings together quantitative approaches used in the study of mechanisms of ruminant digestion and metabolism. 
 

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M. E. Wastney; B.H. Patterson; O.A. Linares; P.C. Greif; R.C. Boston.. 1999.0. 

This book discusses in a hands-on approach how to use mathematical modeling to investigate biological systems. It is written for students and investigators in lay person terms. Examples are used from the fields of physiology, biochemistry, nutrition, agriculture, pharmacology and medicine. 
 

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Ford, A.. 2009.0. 

Modeling the Environment was the first textbook in an emerging field - the modeling techniques that allow managers and researchers to see in advance the consequences of actions and policies in environmental management. This new edition brings the book thoroughly up to date and reaffirms its status as the leading introductory text on the subject. Systems dynamics is one of the most widely known and widely used methods of modeling. The fundamental principles of this approach are demonstrated here with a wide range of examples, including geo-hydrology, population biology, epidemiology and economics. The applications demonstrate the transferability of the systems approach across disciplines, across spatial scales, and across time scales. All of the models are implemented with stock and flow software programs such as Stella and Vensim. These programs are easy and fun to learn, and they allow students to develop realistic models within the first few weeks of a college course. 
 

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J.W. Haefner. 2005.0. 

This is the second edition of a textbook currently published by Springer for a course in mathematical modeling and computer simulation for biologists at the advanced undergraduate and introductory graduate level. The audience for this edition is similar to that of the previous one: advanced level courses in computational biology, as well as researchers retooling themselves 
 

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B. Hannon; M. Ruth. 1997.0. 

Models help us understand the dynamics of real-world processes by using the computer to mimic the actual forces that are known or assumed to result in a system's behavior. This book does not require a substantial background in mathematics or computer science. 
 

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A.M. Law. 2007.0. 

Since the publication of the first edition in 1982, the goal of Simulation Modeling and Analysis has always been to provide a comprehensive, state-of-the-art, and technically correct treatment of all important aspects of a simulation study. The book strives to make this material understandable by the use of intuition and numerous figures, examples, and problems. It is equally well suited for use in university courses, simulation practice, and self study. This book in widely regarded as the \"bible\" of simulation and now has more than 100,000 copies in print. The book can serve as the primary text for a variety of courses.

J.D. Sterman. 2000.0. 

The leading authority on system dynamics explains this approach to organizational problem solving, emphasizing simulation models to understand issues such as fluctuating sales, market growth and stagnation, the reliability of forecasts and the rationality of business decision-making. The CD includes modeling software from Vensim, ithink, and PowerSim.

E. Kebreab; J. Dijkstra; W.J.J. Gerrits; A. Bannink, J. France. 2006.0. 

The book brings together the papers presented orally or as posters at the Sixth International Workshop on Modelling Nutrient Utilization in Farm Animals, held in Wageningen, The Netherlands, 6 - 8 September 2004. The purpose of this book is to present current research in modeling nutrient digestion and utilization in cattle, sheep, pigs, poultry and fish. The book is organized into six sections that cover a range of topics and modeling approaches; these are (I) adsorption and passage; (ii) growth and development; (iii) mineral metabolism; (iv) methodology; (v) environmental impact; and (vi) animal production and feed evaluation. Deterministic, stochastic, empirical and mechanistic modeling approaches are described. This book will be of significant interest to researchers and students of animal science, particularly those concerned with nutrition modeling. 
 

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Model Descriptions

Growth:

Dairy

J. Dijkstra; J. France; M.S. Dhanoa; J.A. Maas; M.D. Hanigan; A.J. Rook; D.E. Beever. 1997.0. J. Dairy Sci.. 80.0:2340-2354 

In this study, a mechanistic model was developed that yielded a single equation to describe the pattern of mammary growth of mammals throughout pregnancy and lactation.

D.G. Fox; M.E. Vn Amburgh; T.P Tylutki. 1999.0. J. Dairy Sci.. 82.0:1968-1977 

The 1996 National Research Council Nutrient Requirements of Beef Cattle equations used to compute growth requirements, target weights, and energy reserves were modified and evaluated for use with dairy cattle. 
 

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Swine

Strathe, A. B., H. Jørgensen, E. Kebreab and A. Danfær.. 2012.0. J. Agric. Sci.. 150::764-774 

The objective of the current study was to develop Bayesian simultaneous equation models for modelling energy intake and partitioning in growing pigs 
 

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D. Bastianelli, D. Sauvant, A. Rerat. 1996.0. J. Anim. Sci.. 74.0:1873- 

A simple simulation model of digestion and absorption in pigs was developed. 
 

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S. Birkett and K. de Lange. 2001.0. Br. J. Nutr.. 86.0:661- 

A computational framework to represent nutrient utilization for body protein and lipid accretion by growing monogastic animals in presented. 
 

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Beef

J.W. Oltjen; A.C. Bywater; R.L Baldwin; W.N. Garrett. 1986.0. J. Anim. Sci.. 62.0:86-97 

A dynamic model of postweaning growth and composition of the beef steer has been developed 
 

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T. Hoch; J. Agabriel. 2004.0. Ag. Syst.. 81.0:1-15 

A mechanistic and dynamic model was designed and constructed to simulate beef cattle growth and related body composition for different animal types under various nutritional conditions. 
 

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L.O. Tedeschi; D.G. Fox; P.J. Guiroy. 2004.0. Ag. Syst.. 79.0:171-204 

A deterministic and mechanistic growth model was developed to dynamically predict growth rate, accumulated weight, days required to reach target body composition, carcass weight (CW) and composition of individual beef cattle for use in individual cattle management systems. 
 

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Poultry

E. Kebreab; J. France; R. P. Kwakkel; S. Leeson; H. Darmani Kuhi ; J. Dijkstra. 2009.0. Poult. Sci.. 88.0:680–689 

A new dynamic and mechanistic model of P and Ca metabolism in layers has been developed to simulate diurnal changes in Ca and P and the hourly requirement of the layer for those minerals. 
 

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H.A. Ahmad. 2011.0. J. Appl. Poult. Res.. 18.0:440-446 

Paper objectives: to simulate data using published literature for different growth periods, and to develop artificial intelligence models with various neural network architectures 
 

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Small Ruminants

J.D. Finlayson; O.J. Cacho; A.C. Bywater. 1995.0. Ag. Syst.. 48.0:1-25 

This paper is the first in a series that presents the development and use of a quantitative model of a sheep grazing system. 
 

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A. Cannas; L.O. Tedeschi; D.G. Fox; A.N. Pell; P.J. Van Soest. 2004.0. J. Anim. Sci.. 82.0:149-169 

The Cornell Net Carbohydrate and Protein System (CNCPS), a mechanistic model that predicts nutrient requirements and biological values of feeds for cattle, was modified for use with sheep. Published equations were added for predicting the energy and protein requirements of sheep, with a special emphasis on dairy sheep, whose specific needs are not considered by most sheep-feeding systems.

L.O. Tedeschi; A. Cannas; D.G. Fox. 2010.0. Small Ruminant Res.. 89.0:174-184 

A mechanistic model that predicts nutrient requirements and biological values of feeds for sheep (Cornell Net Carbohydrate and Protein System; CNCPS-S) was expanded to include goats and the name was changed to the Small Ruminant Nutrition System (SRNS). 
 

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Lactation:

Dairy

J. Dijkstra; J. France; M.S. Dhanoa; J.A. Maas; M.D. Hanigan; A.J. Rook; D.E. Beever. 1997.0. J. Dairy Sci.. 80.0:2340-2354 

In this study, a mechanistic model was developed that yielded a single equation to describe the pattern of mammary growth of mammals throughout pregnancy and lactation.

D.G. Fox; M.E. Vn Amburgh; T.P Tylutki. 1999.0. J. Dairy Sci.. 82.0:1968-1977 

The 1996 National Research Council Nutrient Requirements of Beef Cattle equations used to compute growth requirements, target weights, and energy reserves were modified and evaluated for use with dairy cattle. 
 

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Swine

A.V. Hansen; A. B. Strathe; E. Kebreab; P.K. Theil.. 2012.0. J. Anim. Sci.. 90.0:2285–2298 

The objective of this study was to develop a framework describing the milk production curve in sows as affected by parity, method of milk yield (MY) determination, litter size (LS), and litter gain (LG). 
 

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J.E. Pettigrew; M. Gill; J. France; W.H. Close. 1992.0. J. Anim. Sci.. 70.0:3762-3773 

A mathematical model of lactating sow metabolism was evaluated using three types of tests. 
 

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Beef

W.D. Hohenboken; A. Dudley; D.E. Moody. 1992.0. Anim. Prod.. 55.0:23-28 

Four published equations to characterize individual lactation curves were compared against monthly and fortnightly milk production records from 59 autumn-calving Angus and AngusxHolstein crossbred cows. 
 

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Gestation:

Swine

J.Y. Dourmad; M. Etienne; A. Valancogne; S. Dubois; J. van Milgren; J. Noblet. 2008.0. Anim. Feed Sci. and Tech.. 143.0:372-286 

The objective of this project was to integrate the current state of knowledge in a nutritional model for growing pigs and for sows and make it available as a software tool to end-users, mainly nutritionists involved in the pig industry and students in animal nutrition. The aim of this paper is to describe the basis of the sow model.

C.T. Whittemore; C.A. Morgan. 1990.0. Livestock Prod. Sci.. 26.0:1-37 

Factorial and empirical data from recent work at various research centers provide a quantitative information resource from which nutrient response models may be constructed. 
 

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Grazing:

Beef

M. Freer; A.D. Moore; J.R. Donnelly. 1997.0. Agr. Syst.. 54.0:77-126 

This paper specifies the animal biology module of a model for simulating grazing systems for ruminants on pasture. 
 

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B.B. Baker; R.M. Bourdon; J.D. Hanson. 1992.0. Ecol. Model.. 60.0:257-279 

The model predicts forage intake and diet selection of grazing beef cattle by simulating the mechanistic components of grazing behavior. 
 

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M.W. Tess and B.W. Kolstad. 2000.0. J. Anim. Sci. 78.0:1159-1169 

The objective of this report was to describe the rationale and procedures used to simulate animal and system performance. 
 

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Dairy

A. Rotz; D.R. Buckmaster; D.R. Mertens; J.R. Black. 1989.0. J. Dairy Sci.. 72.0:3050-3063 

The DairyWise model is an empirical model that simulated technical, environmental, and financial processes on a dairy farm. 
 

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J. Baudracco; N. Lopex-Villalobos; C.W. Holmes; E.A. Comeron; K.A. Macdonald; T.N. Barry; N.C. Friggens. 2012.0. Animal. 6.0:980-993 

The model integrates algorithms from three previously published models: a model that predicts herbage dry matter (DM) intake by grazing dairy cows, a mammary gland model that predicts potential milk yield and a body lipid model that predicts genetically driven live weight (LW) and body condition score (BCS).

P. Faverdin; C. Baratte; R. Delagarde; J.L. Peyraud. 2011.0. Grass For. Sci.. 66.0:29-44 

This article presents a model predicting voluntary dry matter intake and milk production by lactating cows fed indoors. This model, with an extension to predict herbage intake at grazing presented in a second article, is used in the Grazemore decision support system.

P. Gregorini; P.C. Beukes; A.J. Romera; G. Levy; M.D. Hanigan. 2013.0. Ecol. Model.. 270.0:11-29 

The objective of the work was to describe the diurnal grazing pattern, including ingestive actions and rumination behaviors, herbage intake, and nutrient supply to the animal in response to the animal's internal state and grazing environment. 
 

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Farm systems:

Dairy

Hill, S. R., K. F. Knowlton, E. Kebreab, J. France, and M. D. Hanigan. 2008.0. J Dairy Sci.. 91.0:2021–2032 

A dynamic, mechanistic, compartmental model of phosphorus (P) digestion and metabolism was constructed in the Advanced Continuous Simulation Language using conservation of mass principles and mass action kinetics.

Ellis, J. L., E. Kebreab, N.E. Odongo, B. W. McBride, E. K. Okine, and J. France.. 2007.0. J. Dairy Sci.. 90.0:3456-3467 

Eighty-three beef and 89 dairy data sets were collected and used to develop statistical models of CH4 production using dietary variables.

C.A. Rotz; D.R. Buckmaster; J.W. Comerford. 2005.0. J. Anim. Sci.. 83.0:231-242 

A beef herd submodel was created for integration with other farm components to form a whole-farm model capable of simulating a wide range of beef production systems. 
 

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Kebreab, E., K. A. Johnson, S. L. Archibeque, D. Pape, and T. Wirth. 2008.0. J. Anim. Sci.. 86.0:2738-2748 

Two empirical and 2 mechanistic models (COWPOLL and MOLLY) were evaluated for their prediction ability using individual cattle measurements. 
 

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R.L.M. Schils; M.H.A. de Haan; J.G.A. Hemmer; A. van der Pol-van Dasselaar; J.A. de Boer; A.G. Evers; G. Holshof; J.C. van Middelkoop; R.L.G. Zom. 2007.0. J. Dairy Sci.. 90.0:5334-5346 

The DairyWise model is an empirical model that simulated technical, environmental, and financial processes on a dairy farm. 
 

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L. Shalloo; P. Dillon; M. Rath; M. Wallace. 2004.0. J. Dairy Sci.. 87.0:1945-1959 

A stochastic budgetary simulation model of a dairy farm was developed to allow investigation of the effects of varying biological, technical and physical processes on farm profitability. 
 

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P. Crosson; P. O'Kiely; F.P. O'Mara; M. Wallace. 2006.0. Agr. Syst.. 89.0:349-370 

A mathematical model, the Grange Beef model, is presented and used to identify optimal beef production systems in Ireland. 
 

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Model Evaluation Methods:

Residuals Analyses:

St-Pierre, N. R.. 2003.0. J. Dairy Sci.. 86.0:344-350 

The objectives of this paper are: 1) to derive the expected relationship between residuals, Y, and Yhat; 2) to determine whether Y or Yhat should be used for the assessment of bias; and 3) to reassess the extent of mean and linear bias in the prediction of N flows to the duodenum by the NRC (2001) 
 

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A.R. Pagan; A.D. Hall. 1983.0. Econ. Rev.. 2.0:159-218 

The present paper derives the formal statistics by concentrating upon the distribution of residuals. 

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R.D. Cook and S. Weisberg. 1982.0. Chapman and Hall, New York NY. 
 

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Sensitivity Analyses:

G. Bellocchi; M. Rivington; M. Bonatelli; K. Matthews.. 2010.0. Agron. Sustain. Dev.. 30.0:109-130 

Here we review validation issues and methods currently available for assessing the quality of biophysical models. The review covers issues of validation purpose, the robustness of model results, data quality, model prediction and model complexity. The importance of assessing input data quality and interpretation of phenomena is also addressed. 
 

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D. G. Altman; J.M. Bland. 1983.0. The Statistician. 32.0:307-317 

Methods of analysis used in the comparison of two methods of measurement are reviewed. The use of correlation, regression and the difference between means is criticized. A simple parametric approach is proposed based on analysis of variance and simple graphical methods.

L.O. Tedeschi. 2006.0. Ag. Syst.. 89.0:225-247 

In this paper we discussed and compared several techniques to evaluate mathematical models designed for predictive purposes.

R. G. Sargent. 1985.0. Winter Simulation Conference. :15-22 

In this expository paper we give a general introduction to verification and validation of simulation models, define the various validation techniques, and present a recommended validation procedure 
 

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R.G. Sargent. 1991.0. Winter Simulation Conference, Syracuse, NY. :37-47 

This paper discusses verification and validation of simulation models. 
 

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E.J. Rykiel. 1996.0. Ecol. Model.. 90.0:229-244 

The ecological literature reveals considerable confusion about the meaning of validationin the context of simulation models. This paper works to clarify that confusion. 
 

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Model Fitting Methods:

A.B. Strathe; A. Danfær; A. Chwalibog; H. Sørensen; E. Kebreab. 2010.0. J. Anim. Sci.. 88.0:2361-2372 

The study developed a multivariate nonlinear mixed effects (MNLME) framework and compared it with an alternative method for estimating parameters in simultaneous equations that described energy metabolism in growing pigs, and then proposed new PD and LD equations. 
 

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Z. Wang; L.A. Goonewardene. 2004.0. Can. J. Anim. Sci.. 84.0:1-11 

The objective of this paper is to provide a background understanding of mixed model methodology in a repeated measures analysis and to use balanced steer data from a growth study to illustrate the use of PROC MIXED in the SAS system using five covariance structures. 
 

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J.D. Hadfield. 2010.0. J. Stat. Software. 33.0:1-22 

Generalized linear mixed models provide a flexible framework for modeling a range of data, although with non-Gaussian response variables the likelihood cannot be obtained in closed form. Markov chain Monte Carlo methods solve this problem by sampling from a series of simpler conditional distributions that can be evaluated. The R package MCMC-glmm, implements such an algorithm for a range of model fitting problems. 
 

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B.P. Carlin; S. Chib. 1995.0. J. Royal Stat. Soc.. 57.0:473-484 

In this paper we present a framework for Bayesian model choice, along with an MCMC algorithm that does not suffer from convergence difficulties 
 

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A.E. Raftery; D. Madigan; J.A. Hoeting. 1997.0. J. Am. Stat. Assn.. 92.0:179-191 

We consider the problem of accounting for model uncertainty in linear regression models 
 

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A. Tarantola. 2005.0. Society for Industrial and Applied Mathematics, Philadelphia, PA. 
 

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Experimental Design

J. Neter; M.H. Kutner; C.J. Nachtsheim; W. Wasserman. 1996.0. McGraw-Hill Publishing Co. Boston, MA. 

There are two approaches to undergraduate and graduate courses in linear statistical models and experimental design in applied statistics. One is a two-term sequence focusing on regression followed by ANOVA/Experimental design. Applied Linear Statistical Models serves that market. It is offered in business, economics, statistics, industrial engineering, public health, medicine, and psychology departments in four-year colleges and universities, and graduate schools. Applied Linear Statistical Models is the leading text in the market. It is noted for its quality and clarity, and its authorship is first-rate. The approach used in the text is an applied one, with an emphasis on understanding of concepts and exposition by means of examples. Sufficient theoretical foundations are provided so that applications of regression analysis can be carried out comfortably. The fourth edition has been updated to keep it current with important new developments in regression analysis

H. Toutenburg. 2009.0. Springer, New York, NY. 

This book is the third revised and updated English edition of the German textbook \\Versuchsplanung und Modellwahl\" by Helge Toutenburg which was based on more than 15 years experience of lectures on the course \\- sign of Experiments\" at the University of Munich and interactions with the statisticians from industries and other areas of applied sciences and engineering. This is a type of resource/ reference book which contains statistical methods used by researchers in applied areas. Because of the diverse examples combined with software demonstrations it is also useful as a textbook in more advanced courses, The applications of design of experiments have seen a significant growth in the last few decades in different areas like industries, pharmaceutical sciences, medical sciences, engineering sciences etc. The second edition of this book received appreciation from academicians, teachers, students and applied statisticians. As a consequence, Springer-Verlag invited Helge Toutenburg to revise it and he invited Shalabh for the third edition of the book. In our experience with students, statisticians from industries and researchers from other fields of experimental sciences, we realized the importance of several topics in the design of experiments which will increase the utility of this book. Moreover we experienced that these topics are mostly explained only theoretically in most of the available books 
 

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R.A. Johnson; D.W. Wichern. 2007.0. Prentice Hall, Upper Saddle River, NJ. 

This market leader offers a readable introduction to the statistical analysis of multivariate observations. Gives readers the knowledge necessary to make proper interpretations and select appropriate techniques for analyzing multivariate data. Starts with a formulation of the population models, delineates the corresponding sample results, and liberally illustrates everything with examples.  Offers an abundance of examples and exercises based on real data.  Appropriate for experimental scientists in a variety of disciplines 
 

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R.O. Kuehl. 1999.0. Duxbury Press New York NY. 

Robert Kuehl's DESIGN OF EXPERIMENTS, Second Edition, prepares students to design and analyze experiments that will help them succeed in the real world. Kuehl uses a large array of real data sets from a broad spectrum of scientific and technological fields. This approach provides realistic settings for conducting actual research projects. Next, he emphasizes the importance of developing a treatment design based on a research hypothesis as an initial step, then developing an experimental or observational study design that facilitates efficient data collection. In addition to a consistent focus on research design, Kuehl offers an interpretation for each analysis.

M.H. Kutner; C.J. Nachtsheim; J. Neter; W. Li. 2004.0. McGraw-Hill Publishing Co. Boston, MA. 

Applied Linear Statistical Models 5e is the long established leading authoritative text and reference on statistical modeling, analysis of variance, and the design of experiments. For students in most any discipline where statistical analysis or interpretation is used, ALSM serves as the standard work. The text proceeds through linear and nonlinear regression and modeling for the first half, and through ANOVA and Experimental Design in the second half. All topics are presented in a precise and clear style supported with solved examples, numbered formulae, graphic illustrations, and \"Comments\" to provide depth and statistical accuracy and precision. Applications used within the text and the hallmark problems, exercises, projects, and case studies are drawn from virtually all disciplines and fields providing motivation for students in virtually any college. The Fifth edition provides an increased use of computing and graphical analysis throughout, without sacrificing concepts or rigor. In general, the 5e uses larger data sets in examples and exercises, and the use of automated software without loss of understanding.

Experimental Analyses

N. R. St-Pierre; W. P. Weiss.. 2009.0. J. Dairy Sci.. 92.0:4581-4588 

The objective of this technical note is to explain the construction of a CCD and its statistical analysis using the Statistical Analysis System 
 

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R.L. Mason; R.F. Gunst; J.L Hess. 2003.0. John Wiley and Sons Inc. Hoboken, NJ. 

Statistical Design and Analysis of Experiments is intended to be a practitioner's guide to statistical methods for designing and analyzing experiments. 
 

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This book is about planning and conducting experiments and about analyzing the resulting data so that valid and objective conclusions are obtained. 
 

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Meta Analyses

N. R. St-Pierre. 2001.0. J. Dairy Sci.. 84.0:741-755. 

The purpose of this review is to help show how improved mathematical and statistical tools and computer technology can help us gain more accurate information from published studies and improve future research. 
 

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W. Arthur Jr; W. Bennett Jr; A.I. Huffcutt. 2001.0. Lawrence Erlbaum Associates. l 

Conducting Meta-Analysis Using SAS reviews the meta-analysis statistical procedure and shows the reader how to conduct one using SAS. It presents and illustrates the use of the PROC MEANS procedure in SAS to perform the data computations called for by the two most commonly used meta-analytic procedures, the Hunter & Schmidt and Glassian approaches. 
 

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L.V. Hedges; I. Olkin.. 1985.0. Academic Press, San Diego CA. 

The main purpose of this book is to address the statistical issues for integrating independent studies. There exist a number of papers and books that discuss the mechanics of collecting, coding and preparing data for a meta-analysis, and we do not deal with these. 
 

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J.E. Hunter; F.L. Schmidt.. 2014.0. SAGE, London, UK. 

Designed to provide researchers clear and informative insight into techniques of meta-analysis, the Third Edition of Methods of Meta-Analysis: Correcting Error and Bias in Research Findings is the most comprehensive text on meta-analysis available today. It is the only book that presents a full and usable treatment of the role of study artifacts in distorting study results, as well as methods for correcting results for such biases and errors 
 

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G.V. Glass. 1976.0. Educ. Res.. 10.0:3-8 

Noted at the original proposal of meta-analysis 
 

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I.J. Lean; A.R. Rabiee; R.F. Duffield; I.R. Dohoo. 2009.0. J. Dairy Sci.. 92.0:3545-3565 

Review of the need to more meta-analyses in animal research 
 

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R.J. Light; D.B Pillemer. 1984.0. Harvard University Press, Cambridge, MA. 
 

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M. Egger; G. Davey Smith; M. Schneider; C. Minder. 1997.0. BMJ. 315.0:629-634 

Explains the use of a funnel plot for assessing sampling bias in data used for meta-analysis

R.M. Harbord; J.P.T. Higgins. 2008.0. Stata J.. 8.0:493-519 

Detailed explanation of the metareg command in STATA 
 

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D.A. Harville. 1977.0. J. Am. Stat. Assoc. 72. 723.0:320-338 

Explanation of REML approaches 
 

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S.G. Thompson; S.J. Sharp. 1999.0. Stat. Med.. 18.0:2693-2708 

A comparison of methods to account for heterogeneity in meta-analyses 
 

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W.H. DuMouchel; J.E. Harris. 1983.0. J. Am Stat. Assoc.. 78.0:293-308 

Explains a Bayesian fitting procedure for meta-analysis studies 
 

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D. Sauvant; P. Schmidely; J.J. Daudin; N.R. St-Pierre. 2008.0. animal. 2.0:1203-1214 

Reviews the importance and appropriate uses for meta-analyses in animal nutrition research

Modeling Websites

L.O. Tedeschi and the Ruminant Nutrition Laboratory of the Texas A&M Department of Animal Science. 2006.0. 

This website provides a synopsis of mathematical nutrition models and their use in livestock management. Specific models, decision support tools and calculators including: (1) the Ruminant Nutrition System, (2) the Large Ruminant Nutrition System, (3) the Small Ruminant Nutrition System, (4) the Cattle Value Discovery System, (5) the Model Evaluation System, (6) the GnG1 Degradation and Passage Models, (7) The Gas Production Fitting System, (8) the Neutral Detergent Fiber Fractional Rate Calculator, (9) the Meal Criterion Calculation, (10) the Hay Game, and (11) the Nim Game are described and available for download. 
 

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L.O. Tedeschi and D.G. Fox. 2014.0. 

This website gives a comprehensive history of applied nutrition models and their use as decision support systems. The advancement and development of nutrition models aimed at improving prediction of animal requirements, nutrient availability and production efficiency is outlined and the co-development of laboratory analytical procedures with these nutrition models is highlighted. Future directions for nutrition modeling are proposed. 
 

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