Least-squares estimation of diet composition from n-alkanes in herbage and faeces using matrix mathematics

It is possible to estimate diet composition from an analysis of n-alkanes in the faeces of ruminant animals. For instance, to estimate the proportion of two species in a diet, two equations are constructed using the known concentrations of two different n-alkanes in the herbage and in the animal's faeces. These two equations are solved for the two unknown quantities of the diet components. Two problems exist with this method. First, it is often the case that we have estimated concentrations of more than two different n-alkanes. This can lead to a problem in deciding which two n-alkanes to use to construct the simultaneous equations. The choice of this pair of n-alkanes is arbitrary in its selection and wasteful of other useful information. The second problem is that sometimes the solution to the simultaneous equations yields nonsensical answers, such as a negative proportion of one species in the diet. In addition to making it difficult to estimate dietary proportions, estimating digestibility becomes impossible. In this paper, we present a technique which provides an estimate of the dietary proportions. This estimate uses information on all the n-alkanes available, and it has a very desirable property of being a least squares estimate. We also present a method for determining the least squares estimate subject to the constraint that all proportions must be non-negative. We provide examples for estimating the proportions of grass and clover in the diet of sheep and the digestibility of those diets.

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The sensitivity of n-alkane analysis to measurement error: implications for use in the study of diet composition

The Journal of Agricultural Science ◽

10.1017/s0021859698005930 ◽

1998 ◽

Vol 131 (4) ◽

pp. 465-476 ◽

Cited By ~ 11

Author(s):

J. A. NEWMAN ◽

F. CRIBARI-NETO ◽

M. J. JENSEN

Keyword(s):

Monte Carlo Simulation ◽

Measurement Error ◽

Diet Composition ◽

Simultaneous Equations ◽

The Other ◽

Analytical Error ◽

The Face ◽

Ruminant Animals ◽

Alkane Analysis

It is possible to estimate diet composition from an analysis of n-alkanes in the faeces of ruminant animals. The method requires the estimation of the concentrations of n-alkanes in the plants and faeces and then the solving of a system of simultaneous equations. There are at least three places in which significant measurement error may be introduced. First, there may be error in the determination of the concentrations of the n-alkanes in the herbage. This error may be the result of analytical error in the chemical analysis, or in the gathering of the representative sample of herbage. In either case, error in this estimate may be particularly important, since this estimate is not independently repeated for each animal in the study, but is conducted once and used throughout the study. Error may also be introduced in the estimates of digestibility of the n-alkanes themselves. The n-alkane method might be ideal if in fact the n-alkanes were completely indigestible – they are not and, furthermore, they are differentially digestible. Lastly, there may be measurement error in the estimate of the n-alkane concentrations in the faeces, which utilize the same analytical procedures that are used on the herbage. That is, if measurement error exists in the herbage estimates, it is quite possible that it also exists in the faeces estimates. We address these issues through the use of Monte Carlo simulation to investigate the likely effects of measurement error on diet composition and digestibility estimates obtained using the n-alkane method. Our results suggest the following conclusions: (1) in the face of any sort of measurement error, estimates of digestibility are likely to be unreliable; (2) when measurement error exists, one of the diet components will usually be under-estimated and the other will usually be over-estimated; (3) any sort of progressive bias in the n-alkane recovery estimates will probably have large and very significant effects on the results; and (4) if measurement error in the estimates of the n-alkane concentrations in the herbage and in the faeces are similar in expectation, then their effects tend to cancel each other out.

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CDSIMEQ: A Program to Implement Two-stage Probit Least Squares

The Stata Journal Promoting communications on statistics and Stata ◽

10.1177/1536867x0300300205 ◽

2003 ◽

Vol 3 (2) ◽

pp. 157-167 ◽

Cited By ~ 82

Author(s):

Omar M. G. Keshk

Keyword(s):

Least Squares ◽

Estimation Method ◽

Least Squares Estimation ◽

Simultaneous Equations ◽

The Other ◽

Endogenous Variable ◽

Standard Errors ◽

Two Stage ◽

Simultaneous Equations Models ◽

Endogenous Variables

The cdsimeq command implements the two-stage probit least squares estimation method described in Maddala (1983) for simultaneous equations models in which one of the endogenous variables is continuous and the other endogenous variable is dichotomous.1 The cdsimeq command implements all the necessary procedures for obtaining consistent estimates for the coefficients, as well as their corrected standard errors.

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The canonical least squares estimation of large-scale simultaneous-equations models

Economic Modelling ◽

10.1016/j.econmod.2007.04.012 ◽

2008 ◽

Vol 25 (2) ◽

pp. 191-200 ◽

Cited By ~ 1

Author(s):

Heejoon Kang

Keyword(s):

Least Squares ◽

Large Scale ◽

Least Squares Estimation ◽

Simultaneous Equations ◽

Simultaneous Equations Models

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Nonparametric Two-Stage Estimation of Simultaneous Equations with Limited Endogenous Regressors

Econometric Theory ◽

10.1017/s0266466600006605 ◽

1996 ◽

Vol 12 (2) ◽

pp. 305-330 ◽

Cited By ~ 9

Author(s):

Myoung-Jae Lee

Keyword(s):

Least Squares ◽

Nuisance Parameter ◽

Least Squares Estimation ◽

Simultaneous Equations ◽

Two Stage ◽

Infinite Dimensional ◽

Second Stage ◽

Endogenous Regressors ◽

Two Stage Least Squares ◽

Stage Estimation

Estimation of simultaneous equations with limited (or transformed) endogenous regressors has been difficult in the parametric literature for various reasons. In this paper, we propose a nonparametric two-stage method that is analogous to two-stage least-squares estimation. A simultaneous censored model is used to illustrate our approach, and then its generalization to other cases is developed. The technical highlight is in handling a nondifferentiable second-stage minimand with an infinite-dimensional first-stage nuisance parameter when the first-stage error is not orthogonal to the second.

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The Estimation of Blood Platelet Survival

Thrombosis and Haemostasis ◽

10.1055/s-0038-1649028 ◽

1972 ◽

Vol 28 (03) ◽

pp. 447-456 ◽

Cited By ~ 3

Author(s):

E. A Murphy ◽

M. E Francis ◽

J. F Mustard

Keyword(s):

Standard Deviation ◽

Least Squares ◽

Experimental Error ◽

Blood Platelet ◽

Least Squares Estimation ◽

Systematic Relationship ◽

Platelet Survival ◽

The Mean ◽

Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

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