Analysis of Sequential Observations with Applications to Experiments on Grazing Animals and Perennial Plants

Evans, John; Roberts, E. A.

doi:10.2307/2530262

Cited by 25 publications

(15 citation statements)

References 4 publications

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“…1) Stepwise use of the Grizzle and Allen test as in Evans and Roberts (1979) i.e. a series of multivariate analyses of variance of the p -q higher-order coefficients testing the hypothesis 8, = j,,, = .…”

Section: Procedures Based On the Grizzle And Allen Testmentioning

confidence: 99%

“…The standard test of adequacy of a polynomial of degree q-1 was given by Rao (1959) and generalised by Grizzle and Allen (1969). This test, which is a multivariate analysis of the coefficients of order zq, is given in Bock (1975, p. 461) and in Goldstein (1979) and was used by Evans and Roberts (1979) to fit polynomials to sequences of treatment contrasts in a designed experiment.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical comparison of some test procedures for determining model adequacy when fitting polynomial equations to sequences of observations

Roberts¹,

Raison²

1986

Journal of Statistical Computation and Simulation

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A number of procedures for testing adequacy of polynomial approximations to growth curves based on Rao's test for additional information, Grizzle and Allen's test --or univariate t-tests were compared using data simulated from quadratic models. Quadratic models were indicated as adequately fitting the data in 95.10k0.10 percent of analyses when the degree of the approximating polynomial was determined by the lowest-order significant coefficient (P=0.05) that was followed by two successive nonsignificant ones according to separate t-tests. Procedures based on the Grizzle and Allen test and modifications of it indicated quadratic models in 86.70k0.41 to 95.34 f 0.21 percent of analyses depending on error structure, variance and the number of coefficients analysed together. The t-test would be preferred in practice as its performance did not depend on the error structure or variance.

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Section: Procedures Based On the Grizzle And Allen Testmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical comparison of some test procedures for determining model adequacy when fitting polynomial equations to sequences of observations

Roberts¹,

Raison²

1986

Journal of Statistical Computation and Simulation

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“…One approach may be to model the deviations of each variety from the harvest means (Evans and Roberts 1979) rather than the actual means themselves. An alternative approach may be to model the genetic response over time.…”

Section: Introductionmentioning

confidence: 99%

Statistical methods for analysis of multi-harvest data from perennial pasture variety selection trials

Faveri¹,

Verbyla

Pitchford

et al. 2015

Crop Pasture Sci.

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Variety selection in perennial pasture crops involves identifying best varieties from data collected from multiple harvest times in field trials. For accurate selection, the statistical methods for analysing such data need to account for the spatial and temporal correlation typically present. This paper provides an approach for analysing multi-harvest data from variety selection trials in which there may be a large number of harvest times. Methods are presented for modelling the variety by harvest effects while accounting for the spatial and temporal correlation between observations. These methods provide an improvement in model fit compared to separate analyses for each harvest, and provide insight into variety by harvest interactions. The approach is illustrated using two traits from a lucerne variety selection trial. The proposed method provides variety predictions allowing for the natural sources of variation and correlation in multi-harvest data.

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“…For instance, Verbyla and Venables [6] demonstrated its wide applicability through some examples such as the longitudinal data from designed experiments. Earlier, Evans and Roberts [7] considered such a generalized growth curve model in an experiment analysis on grazing animals and perennial plants where the interest is the behavior of treatment effects over time (see also [3]). …”

Section: Introductionmentioning

confidence: 99%

Uniformly minimum variance nonnegative quadratic unbiased estimation in a generalized growth curve model

Wu¹,

Zou²,

Li³

2009

Journal of Multivariate Analysis

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a b s t r a c tConsider the generalized growth curve modelwhere B i are the matrices of unknown regression coefficients, and E = (ε 1 , . . . , ε s ) and ε j (j = 1, . . . , s) are independent and identically distributed with the same first four moments as a random vector normally distributed with mean zero and covariance matrix Σ. We derive the necessary and sufficient conditions under which the uniformly minimum variance nonnegative quadratic unbiased estimator (UMVNNQUE) of the parametric function tr(C Σ) with C ≥ 0 exists. The necessary and sufficient conditions for a nonnegative quadratic unbiased estimator y Ay with y = Vec(Y ) of tr(C Σ) to be the UMVNNQUE are obtained as well.

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Analysis of Sequential Observations with Applications to Experiments on Grazing Animals and Perennial Plants

Cited by 25 publications

References 4 publications

Numerical comparison of some test procedures for determining model adequacy when fitting polynomial equations to sequences of observations

Numerical comparison of some test procedures for determining model adequacy when fitting polynomial equations to sequences of observations

Statistical methods for analysis of multi-harvest data from perennial pasture variety selection trials

Uniformly minimum variance nonnegative quadratic unbiased estimation in a generalized growth curve model

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