Lack-of-Fit Testing When Replicates are Not Available

Joglekar, Gitanjali; Schuenemeyer, John H.; LaRiccia, V. N.

doi:10.1080/00031305.1989.10475641

Cited by 13 publications

(5 citation statements)

References 9 publications

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“…This provided the sum of squares of the total error for each model. As no replicates were available, the ‘near replicates’ method (Joglekar et al , 1989) was used to obtain the sum of squares of the pure error of our dataset. Lack of fit and its probability could then be calculated.…”

Section: Methodsmentioning

confidence: 99%

Hierarchical saturation of soil carbon pools near a natural CO₂ spring

Kool

Chung

Tate

et al. 2007

Global Change Biology

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Soil has been identified as a possible carbon (C) sink to mitigate increasing atmospheric CO 2 concentration. However, several recent studies have suggested that the potential of soil to sequester C is limited and that soil may become saturated with C under increasing CO 2 levels. To test this concept of soil C saturation, we studied a gley and organic soil at a grassland site near a natural CO 2 spring. Total and aggregate-associated soil organic C (SOC) concentration showed a significant increase with atmospheric CO 2 concentration. An asymptotic function showed a better fit of SOC and aggregation with CO 2 level than a linear model. There was a shift in allocation of total C from smaller size fractions to the largest aggregate fraction with increasing CO 2 concentration. Litter inputs appeared to be positively related to CO 2 concentration. Based on modeled function parameters and the observed shift in the allocation of the soil C from small to large aggregate-size classes, we postulate that there is a hierarchy in C saturation across different SOC pools. We conclude that the asymptotic response of SOC concentration at higher CO 2 levels indicates saturation of soil C pools, likely because of a limit to physical protection of SOC.

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Section: Methodsmentioning

confidence: 99%

Hierarchical saturation of soil carbon pools near a natural CO₂ spring

Kool

Chung

Tate

et al. 2007

Global Change Biology

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“…It is extremely interesting to note that this is precisely the same numerator sum of squares as used by Shillington (1979), Neill and Johnson (1985) and Joglekar et al (1989). The tests differ from the UMPI between clusters test in that they use different denominator sums of squares hence different estimates of (Tz.…”

Section: The Umpi Test For Orthogonal Lack Of Fit Between Clustersmentioning

confidence: 96%

“…The UMPI tests are Christensen (1989), Atwood and Ryan (1977) and the new test. Shillington's (1979) test ignores C(M*) and Joglekar et al's (1989) test ignores both C(M*) and C(Mp -M xz ) .…”

Section: The Umpi Test For Orthogonal Lack Of Fit Between Clustersmentioning

confidence: 99%

“…There is no such agreement when the clusters consist of near replicates. Various ad hoc tests have been proposed by Shillington (1979), Draper and Smith (1981), Neill andJohnson (1984, 1985), Joglekar, Schuenemeyer, and LaRiccia (1989), and Atwood and Ryan (1977). Recently, Christensen (1989) introduced the concepts of between-cluster and within-cluster lack of fit which allow the theoretical evaluation of near replicate lack-of-fit tests and the construction of optimal tests.…”

Section: Introduction and Notationmentioning

confidence: 98%

“…Christensen's (1989) test has F = 2.282 with P value .109. Neither the Joglekar et al (1989) nor the Atwood and Ryan (1977) tests are defined.…”

Section: Introduction and Notationmentioning

confidence: 99%

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Small-Sample Characterizations of near Replicate Lack-of-Fit Tests

Christensen

1991

Journal of the American Statistical Association

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Several ad hoc tests based on near replicates have been proposed for testing lack of fit in regression analysis. Christensen characterized lack of fit as existing between clusters of near replicates, within clusters, or as a combination of these pure types. Of these, the between-cluster variety is the type commonly associated with the idea of lack of fit. Christensen examined a test that was new to the normal theory regression literature and established uniformly most powerful invariant (UMPI) properties of the test. In particular, the test is UMPI for orthogonal lack of fit within clusters. In this article, a new test is proposed that is UMPI for orthogonal lack of fit between clusters. The relationship of this optimal test to other proposed tests is examined, giving the first small-sample theoretical justification for these tests. The power of the new test is compared to that of others in the literature, and consistency results are discussed.

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