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This article in CS

  1. Vol. 30 No. 4, p. 836-844
     
    Received: Feb 13, 1989
    Published: July, 1990


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doi:10.2135/cropsci1990.0011183X003000040014x

Adequacy of Interval Estimates of Yield Responses to Ozone Estimated from NCLAN Data

  1. M. C. Somerville,
  2. K. A. Dassel and
  3. J. O. Rawlings 
  1. Dep. of Statistics, Box 8208, North Carolina State Univ., Raleigh NC 27695-8203

Abstract

Abstract

Relative yield losses from O3 have been estimated by the National Crop Loss Assessment Network (NCLAN) using a nonlinear Weibull response model. The estimated losses were presented in terms of confidence interval estimates based on first-order linear approximations of variances and normality of estimates. Such interval estimates (Wald estimates) from nonlinear models can be inadequate. Nine Weibull response equations estimated from NCLAN studies were used to assess the adequacy of Wald confidence interval estimates by comparison with interval estimates based on the likelihood ratio test. Three response equations from individual studies were used for illustration of second-order adjustments to the Wald estimates and the use of measures of parameter-effects curvature as flags for cases where linear approximations may be inadequate. The Wald interval estimates were clearly inadequate in two of the three individual studies, which had been chosen to represent cases most likely to show inadequacy because of limited coverage of the response curve and/or high variability. In the third study, which had good coverage of the response curve and relatively low variability, the Wald confidence intervals were nearly identical to the likelihood ratio intervals. Measures of parameter effects curvature identified the two cases where the linear approximation was inadequate and showed whether the second-order adjustments would result in acceptable confidence intervals. Comparisons suggested that Wald confidence interval estimates provided satisfactory approximations for NCLAN response curves that had been computed from data involving more than one experiment, and even for individual experiments where there was adequate coverage of the response curve and moderate variability.

(Current addresses: M.C. Somerville, NSI Environmental Sciences, Research Triangle Park, NC 27709; J.O. Rawlings, Dep. of Statistics, Box 8203, North Carolina State Univ., Raleigh, NC 27695-8203; and K.A. Dassel, Merck, Sharp & Dohme Res. Lab., Rahway, PA 07065-0900).

Paper no. 12049 of the Journal Series of the North Carolina Agric. Res. Service, Raleigh, NC 27695-7643. Research partly supported by Interagency Agreement between the USEPA and the USDA: Interagency Agreement no. DW 12931347, and Specific Cooperative Agreement no. 58-43YK-6-0041 between the USDA and the North Carolina Agric. Res. Service. Although this research was partly funded by the USEPA, it has not been subjected to Agency review and therefore does not necessarily reflect the views of the Agency and no official endorsement should be inferred.

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