Abstract
We review a range of lack-of-fit tests suitable for assessing the appropriateness of the mean function in dose-response models. The review encompasses both well-known tests and new tests based on recent developments in statistics, which we have extended to the dose-response case. We argue that the classical methods are inadequate in certain situations, where the new tests may be applied. Power comparisons are carried out by means of extensive simulation studies, covering both designs with and without replicates at small and large sample sizes. Three datasets from dose-response applications illustrate differences and similarities between the tests. The results suggest that the new tests perform better and exhibit a wider applicability.
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References
Bates DM, Watts DG (1988) Nonlinear regression analysis and its applications. Wiley, New York
Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edn. Springer, New York
Canada Environment (2005) Guidance document on statistical methods for environmental toxicity tests, Environment Canada, Ottawa
Carroll RJ, Ruppert D (1988) Transformation and weighting in regression. Chapman and Hall, New York
Cedergreen N, Ritz C, Streibig JC (2005) Improved empirical models describing hormesis. Environ Toxicol Chem 24: 3166–3172
Christensen AM, Ingerslev F, Baun A (2006) Ecotoxicity of mixtures of antibiotics used in aquacultures. Environ Toxicol Chem 25: 2208–2215
Draper NR, Smith H (1966) Applied regression analysis. Wiley, New York
Huet S, Bouvier A, Poursat M-A, Jolivet E (2004) Statistical tools for nonlinear regression: a practical guide with S-PLUS and R examples, 2nd edn. Springer, New York
Kent JT (1986) The underlying structure of nonnested hypothesis tests. Biometrika 73: 333–343
Lin DY, Wei LJ, Ying Z (1993) Checking the cox model with cumulative sums of martingale-based residuals. Biometrika 80: 557–572
Lin DY, Wei LJ, Ying Z (2002) Model-checking techniques based on cumulative residuals. Biometrics 58: 1–12
López S, France J, Gerrits WJJ, Dhanoa MS, Humphries DJ, Dijkstra J (2000) A generalized Michaelis-Menten equation for the analysis of growth. J Anim Sci 78: 1816–1828
Miller FR, Neill JW, Sherfey BW (1999) Implementation of a maximin power clustering criterion to select near replicates for regression lack-of-fit tests. J Am Stat Assoc 94: 610–620
Mizon GE, Richard J-F (1986) The encompassing principle and its application to testing non-nested hypotheses. Econometrica 54: 657–678
Motulsky HJ, Christopoulos A (2004) Fitting models to biological data using linear and nonlinear regression: a practical guide to curve fitting. Oxford University Press, Oxford
Neill JW (1988) Testing for lack of fit in nonlinear regression. Ann Statist 16: 733–740
OECD (Organisation for Economic Cooperation and Development) (2006a) Current approaches in the statistical analysis of ecotoxicity data: a guidance to application. OECD Environment Health and Safety Publications, Series on testing and assessment, No. 54, Organisation for Economic Cooperation and Development, Paris
OECD (Organisation for Economic Cooperation and Development) (2006b) Current approaches in the statistical analysis of ecotoxicity data: a guidance to application—annexes. OECD Environment Health and Safety Publications, Series on testing and assessment, No. 54, Organisation for Economic Cooperation and Development, Paris
Piegorsch WW, Bailer AJ (2005) Analyzing environmental data. Wiley, Chichester
Pipper CB, Ritz C (2007) Checking the grouped data version of the cox model for interval-grouped survival data. Scand J Statist 34: 405–418
R Development Core Team (2008) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org. ISBN 3-900051-07-0
Scholze M, Boedeker W, Faust M, Backhaus T, Altenburger R, Grimme LH (2001) A general best-fit method for concentration-response curves and the estimation of low-effect concentrations. Environ Toxicol Chem 20: 448–457
Seber GAF, Wild CJ (1989) Nonlinear regression. Wiley, New York
Sparks, T (eds) (2000) Statistics in ecotoxicology. Wiley, Chichester
Su JQ, Wei LJ (1991) A lack-of-fit test for the mean function in a generalized linear model. J Am Statist Assoc 86: 420–426
van Ewijk PH, Hoekstra JA (1993) Calculation of the EC50 and its confidence interval when subtoxic stimulus is present. Ecotoxicol Environ Saf 25: 25–32
Wald A, Wolfowitz J (1940) On a test whether two samples are from the same population. Ann Math Stat 11: 147–162
White H (1981) Consequences and detection of misspecifed nonlinear regression models. J Am Stat Assoc 76: 419–433
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Ritz, C., Martinussen, T. Lack-of-fit tests for assessing mean structures for continuous dose-response data. Environ Ecol Stat 18, 349–366 (2011). https://doi.org/10.1007/s10651-010-0136-x
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DOI: https://doi.org/10.1007/s10651-010-0136-x