Felipe Ortega, Ángel and Menéndez Calleja, María Luisa and Pardo Llorente, Leandro
(2007)
*Order-Restricted Dose-Related Trend Phi-Divergence Tests For Generalized Linear Models.*
Journal of Applied Statistics, 34
(5).
pp. 611-623.
ISSN 0266-4763

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## Abstract

In This Paper A New Family Of Test Statistics Is Presented For Testing The Independence.

Between The Binary Response Y And An Ordered Categorical Explanatory Variable X (Doses) Against The

Alternative Hypothesis Of An Increase Dose-Response Relationship Between A Response Variable Y And

X (Doses). The Properties Of These Test Statistics Are Studied. This New Family Of Test Statistics Is Based

On The Family Of Φ-Divergence Measures And Contains As A Particular Case The Likelihood Ratio Test.

We Pay Special Attention To The Family Of Test Statistics Associated With The Power Divergence Family.

A Simulation Study Is Included In Order To Analyze The Behavior Of The Power Divergence Family Of Test

Statistics

Item Type: | Article |
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Uncontrolled Keywords: | Phi-Divergence Test Statistic; Isotonic Regression; Response Variable; Explanatory Variable;Statistics & Probability |

Subjects: | Sciences > Mathematics > Mathematical statistics |

ID Code: | 15142 |

References: | Agresti, A. & Coull, B.A. (1998) An empirical comparison of inference using a order-restricted and linear logit models for a binary response, Communications in Statistics(Simulation), 27(1), pp. 147–166. Ayer, M., Brunk, H.O., Ewing, G.M., Reid, W.I. & Silverman, E. (1955) An empirical distribution function for sampling with incomplete Information, Annals of Mathematical Statistics, 26, pp. 641–647. Barlow, R.E., Bartholomew, D.J. Bremmer, J.M. & Brunk, H.D. (1972) Statistical Inference Under Order Restrictions(NewYork:Wiley). Collins, B.J., Margolin, B.H.&Ochlert, G.W. (1981)Analyses for binomial data, with application to the fluctuation test for mutageneity, Biometrics, 37, pp. 775–794. Cressie, N. & Read, T.R.C. (1984) Multinomial goodness-of-fit tests, Journal of the Royal Statistical Society,Series B, 46, pp. 440–464. Dale, J.P. (1986) Asymptotic normality of goodness of fit statistics for sparse product multinomials, Journal of the Royal Statistical Society, Series B, 41, pp. 48–59. Leraud, K. & Benichou J. (2001) A comparison of several methods to test for the existence of a monotonic dose-response relationship in clinical and epidemiological studies, Statistics in Medicine, 20, pp. 3335–3351. Mancuso, J.Y., Ahn, H. & Chen, J.J.(2001) Order-restricted dose-related trend tests, Statistics in Medicine, 20, pp. 2305–2318. Mantel, N. (1963) Chi-square Tests with one degree of freedom extensions of the mantel-Haenszel procedure,Journal of the American Statistical Association, 58, pp. 690–700. Mclure, M.&Greenland S. (1992)Tests for trend and dose-response: misinterpretations and alternatives, American Journal of Epidemiology, 135(1), pp. 96–104. Downloaded by [Biblioteca Universidad Complutense de Madrid] at 04:17 29 March 2012 Order-restricted Dose-related Trend Phi-divergence Tests 623 Menéndez, M.L., Pardo, L. & Zografos K. (2002) Tests of hypotheses for and against order restrictions on multinomial parameters based on φ-divergences, Utilitas Mathematica, 61, pp. 209–223. Menéndez, M.L., Morales, D. & Pardo, L. (2003a) Tests based on divergences for and against ordered alternatives in cubic contingency tables, Applied Mathematics and Computation, 134, pp. 207–216. Menéndez, M.L., Pardo, J.A. & Pardo, L. (2003b) Tests based on phi-divergences for bivariate symmetry against ordered alternatives in square contingency tables, Australian and New Zealand Journal of Statistics, 45(1),pp. 1–9. Morton Jones, T., Diggle, P. & Parker, L. (2000) Additive isotonic regression models in Epidemiology, Statistics in Medicine, 19, pp. 849–860. Pardo, L. (2006) Statistical Inference Based on Divergence Measures, Statistics: Textbooks and Monographs (NewYork: Chapman & Hall/CRC). Robertson, T.,Wright, F.T. & Dykstra, R.L. (1988) Order Restricted Statistical Inference (NewYork:Wiley). |

Deposited On: | 09 May 2012 10:50 |

Last Modified: | 06 Feb 2014 10:17 |

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