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1.
The purpose of this paper is to relate a number of multinomial models currently in use for ordinal response data in a unified manner. By studying generalized logit models, proportional generalized odds ratio models and proportional generalized hazard models under different parameterizations, we conclude that there are only four different models and they can be specified genericaUy in a uniform way. These four models all possess the same stochastic ordering property and we compare them graphically in a simple case. Data from the NHLBI TYPE II study (Brensike et al (1984)) is used to illustrate these models. We show that the BMDP programs LE and PR can be employed in computing maximum likelihood estimators for these four models. 相似文献
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A family of log-linear models are proposed to describe contingency tables in which one variable can be considered as the response to the remaining. The proposed models take into account the ordering nature of the response categories and have structure similar to that employed in polynomial regression. Stochastic ordering of the response distributions under the proposed models is discussed and the model-reduction techniques are developed. The proposed models are applied to two data sets previously analysed in the literature. 相似文献
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B. J. Best & J. C. W. Rayner 《Journal of the Royal Statistical Society. Series C, Applied statistics》1998,47(3):439-446
A simple nonparametric method of analysis for contingency tables with an ordinal response and factorial treatment structure is described. The method involves a partition of Pearson's X 2 P -statistic by using orthogonal polynomials so that location and dispersion effects are estimated for each level of the explanatory variable. Analyses of variance are then performed on these effects to determine the important factors. The methods are applied to two examples, where consumers rate their liking for a product on an ordered categorical scale, one of which highlights the need to look at dispersion as well as location effects. 相似文献
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Three regression models for ordinal data, those of Fienberg, McCullagh, and Anderson, are applied to an analysis of kidney function among transplant recipients. The conclusions arising from each model are presented and contrasted. 相似文献
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We propose the L1 distance between the distribution of a binned data sample and a probability distribution from which it is hypothetically drawn as a statistic for testing agreement between the data and a model. We study the distribution of this distance for N-element samples drawn from k bins of equal probability and derive asymptotic formulae for the mean and dispersion of L1 in the large-N limit. We argue that the L1 distance is asymptotically normally distributed, with the mean and dispersion being accurately reproduced by asymptotic formulae even for moderately large values of N and k. 相似文献
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In many toxicological assays, interactions between primary and secondary effects may cause a downturn in mean responses at high doses. In this situation, the typical monotonicity assumption is invalid and may be quite misleading. Prior literature addresses the analysis of response functions with a downturn, but so far as we know, this paper initiates the study of experimental design for this situation. A growth model is combined with a death model to allow for the downturn in mean doses. Several different objective functions are studied. When the number of treatments equals the number of parameters, Fisher information is found to be independent of the model of the treatment means and on the magnitudes of the treatments. In general, A- and DA-optimal weights for estimating adjacent mean differences are found analytically for a simple model and numerically for a biologically motivated model. Results on c-optimality are also obtained for estimating the peak dose and the EC50 (the treatment with response half way between the control and the peak response on the increasing portion of the response function). Finally, when interest lies only in the increasing portion of the response function, we propose composite D-optimal designs. 相似文献
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Partially Efficiency-Balanced (PEB) designs were introduced by Puri and Nigam $year:1977. These designs may be particularly useful for bio-assays and factorial experiments and have a very simple analysis. In the present paper, we give several new systematic procedures of constructing PEB designs with varying replications. A number of practical series of PEB designs are presented. We shall also pre- sent the methods of analysing these designs produced here. 相似文献
9.
Xiaoyu Li 《Journal of statistical planning and inference》2012,142(1):155-170
This paper proposes a class of lack-of-fit tests for fitting a linear regression model when some response variables are missing at random. These tests are based on a class of minimum integrated square distances between a kernel type estimator of a regression function and the parametric regression function being fitted. These tests are shown to be consistent against a large class of fixed alternatives. The corresponding test statistics are shown to have asymptotic normal distributions under null hypothesis and a class of nonparametric local alternatives. Some simulation results are also presented. 相似文献
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In this paper, the regression model with a nonnegativity constraint on the dependent variable is considered. Under weak conditions, L 1 estimates of the regression coefficients are shown to be consistent. 相似文献
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Process capability indices (PCIs) have been widely used in manufacturing industries to previde a quantitative measure of process potential and performance. While some efforts have been dedicated in the literature to the statistical properties of PCIs estimators, scarce attention has been given to the evaluation of these properties when sample data are affected by measurement errors. In this work we deal with the problem of measurement errors effects on the performance of PCIs. The analysis is illustrated with reference toC p , i.e. the simplest and most common measure suggested to evaluate process capability. The authors would like to thank two anonymous referees for their comments and suggestion that were useful in the preparation and improvement of this paper. This work was partially supported by a MURST research grant. 相似文献
14.
Jason S. Bergtold Elizabeth A. Yeager Allen M. Featherstone 《Journal of applied statistics》2018,45(3):528-546
The logistic regression model has been widely used in the social and natural sciences and results from studies using this model can have significant policy impacts. Thus, confidence in the reliability of inferences drawn from these models is essential. The robustness of such inferences is dependent on sample size. The purpose of this article is to examine the impact of alternative data sets on the mean estimated bias and efficiency of parameter estimation and inference for the logistic regression model with observational data. A number of simulations are conducted examining the impact of sample size, nonlinear predictors, and multicollinearity on substantive inferences (e.g. odds ratios, marginal effects) when using logistic regression models. Findings suggest that small sample size can negatively affect the quality of parameter estimates and inferences in the presence of rare events, multicollinearity, and nonlinear predictor functions, but marginal effects estimates are relatively more robust to sample size. 相似文献
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In this paper, estimation of coefficients of simultaneous linear partially explosive model of higher orders with moving average
errors is considered. It has been shown that the above model can be decomposed into a purely explosive model and an autoregressive
model. A two stage estimation, procedure is carried out towards proposing estimators for the partially explosive model. The
asymptotic properties of these estimators are also studied. 相似文献
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In this article we provide saddlepoint approximations for some important models of circular data. The particularity of these saddlepoint approximations is that they do not require solving the saddlepoint equation iteratively, so their evaluation is immediate. We first give very accurate approximations to P-values, critical values and power functions for some optimal tests regarding the concentration parameter under wrapped symmetric α-stable and circular normal models. Then, we consider an approximation to the distribution of a projection of the two-dimensional Pearson random walk with exponential step sizes. 相似文献
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The distributions of some transformations of the sample correlation coefficient r are studied here, when the parent population is a mixture of two standard bivariate normals. The behavior of these transformations is assessed through the first four standard moments. It is shown that there is a close relationship between the behavior of the transformed variables and the lack of normality as evinced by the 'kurtosis' defined in the bivariate population 相似文献
19.
Jorge González Chapela 《Journal of applied statistics》2013,40(7):1572-1585
The constrained, non-normal nature of time-use data poses a challenge to ordinary analysis of variance. This paper investigates a computationally simple variance decomposition technique suitable for those data. As a by-product of the analysis, a measure of fit for systems of time-demand equations is proposed that possesses several useful properties. 相似文献
20.
Yang-Jin Kim Chung Mo Nam Youn Nam Kim Eun Hee Choi Jinheum Kim 《Journal of the Korean Statistical Society》2011,40(3):281-290
In animal tumorigenicity data, the time of occurrence of the tumor is not observed because the existence of the tumor is looked for only at either the time of death or the time of sacrifice of the animal. Such an incomplete data structure makes it difficult to investigate the impact of treatment on the occurrence of tumors. A three-state model (no tumor–tumor–death) is used to model events that occurred sequentially and to connect them. In this paper, we also employed a frailty effect to model the dependency of death on tumor occurrence. For the inference of parameters, an EM algorithm is considered. The method is applied to a real bladder tumor data set and a simulation study is performed to show the behavior of the proposed estimators. 相似文献