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A recent analysis published in this journal found different relationships between mean Ellenberg indicator values and environmental measurements in different vegetation types. The cause was stated as bias in mean Ellenberg values between relevés which in turn suggested to reflect a bias in individual Ellenberg values. We discuss two phenomena that could explain these results without the need to invoke bias in either individual or mean Ellenberg values. Firstly, slopes of linear regression lines underestimate true relationships when analyses involve explanatory variables measured with error. Secondly, syntaxon‐specific distributions of Ellenberg values follow from the floristic definition of phytosociological units. Mean Ellenberg values per relevé therefore carry the stamp of their associated syntaxon even though associated abiotic conditions may vary between relevés. This will lead to variation in slopes and intercepts between vegetation types not because of bias in individual Ellenberg values but because of prescribed bias in the distribution of Ellenberg values between syntaxa. The residual variation in calibrations carried out across vegetation types is undoubtedly reduced by introducing vegetation type as a factor. However users should note that this is unlikely to reflect bias in individual Ellenberg values but is more likely to reflect error in environmental measurements as well the constraint imposed by phytosociological classification. 相似文献
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Summary In most research on smoothing splines the focus has been on estimation, while inference, especially hypothesis testing, has received less attention. By defining design matrices for fixed and random effects and the structure of the covariance matrices of random errors in an appropriate way, the cubic smoothing spline admits a mixed model formulation, which places this nonparametric smoother firmly in a parametric setting. Thus nonlinear curves can be included with random effects and random coefficients. The smoothing parameter is the ratio of the random‐coefficient and error variances and tests for linear regression reduce to tests for zero random‐coefficient variances. We propose an exact F‐test for the situation and investigate its performance in a real pine stem data set and by simulation experiments. Under certain conditions the suggested methods can also be applied when the data are dependent. 相似文献
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When primary endpoints of randomized trials are continuous variables, the analysis of covariance (ANCOVA) with pre-treatment measurements as a covariate is often used to compare two treatment groups. In the ANCOVA, equal slopes (coefficients of pre-treatment measurements) and equal residual variances are commonly assumed. However, random allocation guarantees only equal variances of pre-treatment measurements. Unequal covariances and variances of post-treatment measurements indicate unequal slopes and, usually, unequal residual variances. For non-normal data with unequal covariances and variances of post-treatment measurements, it is known that the ANCOVA with equal slopes and equal variances using an ordinary least-squares method provides an asymptotically normal estimator for the treatment effect. However, the asymptotic variance of the estimator differs from the variance estimated from a standard formula, and its property is unclear. Furthermore, the asymptotic properties of the ANCOVA with equal slopes and unequal variances using a generalized least-squares method are unclear. In this paper, we consider non-normal data with unequal covariances and variances of post-treatment measurements, and examine the asymptotic properties of the ANCOVA with equal slopes using the variance estimated from a standard formula. Analytically, we show that the actual type I error rate, thus the coverage, of the ANCOVA with equal variances is asymptotically at a nominal level under equal sample sizes. That of the ANCOVA with unequal variances using a generalized least-squares method is asymptotically at a nominal level, even under unequal sample sizes. In conclusion, the ANCOVA with equal slopes can be asymptotically justified under random allocation. 相似文献
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In randomized trials, an analysis of covariance (ANCOVA) is often used to analyze post-treatment measurements with pre-treatment measurements as a covariate to compare two treatment groups. Random allocation guarantees only equal variances of pre-treatment measurements. We hence consider data with unequal covariances and variances of post-treatment measurements without assuming normality. Recently, we showed that the actual type I error rate of the usual ANCOVA assuming equal slopes and equal residual variances is asymptotically at a nominal level under equal sample sizes, and that of the ANCOVA with unequal variances is asymptotically at a nominal level, even under unequal sample sizes. In this paper, we investigated the asymptotic properties of the ANCOVA with unequal slopes for such data. The estimators of the treatment effect at the observed mean are identical between equal and unequal variance assumptions, and these are asymptotically normal estimators for the treatment effect at the true mean. However, the variances of these estimators based on standard formulas are biased, and the actual type I error rates are not at a nominal level, irrespective of variance assumptions. In equal sample sizes, the efficiency of the usual ANCOVA assuming equal slopes and equal variances is asymptotically the same as those of the ANCOVA with unequal slopes and higher than that of the ANCOVA with equal slopes and unequal variances. Therefore, the use of the usual ANCOVA is appropriate in equal sample sizes. 相似文献
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V. K. Srivastava G. D. Mishra A. Chaturvedi 《Biometrical journal. Biometrische Zeitschrift》1981,23(1):1-8
For a linear regression model with random coefficients, this paper considers the estimation of the mean of coefficient vector which, in turn, involves the estimation of variances of random coefficients. The conventional estimation methods for it sometimes provides negative estimates. In order to circumvent this kind of difficulty, a proposal is forwarded and is examined in the light of existing ones. 相似文献
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Question: While it is well known that species richness depends on plot size, it is not generally recognised that the same must be true for constancy. Accordingly, many authors use varying plot sizes when classifying vegetation based on the comparison of constancies between groups of plots. We ask whether the constancy‐area relationship follows a general rule, how strong the effect of plot sizes is on constancies, and if it is possible to correct constancies for area. Location: For empirical evaluation, we use data from plant communities in the Czech Republic, Sweden and Russia. Methods: To assess the potential influence of differences in plot size on constancies, we develop a mathematical model. Then, we use series of nested plot species richness data from a wide range of community types (herbaceous and forest) to determine the parameters of the derived function and to test how much the shape of the constancy‐area relationship depends on taxa or vegetation types. Results: Generally, the constancy‐area relationship can be described by C (A)=1?(1?C0)(A/A0)^d, with C being constancy, A area, C0 known constancy on a specific area A0, and d a damping parameter accounting for spatial autocorrelation. As predicted by this function, constancies in plant communities always varied from values near 0% to near 100% if plot sizes were changed sufficiently. For the studied vegetation types, a two‐ to fourfold increase in plot size resulted in a change of conventional constancy classes, i.e. an increase of constancy by 20% or more. Conclusions: Vegetation classification, which largely relies on constancy values, irrespective of whether traditional or modern fidelity definitions are used, is strongly prone to distorting scale effects when relevés of different plot sizes are combined in studies. The constancy‐area functions presented allow an approximate transformation of constancies to other plot sizes but are flawed by idiosyncrasies in taxa and vegetation types. Thus, we conclude that the best solution for future surveys is to apply uniform plot sizes within a few a priori delimited formations and to determine diagnostic species only within these formations. Finally, we suggest that more detailed analyses of constancy‐area relationships can contribute to a better understanding of species‐area relationships because the latter are the summation of the first for all species. 相似文献
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Philip T. Reiss M. Henry H. Stevens Zarrar Shehzad Eva Petkova Michael P. Milham 《Biometrics》2010,66(2):636-643
Summary Permutation tests based on distances among multivariate observations have found many applications in the biological sciences. Two major testing frameworks of this kind are multiresponse permutation procedures and pseudo‐F tests arising from a distance‐based extension of multivariate analysis of variance. In this article, we derive conditions under which these two frameworks are equivalent. The methods and equivalence results are illustrated by reanalyzing an ecological data set and by a novel application to functional magnetic resonance imaging data. 相似文献
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Summary We examine a generalized F ‐test of a nonparametric function through penalized splines and a linear mixed effects model representation. With a mixed effects model representation of penalized splines, we imbed the test of an unspecified function into a test of some fixed effects and a variance component in a linear mixed effects model with nuisance variance components under the null. The procedure can be used to test a nonparametric function or varying‐coefficient with clustered data, compare two spline functions, test the significance of an unspecified function in an additive model with multiple components, and test a row or a column effect in a two‐way analysis of variance model. Through a spectral decomposition of the residual sum of squares, we provide a fast algorithm for computing the null distribution of the test, which significantly improves the computational efficiency over bootstrap. The spectral representation reveals a connection between the likelihood ratio test (LRT) in a multiple variance components model and a single component model. We examine our methods through simulations, where we show that the power of the generalized F ‐test may be higher than the LRT, depending on the hypothesis of interest and the true model under the alternative. We apply these methods to compute the genome‐wide critical value and p ‐value of a genetic association test in a genome‐wide association study (GWAS), where the usual bootstrap is computationally intensive (up to 108 simulations) and asymptotic approximation may be unreliable and conservative. 相似文献
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On the misuse of residuals in ecology: testing regression residuals vs. the analysis of covariance 总被引：28，自引：0，他引：28
Emili García-Berthou 《The Journal of animal ecology》2001,70(4):708-711
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Alan M. Nevill Carlton B. Cooke Roger L. Holder Roger Ramsbottom Clyde Williams 《European journal of applied physiology and occupational physiology》1992,64(5):419-425
This paper examines the problems of modelling bivariate relationships when repeated observations are recorded for each subject. The statistical methods required to test for a common group model were introduced using an example from exercise physiology, where the oxygen cost of running at four different speeds was recorded for a group of 30 recreationally active males. When data for each subject were studied individually, both the plots and correlations suggested the relationship to be linear. Hence, the homogeneity of the subjects' regression lines was compared using the appropriate ANOVA test. The analysis revealed a significant difference in the slopes and intercepts of the lines, thus precluding the use of a single linear model to represent the group. If the subjects were divided into two groups according to the median maximum oxygen consumption (VO2max), a multivariate analysis of variance of the slope and intercept parameters helped to explain some of this heterogeneity (P less than 0.05). However, for physiological rather than statistical reasons, it was necessary to re-analyse the data without the fourth running speed. The revised analysis suggested that the subjects' lines would be better modelled with a common slope but separate intercepts. As before, by dividing the subjects into two groups according to the median VO2max score, a simple t-test indicated that differences in the subjects' intercept parameters were not significant (P = 0.08). Notwithstanding the relatively homogeneous nature of the 30 subjects in terms of VO2max, the statistical methods showed that differences in running economy are, to some extent, dependent on VO2max. 相似文献
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Are Halvor Aastveit 《Biometrical journal. Biometrische Zeitschrift》1983,25(2):129-153
Correlation between adjacent plots in field experiments are common. In this paper the effect of correlation on the usual analysis of variance in a randomized block design is studied. A generalised analysis of variance where correlation is taken into consideration, and the analysis of covariance where the residuals of the neighbouring plots are used as covariates, is discussed. Uniformity trials are used as a basis of a Monte-Carlo study. The generalised analysis improved the power of the tests. The analysis of covariance method was not better than the usual analysis of variance method. 相似文献
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In clinical trials examining the incidence of pneumonia it is a common practice to measure infection via both invasive and non-invasive procedures. In the context of a recently completed randomized trial comparing two treatments the invasive procedure was only utilized in certain scenarios due to the added risk involved, and given that the level of the non-invasive procedure surpassed a given threshold. Hence, what was observed was bivariate data with a pattern of missingness in the invasive variable dependent upon the value of the observed non-invasive observation within a given pair. In order to compare two treatments with bivariate observed data exhibiting this pattern of missingness we developed a semi-parametric methodology utilizing the density-based empirical likelihood approach in order to provide a non-parametric approximation to Neyman-Pearson-type test statistics. This novel empirical likelihood approach has both a parametric and non-parametric components. The non-parametric component utilizes the observations for the non-missing cases, while the parametric component is utilized to tackle the case where observations are missing with respect to the invasive variable. The method is illustrated through its application to the actual data obtained in the pneumonia study and is shown to be an efficient and practical method. 相似文献
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In many scientific problems the purpose of comparing two linear regression models is to demonstrate that they have only negligible differences and so can be regarded as being practically equivalent. The frequently used statistical approach of testing the homogeneity null hypothesis of the two models by using a partial F test is not appropriate for this purpose. In this paper, a simultaneous confidence band is proposed which provides an upper bound on the largest possible difference between the two models, in units of the standard error of the observations, over a given region of the covariates. This is demonstrated to be a more practical method for assessing the equivalence of the two regression models. 相似文献
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Li Zhong-ming 《植物学报(英文版)》1988,30(2)
This paper suggests that the analysis of variance could be used to the distinction of Da- doxylon-like woods and some quantitave characters of Dadoxylon taiyuanensis, Amyelon radicans, A. xui, A. equivius and Billigea resinosa, for example, diameter of ray cells and tracheids, height of rays, and diameter ratio of ray to tracheid, are compared and discussed. The comparision and discussion show quantitave character is more useful to identification of fossil plants than others if analysis Of variance is used. 相似文献
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李中明 《Acta Botanica Sinica》1988,30(2):187-195
本文用方差分析区别具台木类木材的三个种：太原台木(Dadoxylon taiyuanensis),生根无髓根（Amyelon radicans)和徐氏无髓根（A.xui),并同国外的种比较,结果表明,用这种方法能定量地研究植物性状之间的区别,并得到较好的效果。 相似文献