摘要:

After fitting a linear mixed-effects model to a set of repeated-measures or longitudinal data, it is common practice to plot the estimated random effects. On occasion it may be observed that in these plots a straight line may appear. How did this line arise? What influence does it have on the interpretation of the results from the model? This article demonstrates an artifact that can occur in the plots of random effects. If a cluster has exactly one observation, the plot of any estimated random effect against any other estimated random effect will fall on a straight line. The line in the plot of a pair of estimated random effects may even lie in the opposite direction of the direction suggested by the correlation from the random effects covariance matrix. For clusters with two observations at the same design points of the variables for the random effects, the estimated random effects will lie on a plane. Using an example, we demonstrate the patterns in the plots of the estimated random effects. This illustrates that care must be taken when using plots of the estimated random effects.

ISSN:0003-1305    

DOI:10.1080/00031305.2000.10474499

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

We examine a 32factorial experiment that was run on each of 12 days with extra replications of the middle point. Usually, the literature on the analysis of factorial experiments performed in blocks treats the blocks as a fixed effect. Data collected from this experiment, however, were analyzed by treating the block effect as random. The combination of quantitative factor levels and random block effects provides an opportunity to discuss issues that are not commonly encountered in the literature on mixed model analyses of data. In particular, we: (a) discuss modeling the interaction between blocks and regression coefficients; (b) discuss the effect of coding on the estimation of degrees of freedom (df) of the fixed terms; (c) present an oddity with estimating the intercept df; and (d) discuss inference on the mean of the responses. How the experiment may have been run and its consequences are also discussed.

ISSN:0003-1305    

DOI:10.1080/00031305.2000.10474500

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

This article searches for dependence in the decimal expansion of the number π. We systematically test whether the digits of π arek-distributed for greater and greaterk. As it happens, testing whether longer and longer sequences are randomly distributed is a surprisingly interesting problem. We look at a number of approaches to testing independence and find no significant departures from uniform iid behavior in sequences up to 16 digits in length.

ISSN:0003-1305    

DOI:10.1080/00031305.2000.10474501

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Coefficients of determination for continuous predicted values (R2analogs) in logistic regression are examined for their conceptual and mathematical similarity to the familiarR2statistic from ordinary least squares regression, and compared to coefficients of determination for discrete predicted values (indexes of predictive efficiency). An example motivated by substantive concerns and using empirical data from a national household probability sample is presented to illustrate the behavior of the different coefficients of determination in the evaluation of models including dependent variables with different base rates—that is, different proportions of cases or observations with “positive” outcomes. OneR2analog appears to be preferable to the others both in terms of conceptual similarity to the ordinary least squares coefficient of determination, and in terms of its relative independence from the base rate. In addition, base rate should also be considered when selecting an index of predictive efficiency. As expected, the conclusions based onR2analogs are not necessarily consistent with conclusions based on predictive efficiency, with respect to which of several outcomes is better predicted by a given model.

ISSN:0003-1305    

DOI:10.1080/00031305.2000.10474502

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

This article presents necessary and sufficient conditions to be satisfied by the best linear unbiased predictor of future observations in the general linear model in order to have a simple form. Under these conditions, the predictors have an expression similar to that in the uncorrelated case and some parameters related to the covariances between some observations need not to be known.

ISSN:0003-1305    

DOI:10.1080/00031305.2000.10474503

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Multivariate regression is considered with emphasis on prediction. Ordinary least squares tends to yield unstable estimates and consequently uncertain predictions when there are few observations in the training data compared to the number of parameters to be estimated. Thus, there is a need for methods that work well in such situations. This article presents a new alternative prediction method based on reduced-rank regression. The method of reduced-rank regression uses a certain decomposition of the ordinary least squares estimate of the matrix of regression coefficients, and shrinks the last terms of this decomposition exactly to 0. I suggest a new method with soft shrinkage of the terms in the decomposition. Furthermore, the reduced-rank regression, as well as the new softly shrunk reduced-rank regression, are combined with principal components regression. The methods are modified to handle missing observations in the response variables. The various methods are compared through a simulation study. Softly shrunk reduced-rank regression, possibly combined with principal components, turns out to be the best overall method, and the improvement over ordinary least squares is particularly large in situations with few observations.

ISSN:0003-1305    

DOI:10.1080/00031305.2000.10474504

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

It is often desirable to stop a large clinical trial before its planned end if a null result seems inevitable. This early stopping can save considerable resources. It is especially appealing when an experimental treatment is being compared to a standard treatment. Three procedures for early stopping, all with different interpretations and derivations, are described and shown to produce identical rules for normal data and certain parameters. In some cases, this is unexpected and informative. The procedures differ in which of their parameters are adjusted from the fixed sample values to maintain the desired Type I error in this setting of multiple looks at the data.

ISSN:0003-1305    

DOI:10.1080/00031305.2000.10474505

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

This article gives a simple derivation of the smoothing spline based on little more than matrix analysis. Our technique is quite general and extends to nonlinear penalized least squares settings as well as spatial settings. The increasing use of smoothing splines in practice and their availability in many software packages makes a simple derviation worthwhile.

ISSN:0003-1305    

DOI:10.1080/00031305.2000.10474506

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Our focus in this article is on how a course home page can be used to support classroom teaching (not on Web-based education, where the primary teacher-student interaction is by way of the World Wide Web). Our discussion is primarily based on our experiences over the last four years using course home pages to support statistics courses at several levels from introductory to graduate. Over these years we have had the opportunity to try several ideas; seeing some of them work as expected—or better—and seeing others fail to produce any benefits or even detract from the classroom experience. Our discussion should be of value for deciding if your course would benefit from having a home page or for improving an existing one. We also give some advice in the Appendix on how to organize the file structure of a course home page.

ISSN:0003-1305    

DOI:10.1080/00031305.2000.10474507

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

We propose a series of projects for introductory data analysis classes using a single, real multivariate dataset. The assignments combine four current trends in statistics education: Computers, real data, collaborative learning, and writing. Completing the project sequence allows students to appreciate and understand the interconnectedness of statistical concepts. We present rationale for the assignments including five objectives. We provide institutional and course background, an explanation of the data source and variables, grading criteria, a summary of each project, and an assessment of student learning. We conclude with a Web address to facilitate implementation of this approach.

ISSN:0003-1305    

DOI:10.1080/00031305.2000.10474508

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor