Abstract: (2003). Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis. Journal of the American Statistical Association: Vol. 98, No. 461, pp. 257-258.

Abstract: Cross-sectional studies with binary outcomes analyzed by logistic regression are frequent in the epidemiological literature. However, the odds ratio can importantly overestimate the prevalence ratio, the measure of choice in these studies. Also, controlling for confounding is not equivalent for the two measures. In this paper we explore alternatives for modeling data of such studies with techniques that directly estimate the prevalence ratio. We compared Cox regression with constant time at risk, Poisson regression and log-binomial regression against the standard Mantel-Haenszel estimators. Models with robust variance estimators in Cox and Poisson regressions and variance corrected by the scale parameter in Poisson regression were also evaluated. Three outcomes, from a cross-sectional study carried out in Pelotas, Brazil, with different levels of prevalence were explored: weight-for-age deficit (4%), asthma (31%) and mother in a paid job (52%). Unadjusted Cox/Poisson regression and Poisson regression with scale parameter adjusted by deviance performed worst in terms of interval estimates. Poisson regression with scale parameter adjusted by χ2 showed variable performance depending on the outcome prevalence. Cox/Poisson regression with robust variance, and log-binomial regression performed equally well when the model was correctly specified. Cox or Poisson regression with robust variance and log-binomial regression provide correct estimates and are a better alternative for the analysis of cross-sectional studies with binary outcomes than logistic regression, since the prevalence ratio is more interpretable and easier to communicate to non-specialists than the odds ratio. However, precautions are needed to avoid estimation problems in specific situations.

Abstract: Clarify is a program that uses Monte Carlo simulation to convert the raw output of statistical procedures into results that are of direct interest to researchers, without changing statistical assumptions or requiring new statistical models. The program, designed for use with the Stata statistics package, offers a convenient way to implement the techniques described in: Gary King, Michael Tomz, and Jason Wittenberg (2000). "Making the Most of Statistical Analyses: Improving Interpretation and Presentation." American Journal of Political Science 44, no. 2 (April 2000): 347-61. We recommend that you read this article before using the software. Clarify simulates quantities of interest for the most commonly used statistical models, including linear regression, binary logit, binary probit, ordered logit, ordered probit, multinomial logit, Poisson regression, negative binomial regression, weibull regression, seemingly unrelated regression equations, and the additive logistic normal model for compositional data. Clarify Version 2.1 is forthcoming (2003) in Journal of Statistical Software.

Abstract: discuss the production of low rank smoothers for d greater than or equal to 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thin plate spline smoothing problem and are optimal in the sense that the truncation is designed to result in the minimum possible perturbation of the thin plate spline smoothing problem given the dimension of the basis used to construct the smoother. By making use of Lanczos iteration the basis change and truncation are computationally efficient. The smoothers allow the use of approximate thin plate spline models with large data sets, avoid the problems that are associated with 'knot placement' that usually complicate modelling with regression splines or penalized regression splines, provide a sensible way of modelling interaction terms in generalized additive models, provide low rank approximations to generalized smoothing spline models, appropriate for use with large data sets, provide a means for incorporating smooth functions of more than one variable into non-linear models and improve the computational efficiency of penalized likelihood models incorporating thin plate splines. Given that the approach produces spline-like models with a sparse basis, it also provides a natural way of incorporating unpenalized spline-like terms in linear and generalized linear models, and these can be treated just like any other model terms from the point of view of model selection, inference and diagnostics

Abstract: This paper deals with fitting piecewise terms in regression models where one or more break-points are true parameters of the model For estimation, a simple linearization technique is called for, taking advantage of the linear formulation of the problem As a result, the method is suitable for any regression model with linear predictor and so current software can be used; threshold modelling as function of explanatory variables is also allowed Differences between the other procedures available are shown and relative merits discussed Simulations and two examples are presented to illustrate the method

Abstract: FUNDAMENTALS Statistical Inference I: Descriptive Statistics Measures of Relative Standing Measures of Central Tendency Measures of Variability Skewness and Kurtosis Measures of Association Properties of Estimators Methods of Displaying Data Statistical Inference II: Interval Estimation, Hypothesis Testing, and Population Comparisons Confidence Intervals Hypothesis Testing Inferences Regarding a Single Population Comparing Two Populations Nonparametric Methods CONTINUOUS DEPENDENT VARIABLE MODELS Linear Regression Assumptions of the Linear Regression Model Regression Fundamentals Manipulating Variables in Regression Estimate a Single Beta Parameter Estimate Beta Parameter for Ranges of a Variable Estimate a Single Beta Parameter for m - 1 of the m Levels of a Variable Checking Regression Assumptions Regression Outliers Regression Model GOF Measures Multicollinearity in the Regression Regression Model-Building Strategies Estimating Elasticities Censored Dependent Variables-Tobit Model Box-Cox Regression Violations of Regression Assumptions Zero Mean of the Disturbances Assumption Normality of the Disturbances Assumption Uncorrelatedness of Regressors and Disturbances Assumption Homoscedasticity of the Disturbances Assumption No Serial Correlation in the Disturbances Assumption Model Specification Errors Simultaneous-Equation Models Overview of the Simultaneous-Equations Problem Reduced Form and the Identification Problem Simultaneous-Equation Estimation Seemingly Unrelated Equations Applications of Simultaneous Equations to Transportation Data Panel Data Analysis Issues in Panel Data Analysis One-Way Error Component Models Two-Way Error Component Models Variable-Parameter Models Additional Topics and Extensions Background and Exploration in Time Series Exploring a Time Series Basic Concepts: Stationarity and Dependence Time Series in Regression Forecasting in Time Series: Autoregressive Integrated Moving Average (ARIMA) Models and Extensions Autoregressive Integrated Moving Average Models The Box-Jenkins Approach Autoregressive Integrated Moving Average Model Extensions Multivariate Models Nonlinear Models Latent Variable Models Principal Components Analysis Factor Analysis Structural Equation Modeling Duration Models Hazard-Based Duration Models Characteristics of Duration Data Nonparametric Models Semiparametric Models Fully Parametric Models Comparisons of Nonparametric, Semiparametric, and Fully Parametric Models Heterogeneity State Dependence Time-Varying Covariates Discrete-Time Hazard Models Competing Risk Models COUNT AND DISCRETE DEPENDENT VARIABLE MODELS Count Data Models Poisson Regression Model Interpretation of Variables in the Poisson Regression Model Poisson Regression Model Goodness-of-Fit Measures Truncated Poisson Regression Model Negative Binomial Regression Model Zero-Inflated Poisson and Negative Binomial Regression Models Random-Effects Count Models Logistic Regression Principles of Logistic Regression The Logistic Regression Model Discrete Outcome Models Models of Discrete Data Binary and Multinomial Probit Models Multinomial Logit Model Discrete Data and Utility Theory Properties and Estimation of MNL Models The Nested Logit Model (Generalized Extreme Value Models) Special Properties of Logit Models Ordered Probability Models Models for Ordered Discrete Data Ordered Probability Models with Random Effects Limitations of Ordered Probability Models Discrete/Continuous Models Overview of the Discrete/Continuous Modeling Problem Econometric Corrections: Instrumental Variables and Expected Value Method Econometric Corrections: Selectivity-Bias Correction Term Discrete/Continuous Model Structures Transportation Application of Discrete/Continuous Model Structures OTHER STATISTICAL METHODS Random-Parameter Models Random-Parameters Multinomial Logit Model (Mixed Logit Model) Random-Parameter Count Models Random-Parameter Duration Models Bayesian Models Bayes' Theorem MCMC Sampling-Based Estimation Flexibility of Bayesian Statistical Models via MCMC Sampling-Based Estimation Convergence and Identifi ability Issues with MCMC Bayesian Models Goodness-of-Fit, Sensitivity Analysis, and Model Selection Criterion using MCMC Bayesian Models Appendix A: Statistical Fundamentals Appendix B: Glossary of Terms Appendix C: Statistical Tables Appendix D: Variable Transformations References Index

Abstract: This paper describes the implementation in R of a method for tabular or graphical display of terms in a complex generalised linear model. By complex, I mean a model that contains terms related by marginality or hierarchy, such as polynomial terms, or main effects and interactions. I call these tables or graphs effect displays. Effect displays are constructed by identifying high-order terms in a generalised linear model. Fitted values under the model are computed for each such term. The lower-order "relatives" of a high-order term (e.g., main effects marginal to an interaction) are absorbed into the term, allowing the predictors appearing in the high-order term to range over their values. The values of other predictors are fixed at typical values: for example, a covariate could be fixed at its mean or median, a factor at its proportional distribution in the data, or to equal proportions in its several levels. Variations of effect displays are also described, including representation of terms higher-order to any appearing in the model.

Abstract: Many computer vision, signal processing and statistical problems can be posed as problems of learning low dimensional linear or multi-linear models These models have been widely used for the representation of shape, appearance, motion, etc, in computer vision applications Methods for learning linear models can be seen as a special case of subspace fitting One draw-back of previous learning methods is that they are based on least squares estimation techniques and hence fail to account for “outliers” which are common in realistic training sets We review previous approaches for making linear learning methods robust to outliers and present a new method that uses an intra-sample outlier process to account for pixel outliers We develop the theory of Robust Subspace Learning (RSL) for linear models within a continuous optimization framework based on robust M-estimation The framework applies to a variety of linear learning problems in computer vision including eigen-analysis and structure from motion Several synthetic and natural examples are used to develop and illustrate the theory and applications of robust subspace learning in computer vision

Abstract: We explore the use of the so-called zero-norm of the parameters of linear models in learning. Minimization of such a quantity has many uses in a machine learning context: for variable or feature selection, minimizing training error and ensuring sparsity in solutions. We derive a simple but practical method for achieving these goals and discuss its relationship to existing techniques of minimizing the zero-norm. The method boils down to implementing a simple modification of vanilla SVM, namely via an iterative multiplicative rescaling of the training data. Applications we investigate which aid our discussion include variable and feature selection on biological microarray data, and multicategory classification.

Abstract: In many applications, the objective is to build regression models to explain a response variable over a region of interest under the assumption that the responses are spatially correlated. In nearly all of this work, the regression coefficients are assumed to be constant over the region. However, in some applications, coefficients are expected to vary at the local or subregional level. Here we focus on the local case. Although parametric modeling of the spatial surface for the coefficient is possible, here we argue that it is more natural and flexible to view the surface as a realization from a spatial process. We show how such modeling can be formalized in the context of Gaussian responses providing attractive interpretation in terms of both random effects and explaining residuals. We also offer extensions to generalized linear models and to spatio-temporal setting. We illustrate both static and dynamic modeling with a dataset that attempts to explain (log) selling price of single-family houses.

Abstract: We consider a regression setting where the response is a scalar and the predictor is a random function defined on a compact set of R. Many fields of appli- cations are concerned with this kind of data, for instance chemometrics when the predictor is a signal digitized in many points. Then, people have mainly considered the multivariate linear model and have adapted the least squares procedure to take care of highly correlated predictors. Another point of view is to introduce a con- tinuous version of this model, i.e., the functional linear model with scalar response. We are then faced with the estimation of a functional coefficient or, equivalently, of a linear functional. We first study an estimator based on a B-splines expansion of the functional coefficient which in some way generalizes ridge regression. We derive an upper bound for the L 2 rate of convergence of this estimator. As an alternative we also introduce a smooth version of functional principal components regression for which L 2 convergence is achieved. Finally both methods are compared by means

Abstract: This paper deals with data (or information) fusion for the purpose of estimation. Three estimation fusion architectures are considered: centralized, distributed, and hybrid. A unified linear model and a general framework for these three architectures are established. Optimal fusion rules based on the best linear unbiased estimation (BLUE), the weighted least squares (WLS), and their generalized versions are presented for cases with complete, incomplete, or no prior information. These rules are more general and flexible, and have wider applicability than previous results. For example, they are in a unified form that is optimal for all of the three fusion architectures with arbitrary correlation of local estimates or observation errors across sensors or across time. They are also in explicit forms convenient for implementation. The optimal fusion rules presented are not limited to linear data models. Illustrative numerical results are provided to verify the fusion rules and demonstrate how these fusion rules can be used in cases with complete, incomplete, or no prior information.

Abstract: Preface to the Second Edition.Preface to the First Edition.PART I: REGRESSION MODELS.Introduction to Linear Models.Regression on Functions of One Variable.Transforming the Data.Regression of Functions of Several Variables.Collinearity in Multiple Linear Regression.Influential Observations in Multiple Linear Regression.Polynomial Models and Qualitative Predictors.Additional Topics.PART II: ANALYSIS OF VARIANCE MODELS.Introduction to Analysis of Variance Models.Fixed Effects Models I: One-Way Classification of Means.Fixed Effects Models II: Two-Way Classification of Means.Fixed Effects Models III: Multiple Crossed and Nested Factors.Mixed Models I: The AOV Method with Balanced Data.Mixed Models II: The AVE Method with Balanced Data.Mixed Models III: Unbalanced Data.PART III: MATHEMATICAL THEORY OF LINEAR MODELS.Distribution of Linear and Quadratic Forms.Estimation and Inference for Linear Models.Simultaneous Inference: Tests and Confidence Intervals .Appendix A. Mathematics.Appendix B. Statistics.Appendix C. Statistical Tables.Appendix D. Data Tables.References.Index.

Abstract: We study the problem of aggregation of M arbitrary estimators of a regression function with respect to the mean squared risk Three main types of aggregation are considered: model selection, convex and linear aggregation We define the notion of optimal rate of aggregation in an abstract context and prove lower bounds valid for any method of aggregation We then construct procedures that attain these bounds, thus establishing optimal rates of linear, convex and model selection type aggregation

Abstract: In a recent paper, Bai and Perron (1998) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This algorithm is based on the principle of dynamic programming and requires at most least-squares operations of order O T2 for any number of breaks. Our method can be applied to both pure and partial structural change models. Second, we consider the problem of forming confidence intervals for the break dates under various hypotheses about the structure of the data and the errors across segments. Third, we address the issue of testing for structural changes under very general conditions on the data and the errors. Fourth, we address the issue of estimating the number of breaks. Finally, a few empirical applications are presented to illustrate the usefulness of the procedures. All methods discussed are implemented in a GAUSS program. Copyright  2002 John Wiley & Sons, Ltd.

Abstract: INTRODUCTION Examples of Mismeasurement The Mismeasurement Phenomenon What is Ahead? THE IMPACT OF MISMEASURED CONTINUOUS VARIABLES The Archetypical Scenario More General Impact Multiplicative Measurement Error Multiple Mismeasured Predictors What about Variability and Small Samples? Logistic Regression Beyond Nondifferential and Unbiased Measurement Error Summary Mathematical Details THE IMPACT OF MISMEASURED CATEGORICAL VARIABLES The Linear Model Case More General Impact Inferences on Odds-Ratios Logistic Regression Differential Misclassification Polychotomous Variables Summary Mathematical Details ADJUSTMENT FOR MISMEASURED CONTINUOUS VARIABLES Posterior Distributions A Simple Scenario Nonlinear Mixed Effects Model: Viral Dynamics Logistic Regression I: Smoking and Bladder Cancer Logistic Regression II: Framingham Heart Study Issues in Specifying the Exposure Model More Flexible Exposure Models Retrospective Analysis Comparison with Non-Bayesian Approaches Summary Mathematical Details ADJUSTMENT FOR MISMEASURED CATEGORICAL VARIABLES A Simple Scenario Partial Knowledge of Misclassification Probabilities Dual Exposure Assessment Models with Additional Explanatory Variables Summary Mathematical Details FURTHER TOPICS Dichotomization of Mismeasured Continuous Variables Mismeasurement Bias and Model Misspecification Bias Identifiability in Mismeasurement Models Further Remarks APPENDIX: BAYES-MCMC INFERENCE Bayes Theorem Point and Interval Estimates Markov Chain Monte Carlo Prior Selection MCMC and Unobserved Structure REFERENCES

Abstract: Summary A study into geographical variability of reproductive health outcomes (e.g. birth weight) in Upper Cape Cod, Massachusetts, USA, benefits from geostatistical mapping or kriging. However, also observed are some continuous covariates (e.g. maternal age) that exhibit pronounced non-linear relationships with the response variable. To account for such effects properly we merge kriging with additive models to obtain what we call geoadditive models. The merging becomes effortless by expressing both as linear mixed models. The resulting mixed model representation for the geoadditive model allows for fitting and diagnosis using standard methodology and software.

Abstract: A systematic strategy for stochastic mode reduction is applied here to three prototype ‘‘toy’’ models with nonlinear behavior mimicking several features of low-frequency variability in the extratropical atmosphere. Two of the models involve explicit stable periodic orbits and multiple equilibria in the projected nonlinear climate dynamics. The systematic strategy has two steps: stochastic consistency and stochastic mode elimination. Both aspects of the mode reduction strategy are tested in an a priori fashion in the paper. In all three models the stochastic mode elimination procedure applies in a quantitative fashion for moderately large values of « 0.5 or even « 1, where the parameter « roughly measures the ratio of correlation times of unresolved variables to resolved climate variables, even though the procedure is only justified mathematically for « K 1. The results developed here provide some new perspectives on both the role of stable nonlinear structures in projected nonlinear climate dynamics and the regression fitting strategies for stochastic climate modeling. In one example, a deterministic system with 102 degrees of freedom has an explicit stable periodic orbit for the projected climate dynamics in two variables; however, the complete deterministic system has instead a probability density function with two large isolated peaks on the ‘‘ghost’’ of this periodic orbit, and correlation functions that only weakly ‘‘shadow’’ this periodic orbit. Furthermore, all of these features are predicted in a quantitative fashion by the reduced stochastic model in two variables derived from the systematic theory; this reduced model has multiplicative noise and augmented nonlinearity. In a second deterministic model with 101 degrees of freedom, it is established that stable multiple equilibria in the projected climate dynamics can be either relevant or completely irrelevant in the actual dynamics for the climate variable depending on the strength of nonlinearity and the coupling to the unresolved variables. Furthermore, all this behavior is predicted in a quantitative fashion by a reduced nonlinear stochastic model for a single climate variable with additive noise, which is derived from the systematic mode reduction procedure. Finally, the systematic mode reduction strategy is applied in an idealized context to the stochastic modeling of the effect of mountain torque on the angular momentum budget. Surprisingly, the strategy yields a nonlinear stochastic equation for the large-scale fluctuations, and numerical simulations confirm significantly improved predicted correlation functions from this model compared with a standard linear model with damping and white noise forcing.

Abstract: This 4th edition (4E) retains the general structure of the 3rd edition (3E), but covers a somewhat broader range of topics, with more detailed examples and updated software features. The greatest enhancement is in terms of the discussion and examples of linear and mixed-model methods throughout the book. Examples in most chapters focus on the GLM and/or the MIXED procedures, how they compare, how they can be used to compliment each other and the limits of each. Other enhancements include the use of version 8 and ODS, discussions and examples on Ž xed versus random block effects, analysis of multilocation data, a new chapter on unbalanced data analysis, and a new chapter on generalized linear models and PROC GENMOD. Additional graphics have been included in certain sections, helping a great deal. The SAS Books by Users’ companion website (http://www.sas.com/service/doc/bbu/companion_site/56655.html) contains the datasets and SAS code (release 8.2) to perform the analyses described throughout the book. An introductory chapter describes the scope of the book and chapter summaries where updates and enhancements have occurred. Chapter 2, “Regression,” reviews the basics of linear models in terms of simple linear and multiple regression, similar to the 3E. Discussion focuses on testing hypotheses and estimating linear combinations of parameters. Type I, II, and III sums of squares are introduced along with the concept of partitioning sums of squares and Ž tting full versus reduced models. The REG procedure is used to demonstrate the concepts, and GLM is introduced toward the end of the chapter. The contents of Chapter 3, “Analysis of Variance for Balanced Data,” are similar to the 3E, covering the basic designs of one-way ANOVA, randomized block designs with Ž xed blocks, two-way factorial designs, and a latin square design. However, emphasis is placed on the GLM rather than on the ANOVA procedure in the examples. The MIXED procedure is also introduced here. The chapter contains a good review of multiple comparison of means methods, and an excellent discussion on model parameterization and how to go from a “means” model to an “effects” model. There are some minor errors in the equations in the “Simple Effect Comparisons” section. Chapter 4, “Analyzing Data With Random Effects,” focuses on the issues pertaining to mixed-model inferences. A good introduction section has been added that discusses Ž xed versus random effects. The chapter focuses on the MIXED and GLM procedures and how they compare, rather than on the NESTED and GLM procedures of the 3E. More discussion on calculating standard errors from ESTIMATE and LSMEANS statements, and on the differences between GLM and MIXED, has been added. Also, discussion and examples on the likelihood ratio test and the Wald test options in MIXED are included. There is an additional section that explores blocked designs with random blocks and how the results/interpretations compare to the Ž xed-block designs discussed in Chapter 3. The comparisons made between GLM and MIXED are excellent in terms of why the outputs from the two procedures differ, what information one can and cannot get from each procedure, and whether the information obtained from each is correct (i.e., what are the limits for GLM). There are some minor typos throughout the chapter in the reference tables and some of the equations. Chapter 5, “Unbalanced Data Analysis: Basic Methods,” is a new chapter to the 4E. The chapter discusses the issues that arise with unbalanced data and missing or empty cells. The examples and explanations are clear in terms of what to be careful of in each case and when to use either GLM or MIXED over the other. An excellent discussion is included about how estimability is treated under both GLM and MIXED and how they compare when data have missing cells. Also, included is a good discussion on the differences in the four types of sums of squares and where each would or would not be applicable. Chapter 6, “Understanding Linear Models Concepts,” is similar in content to the previous edition, however, a section at the end has been added introducing generalized least squares and the methodology used by MIXED. Chapter 6 is the most demanding chapter in the book. It goes into more depth than previous chapters about how GLM and MIXED parameterize models and how this is effected by Ž xed versus random effects. How to generate the estimable functions of an analysis, and how to understand the output that GLM provides, are also discussed. Again, there are minor typos in some of the equations. Chapter 7, “Analysis of Covariance,” provides a good overview of the different models and analyses involved in ANCOVA and has been expanded somewhat from the 3E. Additional discussion on adjusted and unadjusted means and how to estimate them has been added, with graphics. Also, more details are included on the analysis under an unequal slopes model. The example with multiple error terms from the previous edition has been updated with discussion and analysis to cover both GLM and MIXED output results. An additional section at the end of the chapter discusses orthogonal polynomials and how they relate to analysis of covariance. The example used very effectively demonstrates the link between traditional ANOVA methods for multilevel factorial experiments and ANCOVA methods. Chapter 8, “Repeated-Measures Analysis,” underwent major revisions due to the inclusion of MIXED. A substantial section on mixed-model analysis of repeated measures has been added. The chapter begins with a good discussion of the different analysis methods used for repeated measures, in which mixedmodel methods have been included. It also introduces the covariance structure of repeated measures and how it differs from traditional split-plot models. A large part of the chapter focuses on the different covariance models that are common for repeated measures and how to Ž t them using PROC MIXED. There is a good review on deŽ ning the basic error covariance structure of a model, covering the different common structures and how they differ. Covariance structures from the simplest to the most complex are discussed, along with examples showing how to Ž t these structures using MIXED. The graphics are most helpful. Details on determining which covariance structure best Ž ts one’s data using the diagnostic tools available in MIXED is also included. Chapter 9, “Multivariate Linear Models,” gives a brief overview and introduction to MANOVA. It is similar to the chapter in the 3E; however, emphasis is placed on the GLM procedure rather than on the ANOVA procedure. Chapter 10, “Generalized Linear Models,” is another chapter new to the 4E. This chapter is an excellent overview of the basic differences between “standard” linear models and generalized linear models. The chapter gives a good overview of the capabilities of the GENMOD procedure in Ž tting a variety of models. It begins with a binary response variable example, reviewing both the logit and probit regression models. Model goodness of Ž t and how to assess Ž t are addressed. Applications of using the inverse link and delta rule are shown. The problem of overdispersion and correction for it is addressed with a third example using count data. The last example in this chapter is a repeated-measures scenario and is used to introduce generalized estimating equations and how to specify the covariance structure in GENMOD and how it compares to MIXED. Chapter 11, “Examples of Special Applications,” has been updated from the 3E to include additional examples, with discussion focusing on GLM and MIXED procedures. A fractional factorial example has been added; the balanced incomplete-block design example is analyzed in both GLM and MIXED. The crossover design has been enhanced with an example from Cochran and Cox (1957) and is analyzed with both GLM and MIXED and compared. A large section on the analysis of multilocation data has been added at the end of this chapter. One example dataset is used here to demonstrate the current issues involved with this type of dataset and several alternative analyses, using both linear and mixed-model methods. Unlike for the previous chapters, however, there does not appear to be any of the SAS code recreated on the website for this chapter. Similar to the 3E, the 4E covers a very broad range of topics, which is the authors’ intent. It is an excellent reference for speciŽ c linear models procedures available in SAS under a broad range of scenarios. As mentioned previously, the companion website gives the data and SAS code used in the examples; however, it must be noted that some minor changes in the code are required for it to run without errors (speciŽ cally, Chaps. 6, 7, 8, and 10). SAS for Linear Models is an excellent resource for the intermediate to advanced SAS statistical user with a basic understanding of linear models. It would also serve well as a supplemental textbook for an applied linear models course where SAS is the software package for analysis. The authors have done an excellent job incorporating the latest analysis methods and latest software

Abstract: The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three-features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure.

Abstract: Summary. We estimate cause–effect relationships in empirical research where exposures are not completely controlled, as in observational studies or with patient non-compliance and self-selected treatment switches in randomized clinical trials. Additive and multiplicative structural mean models have proved useful for this but suffer from the classical limitations of linear and log-linear models when accommodating binary data. We propose the generalized structural mean model to overcome these limitations. This is a semiparametric two-stage model which extends the structural mean model to handle non-linear average exposure effects. The first-stage structural model describes the causal effect of received exposure by contrasting the means of observed and potential exposure-free outcomes in exposed subsets of the population. For identification of the structural parameters, a second stage ‘nuisance’ model is introduced. This takes the form of a classical association model for expected outcomes given observed exposure. Under the model, we derive estimating equations which yield consistent, asymptotically normal and efficient estimators of the structural effects. We examine their robustness to model misspecification and construct robust estimators in the absence of any exposure effect. The double-logistic structural mean model is developed in more detail to estimate the effect of observed exposure on the success of treatment in a randomized controlled blood pressure reduction trial with self-selected non-compliance.

Abstract: In this paper, I consider the estimation of dynamic binary choice panel data models with fixed effects. I use a Modified Maximum Likelihood Estimator (MMLE) that reduces the order of the bias in the Maximum Likelihood Estimator from O(T-1) to O(T-2), without increasing the asymptotic variance. I evaluate its performance in finite samples where T is not large, using Monte Carlo simulations. In Probit and Logit models containing lags of the endogenous variable and exogenous variables, the estimator is found to have a small bias in a panel with eight periods. A distinctive advantage of the MMLE is its general applicability. Identification issues about policy parameters of interest that arise in this kind of models are also addressed. In contrast with linear models, parameters of interest typically depend on the distribution of the individual effects. I discuss the relevance of mean effects across individuals and show an instance in which the entire distribution is needed. Compared with simple MLE, simulation results show that MMLE improves significantly the estimation of the distribution of the effect of interest.

Abstract: This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability, of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model provides information about the mean-square deviation and mean-square error performance of the filters. In addition to deriving earlier results in a unified manner, the approach leads to stability and performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and does not require an explicit recursion for the covariance matrix of the weight-error vector.