An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

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Experimental Design and Data Analysis for Biologists

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Modern Applied Statistics With S

1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

From the Book:
“Clean code that works” is Ron Jeffries’ pithy phrase. The goal is clean code that works, and for a whole bunch of reasons:
Clean code that works is a predictable way to develop. You know when you are finished, without having to worry about a long bug trail.Clean code that works gives you a chance to learn all the lessons that the code has to teach you. If you only ever slap together the first thing you think of, you never have time to think of a second, better, thing. Clean code that works improves the lives of users of our software.Clean code that works lets your teammates count on you, and you on them.Writing clean code that works feels good.But how do you get to clean code that works? Many forces drive you away from clean code, and even code that works. Without taking too much counsel of our fears, here’s what we do—drive development with automated tests, a style of development called “Test-Driven Development” (TDD for short). 
In Test-Driven Development, you:
Write new code only if you first have a failing automated test.Eliminate duplication.

Two simple rules, but they generate complex individual and group behavior. Some of the technical implications are:You must design organically, with running code providing feedback between decisionsYou must write your own tests, since you can’t wait twenty times a day for someone else to write a testYour development environment must provide rapid response to small changesYour designs must consist of many highly cohesive, loosely coupled components, just to make testing easy

The two rules imply an order to the tasks ofprogramming:
1. Red—write a little test that doesn’t work, perhaps doesn’t even compile at first
2. Green—make the test work quickly, committing whatever sins necessary in the process
3. Refactor—eliminate all the duplication created in just getting the test to work


Red/green/refactor. The TDD’s mantra.

Assuming for the moment that such a style is possible, it might be possible to dramatically reduce the defect density of code and make the subject of work crystal clear to all involved. If so, writing only code demanded by failing tests also has social implications:
If the defect density can be reduced enough, QA can shift from reactive to pro-active workIf the number of nasty surprises can be reduced enough, project managers can estimate accurately enough to involve real customers in daily developmentIf the topics of technical conversations can be made clear enough, programmers can work in minute-by-minute collaboration instead of daily or weekly collaborationAgain, if the defect density can be reduced enough, we can have shippable software with new functionality every day, leading to new business relationships with customers


So, the concept is simple, but what’s my motivation? Why would a programmer take on the additional work of writing automated tests? Why would a programmer work in tiny little steps when their mind is capable of great soaring swoops of design? Courage.
Courage
Test-driven development is a way of managing fear during programming. I don’t mean fear in a bad way, pow widdle prwogwammew needs a pacifiew, but fear in the legitimate, this-is-a-hard-problem-and-I-can’t-see-the-end-from-the-beginning sense. If pain is nature’s way of saying “Stop!”, fear is nature’s way of saying “Be careful.” Being careful is good, but fear has a host of other effects:
Makes you tentativeMakes you want to communicate lessMakes you shy from feedbackMakes you grumpy

None of these effects are helpful when programming, especially when programming something hard. So, how can you face a difficult situation and:
Instead of being tentative, begin learning concretely as quickly as possible.Instead of clamming up, communicate more clearly.Instead of avoiding feedback, search out helpful, concrete feedback.(You’ll have to work on grumpiness on your own.) 

Imagine programming as turning a crank to pull a bucket of water from a well. When the bucket is small, a free-spinning crank is fine. When the bucket is big and full of water, you’re going to get tired before the bucket is all the way up. You need a ratchet mechanism to enable you to rest between bouts of cranking. The heavier the bucket, the closer the teeth need to be on the ratchet.

The tests in test-driven development are the teeth of the ratchet. Once you get one test working, you know it is working, now and forever. You are one step closer to having everything working than you were when the test was broken. Now get the next one working, and the next, and the next. By analogy, the tougher the programming problem, the less ground should be covered by each test.

Readers of Extreme Programming Explained will notice a difference in tone between XP and TDD. TDD isn’t an absolute like Extreme Programming. XP says, “Here are things you must be able to do to be prepared to evolve further.” TDD is a little fuzzier. TDD is an awareness of the gap between decision and feedback during programming, and techniques to control that gap. “What if I do a paper design for a week, then test-drive the code? Is that TDD?” Sure, it’s TDD. You were aware of the gap between decision and feedback and you controlled the gap deliberately.

That said, most people who learn TDD find their programming practice changed for good. “Test Infected” is the phrase Erich Gamma coined to describe this shift. You might find yourself writing more tests earlier, and working in smaller steps than you ever dreamed would be sensible. On the other hand, some programmers learn TDD and go back to their earlier practices, reserving TDD for special occasions when ordinary programming isn’t making progress.

There are certainly programming tasks that can’t be driven solely by tests (or at least, not yet). Security software and concurrency, for example, are two topics where TDD is not sufficient to mechanically demonstrate that the goals of the software have been met. Security relies on essentially defect-free code, true, but also on human judgement about the methods used to secure the software. Subtle concurrency problems can’t be reliably duplicated by running the code.

Once you are finished reading this book, you should be ready to:
Start simplyWrite automated testsRefactor to add design decisions one at a time

This book is organized into three sections.
An example of writing typical model code using TDD. The example is one I got from Ward Cunningham years ago, and have used many times since, multi-currency arithmetic. In it you will learn to write tests before code and grow a design organically.An example of testing more complicated logic, including reflection and exceptions, by developing a framework for automated testing. This example also serves to introduce you to the xUnit architecture that is at the heart of many programmer-oriented testing tools. In the second example you will learn to work in even smaller steps than in the first example, including the kind of self-referential hooha beloved of computer scientists.Patterns for TDD. Included are patterns for the deciding what tests to write, how to write tests using xUnit, and a greatest hits selection of the design patterns and refactorings used in the examples.

I wrote the examples imagining a pair programming session. If you like looking at the map before wandering around, you may want to go straight to the patterns in Section 3 and use the examples as illustrations. If you prefer just wandering around and then looking at the map to see where you’ve been, try reading the examples through and refering to the patterns when you want more detail about a technique, then using the patterns as a reference.

Several reviewers have commented they got the most out of the examples when they started up a programming environment and entered the code and ran the tests as they read.

A note about the examples. Both examples, multi-currency calculation and a testing framework, appear simple. There are (and I have seen) complicated, ugly, messy ways of solving the same problems. I could have chosen one of those complicated, ugly, messy solutions to give the book an air of “reality.” However, my goal, and I hope your goal, is to write clean code that works. Before teeing off on the examples as being too simple, spend 15 seconds imagining a programming world in which all code was this clear and direct, where there were no complicated solutions, only apparently complicated problems begging for careful thought. TDD is a practice that can help you lead yourself to exactly that careful thought.

Test Driven Development: By Example

Repeated measurement designs occur in many areas of statistical research. In 1986, Liang and Zeger offered an elegant analysis of these problems based on a set of generalized estimating equations (GEEs) for regression parameters, that specify only the relationship between the marginal mean of the response variable and covariates. Their solution is based on iterated reweighted least squares fitting. In this paper, we propose a rank-based fitting procedure that only involves substituting a norm based on a score function for the Euclidean norm used by Liang and Zeger. Our subsequent fitting, while also an iterated reweighted least squares solution to GEEs, is robust to outliers in response space and the weights can easily be adapted for robustness in factor space. As with the fitting of Liang and Zeger, our rank-based fitting utilizes a working covariance matrix. We prove that our estimators of the regression coefficients are asymptotically normal. The results of a simulation study show that the our proposed estimators are empirically efficient and valid. We illustrate our analysis on a real data set drawn from a hierarchical (three-way nested) design.

Iterated reweighted rank-based estimates for GEE models

For multivariate data collected over groups, discriminant analysis is a two-stage procedure: separation and allocation. For the traditional least squares procedure, separation of training data into groups is accomplished by the maximization of the Lawley–Hotelling test for differences between group means. This produces a set of discriminant coordinates which are used to visualize the data. Using the nearest center rule, the discriminant representation can be used for allocation of data of unknown group membership. In this paper, we propose an approach to discriminant analysis based on efficient robust discriminant coordinates. These coordinates are obtained by the maximization of a Lawley–Hotelling test based on robust estimates. The design matrix used in the fitting is the usual one-way incidence matrix of zeros and ones; hence, our procedure uses highly efficient robust estimators to do the fitting. This produces efficient robust discriminant coordinates which allow the user to visually assess the diffe...

Discriminant procedures based on efficient robust discriminant coordinates

On the robust rank analysis of linear models with nonsymmetric error distributions

The finite sample performance of a number of tests for symmetry of the distribution of the errors of a linear model is considered. The first family of tests is based on the discrepancy between two regression fits. The first fit is appropriate under symmetric errors while the second is appropriate for skewed as well as symmetric error distributions. The second family of procedures consists of tests for the univariate symmetry problem. Thus, in the linear model setting these tests are based on residuals. An extensive empirical study of the finite sample, null behavior of the tests is presented. The results of a power comparison among the tests is also discussed.

Finite sample performance of tests for symmetry of the errors in a linear model

This article examines the stability properties of the least median of squares (LMS) estimate. Attention is focussed on LMS since it is arguably the most widely used high breakdown regression estimate. The differing roles of breakdown point and influence function in producing estimates which are stable to changes in the data are discussed. Simulations and real examples are used to illustrate the extent to which the LMS estimate can change when small changes are made to centrally located data. It is shown that this instability is a consequence of the fact that the LMS estimate has an influence function which is unbounded to the effects of centrally located x's and is not merely a consequence of the exact fit property and the curse of dimensionality, as argued by Rousseeuw (1994).

Joseph W. McKean

Papers

Iterated reweighted rank-based estimates for GEE models

Discriminant procedures based on efficient robust discriminant coordinates

On the robust rank analysis of linear models with nonsymmetric error distributions

Finite sample performance of tests for symmetry of the errors in a linear model

Finite sample stability properties of the least median of squares estimator