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Visualizing Longitudinal Data With Dropouts
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| Pengarang | : | Mithat Gönen |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 67 (No. 2) |
| Halaman | : | 97-103 |
| Abstrak | : | This article proposes a triangle plot to display longitudinal data with dropouts. The triangle plot is a tool of data visualization that can also serve as a graphical check for informativeness of the dropout process. There are similarities between the lasagna plot and the triangle plot, but the explicit use of dropout time as an axis is an advantage of the triangle plot over the more commonly used graphical strategies for longitudinal data. It is possible to interpret the triangle plot as a trellis plot, which gives rise to several extensions such as the triangle histogram and the triangle boxplot. R code is available to streamline the use of the triangle plot in practice. Supplementary materials for this article are available online. |
Majority Voting by Independent Classifiers Can Increase Error Rates
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 67 (No. 2) |
| Halaman | : | 94-96 |
| Abstrak | : | The technique of “majority voting” of classifiers is used in machine learning with the aim of constructing a new combined classification rule that has better characteristics than any of a given set of rules. The “Condorcet Jury Theorem” is often cited, incorrectly, as support for a claim that this practice leads to an improved classifier (i.e., one with smaller error probabilities) when the given classifiers are sufficiently good and are uncorrelated. We specifically address the case of two-category classification, and argue that a correct claim can be made for independent (not just uncorrelated) classification errors (not the classifiers themselves), and offer an example demonstrating that the common claim is false. Supplementary materials for this article are available online. |
A Bayesian Look at Nonidentifiability: A Simple Example
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 67 (No. 2) |
| Halaman | : | 90-93 |
| Abstrak | : | This article discusses the concept of identifiability in simple probability calculus. Emphasis is given to Bayesian solutions. In particular, we compare Bayes and maximum likelihood estimators. We advocate adoption of informative prior probabilities for the Bayesian operation in place of diffuse or reference priors. We also discuss the concept of identifying functions. |
Estimating Omissions From Searches
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 67 (No. 2) |
| Halaman | : | 82-89 |
| Abstrak | : | The mark-recapture method was devised by Petersen in Citation1896 to estimate the number of fish migrating into the Limfjord, and independently by Lincoln in Citation1930 to estimate waterfowl abundance. The technique can be applied to any search for a finite number of items by two or more people or agents, allowing the number of searched-for items to be estimated. This ubiquitous problem appears in fields from ecology and epidemiology, through to mathematics, social sciences, and computing. Here, we exactly calculate the moments of the hypergeometric distribution associated with this longstanding problem, confirming that widely used estimates conjectured in 1951 are often too small. Our Bayesian approach highlights how different search strategies will modify the estimates. The estimates are applied to several examples. For some published applications, substantial errors are found to result from using the Chapman or Lincoln–Petersen estimates. Supplementary materials for this article are available online. |
Simulation-Based Confidence Intervals for Functions With Complicated Derivatives Micha Mandel
| Pengarang | : | Micha Mandel |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 67 (No. 2) |
| Halaman | : | Micha Mand |
| Abstrak | : | In many scientific problems, the quantity of interest is a function of parameters that index the model, and confidence intervals are constructed by applying the delta method. However, when the function of interest has complicated derivatives, this standard approach is unattractive and alternative algorithms are required. This article discusses a simple simulation-based algorithm for estimating the variance of a transformation, and demonstrates its simplicity and accuracy by applying it to several statistical problems. |
Using the Exterior Match to Compare Two Entwined Matched Control Groups
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 67 (No. 2) |
| Halaman | : | 67-75 |
| Abstrak | : | When comparing outcomes, such as survival, in two groups— say a focal group and a comparison group—a common question is whether an adjustment for certain baseline differences that separate these two groups actually matters for the difference in outcomes. Did the adjustment matter? If it did matter, to what quantitative extent did it matter? This question is quite distinct from whether the baseline variables predict the outcome: baseline variables may predict the outcome, yet explain no part of the difference in outcomes in two groups. The question is also distinct from whether a difference between the groups remains after adjustment: an adjustment may matter quite a bit, yet fail to explain a substantial part of the difference in outcomes, and, indeed, adjustment may increase the difference. Whether an adjustment for (x 1, x 2) matters over and above an adjustment for x 1 alone can be addressed by comparing outcomes in two control groups formed from the comparison group, one matched to the focal group for x 1 alone, the other matched to focal group for (x 1, x 2). How do outcomes differ in these two matched control groups? If two control groups are each pair-matched to the same focal group, then the result is a set of matched triples, so controls in the two groups are implicitly matched to each other by virtue of being matched to the same person in the focal group. When the comparison group is vastly larger than the focal group and their distributions exhibit extensive overlap on (x 1, x 2), it may be possible to construct nonintersecting matched control groups, but quite often the comparison group is large enough to yield closely matched groups one at a time, but is not large enough to produce several nonintersecting matched control groups. How can one compare two matched control groups that are entwined, with some of the same controls in both groups? Two entwined control groups have a nonempty intersection: some of the same controls appear in both groups as duplicates. These duplicates may appear in the same matched triple, but more commonly they appear in different matched triples. This structure yields a new nonintersecting match that we call the exterior match. Properties of the exterior match are discussed. Our on-going study of black-versus-white disparities in survival following breast cancer in Medicare motivated this work and is used to illustrate. |
Logistic Regression With Multiple Random Effects: A Simulation Study of Estimation Methods and Statistical Packages
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 67 (No. 3) |
| Halaman | : | 171-182 |
| Abstrak | : | Several statistical packages are capable of estimating generalized linear mixed models and these packages provide one or more of three estimation methods: penalized quasi-likelihood, Laplace, and Gauss–Hermite. Many studies have investigated these methods’ performance for the mixed-effects logistic regression model. However, the authors focused on models with one or two random effects and assumed a simple covariance structure between them, which may not be realistic. When there are multiple correlated random effects in a model, the computation becomes intensive, and often an algorithm fails to converge. Moreover, in our analysis of smoking status and exposure to antitobacco advertisements, we have observed that when a model included multiple random effects, parameter estimates varied considerably from one statistical package to another even when using the same estimation method. This article presents a comprehensive review of the advantages and disadvantages of each estimation method. In addition, we compare the performances of the three methods across statistical packages via simulation, which involves two- and three-level logistic regression models with at least three correlated random effects. We apply our findings to a real dataset. Our results suggest that two packages—SAS GLIMMIX Laplace and SuperMix Gaussian quadrature—perform well in terms of accuracy, precision, convergence rates, and computing speed. We also discuss the strengths and weaknesses of the two packages in regard to sample sizes. |
Better Articulating Normal Curve Theory for Introductory Mathematical Statistics Students: Power Transformations and Their Back-Transformations
| Pengarang | : | Daniel A. Griffith |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 67 (No. 3) |
| Halaman | : | 157-169 |
| Abstrak | : | This article addresses a gap in many, if not all, introductory mathematical statistics textbooks, namely, transforming a random variable so that it better mimics a normal distribution. Virtually all such textbooks treat the subject of variable transformations, which furnishes a nice opportunity to introduce and study this transformation-to-normality topic, a topic students frequently encounter in subsequent applied statistics courses. Accordingly, this article reviews variable power transformations of the Box–Cox type within the context of normal curve theory, as well as addresses their corresponding back-transformations. It presents four theorems and a conjecture that furnish the basics needed to derive equivalent results for all nonnegative values of the Box–Cox power transformation exponent. Results are illustrated with the exponential random variable. This article also includes selected pedagogic tools created with R code. |
Bayesian Multimodel Inference by RJMCMC: A Gibbs Sampling Approach
| Pengarang | : | Richard J. Barker |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 67 (No. 3) |
| Halaman | : | 150-156 |
| Abstrak | : | Bayesian multimodel inference treats a set of candidate models as the sample space of a latent categorical random variable, sampled once; the data at hand are modeled as having been generated according to the sampled model. Model selection and model averaging are based on the posterior probabilities for the model set. Reversible-jump Markov chain Monte Carlo (RJMCMC) extends ordinary MCMC methods to this meta-model. We describe a version of RJMCMC that intuitively represents the process as Gibbs sampling with alternating updates of a categorical variable M (for Model) and a “palette” of parameters , from which any of the model-specific parameters can be calculated. Our representation makes plain how model-specific Monte Carlo outputs (analytical or numerical) can be post-processed to compute model weights or Bayes factors. We illustrate the procedure with several examples. |
Are Independent Parameter Draws Necessary for Multiple Imputation?
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 67 (No. 3) |
| Halaman | : | 143-149 |
| Abstrak | : | In typical implementations of multiple imputation for missing data, analysts create m completed datasets based on approximately independent draws of imputation model parameters. We use theoretical arguments and simulations to show that, provided m is large, the use of independent draws is not necessary. In fact, appropriate use of dependent draws can improve precision relative to the use of independent draws. It also eliminates the sometimes difficult task of obtaining independent draws; for example, in fully Bayesian imputation models based on MCMC, analysts can avoid the search for a subsampling interval that ensures approximately independent draws for all parameters. We illustrate the use of dependent draws in multiple imputation with a study of the effect of breast feeding on children’s later cognitive abilities. |