Longitudinal data from factorial experiments frequently arise in various fields of study, ranging from medicine and biology to public policy and sociology. In most practical situations, the distribution of observed data is unknown and there may exist a number of atypical measurements and outliers. Hence, use of parametric and semiparametric procedures that impose restrictive distributional assumptions on observed longitudinal samples becomes questionable. This, in turn, has led to a substantial demand for statistical procedures that enable us to accurately and reliably analyze longitudinal measurements in factorial experiments with minimal conditions on available data, and robust nonparametric methodology offering such a possibility becomes of particular practical importance. In this article, we introduce a new R package nparLD which provides statisticians and researchers from other disciplines an easy and user-friendly access to the most up-todate robust rank-based methods for the analysis of longitudinal data in factorial settings. We illustrate the implemented procedures by case studies from dentistry, biology, and medicine.

In many applications, the underlying scientific question concerns whether the variances of k samples are equal. There are a substantial number of tests for this problem. Many of them rely on the assumption of normality and are not robust to its violation. In 1960 Professor Howard Levene proposed a new approach to this problem by applying the F -test to the absolute deviations of the observations from their group means. Levene's approach is powerful and robust to nonnormality and became a very popular tool for checking the homogeneity of variances.This paper reviews the original method proposed by Levene and subsequent robust modifications. A modification of Levene-type tests to increase their power to detect monotonic trends in variances is discussed. This procedure is useful when one is concerned with an alternative of increasing or decreasing variability, for example, increasing volatility of stocks prices or "open or closed gramophones" in regression residual analysis. A major section of the paper is devoted to discussion of various scientific problems where Levene-type tests have been used, for example, economic anthropology, accuracy of medical measurements, volatility of the price of oil, studies of the consistency of jury awards in legal cases and the effect of hurricanes on ecological systems.

BackgroundWe developed a practical influenza forecast model based on real-time, geographically focused, and easy to access data, designed to provide individual medical centers with advanced warning of the expected number of influenza cases, thus allowing for sufficient time to implement interventions. Secondly, we evaluated the effects of incorporating a real-time influenza surveillance system, Google Flu Trends, and meteorological and temporal information on forecast accuracy.MethodsForecast models designed to predict one week in advance were developed from weekly counts of confirmed influenza cases over seven seasons (2004–2011) divided into seven training and out-of-sample verification sets. Forecasting procedures using classical Box-Jenkins, generalized linear models (GLM), and generalized linear autoregressive moving average (GARMA) methods were employed to develop the final model and assess the relative contribution of external variables such as, Google Flu Trends, meteorological data, and temporal information.ResultsA GARMA(3,0) forecast model with Negative Binomial distribution integrating Google Flu Trends information provided the most accurate influenza case predictions. The model, on the average, predicts weekly influenza cases during 7 out-of-sample outbreaks within 7 cases for 83% of estimates. Google Flu Trend data was the only source of external information to provide statistically significant forecast improvements over the base model in four of the seven out-of-sample verification sets. Overall, the p-value of adding this external information to the model is 0.0005. The other exogenous variables did not yield a statistically significant improvement in any of the verification sets.ConclusionsInteger-valued autoregression of influenza cases provides a strong base forecast model, which is enhanced by the addition of Google Flu Trends confirming the predictive capabilities of search query based syndromic surveillance. This accessible and flexible forecast model can be used by individual medical centers to provide advanced warning of future influenza cases.

BackgroundThe objective of this study is to investigate predictive utility of online social media and web search queries, particularly, Google search data, to forecast new cases of influenza-like-illness (ILI) in general outpatient clinics (GOPC) in Hong Kong. To mitigate the impact of sensitivity to self-excitement (i.e., fickle media interest) and other artifacts of online social media data, in our approach we fuse multiple offline and online data sources.MethodsFour individual models: generalized linear model (GLM), least absolute shrinkage and selection operator (LASSO), autoregressive integrated moving average (ARIMA), and deep learning (DL) with Feedforward Neural Networks (FNN) are employed to forecast ILI-GOPC both one week and two weeks in advance. The covariates include Google search queries, meteorological data, and previously recorded offline ILI. To our knowledge, this is the first study that introduces deep learning methodology into surveillance of infectious diseases and investigates its predictive utility. Furthermore, to exploit the strength from each individual forecasting models, we use statistical model fusion, using Bayesian model averaging (BMA), which allows a systematic integration of multiple forecast scenarios. For each model, an adaptive approach is used to capture the recent relationship between ILI and covariates.ResultsDL with FNN appears to deliver the most competitive predictive performance among the four considered individual models. Combing all four models in a comprehensive BMA framework allows to further improve such predictive evaluation metrics as root mean squared error (RMSE) and mean absolute predictive error (MAPE). Nevertheless, DL with FNN remains the preferred method for predicting locations of influenza peaks.ConclusionsThe proposed approach can be viewed a feasible alternative to forecast ILI in Hong Kong or other countries where ILI has no constant seasonal trend and influenza data resources are limited. The proposed methodology is easily tractable and computationally efficient.

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We present a new R software package lawstat that contains statistical tests and procedures that are utilized in various litigations on securities law, antitrust law, equal employment and discrimination as well as in public policy and biostatistics. Along with the well known tests such as the Bartels test, runs test, tests of homogeneity of several sample proportions, the Brunner-Munzel tests, the Lorenz curve, the Cochran-Mantel-Haenszel test and others, the package contains new distribution-free robust tests for symmetry, robust tests for normality that are more sensitive to heavy-tailed departures, measures of relative variability, Levene-type tests against trends in variances etc. All implemented tests and methods are illustrated by simulations and real-life examples from legal cases, economics and biostatistics. Although the package is called lawstat, it presents implementation and discussion of statistical procedures and tests that are also employed in a variety of other applications, e.g., biostatistics, environmental studies, social sciences and others, in other words, all applications utilizing statistical data analysis. Hence, name of the package should not be considered as a restriction to legal statistics. The package will be useful to applied statisticians and "quantitatively alert practitioners" of other subjects as well as an asset in teaching statistical courses.

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We sought to develop a practical influenza forecast model, based on real-time, geographically focused, and easy to access data, to provide individual medical centers with advanced warning of the number of influenza cases, thus allowing sufficient time to implement an intervention. Secondly, we evaluated how the addition of a real-time influenza surveillance system, Google Flu Trends, would impact the forecasting capabilities of this model.