Regression models allow one to isolate the relationship between the outcome and an explanatory variable while the other variables are held constant. Here, we introduce an R package, visreg, for the convenient visualization of this relationship via short, simple function calls. In addition to estimates of this relationship, the package also provides pointwise condence bands and partial residuals to allow assessment of variability as well as outliers and other deviations from modeling assumptions. The package provides several options for visualizing models with interactions, including lattice plots, contour plots, and both static and interactive perspective plots. The implementation of the package is designed to be fully object-oriented and interface seamlessly with R’s rich collection of model classes, allowing a consistent interface for visualizing not only linear models, but generalized linear models, proportional hazards models, generalized additive models, robust regression models, and many more.

/pdf/visualization-of-regression-models-using-visreg-3kce0jqvd5.pdf

Visualization of Regression Models Using visreg

Visualizing outliers in massive datasets requires statistical pre-processing in order to reduce the scale of the problem to a size amenable to rendering systems like D3, Plotly or analytic systems like R or SAS. This paper presents a new algorithm, called hdoutliers , for detecting multidimensional outliers. It is unique for a) dealing with a mixture of categorical and continuous variables, b) dealing with big-p (many columns of data), c) dealing with big- $n$ (many rows of data), d) dealing with outliers that mask other outliers, and e) dealing consistently with unidimensional and multidimensional datasets. Unlike ad hoc methods found in many machine learning papers, hdoutliers is based on a distributional model that allows outliers to be tagged with a probability. This critical feature reduces the likelihood of false discoveries.

Visualizing Big Data Outliers Through Distributed Aggregation

Abstract The beta distribution is a versatile function that accommodates a broad range of probability distribution shapes. Beta regression based on the beta distribution can be used to model a response variable y that takes values in open unit interval (0, 1). Zero/one inflated beta (ZOIB) regression models can be applied when y takes values from closed unit interval [0, 1]. The ZOIB model is based a piecewise distribution that accounts for the probability mass at 0 and 1, in addition to the probability density within (0, 1). This paper introduces an R package – zoib that provides Bayesian inferences for a class of ZOIB models. The statistical methodology underlying the zoib package is discussed, the functions coved by the package are outlined, and the usage of the package is illustrated with three examples of different data and model types. The package is comprehensive and versatile in that it can model data with or without inflation at 0 or 1, accommodate clustered and correlated data via latent variables, perform penalized regression as needed, and allow for model comparison via the computation of the DIC criterion.

/pdf/zoib-an-r-package-for-bayesian-inference-for-beta-regression-2j1dr1fe20.pdf

zoib: An R Package for Bayesian Inference for Beta Regression and Zero/One Inflated Beta Regression

Drawing on the attention-based view of the firm and the experiential learning literature, this paper develops and tests a theory on how firms learn to cope with the strains of activity load. We first empirically test the impact of activity load on the performance of a focal activity. We then study how this relationship is moderated by four dimensions of experiential learning: stock, homogeneity, pacing, and past success. We test our hypotheses on a proprietary database of 6,913 investments by 248 private equity firms in 77 countries between 1973 and 2008. We find that heavier activity loads exact a smaller toll on performance when firms have larger and more homogenous stocks of prior experience. However, when firms' prior experience is more rapidly paced or successful, the toll of heavier activity loads on performance grows. Taken together, these four dimensions of experiential learning provide an initial theoretical basis for the development of a capability that we term “attention modulation capability.”

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID2398104_code834846.pdf?abstractid=2398104&mirid=1&type=2

The Dimensions of Experiential Learning in the Management of Activity Load

Statistical analyses are an integral component of scientific research, and for decades, biologists have applied transformations to data to meet the normal error assumptions for F and t tests. Over the years, there has been a movement from data transformation toward model reformation-the use of non-normal error structures within the framework of the generalized linear model (GLM). The principal advantage of model reformation is that parameters are estimated on the original, rather than the transformed scale. However, data transformation has been shown to give better control over type I error, for simulated data with known error structures. We conducted a literature review of statistical textbooks directed toward biologists and of journal articles published in the primary literature to determine temporal trends in both the text recommendations and the practice in the refereed literature over the past 35 years. In this review, a trend of increasing use of reformation in the primary literature was evident, moving from no use of reformation before 1996 to >50% of the articles reviewed applying GLM after 2006. However, no such trend was observed in the recommendations in statistical textbooks. We then undertook 12 analyses based on published datasets in which we compared the type I error estimates, residual plot diagnostics, and coefficients yielded by analyses using square root transformations, log transformations, and the GLM. All analyses yielded acceptable residual versus fit plots and had similar p-values within each analysis, but as expected, the coefficient estimates differed substantially. Furthermore, no consensus could be found in the literature regarding a procedure to back-transform the coefficient estimates obtained from linear models performed on transformed datasets. This lack of consistency among coefficient estimates constitutes a major argument for model reformation over data transformation in biology.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/ece3.3807

Count data in biology—Data transformation or model reformation?

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Plots Transformations And Regression An Introduction To Graphical Methods Of Diagnostic Regression Analysis