M. W. McLean, M. P. Wand.

Source: Bayesian Analysis, Volume 14, Number 2, 371--398.

Abstract:
We build on recent work concerning message passing approaches to approximate fitting and inference for arbitrarily large regression models. The focus is on regression models where the response variable is modeled to have an elaborate distribution, which is loosely defined to mean a distribution that is more complicated than common distributions such as those in the Bernoulli, Poisson and Normal families. Examples of elaborate response families considered here are the Negative Binomial and $t$ families. Variational message passing is more challenging due to some of the conjugate exponential families being non-standard and numerical integration being needed. Nevertheless, a factor graph fragment approach means the requisite calculations only need to be done once for a particular elaborate response distribution family. Computer code can be compartmentalized, including that involving numerical integration. A major finding of this work is that the modularity of variational message passing extends to elaborate response regression models.

Roderick J. Little.

Source: Statistical Science, Volume 34, Number 4, 580--583.

Andreas Buja, Lawrence Brown, Arun Kumar Kuchibhotla, Richard Berk, Edward George, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 545--565.

Abstract:
We develop a model-free theory of general types of parametric regression for i.i.d. observations. The theory replaces the parameters of parametric models with statistical functionals, to be called “regression functionals,” defined on large nonparametric classes of joint ${x extrm{-}y}$ distributions, without assuming a correct model. Parametric models are reduced to heuristics to suggest plausible objective functions. An example of a regression functional is the vector of slopes of linear equations fitted by OLS to largely arbitrary ${x extrm{-}y}$ distributions, without assuming a linear model (see Part I). More generally, regression functionals can be defined by minimizing objective functions, solving estimating equations, or with ad hoc constructions. In this framework, it is possible to achieve the following: (1) define a notion of “well-specification” for regression functionals that replaces the notion of correct specification of models, (2) propose a well-specification diagnostic for regression functionals based on reweighting distributions and data, (3) decompose sampling variability of regression functionals into two sources, one due to the conditional response distribution and another due to the regressor distribution interacting with misspecification, both of order $N^{-1/2}$, (4) exhibit plug-in/sandwich estimators of standard error as limit cases of ${x extrm{-}y}$ bootstrap estimators, and (5) provide theoretical heuristics to indicate that ${x extrm{-}y}$ bootstrap standard errors may generally be preferred over sandwich estimators.

Andreas Buja, Lawrence Brown, Richard Berk, Edward George, Emil Pitkin, Mikhail Traskin, Kai Zhang, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 523--544.

Abstract:
In the early 1980s, Halbert White inaugurated a “model-robust” form of statistical inference based on the “sandwich estimator” of standard error. This estimator is known to be “heteroskedasticity-consistent,” but it is less well known to be “nonlinearity-consistent” as well. Nonlinearity, however, raises fundamental issues because in its presence regressors are not ancillary, hence cannot be treated as fixed. The consequences are deep: (1) population slopes need to be reinterpreted as statistical functionals obtained from OLS fits to largely arbitrary joint ${x extrm{-}y}$ distributions; (2) the meaning of slope parameters needs to be rethought; (3) the regressor distribution affects the slope parameters; (4) randomness of the regressors becomes a source of sampling variability in slope estimates of order $1/sqrt{N}$; (5) inference needs to be based on model-robust standard errors, including sandwich estimators or the ${x extrm{-}y}$ bootstrap. In theory, model-robust and model-trusting standard errors can deviate by arbitrary magnitudes either way. In practice, significant deviations between them can be detected with a diagnostic test.

Jacqueline J. Meulman, Anita J. van der Kooij, Kevin L. W. Duisters.

Source: Statistical Science, Volume 34, Number 3, 361--390.

Abstract:
We present a methodology for multiple regression analysis that deals with categorical variables (possibly mixed with continuous ones), in combination with regularization, variable selection and high-dimensional data ($Pgg N$). Regularization and optimal scaling (OS) are two important extensions of ordinary least squares regression (OLS) that will be combined in this paper. There are two data analytic situations for which optimal scaling was developed. One is the analysis of categorical data, and the other the need for transformations because of nonlinear relationships between predictors and outcome. Optimal scaling of categorical data finds quantifications for the categories, both for the predictors and for the outcome variables, that are optimal for the regression model in the sense that they maximize the multiple correlation. When nonlinear relationships exist, nonlinear transformation of predictors and outcome maximize the multiple correlation in the same way. We will consider a variety of transformation types; typically we use step functions for categorical variables, and smooth (spline) functions for continuous variables. Both types of functions can be restricted to be monotonic, preserving the ordinal information in the data. In combination with optimal scaling, three popular regularization methods will be considered: Ridge regression, the Lasso and the Elastic Net. The resulting method will be called ROS Regression (Regularized Optimal Scaling Regression). The OS algorithm provides straightforward and efficient estimation of the regularized regression coefficients, automatically gives the Group Lasso and Blockwise Sparse Regression, and extends them by the possibility to maintain ordinal properties in the data. Extended examples are provided.

Gregorio Quintana-Ortí, Amelia Simó.

Source: Statistical Science, Volume 34, Number 2, 236--252.

Abstract:
This paper is focused on kernel regression when the response variable is the shape of a 3D object represented by a configuration matrix of landmarks. Regression methods on this shape space are not trivial because this space has a complex finite-dimensional Riemannian manifold structure (non-Euclidean). Papers about it are scarce in the literature, the majority of them are restricted to the case of a single explanatory variable, and many of them are based on the approximated tangent space. In this paper, there are several methodological innovations. The first one is the adaptation of the general method for kernel regression analysis in manifold-valued data to the three-dimensional case of Kendall’s shape space. The second one is its generalization to the multivariate case and the addressing of the curse-of-dimensionality problem. Finally, we propose bootstrap confidence intervals for prediction. A simulation study is carried out to check the goodness of the procedure, and a comparison with a current approach is performed. Then, it is applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children’s wear.

Many complex human traits exhibit differences between sexes. While numerous factors likely contribute to this phenomenon, growing evidence from genome-wide studies suggest a partial explanation: that males and females from the same population possess differing genetic architectures. Despite this, mapping gene-by-sex (GxS) interactions remains a challenge likely because the magnitude of such an interaction is typically and exceedingly small; traditional genome-wide association techniques may be underpowered to detect such events, due partly to the burden of multiple test correction. Here, we developed a local Bayesian regression (LBR) method to estimate sex-specific SNP marker effects after fully accounting for local linkage-disequilibrium (LD) patterns. This enabled us to infer sex-specific effects and GxS interactions either at the single SNP level, or by aggregating the effects of multiple SNPs to make inferences at the level of small LD-based regions. Using simulations in which there was imperfect LD between SNPs and causal variants, we showed that aggregating sex-specific marker effects with LBR provides improved power and resolution to detect GxS interactions over traditional single-SNP-based tests. When using LBR to analyze traits from the UK Biobank, we detected a relatively large GxS interaction impacting bone mineral density within ABO, and replicated many previously detected large-magnitude GxS interactions impacting waist-to-hip ratio. We also discovered many new GxS interactions impacting such traits as height and body mass index (BMI) within regions of the genome where both male- and female-specific effects explain a small proportion of phenotypic variance (R² < 1 x 10^–4), but are enriched in known expression quantitative trait loci.

A logistic regression model and a bivariate statistical analysis were used in this paper to evaluate the groundwater recharge susceptibility. The approach is based on the assessment of the relationship involving groundwater recharge and parameters that influence this hydrological process. Surface parameters and aquifer-related parameters were evaluated as thematic map layers using ArcGIS. Then, a weighted-rating method was adopted to categorize each parameter's map. To assess the role of each parameter in the aquifer recharge, a logistic regression model and a bivariate statistical analysis were applied to the Guenniche phreatic aquifer (Tunisia). Models are explored to establish a map showing the aquifer recharge susceptibility. The code Modflow was used to simulate the consequence of the recharge. The recharge amount was introduced in the model and was tested to verify the recharge effect on the hydraulic head for the two models. The obtained results reveal that the recharge as mapped in the bivariate statistical model has a minor impact on the hydraulic head. Results of the logistic regression model are more significant as the hydraulic head is widely affected. This model provides good results in mapping the spatial distribution of the aquifer recharge susceptibility.

Due to schedule disruptions, stress, and being stuck inside, many babies and children are experiencing sleep regression amid the coronavirus pandemic.Dr. Harvey Karp, a pediatrician and sleep expert who created the SNOO crib, shares some tips on how parents can effectively address sleep regression.Karp recommends a consistent bedtime routine, spending time outdoors, and engaging in soothing talk before bed.Visit Insider's homepage for more stories.If your child's sleep has become more erratic during the coronavirus crisis, know that you're not alone. In fact, Italian pediatricians reported widespread sleep disturbances among their young patients as the pandemic hit its peak there.Between our new home-bound lives and the stress of a global pandemic, many factors can compromise our kids' sleep

Online Resource

Mendenhall, William, author

Riazoshams, Hossein, 1971- author

Gujarati, Damodar N., author

Dewey Library - QA278.2.F53 2020

Online Resource

Tokyo : Springer Japan : Imprint: Springer, 2014