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We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce dimensionality, while also exploiting regularization techniques like ridge regression for addressing multicollinearity. With the learned Hamiltonian we can solve the Time-Dependent Hartree-Fock (TDHF) equation to propagate the electron density in time, and predict its dynamics for field-free and field-on scenarios. We observe close quantitative agreement between the predicted dynamics and ground truth for both field-off trajectories similar to the training data, and field-on trajectories outside of the training data.

The main objective of this article is to investigate how national culture and sociopolitical environment influence the level of wine consumption in a representative panel of countries. Culture is defined as the consumption practices related to economic, social, and cultural aspects and institutional factors. A single equation analysis is based on a cross section of countries representing 90% of wine consumption in the world for the period 2003–2017. In order to draw a final model explaining wine consumption through the cultural peculiarities of a country and to avoid multicollinearity among independent variables, a principal component analysis is performed and a random‐effects GLS regression model is applied to determine the set of cultural variables which are the most significant in affecting wine consumption.

Aim The present study aimed to investigate factors relating to discharge to home of elderly patients with heart failure. Method After applying exclusion criteria and excluding patients with missing data, 110 of 165 elderly patients with heart failure aged at least 75 years admitted to our institution were divided into discharge to home (n = 85) and non-discharge to home (n = 25) groups. Clinical characteristics, comorbidities, blood test data and echocardiographic data were retrospectively investigated and compared based on patients' medical records. Nutritional status was assessed using the Geriatric Nutritional Risk Index (GNRI) upon admission and at 2 weeks after admission (2-week GNRI). Correlations with discharge to home were investigated using multiple logistic regression analysis with discharge to home as the dependent variable and parameters for which significant intergroup differences were observed as explanatory variables, when considering multicollinearity. Ratio scales selected by multiple logistic regression analysis were analyzed using a receiver operating characteristic curve and cut-off values were calculated. Results Independent factors predicting discharge to home were 100-m walk achievement (P = 0.037; odds ratio [OR], 3.057; 95% confidence interval [CI], 2.418-8.751) and 2-week GNRI (P = 0.006; OR, 1.083; 95% CI, 1.023-1.146). Area under the receiver operating characteristic curve for 2-week GNRI was 0.735 (95% CI, 0.622-0.847) with a cut-off value for 2-week GNRI to determine discharge to home of 75.29 (sensitivity, 78.8%; specificity, 60.0%). Conclusion The present findings suggest that 100-m walk achievement and 2-week GNRI may be predictors for discharge to home in elderly patients with heart failure. Geriatr Gerontol Int 2020; 20: 1029-1035..

In this study, we propose shrinkage methods based on {\it generalized ridge regression} (GRR) estimation which is suitable for both multicollinearity and high dimensional problems with small number of samples (large $p$, small $n$). Also, it is obtained theoretical properties of the proposed estimators for Low/High Dimensional cases. Furthermore, the performance of the listed estimators is demonstrated by both simulation studies and real-data analysis, and compare its performance with existing penalty methods. We show that the proposed methods compare well to competing regularization techniques.

The aim of this work was the foodinformatic (chemoinformatic) modeling of volatile organic compounds (VOCs) of different samples of peppers based on a quantitative structure-property relationship (QSPR) for the retention indices of 273 identified compounds. The experimental retention indices were measured by means of comprehensive two-dimensional gas chromatography combined with quadrupole-mass spectrometry (GC × GC/qMS) using the BPX5 and BP20 column coupled system. All the VOCs were represented by means of both conformation-independent molecular descriptors and molecular fingerprints calculated in the Dragon and PaDEL-Descriptor software. The dataset was divided into training, validation and test sets of molecules according to the Balanced Subsets Method (BSM). Subsequently, the V-WSP unsupervised variable reduction method was used to reduce the presence of multicollinearity, redundancy, and noise in the initial pool of 4,336 molecular descriptors and fingerprints. Using this method, a reduced pool of 1,664 was submitted to the supervised selection by means of the replacement method (RM) variable subset selection in order to define a four-descriptor model. The quality of the model was measured by means of the coefficient of determination and the root-mean-square deviation in fitting ( [Formula: see text] and [Formula: see text] ), validation ( [Formula: see text] and [Formula: see text] ), and prediction ( [Formula: see text] and [Formula: see text] ). The negligible differences among the parameters in the three sets indicate a stable and predictive QSPR model. This quantitative structure-activity relationship was developed keeping in mind the five principles defined by the Organization for Economic Co-operation and Development (OECD) to make it applicable. PRACTICAL APPLICATION: This predictive mathematical model developed from the retention indices of 273 volatile organic compounds (VOCs) detected in pepper samples could be useful for chromatographers working on the identification of other common VOCs in peppers or other foods by means of comprehensive two-dimensional gas chromatography combined with quadrupole-mass spectrometry (GC × GC/qMS) using a bi-dimensional stationary phase coupled system (BPX5 and BP20).; © 2019 Institute of Food Technologists®.

Investigating physical activity (PA) patterns as a detailed intensity spectrum instead of crude intensity categories have improved the ability to analyze the relationship between measured PA and health variables. The aim of this methodological study was to introduce and investigate the utility of using detailed PA intensity spectrum compared to crude PA intensity categories for comparison of PA between groups and between repeated measures. The study sample consisted of two groups of children, where one group was scheduled for extended physical education (PE) by daily classes while the other group followed usual PE schedule. Accelerometer data was processed into traditional crude PA intensity categories and into detailed PA intensity spectrum. Multivariate partial least squares regression for discriminant analysis (PLS-DA) was applied for PA intensity spectrum group comparison and compared to traditional univariate statistical analysis. Repeated measures were investigated using independent PLS-DA as well as multilevel PLS-DA for paired analysis. While traditional analysis of crude PA intensity categories was unable to find any group differences, multivariate analysis of the PA intensity spectrum identified statistically significant differences. By the extension of multilevel PLS-DA for paired comparison, a clear difference in the PA intensity spectrum was demonstrated between repeated measures. In conclusion, analysis of detailed PA intensity spectrum demonstrates utility for comparing detailed PA data between groups and between repeated measures in interventional and observational research.

International audience; Abstract In a large variety of fields such as epidemiology, process monitoring, chemometrics, marketing, and social sciences among others, many research questions pertain to regression analysis from large data sets. Although in some cases standard regression will suffice, modeling is sometimes more challenging for various reasons (i) explain several variables; (ii) with a large number of explanatory variables organized into meaningful, usually ill?conditioned, multidimensional matrices; (iii) where observations come from different subpopulations; and (iv) with the opportunity to predict new observations. Although some developed methods partially meet these challenges, none of them covers all these aspects. To fill this gap, a new method, called regularized clusterwise multiblock regression (CW.rMBREG), is proposed. The method CW.rMBREG combines clustering and a component?based (multiblock) model associated with a well?defined criterion to optimize. It provides simultaneously a partition of the observations into clusters along with the regression coefficients associated with each cluster. To go further, we propose to investigate a key feature generally neglected in clusterwise regression, ie, the prediction of new observations. The usefulness of CW.rMBREG is illustrated on the basis of both a simulation study and a real example in the field of indoor air quality. It results that CW.rMBREG improves the quality of the prediction and facilitates the interpretation of complex ill?conditioned data. The proposed method is available for users through the R package mbclusterwise.

Research Summary: In multivariate regression analyses of correlated variables, we sometimes observe pairs of estimated beta coefficients large in absolute magnitude and opposite in sign. T‐statistics are also large, suggesting meaningful findings. I found 64 recently published Strategic Management Journal articles with results exhibiting these characteristics. In this article, I demonstrate that such results may be Type 1 errors (false positives): If regressors are correlated via an unobservable common factor, estimated beta coefficients will misleadingly tend toward infinite magnitudes in opposite directions, even if the variables’ real effects are small and of the same sign. Diagnostics such as Variance Inflation Factors (VIF) will misleadingly validate Type 1 errors as legitimate results. After establishing general results via mathematical analysis and simulation, I provide guidelines for detection and mitigation. Managerial Summary: This article demonstrates mathematically how regression analyses with correlated independent variables may generate beta coefficients of opposite sign to the variables’ true effects. To assess the likelihood of this possibility, I propose that: if (a) absolute correlation of two independent variables is about ±0.3 or more (smaller correlations may be problematic for large data sets), (b) the two variables have beta coefficients of opposite sign, if correlated positively, and of the same sign, if correlated negatively, and (c) the bivariate correlation of one independent variable with the dependent variable is of the opposite sign from the beta coefficient, then the beta might be a false positive. To facilitate such analysis, authors should provide complete correlation tables, including dependent variables, interaction terms, and quadratic terms.

Our goal in this study was to investigate antecedents to formation of leadership self‐efficacy (LSE) for men versus women. We used a relative importance analysis, which allows more precise identification of important predictors without concern of multicollinearity effects on R2. Using a sample of 325 business students, we found that extraversion, conscientiousness and openness to experience each explained significant variance in LSE. Conscientiousness and openness to experience were stronger predictors of LSE for women than men, whereas extraversion was a stronger predictor of LSE for men than women. We provide a literature review with hypotheses, methods and analysis. We discuss the results with respect to the role congruency and leadership self‐perceptions and provide implications for future research and practice of leadership development.

We propose a method for improving the predictive ability of standard forecasting models used in financial economics. Our approach is based on the functional partial least squares (FPLS) model, which is capable of avoiding multicollinearity in regression by efficiently extracting information from the high-dimensional market data. By using its well-known ability, we can incorporate auxiliary variables that improve the predictive accuracy. We provide an empirical application of our proposed methodology in terms of its ability to predict the conditional average log return and the volatility of crude oil prices via exponential smoothing, Bayesian stochastic volatility, and GARCH (generalized autoregressive conditional heteroskedasticity) models, respectively. In particular, what we call functional data analysis (FDA) traces in this article are obtained via the FPLS regression from both the crude oil returns and auxiliary variables of the exchange rates of major currencies. For forecast performance evaluation, we compare out-of-sample forecasting accuracy of the standard models with FDA traces to the accuracy of the same forecasting models with the observed crude oil returns, principal component regression (PCR), and least absolute shrinkage and selection operator (LASSO) models. We find evidence that the standard models with FDA traces significantly outperform our competing models. Finally, they are also compared with the test for superior predictive ability and the reality check for data snooping. Our empirical results show that our new methodology significantly improves predictive ability of standard models in forecasting the latent average log return and the volatility of financial time series.

This article presents a Bayesian method based on spatial filtering to estimate hedonic models for dwelling prices with geographically varying coefficients. A Bayesian Adaptive Sampling algorithm for variable selection is used, which makes it possible to select the most appropriate filters for each hedonic coefficient. This approach explores the model space more systematically and takes into account the uncertainty associated with model estimation and selection processes. The methodology is illustrated with an application for the real estate market in the Spanish city of Zaragoza and with simulated data. In addition, an exhaustive comparison study with a set of alternatives strategies used in the literature is carried out. Our results show that the proposed Bayesian procedures are competitive in terms of prediction; more accurate results are obtained in the estimation of the regression coefficients of the model, and the multicollinearity problems associated with the estimation of the regression coefficients are solved.

The main thrust of this study is to consider the problem of simultaneous prediction of actual and average values of the simultaneous equations model through the target function of Shalabh (Bulletin of International Statistical Institute, 1995, 56, 1375–1390). We focus on the predictive performance of the two-stage ridge estimator with the motivation for eliminating the disorder arising from multicollinearity. An optimal biasing parameter of the two-stage ridge estimator is derived by a minimization process of prediction mean square error. In addition, an optimal estimator for the weight of observed value in target function is attained theoretically. The results inferred from a numerical example and a Monte Carlo experiment provide a dramatic improvement in the predictive ability of the two-stage ridge estimator. © 2019 John Wiley & Sons, Ltd.

With many predictors in regression, fitting the full model can induce multicollinearity problems. Least Absolute Shrinkage and Selection Operation (LASSO) is useful when the effects of many explanatory variables are sparse in a high-dimensional dataset. Influential points can have a disproportionate impact on the estimated values of model parameters. This paper describes a new influence plot that can be used to increase understanding of the contributions of individual observations and the robustness of results. This can serve as a complement to other regression diagnostics techniques in the LASSO regression setting. Using this influence plot, we can find influential points and their impact on shrinkage of model parameters and model selection. We illustrate the methods with two examples. Copyright © 2016 John Wiley & Sons, Ltd.

Understanding the impacts of land cover pattern on the heat island effect is essential for sustainable urban development. Conventional model fitting methods have restricted ability to produce accurate estimates of the land cover-temperature association due to the lack of procedures to address two important issues: spatial dependence in proximal spatial units and high correlations among predictor variables. In this study, we seek to develop an effective framework called spatially filtered ridge regression (SFRR) to estimate the variations in the quantity and distribution of land surface temperature (LST) in response to various land cover patterns. The SFRR effectively integrates spatial autoregressive models and ridge regression, and it achieves reliable parameter estimates with substantially reduced mean square errors. We show this by comparing the performance of the SFRR to other widely adopted models using Monte Carlo simulation followed by an empirical study over central Phoenix. Results highlight the great potential of the SFRR in producing accurate statistical estimates, providing a positive step toward informed and unbiased decision-making across a wide variety of disciplines. (Code and data to reproduce the results in the case study are available at: https://github.com/cfan13/SFRRTGIS.git.)

Objective To change the common practice of eliminating independent variables from models because they produce multicollinearity in an independent variable of special interest. Methods I supplement my presentation, which is based on the purposes of regression analysis, by using Venn diagrams, simple formulas, and two small simulations. Results Independent variables that when removed from a model substantially change the statistics associated with the independent variable(s) of most interest are variables that should typically be kept in the model. Multicollinearity is not a sufficient reason to drop variables from a model. Conclusion I argue against the routine dropping of variables that cause multicollinearity in an independent variable of interest from regression models. A more important criterion to consider when contemplating dropping a variable from a model is “model influence.”

Summary One of the standard variable selection procedures in multiple linear regression is to use a penalisation technique in least-squares (LS) analysis. In this setting, many different types of penalties have been introduced to achieve variable selection. It is well known that LS analysis is sensitive to outliers, and consequently outliers can present serious problems for the classical variable selection procedures. Since rank-based procedures have desirable robustness properties compared to LS procedures, we propose a rank-based adaptive lasso-type penalised regression estimator and a corresponding variable selection procedure for linear regression models. The proposed estimator and variable selection procedure are robust against outliers in both response and predictor space. Furthermore, since rank regression can yield unstable estimators in the presence of multicollinearity, in order to provide inference that is robust against multicollinearity, we adjust the penalty term in the adaptive lasso function by incorporating the standard errors of the rank estimator. The theoretical properties of the proposed procedures are established and their performances are investigated by means of simulations. Finally, the estimator and variable selection procedure are applied to the Plasma Beta-Carotene Level data set.

“Species distribution modeling” was recently ranked as one of the top five “research fronts” in ecology and the environmental sciences by ISI's Essential Science Indicators (Renner and Warton 2013), reflecting the importance of predicting how species distributions will respond to anthropogenic change. Unfortunately, species distribution models (SDMs) often perform poorly when applied to novel environments. Compounding on this problem is the shortage of methods for evaluating SDMs (hence, we may be getting our predictions wrong and not even know it). Traditional methods for validating SDMs quantify a model's ability to classify locations as used or unused. Instead, we propose to focus on how well SDMs can predict the characteristics of used locations. This subtle shift in viewpoint leads to a more natural and informative evaluation and validation of models across the entire spectrum of SDMs. Through a series of examples, we show how simple graphical methods can help with three fundamental challenges of habitat modeling: identifying missing covariates, non-linearity, and multicollinearity. Identifying habitat characteristics that are not well-predicted by the model can provide insights into variables affecting the distribution of species, suggest appropriate model modifications, and ultimately improve the reliability and generality of conservation and management recommendations.

Summary The sum of Akaike weights (SW) is often used to quantify relative variable importance (RVI) within the information-theoretic (IT) multimodel inference framework. A recent study (Galipaud et al. 2014, Methods in Ecology and Evolution 5: 983) questioned the validity of the SW approach. Regrettably, this study is flawed because SW was evaluated with an inappropriate benchmark. Irrespective of this study's methodological issues, RVI metrics based on the relative contribution of explanatory variables in explaining the variance in the response variable (partitioned R2-based) are lacking in multimodel inference. We re-evaluated the validity of SW by repeating Galipaud et al.'s experiment but with an appropriate benchmark. When explanatory variables are uncorrelated, the quantity that SW estimates (i.e. the probability that a variable is included in the actual best IT model) is monotonically related to squared zero-order correlation coefficients (r2) between explanatory variables and the response variable. The degree of correspondence between SW and r2 rankings (not values) of variables in data sets with uncorrelated explanatory variables was therefore used as a benchmark to evaluate the validity of SW as a RVI metric. To address the lack of partitioned R2-based RVI metrics in multimodel inference, we proposed 2 metrics: (a) Iweighted, the average model probability-weighted partitioned R2; and (b) Ibest, the partitioned R2 derived from the best IT model. We performed Monte Carlo simulations to evaluate the utility of Iweighted and Ibest versus partitioned R2 derived from the global model (Iglobal). SW rankings matched r2 rankings of variables; therefore, SW is a valid measure of RVI. Among partitioned R2-based metrics, Iweighted and Iglobal were generally more accurate in estimating the population partitioned R2. Iweighted performed better when explanatory variables were uncorrelated, whereas Iglobal was better in smaller data sets with correlated explanatory variables. To improve the utility of Iweighted in such data sets, we proposed approaches to eliminate or reduce the influence of correlated variables. Despite recent criticisms, our results show that SW is a valid RVI metric. To quantify RVI in terms of the R2 explained by each variable, Iweighted and Iglobal are the preferred RVI metrics.

In this paper we compare conceptualising single factor technical and allocative efficiency as indicators of a single latent variable, or as separate observed variables. In the former case, the impacts on both efficiency types are analysed by means of structural equationmodeling (SEM), in the latter by seemingly unrelated regression (SUR). We compare estimation results of the two approaches based on a dataset on single factor irrigation water use efficiency obtained from a survey of 360 farmers in the Guanzhong Plain, China. The main methodological findings are that SEM allows identification of the most important dimension of irrigation water efficiency (technical efficiency) via comparison of their factor scores and reliability. Moreover, it reduces multicollinearity and attenuation bias. It thus is preferable to SUR. The SEM estimates show that perception of water scarcity is the most important positive determinant of both types of efficiency, followed by irrigation infrastructure, income and water price. Furthermore, there is a strong negative reverse effect from efficiency on perception.

Three flawed practices associated with model averaging coefficients for predictor variables in regression models commonly occur when making multimodel inferences in analyses of ecological data. Model-averaged regression coefficients based on Akaike information criterion (AIC) weights have been recommended for addressing model uncertainty but they are not valid, interpretable estimates of partial effects for individual predictors when there is multicollinearity among the predictor variables. Multicollinearity implies that the scaling of units in the denominators of the regression coefficients may change across models such that neither the parameters nor their estimates have common scales, therefore averaging them makes no sense. The associated sums of AIC model weights recommended to assess relative importance of individual predictors are really a measure of relative importance of models, with little information about contributions by individual predictors compared to other measures of relative importance based on effects size or variance reduction. Sometimes the model-averaged regression coefficients for predictor variables are incorrectly used to make model-averaged predictions of the response variable when the models are not linear in the parameters. I demonstrate the issues with the first two practices using the college grade point average example extensively analyzed by Burnham and Anderson. I show how partial standard deviations of the predictor variables can be used to detect changing scales of their estimates with multicollinearity. Standardizing estimates based on partial standard deviations for their variables can be used to make the scaling of the estimates commensurate across models, a necessary but not sufficient condition for model averaging of the estimates to be sensible. A unimodal distribution of estimates and valid interpretation of individual parameters are additional requisite conditions. The standardized estimates or equivalently the t statistics on unstandardized estimates also can be used to provide more informative measures of relative importance than sums of AIC weights. Finally, I illustrate how seriously compromised statistical interpretations and predictions can be for all three of these flawed practices by critiquing their use in a recent species distribution modeling technique developed for predicting Greater Sage-Grouse (Centrocercus urophasianus) distribution in Colorado, USA. These model averaging issues are common in other ecological literature and ought to be discontinued if we are to make effective scientific contributions to ecological knowledge and conservation of natural resources.

The mineral particles are classified in different textural classes according to their size. Reflectance spectrometry and spectra can be valid instruments to classify the soils according to their texture. This is possible using different statistical methods, for example, discriminant analysis. However, other multivariate methods, like multinomial logistic regression, can be used, but the presence of multicollinearity among explicative variables could affect the estimation of the parameters. The solution proposed to remedy this problem is an alternative way to apply the multinomial logit model. To evaluate its performances, we compare the results with both classical multinomial logit and discriminant analysis ones. Copyright © 2015 John Wiley & Sons, Ltd.

We consider a variety of regression modeling strategies for analyzing observational data associated with typical wildlife studies, including all subsets and stepwise regression, a single full model, and Akaike's Information Criterion (AIC)-based multimodel inference. Although there are advantages and disadvantages to each approach, we suggest that there is no unique best way to analyze data. Further, we argue that, although multimodel inference can be useful in natural resource management, the importance of considering causality and accurately estimating effect sizes is greater than simply considering a variety of models. Determining causation is far more valuable than simply indicating how the response variable and explanatory variables covaried within a data set, especially when the data set did not arise from a controlled experiment. Understanding the causal mechanism will provide much better predictions beyond the range of data observed. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

1. Prediction is fundamental to scientific enquiry and application; however, ecologists tend to favour explanatory modelling. We discuss a predictive modelling framework to evaluate ecological hypotheses and to explore novel/unobserved environmental scenarios to assist conservation and management decision-makers. We apply this framework to develop an optimal predictive model for juvenile (

A gene expression programming (GEP)-based approach that shows prospects how to estimate bus dwell time (BDT) more accurately and overcome some of the issues associated with the multiple linear regression (MLR) method is proposed in this article. The model is calibrated and validated using the data collected from 22 bus stops in Auckland and compared against the MLR model based on five different performance measures: mean error, mean absolute error, root mean square error, mean absolute percentage error, and R² value. The restrictions to stick with a predefined model and the need to satisfy assumptions made on multicollinearity, homoscedasticity, and the normality of random error are often difficult to satisfy.

When the interdependence of disturbances is present in a regression model, the pattern of sample residuals contains information which is useful in the prediction of post-sample drawings and when multicollinearity among regressors is also present, it is useful to use biased regression estimators. This information is exploited in the biased predictors derived here. Also, the predictive performance of various biased predictors with correlated errors is discussed and all pair-wise comparisons are made among these predictors. The theoretical results are illustrated by a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.

International audience; Direct gradient analyses in spatial genetics provide unique opportunities to describe the inherent complexity of genetic variation in wildlife species and are the object of many methodological developments. However, multicollinearity among explanatory variables is a systemic issue in multivariate regression analyses and is likely to cause serious difficulties in properly interpreting results of direct gradient analyses, with the risk of erroneous conclusions, misdirected research and inefficient or counterproductive conservation measures. Using simulated data sets along with linear and logistic regressions on distance matrices, we illustrate how commonality analysis (CA), a detailed variance-partitioning procedure that was recently introduced in the field of ecology, can be used to deal with nonindependence among spatial predictors. By decomposing model fit indices into unique and common (or shared) variance components, CA allows identifying the location and magnitude of multicollinearity, revealing spurious correlations and thus thoroughly improving the interpretation of multivariate regressions. Despite a few nherent limitations, especially in the case of resistance model optimization, this review highlights the great potential of CA to account for complex multicollinearity patterns in spatial genetics and identifies future applications and lines of research. We strongly urge spatial geneticists to systematically investigate commonalities when performing direct gradient analyses.

Many existing cohort studies designed to investigate health effects of environmental exposures also collect data on genetic markers. The Early Life Exposures in Mexico to Environmental Toxicants project, for instance, has been genotyping single nucleotide polymorphisms on candidate genes involved in mental and nutrient metabolism and also in potentially shared metabolic pathways with the environmental exposures. Given the longitudinal nature of these cohort studies, rich exposure and outcome data are available to address novel questions regarding gene-environment interaction (G × E). Latent variable (LV) models have been effectively used for dimension reduction, helping with multiple testing and multicollinearity issues in the presence of correlated multivariate exposures and outcomes. In this paper, we first propose a modeling strategy, based on LV models, to examine the association between repeated outcome measures (e.g., child weight) and a set of correlated exposure biomarkers (e.g., prenatal lead exposure). We then construct novel tests for G × E effects within the LV framework to examine effect modification of outcome-exposure association by genetic factors (e.g., the hemochromatosis gene). We consider two scenarios: one allowing dependence of the LV models on genes and the other assuming independence between the LV models and genes. We combine the two sets of estimates by shrinkage estimation to trade off bias and efficiency in a data-adaptive way. Using simulations, we evaluate the properties of the shrinkage estimates, and in particular, we demonstrate the need for this data-adaptive shrinkage given repeated outcome measures, exposure measures possibly repeated and time-varying gene-environment association.

This is the final draft, after peer-review, of a manuscript published in Higher Education Quarterly. The published version is available online at http://dx.doi.org/ 10.1111/hequ.12058

Bernoulli (or binomial) regression using a generalized linear model with a log link function, where the exponentiated regression parameters have interpretation as relative risks, is often more appropriate than logistic regression for prospective studies with common outcomes. In particular, many researchers regard relative risks to be more intuitively interpretable than odds ratios. However, for the log link, when the outcome is very prevalent, the likelihood may not have a unique maximum. To circumvent this problem, a 'COPY method' has been proposed, which is equivalent to creating for each subject an additional observation with the same covariates except the response variable has the outcome values interchanged (1's changed to 0's and 0's changed to 1's). The original response is given weight close to 1, while the new observation is given a positive weight close to 0; this approach always leads to convergence of the maximum likelihood algorithm, except for problems with convergence due to multicollinearity among covariates. Even though this method produces a unique maximum, when the outcome is very prevalent, and/or the sample size is relatively small, the COPY method can yield biased estimates. Here, we propose using the jackknife as a bias-reduction approach for the COPY method. The proposed method is motivated by a study of patients undergoing colorectal cancer surgery.

When the component proportions in mixture experiments are restricted by lower and upper bounds, the input space of a designed experiment space can become an irregular region that can induce multicollinearity problems when estimating the component proportion parameters. Thus, ridge regression provides a beneficial means of stabilizing the coefficient estimates in the fitted model. Previous research has focused on using prediction variance as a metric for determining an appropriate value of the ridge constant, k. We use visualization techniques to illustrate and evaluate ridge regression estimators and the robustness of estimation with respect to the variance and the bias. The addition of bias allows better balancing between the stability of the estimators and minimally changing the estimates. We illustrate the graphical methods with mixture and mixture-process examples from the literature. Copyright © 2014 John Wiley & Sons, Ltd.

We examine theoretical and methodological issues associated with the roles of individual and group-normative importance in self-esteem determination. Critical issues include multicollinearity among the physical self-subdomains, which may have affected previous results, and the need for a multidimensional perspective on importance models. Using Lindwall, Asci, Palmeira, Fox, & Hagger (2011)’s database, we apply state-of-the-art methodologies, including Exploratory Structural Equation Modeling and the product-of-indicators approach to latent interactions. Positive interactions would be required to support the Individually Importance-Weighted Average model, but none were observed in the multidimensional model, including all interaction effects; nonetheless, some effects were found in the country-based version of the model. Rather, we found support for the alternative Group Importance-Weighted Average model. We conclude that domain-specific self-concepts are weighted differently and thus differentially affect self-esteem, but these weights do not seem to depend on individual differences in importance. Although awaiting confirmation from further studies, our results suggest the idea that individuals use mainly normative importance processes based on cultural factors in weighting each domain specific component of self-concept.