A Censored Mixture Model for Modeling Risk Taking

Risk behavior has substantial consequences for health, well-being, and general behavior. The association between real-world risk behavior and risk behavior on experimental tasks is well documented, but their modeling is challenging for several reasons. First, many experimental risk tasks may end prematurely leading to censored observations. Second, certain outcome values can be more attractive than others. Third, a priori unknown groups of participants can react differently to certain risk-levels. Here, we propose the censored mixture model which models risk taking while dealing with censoring, attractiveness to certain outcomes, and unobserved individual risk preferences, next to experimental conditions.

Multivariate estimation of factor structures of complex traits using SNP-based genomic relationships

Background

Heritability and genetic correlation can be estimated from genome-wide single-nucleotide polymorphism (SNP) data using various methods. We recently developed multivariate genomic-relatedness-based restricted maximum likelihood (MGREML) for statistically and computationally efficient estimation of SNP-based heritability (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h^2_{\text{SNP}}$$\end{document}hSNP2) and genetic correlation (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _G$$\end{document}ρG) across many traits in large datasets. Here, we extend MGREML by allowing it to fit and perform tests on user-specified factor models, while preserving the low computational complexity.

Results

Using simulations, we show that MGREML yields consistent estimates and valid inferences for such factor models at low computational cost (e.g., for data on 50 traits and 20,000 individuals, a saturated model involving 50 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h^2_{\text{SNP}}$$\end{document}hSNP2’s, 1225 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _G$$\end{document}ρG’s, and 50 fixed effects is estimated and compared to a restricted model in less than one hour on a single notebook with two 2.7 GHz cores and 16 GB of RAM). Using repeated measures of height and body mass index from the US Health and Retirement Study, we illustrate the ability of MGREML to estimate a factor model and test whether it fits the data better than a nested model. The MGREML tool, the simulation code, and an extensive tutorial are freely available at https://github.com/devlaming/mgreml/.

Conclusion

MGREML can now be used to estimate multivariate factor structures and perform inferences on such factor models at low computational cost. This new feature enables simple structural equation modeling using MGREML, allowing researchers to specify, estimate, and compare genetic factor models of their choosing using SNP data.

Least-squares bilinear clustering of three-way data

A least-squares bilinear clustering framework for modelling three-way data, where each observation consists of an ordinary two-way matrix, is introduced. The method combines bilinear decompositions of the two-way matrices with clustering over observations. Different clusterings are defined for each part of the bilinear decomposition, which decomposes the matrix-valued observations into overall means, row margins, column margins and row–column interactions. Therefore up to four different classifications are defined jointly, one for each type of effect. The computational burden is greatly reduced by the orthogonality of the bilinear model, such that the joint clustering problem reduces to separate problems which can be handled independently. Three of these sub-problems are specific cases of k-means clustering; a special algorithm is formulated for the row–column interactions, which are displayed in clusterwise biplots. The method is illustrated via an empirical example and interpreting the interaction biplots are discussed. Supplemental materials for this paper are available online, which includes the dedicated R package, .

Multivariate analysis reveals shared genetic architecture of brain morphology and human behavior

Human variation in brain morphology and behavior are related and highly heritable. Yet, it is largely unknown to what extent specific features of brain morphology and behavior are genetically related. Here, we introduce a computationally efficient approach for multivariate genomic-relatedness-based restricted maximum likelihood (MGREML) to estimate the genetic correlation between a large number of phenotypes simultaneously. Using individual-level data (N = 20,190) from the UK Biobank, we provide estimates of the heritability of gray-matter volume in 74 regions of interest (ROIs) in the brain and we map genetic correlations between these ROIs and health-relevant behavioral outcomes, including intelligence. We find four genetically distinct clusters in the brain that are aligned with standard anatomical subdivision in neuroscience. Behavioral traits have distinct genetic correlations with brain morphology which suggests trait-specific relevance of ROIs. These empirical results illustrate how MGREML can be used to estimate internally consistent and high-dimensional genetic correlation matrices in large datasets.

A Robust Bootstrap Test for Mediation Analysis

Mediation analysis is central to theory building and testing in organizational sciences. Scholars often use linear regression analysis based on normal-theory maximum likelihood estimators to test mediation. However, these estimators are very sensitive to deviations from normality assumptions, such as outliers, heavy tails, or skewness of the observed distribution. This sensitivity seriously threatens the empirical testing of theory about mediation mechanisms. To overcome this threat, we develop a robust mediation method that yields reliable results even when the data deviate from normality assumptions. We demonstrate the mechanics of our proposed method in an illustrative case, while simulation studies show that our method is both superior in estimating the effect size and more reliable in assessing its significance than the existing methods. Furthermore, we provide freely available software in R and SPSS to enhance its accessibility and adoption by empirical researchers.

Genome-wide association analyses of risk tolerance and risky behaviors in over 1 million individuals identify hundreds of loci and shared genetic influences

Humans vary substantially in their willingness to take risks. In a combined sample of over 1 million individuals, we conducted genome-wide association studies (GWAS) of general risk tolerance, adventurousness, and risky behaviors in the driving, drinking, smoking, and sexual domains. Across all GWAS, we identified hundreds of associated loci, including 99 loci associated with general risk tolerance. We report evidence of substantial shared genetic influences across risk tolerance and the risky behaviors: 46 of the 99 general risk tolerance loci contain a lead SNP for at least one of our other GWAS, and general risk tolerance is genetically correlated ([Formula: see text] ~ 0.25 to 0.50) with a range of risky behaviors. Bioinformatics analyses imply that genes near SNPs associated with general risk tolerance are highly expressed in brain tissues and point to a role for glutamatergic and GABAergic neurotransmission. We found no evidence of enrichment for genes previously hypothesized to relate to risk tolerance.

Genome-wide Analysis of Large-scale Longitudinal Outcomes using Penalization -GALLOP algorithm

Genome-wide association studies (GWAS) with longitudinal phenotypes provide opportunities to identify genetic variations associated with changes in human traits over time. Mixed models are used to correct for the correlated nature of longitudinal data. GWA studies are notorious for their computational challenges, which are considerable when mixed models for thousands of individuals are fitted to millions of SNPs. We present a new algorithm that speeds up a genome-wide analysis of longitudinal data by several orders of magnitude. It solves the equivalent penalized least squares problem efficiently, computing variances in an initial step. Factorizations and transformations are used to avoid inversion of large matrices. Because the system of equations is bordered, we can re-use components, which can be precomputed for the mixed model without a SNP. Two SNP effects (main and its interaction with time) are obtained. Our method completes the analysis a thousand times faster than the R package lme4, providing an almost identical solution for the coefficients and p-values. We provide an R implementation of our algorithm.

Competing for the same value segments? Insight into the volatile Dutch political landscape

Values are central to public debates today. Human values convey broad goals that serve as guiding principles in a person’s life and value priorities differ across people in society. Groups in society holding opposing values (e.g., universalism versus security) will make different choices when voting in an election. Whereas over time, values are relatively stable, the number and type of political parties as well as the political values they communicate and disseminate have been changing. Groups of people holding the same human values may therefore vote for another (new) party in a later election. We focus on analyzing the relationship between human values and voting in elections, introducing a new methodology to analyze how value profiles relate to political support over time. We investigate the Dutch multi-party political system over five waves of the European Social Survey, spanning 2002 until 2010. Whilst previous research has focused on individual values separately and focused on voters only, we (1) distinguish groups holding a similar set of opposing and compatible values (value profile) instead of focusing on single values in the the entire population; (2) incorporate a correction for differences in scale use in our model; (3) compare voting over time; (4) include non-voters, a growing group in Dutch society. We find evidence that specific value profiles are related to voting for a specific set of political parties. We also find that specific value profiles distinguish non-voters from voters and that voters for populist parties resemble non-voters.

Regularized Generalized Canonical Correlation Analysis: A Framework for Sequential Multiblock Component Methods

A new framework for sequential multiblock component methods is presented. This framework relies on a new version of regularized generalized canonical correlation analysis (RGCCA) where various scheme functions and shrinkage constants are considered. Two types of between block connections are considered: blocks are either fully connected or connected to the superblock (concatenation of all blocks). The proposed iterative algorithm is monotone convergent and guarantees obtaining at convergence a stationary point of RGCCA. In some cases, the solution of RGCCA is the first eigenvalue/eigenvector of a certain matrix. For the scheme functions x, [Formula: see text], [Formula: see text] or [Formula: see text] and shrinkage constants 0 or 1, many multiblock component methods are recovered.

Regularized Generalized Canonical Correlation Analysis: A Framework for Sequential Multiblock Component Methods

A new framework for sequential multiblock component methods is presented. This framework relies on a new version of regularized generalized canonical correlation analysis (RGCCA) where various scheme functions and shrinkage constants are considered. Two types of between block connections are considered: blocks are either fully connected or connected to the superblock (concatenation of all blocks). The proposed iterative algorithm is monotone convergent and guarantees obtaining at convergence a stationary point of RGCCA. In some cases, the solution of RGCCA is the first eigenvalue/eigenvector of a certain matrix. For the scheme functions x, [Formula: see text], [Formula: see text] or [Formula: see text] and shrinkage constants 0 or 1, many multiblock component methods are recovered.

Meta-GWAS Accuracy and Power (MetaGAP) Calculator Shows that Hiding Heritability Is Partially Due to Imperfect Genetic Correlations across Studies

Large-scale genome-wide association results are typically obtained from a fixed-effects meta-analysis of GWAS summary statistics from multiple studies spanning different regions and/or time periods. This approach averages the estimated effects of genetic variants across studies. In case genetic effects are heterogeneous across studies, the statistical power of a GWAS and the predictive accuracy of polygenic scores are attenuated, contributing to the so-called ‘missing heritability’. Here, we describe the online Meta-GWAS Accuracy and Power (MetaGAP) calculator (available at www.devlaming.eu) which quantifies this attenuation based on a novel multi-study framework. By means of simulation studies, we show that under a wide range of genetic architectures, the statistical power and predictive accuracy provided by this calculator are accurate. We compare the predictions from the MetaGAP calculator with actual results obtained in the GWAS literature. Specifically, we use genomic-relatedness-matrix restricted maximum likelihood to estimate the SNP heritability and cross-study genetic correlation of height, BMI, years of education, and self-rated health in three large samples. These estimates are used as input parameters for the MetaGAP calculator. Results from the calculator suggest that cross-study heterogeneity has led to attenuation of statistical power and predictive accuracy in recent large-scale GWAS efforts on these traits (e.g., for years of education, we estimate a relative loss of 51–62% in the number of genome-wide significant loci and a relative loss in polygenic score R² of 36–38%). Hence, cross-study heterogeneity contributes to the missing heritability.

Large-scale genome-wide association studies are uncovering the genetic architecture of traits which are affected by many genetic variants. In such efforts, one typically meta-analyzes association results from multiple studies spanning different regions and/or time periods. Results from such efforts do not yet capture a large share of the heritability. The origins of this so-called ‘missing heritability’ have been strongly debated. One factor exacerbating the missing heritability is heterogeneity in the effects of genetic variants across studies. The effect of this type of heterogeneity on statistical power to detect associated genetic variants and the accuracy of polygenic predictions is poorly understood. In the current study, we derive the precise effects of heterogeneity in genetic effects across studies on both the statistical power to detect associated genetic variants as well as the accuracy of polygenic predictions. We present an online calculator, available at www.devlaming.eu, which accounts for these effects. By means of this calculator, we show that imperfect genetic correlations between studies substantially decrease statistical power and predictive accuracy and, thereby, contribute to the missing heritability. The MetaGAP calculator helps researchers to gauge how sensitive their results will be to heterogeneity in genetic effects across studies. If strong heterogeneity is expected, random-effects meta-analysis methods should be used instead of fixed-effects methods.

Genetic variants associated with subjective well-being, depressive symptoms, and neuroticism identified through genome-wide analyses

Very few genetic variants have been associated with depression and neuroticism, likely because of limitations on sample size in previous studies. Subjective well-being, a phenotype that is genetically correlated with both of these traits, has not yet been studied with genome-wide data. We conducted genome-wide association studies of three phenotypes: subjective well-being (n = 298,420), depressive symptoms (n = 161,460), and neuroticism (n = 170,911). We identify 3 variants associated with subjective well-being, 2 variants associated with depressive symptoms, and 11 variants associated with neuroticism, including 2 inversion polymorphisms. The two loci associated with depressive symptoms replicate in an independent depression sample. Joint analyses that exploit the high genetic correlations between the phenotypes (|ρ^| ≈ 0.8) strengthen the overall credibility of the findings and allow us to identify additional variants. Across our phenotypes, loci regulating expression in central nervous system and adrenal or pancreas tissues are strongly enriched for association.

Genome-wide association study identifies 74 loci associated with educational attainment

Educational attainment is strongly influenced by social and other environmental factors, but genetic factors are estimated to account for at least 20% of the variation across individuals. Here we report the results of a genome-wide association study (GWAS) for educational attainment that extends our earlier discovery sample of 101,069 individuals to 293,723 individuals, and a replication study in an independent sample of 111,349 individuals from the UK Biobank. We identify 74 genome-wide significant loci associated with the number of years of schooling completed. Single-nucleotide polymorphisms associated with educational attainment are disproportionately found in genomic regions regulating gene expression in the fetal brain. Candidate genes are preferentially expressed in neural tissue, especially during the prenatal period, and enriched for biological pathways involved in neural development. Our findings demonstrate that, even for a behavioural phenotype that is mostly environmentally determined, a well-powered GWAS identifies replicable associated genetic variants that suggest biologically relevant pathways. Because educational attainment is measured in large numbers of individuals, it will continue to be useful as a proxy phenotype in efforts to characterize the genetic influences of related phenotypes, including cognition and neuropsychiatric diseases.

Constrained Dual Scaling for Detecting Response Styles in Categorical Data

Dual scaling (DS) is a multivariate exploratory method equivalent to correspondence analysis when analysing contingency tables. However, for the analysis of rating data, different proposals appear in the DS and correspondence analysis literature. It is shown here that a peculiarity of the DS method can be exploited to detect differences in response styles. Response styles occur when respondents use rating scales differently for reasons not related to the questions, often biasing results. A spline-based constrained version of DS is devised which can detect the presence of four prominent types of response styles, and is extended to allow for multiple response styles. An alternating nonnegative least squares algorithm is devised for estimating the parameters. The new method is appraised both by simulation studies and an empirical application.

When does power disparity help or hurt group performance?

Power differences are ubiquitous in social settings. However, the question of whether groups with higher or lower power disparity achieve better performance has thus far received conflicting answers. To address this issue, we identify 3 underlying assumptions in the literature that may have led to these divergent findings, including a myopic focus on static hierarchies, an assumption that those at the top of hierarchies are competent at group tasks, and an assumption that equality is not possible. We employ a multimethod set of studies to examine these assumptions and to understand when power disparity will help or harm group performance. First, our agent-based simulation analyses show that by unpacking these common implicit assumptions in power research, we can explain earlier disparate findings--power disparity benefits group performance when it is dynamically aligned with the power holder's task competence, and harms group performance when held constant and/or is not aligned with task competence. Second, our empirical findings in both a field study of fraud investigation groups and a multiround laboratory study corroborate the simulation results. We thereby contribute to research on power by highlighting a dynamic understanding of power in groups and explaining how current implicit assumptions may lead to opposing findings.

GWAS of 126,559 individuals identifies genetic variants associated with educational attainment

A genome-wide association study (GWAS) of educational attainment was conducted in a discovery sample of 101,069 individuals and a replication sample of 25,490. Three independent single-nucleotide polymorphisms (SNPs) are genome-wide significant (rs9320913, rs11584700, rs4851266), and all three replicate. Estimated effects sizes are small (coefficient of determination R(2) ≈ 0.02%), approximately 1 month of schooling per allele. A linear polygenic score from all measured SNPs accounts for ≈2% of the variance in both educational attainment and cognitive function. Genes in the region of the loci have previously been associated with health, cognitive, and central nervous system phenotypes, and bioinformatics analyses suggest the involvement of the anterior caudate nucleus. These findings provide promising candidate SNPs for follow-up work, and our effect size estimates can anchor power analyses in social-science genetics.

The molecular genetic architecture of self-employment

Economic variables such as income, education, and occupation are known to affect mortality and morbidity, such as cardiovascular disease, and have also been shown to be partly heritable. However, very little is known about which genes influence economic variables, although these genes may have both a direct and an indirect effect on health. We report results from the first large-scale collaboration that studies the molecular genetic architecture of an economic variable-entrepreneurship-that was operationalized using self-employment, a widely-available proxy. Our results suggest that common SNPs when considered jointly explain about half of the narrow-sense heritability of self-employment estimated in twin data (σ(g)(2)/σ(P)(2) = 25%, h(2) = 55%). However, a meta-analysis of genome-wide association studies across sixteen studies comprising 50,627 participants did not identify genome-wide significant SNPs. 58 SNPs with p<10(-5) were tested in a replication sample (n = 3,271), but none replicated. Furthermore, a gene-based test shows that none of the genes that were previously suggested in the literature to influence entrepreneurship reveal significant associations. Finally, SNP-based genetic scores that use results from the meta-analysis capture less than 0.2% of the variance in self-employment in an independent sample (p≥0.039). Our results are consistent with a highly polygenic molecular genetic architecture of self-employment, with many genetic variants of small effect. Although self-employment is a multi-faceted, heavily environmentally influenced, and biologically distal trait, our results are similar to those for other genetically complex and biologically more proximate outcomes, such as height, intelligence, personality, and several diseases.

Fast linear mixed model computations for genome-wide association studies with longitudinal data

Genome-wide association studies are characterized by a huge number of statistical tests performed to discover new disease-related genetic variants [in the form of single-nucleotide polymorphisms (SNPs)] in human DNA. Many SNPs have been identified for cross-sectionally measured phenotypes. However, there is a growing interest in genetic determinants of the evolution of traits over time. Dealing with correlated observations from the same individual, we need to apply advanced statistical techniques. The linear mixed model is popular but also much more computationally demanding than fitting a linear regression model to independent observations. We propose a conditional two-step approach as an approximate method to explore the longitudinal relationship between the trait and the SNP. In a simulation study, we compare several fast methods with respect to their accuracy and speed. The conditional two-step approach is applied to relate SNPs to longitudinal bone mineral density responses collected in the Rotterdam Study.

Molecular Genetics and Economics

The costs of comprehensively genotyping human subjects have fallen to the point where major funding bodies, even in the social sciences, are beginning to incorporate genetic and biological markers into major social surveys. How, if at all, should economists use and combine molecular genetic and economic data from these surveys? What challenges arise when analyzing genetically informative data? To illustrate, we present results from a “genome-wide association study” of educational attainment. We use a sample of 7,500 individuals from the Framingham Heart Study; our dataset contains over 360,000 genetic markers per person. We get some initially promising results linking genetic markers to educational attainment, but these fail to replicate in a second large sample of 9,500 people from the Rotterdam Study. Unfortunately such failure is typical in molecular genetic studies of this type, so the example is also cautionary. We discuss a number of methodological challenges that face researchers who use molecular genetics to reliably identify genetic associates of economic traits. Our overall assessment is cautiously optimistic: this new data source has potential in economics. But researchers and consumers of the genoeconomic literature should be wary of the pitfalls, most notably the difficulty of doing reliable inference when faced with multiple hypothesis problems on a scale never before encountered in social science.

Embedding the Organizational Culture Profile Into Schwartz’s Theory of Universals in Values

Person-organization fit (P-O fit) is often measured by the congruence of a person’s values and the values that he or she ascribes to the organization. A popular instrument used in this context is the Organizational Culture Profile (OCP; O’Reilly, Chatman, & Caldwell, 1991). The OCP uses 54 items that form eight factors in exploratory factor analysis. We investigate the extent to which the OCP can be embedded into Schwartz’s Theory of Universals in Values (TUV) that is formulated in terms of a circumplex in a two-dimensional plane. To address this question, we develop a nonstandard multidimensional scaling (MDS) method that enforces a TUV-based axial regionality onto the solution space together with a permutation test that assesses the consistency of the side constraints with the MDS representation. We find that the OCP can indeed be embedded into the TUV. The practical implication is that P-O fit can be assessed more simply by the congruence of the person’s and the organization’s positions on two value dimensions: risk versus rules and results versus relations.

Optimal Scaling of Interaction Effects in Generalized Linear Models

Multiplicative interaction models, such as Goodman's (1981) RC(M) association models, can be a useful tool for analyzing the content of interaction effects. However, most models for interaction effects are suitable only for data sets with two or three predictor variables. Here, we discuss an optimal scaling model for analyzing the content of interaction effects in generalized linear models with any number of categorical predictor variables. This model, which we call the optimal scaling of interactions model, is a parsimonious, one-dimensional multiplicative interaction model. We discuss how the model can be used to visually interpret the interaction effects. Several extensions of the one-dimensional model are also explored. Finally, two data sets are used to show how the results of the model can be applied and interpreted. The first data set is based on the Student/Teacher Achievement Ratio project and is used to investigate the effects of class size on the performance of primary school students. The second data set comprises four questions from the 1994 General Social Survey ( Davis & Smith, 1996 ) on attitudes of the labor roles of women.

Nonlinear principal components analysis: introduction and application

The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover nonlinear relationships between variables. Also, nonlinear PCA can deal with variables at their appropriate measurement level; for example, it can treat Likert-type scales ordinally instead of numerically. Every observed value of a variable can be referred to as a category. While performing PCA, nonlinear PCA converts every category to a numeric value, in accordance with the variable's analysis level, using optimal quantification. The authors discuss how optimal quantification is carried out, what analysis levels are, which decisions have to be made when applying nonlinear PCA, and how the results can be interpreted. The strengths and limitations of the method are discussed. An example applying nonlinear PCA to empirical data using the program CATPCA (J. J. Meulman, W. J. Heiser, & SPSS, 2004) is provided.

Stability of nonlinear principal components analysis: An empirical study using the balanced bootstrap

Principal components analysis (PCA) is used to explore the structure of data sets containing linearly related numeric variables. Alternatively, nonlinear PCA can handle possibly nonlinearly related numeric as well as nonnumeric variables. For linear PCA, the stability of its solution can be established under the assumption of multivariate normality. For nonlinear PCA, however, standard options for establishing stability are not provided. The authors use the nonparametric bootstrap procedure to assess the stability of nonlinear PCA results, applied to empirical data. They use confidence intervals for the variable transformations and confidence ellipses for the eigenvalues, the component loadings, and the person scores. They discuss the balanced version of the bootstrap, bias estimation, and Procrustes rotation. To provide a benchmark, the same bootstrap procedure is applied to linear PCA on the same data. On the basis of the results, the authors advise using at least 1,000 bootstrap samples, using Procrustes rotation on the bootstrap results, examining the bootstrap distributions along with the confidence regions, and merging categories with small marginal frequencies to reduce the variance of the bootstrap results.