Multidimensional scaling (MDS) is an extremely general scaling procedure that has seen little application in educational measurement. This lack of application is unfortunate because, among its other uses, MDS can help us better understand what educational tests are measuring, examine the structure of educational test data, evaluate the stability of test structure across test forms or groups, and investigate differences across individuals with respect to their perceptions of test items.Perhaps one of the reasons MDS has not been widely applied to measurement problems is that many of the textbooks in this area are either dated or out of print. Therefore, I was pleased to see Borg and Groenen's comprehensive text and even more pleased to be asked to review it for the educational measurement community.Modern Multidimensional Scaling contains 22 chapters, 470 pages, and more than enough equations to satisfy the most mathematically inquisitive among us. I do not recommend trying to read it in 1 night. The book is divided into five parts: (a) Introduction, (b) MDS Models and Solving MDS Problems, (c) Unfolding, (d) MDS Geometry as a Substantive Model, and (e) MDS and Related Methods.Those who are generally familiar with MDS, but who want a more comprehensive understanding of the different models and how they work, will want this book. Borg and Groenen synthesize the contributions of many different MDS pioneers and leave no stone unturned. For example, Guttman's smallest scaling analysis is appropriately described as an MDS model and is integrated into discussions of the models proposed by Torgerson, Shepard, Kruskal, and others. Their discussion of simulation research is also comprehensive and provides an empirical basis for their suggestions regarding selecting dimensionality and choosing an appropriate distance formula. Appropriate attention is also paid to the major types of data analyzed by MDS such as derived similarity data (e.g., computing correlations among test items from the individuals who responded to them) and direct similarity data (e.g., asking participants to rate the similarity of given object pairs).Readers relatively unfamiliar with MDS will also find the book helpful. Borg and Groenen claim that part one, which contains six chapters, can be used as an introductory course in MDS that requires little mathematical sophistication. This introductory section covers the history, purposes, and theory of MDS, and illustrates how MDS can be used to address a variety of research questions. The distinction between metric and nonmetric (ordinal) MDS is clearly described, and the authors provide a conceptual understanding of MDS by showing how an MDS solution can be computed by hand-using only a ruler and a compass. Another

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, 1. CC-BY-NC-ND 4.0 International license It is made available under a (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.The copyright holder for this preprint . http://dx.doi.org/10.1101/048322 doi: bioRxiv preprint first posted online Apr. 13, 2016; contributing to the so-called 'missing heritability'. Here, we describe the online Meta-GWAS Accuracy and Power calculator (MetaGAP; 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 MetaGAP with actual results obtained in the GWAS literature. Specifically, we use genomic-relatedness-matrix restricted maximum likelihood (GREML) 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 R 2 of 36-38%). Hence, cross-study heterogeneity contributes to the missing heritability. Author SummaryLarge-scale genome-wide association studies are uncovering the genetic architecture of traits which are affected by many genetic variants. Such studies typically meta-analyze association results from multiple studies spanning different regions and/or time periods. GWAS results do not yet capture a large share of the total proportion of trait variation attributable to genetic variation. 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. Its influence 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 provide an online calculator, available at www.devlaming.eu, which accounts for these ...

In the current era of systems biological research there is a need for the integrative analysis of binary and quantitative genomics data sets measured on the same objects. One standard tool of exploring the underlying dependence structure present in multiple quantitative data sets is simultaneous component analysis (SCA) model. However, it does not have any provisions when a part of the data are binary. To this end, we propose the generalized SCA (GSCA) model, which takes into account the distinct mathematical properties of binary and quantitative measurements in the maximum likelihood framework. Like in the SCA model, a common low dimensional subspace is assumed to represent the shared information between these two distinct types of measurements. However, the GSCA model can easily be overfitted when a rank larger than one is used, leading to some of the estimated parameters to become very large. To achieve a low rank solution and combat overfitting, we propose to use a concave variant of the nuclear norm penalty. An efficient majorization algorithm is developed to fit this model with different concave penalties. Realistic simulations (low signal-to-noise ratio and highly imbalanced binary data) are used to evaluate the performance of the proposed model in recovering the underlying structure. Also, a missing value based cross validation procedure is implemented for model selection. We illustrate the usefulness of the GSCA model for exploratory data analysis of quantitative gene expression and binary copy number aberration (CNA) measurements obtained from the GDSC1000 data sets.

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AND KEYWORDS AbstractTraditionally, recommender systems present recommendations in lists to the user. In contentand knowledge-based recommendation systems these list are often sorted on some notion of similarity with a query, ideal product specification, or sample product. However, a lot of information is lost in this way, since two even similar products can differ from the query on a completely different set of product characteristics. When using a two dimensional, that is, a map-based, representation of the recommendations, it is possible to retain this information. In the map we can then position recommendations that are similar to each other in the same area of the map.Both in science and industry an increasing number of two dimensional graphical interfaces have been introduced over the last years. However, some of them lack a sound scientific foundation, while other approaches are not applicable in a recommendation setting. In our chapter, we will describe a framework, which has a solid scientific foundation (using state-of-the-art statistical models) and is specifically designed to work with e-commerce product catalogs. Basis of the framework is the Product Catalog Map interface based on multidimensional scaling. Also, weshow another type of interface based on nonlinear principal components analysis, which provides an easy way in constraining the space based on specific characteristic values. Then, we discuss some advanced issues. Firstly, we discuss how the product catalog interface can be adapted to better fit the users' notion of importance of attributes using click stream analysis.Secondly, we show an user interface that combines recommendation by proposing with the map based approach. Finally, we show how these methods can be applied to a real e-commerce product catalog of MP3-players.Free Keywords map-based interface, multidimensional scaling, nonlinear principal components analysis, recommender systems, dissimilarity measure Availability The ERIM Report Series is distributed through the following platforms: