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Network Psychometrics
TL;DR: In this paper, a general introduction to network modeling in psychometrics is provided, with an introduction to the statistical model formulation of pairwise Markov random fields (PMRF), followed by an introduction of the Ising model suitable for binary data.
Abstract: This chapter provides a general introduction of network modeling in psychometrics. The chapter starts with an introduction to the statistical model formulation of pairwise Markov random fields (PMRF), followed by an introduction of the PMRF suitable for binary data: the Ising model. The Ising model is a model used in ferromagnetism to explain phase transitions in a field of particles. Following the description of the Ising model in statistical physics, the chapter continues to show that the Ising model is closely related to models used in psychometrics. The Ising model can be shown to be equivalent to certain kinds of logistic regression models, loglinear models and multi-dimensional item response theory (MIRT) models. The equivalence between the Ising model and the MIRT model puts standard psychometrics in a new light and leads to a strikingly different interpretation of well-known latent variable models. The chapter gives an overview of methods that can be used to estimate the Ising model, and concludes with a discussion on the interpretation of latent variables given the equivalence between the Ising model and MIRT.
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TL;DR: The network theory has direct implications for how to understand diagnosis and treatment, and suggests a clear agenda for future research in psychiatry and associated disciplines.
1,311 citations
TL;DR: In this article, the authors describe how regularization techniques can be used to efficiently estimate a parsimonious and interpretable network structure in psychological data, and demonstrate the method in an empirical example on post-traumatic stress disorder data.
Abstract: Recent years have seen an emergence of network modeling applied to moods, attitudes, and problems in the realm of psychology. In this framework, psychological variables are understood to directly affect each other rather than being caused by an unobserved latent entity. In this tutorial, we introduce the reader to estimating the most popular network model for psychological data: the partial correlation network. We describe how regularization techniques can be used to efficiently estimate a parsimonious and interpretable network structure in psychological data. We show how to perform these analyses in R and demonstrate the method in an empirical example on post-traumatic stress disorder data. In addition, we discuss the effect of the hyperparameter that needs to be manually set by the researcher, how to handle non-normal data, how to determine the required sample size for a network analysis, and provide a checklist with potential solutions for problems that can arise when estimating regularized partial correlation networks.
839 citations
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TL;DR: The current state-of-the-art of network estimation is introduced and a rationale why researchers should investigate the accuracy of psychological networks is provided, and the free R-package bootnet is developed that allows for estimating psychological networks in a generalized framework in addition to the proposed bootstrap methods.
Abstract: The usage of psychological networks that conceptualize psychological behavior as a complex interplay of psychological and other components has gained increasing popularity in various fields of psychology. While prior publications have tackled the topics of estimating and interpreting such networks, little work has been conducted to check how accurate (i.e., prone to sampling variation) networks are estimated, and how stable (i.e., interpretation remains similar with less observations) inferences from the network structure (such as centrality indices) are. In this tutorial paper, we aim to introduce the reader to this field and tackle the problem of accuracy under sampling variation. We first introduce the current state-of-the-art of network estimation. Second, we provide a rationale why researchers should investigate the accuracy of psychological networks. Third, we describe how bootstrap routines can be used to (A) assess the accuracy of estimated network connections, (B) investigate the stability of centrality indices, and (C) test whether network connections and centrality estimates for different variables differ from each other. We introduce two novel statistical methods: for (B) the correlation stability coefficient, and for (C) the bootstrapped difference test for edge-weights and centrality indices. We conducted and present simulation studies to assess the performance of both methods. Finally, we developed the free R-package bootnet that allows for estimating psychological networks in a generalized framework in addition to the proposed bootstrap methods. We showcase bootnet in a tutorial, accompanied by R syntax, in which we analyze a dataset of 359 women with posttraumatic stress disorder available online.
606 citations
TL;DR: A review of all empirical network studies published between 2010 and 2016 concludes that network analysis has yielded important insights and may provide an important inroad towards personalized medicine by investigating the network structures of individual patients.
Abstract: Purpose
The network perspective on psychopathology understands mental disorders as complex networks of interacting symptoms. Despite its recent debut, with conceptual foundations in 2008 and empirical foundations in 2010, the framework has received considerable attention and recognition in the last years.
515 citations
TL;DR: Challenges to network theory may propel the network approach from its adolescence into adulthood and promises advances in understanding psychopathology both at the nomothetic and idiographic level.
Abstract: Since the introduction of mental disorders as networks of causally interacting symptoms, this novel framework has received considerable attention. The past years have resulted in over 40 scientific publications and numerous conference symposia and workshops. Now is an excellent moment to take stock of the network approach: What are its most fundamental challenges, and what are potential ways forward in addressing them? After a brief conceptual introduction, we first discuss challenges to network theory: (1) What is the validity of the network approach beyond some commonly investigated disorders such as major depression? (2) How do we best define psychopathological networks and their constituent elements? And (3) how can we gain a better understanding of the causal nature and real-life underpinnings of associations among symptoms? Next, after a short technical introduction to network modeling, we discuss challenges to network methodology: (4) heterogeneity of samples studied with network analytic models, and (5) a lurking replicability crisis in this strongly data-driven and exploratory field. Addressing these challenges may propel the network approach from its adolescence into adulthood and promises advances in understanding psychopathology both at the nomothetic and idiographic level.
485 citations
References
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Journal Article•
TL;DR: Copyright (©) 1999–2012 R Foundation for Statistical Computing; permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and permission notice are preserved on all copies.
Abstract: Copyright (©) 1999–2012 R Foundation for Statistical Computing. Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions, except that this permission notice may be stated in a translation approved by the R Core Team.
272,030 citations
"Network Psychometrics" refers methods in this paper
...For example, the iterative proportional fitting algorithm (Haberman, 1972), which is implemented in the loglin function in the statistical programming language R (R Core Team, 2016), can be used to estimate the parameters of the Ising model....
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...R Core Team (2016)....
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TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
Abstract: SUMMARY We propose a new method for estimation in linear models. The 'lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.
40,785 citations
"Network Psychometrics" refers methods in this paper
...The most common regularization method is `1 regularization–commonly known as the least absolute shrinkage and selection operator (LASSO; Tibshirani 1996)–in which the sum of absolute parameter values is penalized to be under some value....
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TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Abstract: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
33,771 citations
TL;DR: It is shown that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation, and an algorithm called LARS‐EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lamba.
Abstract: Summary. We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together.The elastic net is particularly useful when the number of predictors (p) is much bigger than the number of observations (n). By contrast, the lasso is not a very satisfactory variable selection method in the
16,538 citations
"Network Psychometrics" refers background in this paper
...Zou and Hastie (2005) proposed a compromise between both penalty functions in the elastic net, which uses another tuning parameter, α, to mix between `1 and `2 regularization: PenElasticNet (ω i) = k∑ j=1,j!=i 1 2(1− α)ω 2 ij + α|ωij | If α = 1, the elastic net reduces to the LASSO penalty, and if…...
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TL;DR: In comparative timings, the new algorithms are considerably faster than competing methods and can handle large problems and can also deal efficiently with sparse features.
Abstract: We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, two-class logistic regression, and multinomial regression problems while the penalties include l(1) (the lasso), l(2) (ridge regression) and mixtures of the two (the elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.
13,656 citations
"Network Psychometrics" refers background or methods in this paper
...For each node i the following expression is maximized (Friedman et al., 2010): max τi,ωi [Li (τ ,Ω;x)− λPen (ω i)] (17) Where ω i is the ith row (or column due to symmetry) of Ω and Pen (ω i) denotes the penalty function, which is defined in the LASSO as follows: Pen`1 (ω i) = ||ω i||1 =…...
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...We have implemented `1-regularized disjoint pseudolikelihood estimation of the Ising model using EBIC to select a tuning parameter per node in the R package IsingFit (van Borkulo and Epskamp, 2014; van Borkulo et al., 2014), which uses glmnet for optimization (Friedman et al., 2010)....
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...For each node i the following expression is maximized (Friedman et al., 2010):...
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..., 2014), which uses glmnet for optimization (Friedman et al., 2010)....
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...Again, the R package glmnet (Friedman et al., 2010) can be used for estimating parameters using the elastic net....
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