arXiv subjects

Lourens Waldorp

Publications and source records attributed to Lourens Waldorp.

At least 19 recordsLinked to original sources

arXiv2026

Measurement error and reliability from a different perspective: Reliability of decision functions and the sum score

We propose an alternative framework for measurement error that allows us to determine reliability at the level of the decision, such as the decision to pass or fail. This framework makes it possible to answer the question which properties of a decision function are relevant to make decisions. The mechanism is relatively simple for dichotomous items: The response to any item has probability $\tfrac{1}{2}(1-ρ)$, with $ρ\in [-1,1]$, to be different from the original response. We show that this framework satisfies the classical axioms (those of Lord and Novick) and can therefore be considered as being aligned with classical test theory. We also show some relations to modern test theory and its connections to graphs. We then connect the idea of reliability at the level of the decision to the idea of how many of the (two-response) items are required to be flipped to change the decision; this is referred to as stability. Finally, we argue that from this perspective the best decision function (with respect to a set of properties including stability) is a weighted sum score with threshold value.

stat.ME↗

arXiv2026

High-dimensional networks and mean squared error for possibly misspecified models

To avoid missing important variables and their connections in networks, more and more variables are included in network analysis. Here we show that in a setting with many more parameters than observations (high-dimensional) it is possible to get a conservative (i.e., low false positive rate) estimate of the neighbourhood for each node (which connections are in the network). A neighbourhood is often estimated with a linear model, and this leads to two interesting cases: (i) If the true model is linear, then neighbourhood selection work reasonably well, and (ii) if the true model is nonlinear, then neighbourhood selection requires a penalty for the high dimensions. Here we show the impact of the ridge parameter on the mean squared error, and how this leads to low test variance and hence to neighbourhoods with large numbers of edges. We connect these insights with results from machine learning, where the so-called double descent (when more parameters are included than observations, the mean squared error goes down a second time) has put the traditional view on model selection upside down. Essentially, for adequate neighbourhood selection in models with a large number of parameters, the volume of the model space needs to be included in the penalty. Most neighbourhood selection methods (e.g., Lasso, AIC, BIC) lead to spurious edges (high false positive rate), but we prove that in the high-dimensional setting, minimum description length leads to correct neighbourhood selection or smaller (low false positive rates) in both cases when either the model is correctly or incorrectly assumed linear

stat.ML↗

arXiv2026

What is your Prior Worth? Effective Sample Size and Sample Size Planning for Gaussian Graphical Models

In Bayesian analysis, the prior effective sample size (ESS) expresses the information carried by a prior distribution in units of observations, quantifying how much independent information the prospective data must provide to outweigh an informative prior elicited from a previous study. For network models such as Gaussian graphical models (GGMs), the prior ESS is not straightforward to compute. The Wishart and G-Wishart priors induce dependence among the entries of the precision matrix, and their informativeness has never been expressed in an interpretable, observation-equivalent unit. As a result, researchers eliciting an informative prior for a GGM have had no principled basis for sample size planning. In this paper, we close this gap by formalizing a pre-data ESS for GGMs under the Wishart and G-Wishart priors. We adapt five ESS estimators to the GGM setting and compute each through two aggregation schemes: a global ESS measure based on a determinant ratio, and a parameterwise version based on a Cholesky decomposition. Building on these measures, we introduce two complementary planning strategies: the Data-to-Prior Information Ratio (DPIR), which determines the sample size at which the data dominate the prior, and a GGM extension of Bayes Factor Design Analysis (BFDA), which determines the sample size required for conclusive edge-based evidence. Simulation studies show that the two procedures target complementary design goals and that the ESS estimators differ systematically in their sensitivity to network structure and geometry. We conclude by outlining extensions to other graphical models, including time-dependent variants, as well as to matrix-variate mixture priors.

stat.ME↗

arXiv2026

Towards personalised intervention: A causal-dynamical framework to determine psychological treatment trajectories

For approximately half of the individuals receiving mental health care, the results are suboptimal, even when treatments align with evidence-based guidelines. These limited effects may partly stem from how clinical decisions on treatment focus are made in mental health care. Typically, treatment strategy is guided by the diagnostic classification combined with the individualized case conceptualization. While standard, this approach may fall short for several reasons such as biases on the part of both the patient and therapist, and treatment guidelines being based on average effects that may not (exactly) suit the individual patient. To address these challenges, we propose a novel framework that reduces biases in clinical decision-making and makes it genuinely possible to tailor treatment focus to the individual patient. This framework involves (a) constructing causal graphs and estimating causal effects from intensively collected, longitudinal patient data, (b) simulating new time series based upon the causal relationships, and (c) using these simulations to identify the most effective treatment focus for the individual patient. By simulating and comparing different intervention strategies and examining both the estimated individual's responsiveness and its long-term effectiveness, this approach may generate useful insights to guide treatment focus and strategy, which can lead to a significant improvement of treatment outcomes in mental health care.

nlin.AO↗

arXiv2026

Blume-Capel model: Estimation of a three stable state network for $-\bf 1$, $\bf 0$ and $\bf +1$ data

An extension of the Ising model is proposed as a viable alternative for data with values $-1$, $0$ and $+1$ in the inverse problem, i.e., estimation of the parameters. This model is called the Blume-Capel (BC) model, adapted from physics for small networks. The advantage of the BC model is not only the fact that it is possible to have a neutral (centrist) position on the response scale, but also that this model allows for three stable states. We illustrate magnetisation properties of the BC model using simulations and mean field results. For estimation of the BC parameters, we show that the BC model is part of the exponential family of distributions and show that the model is identified, except for the (inverse) temperature. We then show that combining pseudo-likelihood with lasso yields accurate parameter recovery for the BC model, even in small networks. Moreover, confidence intervals with good coverage properties can be obtained using the desparsified lasso together with sandwich and shrinkage techniques. We apply the methods to data obtained from the online platform \textit{Stemwijzer}, intended to aid people in deciding for whom to vote.

stat.AP↗

arXiv2025

Polarisation in increasingly connected societies

Explanations of polarization often rely on one of the three mechanisms: homophily, bounded confidence, and community-based interactions. Models based on these mechanisms consider the lack of interactions as the main cause of polarization. Given the increasing connectivity in modern society, this explanation of polarization may be insufficient. We aim to show that in involvement-based models, society becomes more polarized as its connectedness increases. To this end, we propose a minimal voter-type model (called I-voter) that incorporates involvement as a key mechanism in opinion formation and study its dependence on network connectivity. We describe the steady-state behaviour of the model analytically, at the mean-field and the moment-hierarchy levels and stress the generality of our findings by considering various extensions and different network topologies.

physics.soc-ph↗

arXiv2025

Mean-field theory of the general-spin Ising model

Motivated by modelling in physics and other disciplines, such as sociology and psychology, we derive the mean field of the general-spin Ising model from the variational principle of the Gibbs free energy. The general-spin Ising model has $2k+1$ spin values, generated by $-(k-j)/k$, with $j=0,1,2\ldots,2k$, such that for $k=1$ we obtain $-1,0,1$, for example; the Hamiltonian is identical to that of the standard Ising model. The general-spin Ising model exhibits spontaneous magnetisation, similar to the standard Ising model, but with the location translated by a factor depending on the number of categories $2k+1$. We also show how the accuracy of the mean field depends on both the number of nodes and node degree, and that the hysteresis effect decreases and saturates with the number of categories $2k+1$. Monte Carlo simulations confirm the theoretical results.

cond-mat.stat-mech↗

arXiv2025

The Principle of Redundant Reflection

The fact that redundant information does not update a rational belief implies that rational beliefs are updated using Bayes rule. In the framework of Hild (1998a), this is true under mild conditions for discrete, continuous, and arbitrary measure spaces. We prove this result and illustrate it with two examples.

stat.ME↗

arXiv2024

Perturbation graphs, invariant prediction and causal relations in psychology

Networks (graphs) in psychology are often restricted to settings without interventions. Here we consider a framework borrowed from biology that involves multiple interventions from different contexts (observations and experiments) in a single analysis. The method is called perturbation graphs. In gene regulatory networks, the induced change in one gene is measured on all other genes in the analysis, thereby assessing possible causal relations. This is repeated for each gene in the analysis. A perturbation graph leads to the correct set of causes (not necessarily direct causes). Subsequent pruning of paths in the graph (called transitive reduction) should reveal direct causes. We show that transitive reduction will not in general lead to the correct underlying graph. We also show that invariant causal prediction is a generalisation of the perturbation graph method, where including additional variables does reveal direct causes, and thereby replacing transitive reduction. We conclude that perturbation graphs provide a promising new tool for experimental designs in psychology, and combined with invariant causal prediction make it possible to reveal direct causes instead of causal paths. As an illustration we apply the perturbation graphs and invariant causal prediction to a data set about attitudes on meat consumption and to a time series of a patient diagnosed with major depression disorder.

stat.ME↗

arXiv2024

Explaining Clustering of Ecological Momentary Assessment Data Through Temporal and Feature Attention

In the field of psychopathology, Ecological Momentary Assessment (EMA) studies offer rich individual data on psychopathology-relevant variables (e.g., affect, behavior, etc) in real-time. EMA data is collected dynamically, represented as complex multivariate time series (MTS). Such information is crucial for a better understanding of mental disorders at the individual- and group-level. More specifically, clustering individuals in EMA data facilitates uncovering and studying the commonalities as well as variations of groups in the population. Nevertheless, since clustering is an unsupervised task and true EMA grouping is not commonly available, the evaluation of clustering is quite challenging. An important aspect of evaluation is clustering explainability. Thus, this paper proposes an attention-based interpretable framework to identify the important time-points and variables that play primary roles in distinguishing between clusters. A key part of this study is to examine ways to analyze, summarize, and interpret the attention weights as well as evaluate the patterns underlying the important segments of the data that differentiate across clusters. To evaluate the proposed approach, an EMA dataset of 187 individuals grouped in 3 clusters is used for analyzing the derived attention-based importance attributes. More specifically, this analysis provides the distinct characteristics at the cluster-, feature- and individual level. Such clustering explanations could be beneficial for generalizing existing concepts of mental disorders, discovering new insights, and even enhancing our knowledge at an individual level.

cs.LG↗

arXiv2024

Exploiting Individual Graph Structures to Enhance Ecological Momentary Assessment (EMA) Forecasting

In the evolving field of psychopathology, the accurate assessment and forecasting of data derived from Ecological Momentary Assessment (EMA) is crucial. EMA offers contextually-rich psychopathological measurements over time, that practically lead to Multivariate Time Series (MTS) data. Thus, many challenges arise in analysis from the temporal complexities inherent in emotional, behavioral, and contextual EMA data as well as their inter-dependencies. To address both of these aspects, this research investigates the performance of Recurrent and Temporal Graph Neural Networks (GNNs). Overall, GNNs, by incorporating additional information from graphs reflecting the inner relationships between the variables, notably enhance the results by decreasing the Mean Squared Error (MSE) to 0.84 compared to the baseline LSTM model at 1.02. Therefore, the effect of constructing graphs with different characteristics on GNN performance is also explored. Additionally, GNN-learned graphs, which are dynamically refined during the training process, were evaluated. Using such graphs showed a similarly good performance. Thus, graph learning proved also promising for other GNN methods, potentially refining the pre-defined graphs.

cs.LG↗

arXiv2023

Model-based Clustering of Individuals' Ecological Momentary Assessment Time-series Data for Improving Forecasting Performance

Through Ecological Momentary Assessment (EMA) studies, a number of time-series data is collected across multiple individuals, continuously monitoring various items of emotional behavior. Such complex data is commonly analyzed in an individual level, using personalized models. However, it is believed that additional information of similar individuals is likely to enhance these models leading to better individuals' description. Thus, clustering is investigated with an aim to group together the most similar individuals, and subsequently use this information in group-based models in order to improve individuals' predictive performance. More specifically, two model-based clustering approaches are examined, where the first is using model-extracted parameters of personalized models, whereas the second is optimized on the model-based forecasting performance. Both methods are then analyzed using intrinsic clustering evaluation measures (e.g. Silhouette coefficients) as well as the performance of a downstream forecasting scheme, where each forecasting group-model is devoted to describe all individuals belonging to one cluster. Among these, clustering based on performance shows the best results, in terms of all examined evaluation measures. As another level of evaluation, those group-models' performance is compared to three baseline scenarios, the personalized, the all-in-one group and the random group-based concept. According to this comparison, the superiority of clustering-based methods is again confirmed, indicating that the utilization of group-based information could be effectively enhance the overall performance of all individuals' data.

cs.LG↗

arXiv2022

Clustering individuals based on multivariate EMA time-series data

In the field of psychopathology, Ecological Momentary Assessment (EMA) methodological advancements have offered new opportunities to collect time-intensive, repeated and intra-individual measurements. This way, a large amount of data has become available, providing the means for further exploring mental disorders. Consequently, advanced machine learning (ML) methods are needed to understand data characteristics and uncover hidden and meaningful relationships regarding the underlying complex psychological processes. Among other uses, ML facilitates the identification of similar patterns in data of different individuals through clustering. This paper focuses on clustering multivariate time-series (MTS) data of individuals into several groups. Since clustering is an unsupervised problem, it is challenging to assess whether the resulting grouping is successful. Thus, we investigate different clustering methods based on different distance measures and assess them for the stability and quality of the derived clusters. These clustering steps are illustrated on a real-world EMA dataset, including 33 individuals and 15 variables. Through evaluation, the results of kernel-based clustering methods appear promising to identify meaningful groups in the data. So, efficient representations of EMA data play an important role in clustering.

cs.LG↗

arXiv2022

Using Explainable Boosting Machine to Compare Idiographic and Nomothetic Approaches for Ecological Momentary Assessment Data

Previous research on EMA data of mental disorders was mainly focused on multivariate regression-based approaches modeling each individual separately. This paper goes a step further towards exploring the use of non-linear interpretable machine learning (ML) models in classification problems. ML models can enhance the ability to accurately predict the occurrence of different behaviors by recognizing complicated patterns between variables in data. To evaluate this, the performance of various ensembles of trees are compared to linear models using imbalanced synthetic and real-world datasets. After examining the distributions of AUC scores in all cases, non-linear models appear to be superior to baseline linear models. Moreover, apart from personalized approaches, group-level prediction models are also likely to offer an enhanced performance. According to this, two different nomothetic approaches to integrate data of more than one individuals are examined, one using directly all data during training and one based on knowledge distillation. Interestingly, it is observed that in one of the two real-world datasets, knowledge distillation method achieves improved AUC scores (mean relative change of +17\% compared to personalized) showing how it can benefit EMA data classification and performance.

cs.LG↗

arXiv2020

Relations between networks, regression, partial correlation, and latent variable model

The Gaussian graphical model (GGM) has become a popular tool for analyzing networks of psychological variables. In a recent paper in this journal, Forbes, Wright, Markon, and Krueger (FWMK) voiced the concern that GGMs that are estimated from partial correlations wrongfully remove the variance that is shared by its constituents. If true, this concern has grave consequences for the application of GGMs. Indeed, if partial correlations only capture the unique covariances, then the data that come from a unidimensional latent variable model ULVM should be associated with an empty network (no edges), as there are no unique covariances in a ULVM. We know that this cannot be true, which suggests that FWMK are missing something with their claim. We introduce a connection between the ULVM and the GGM and use that connection to prove that we find a fully-connected and not an empty network associated with a ULVM. We then use the relation between GGMs and linear regression to show that the partial correlation indeed does not remove the common variance.

stat.ME↗

arXiv2020

Interpreting the Ising Model: The Input Matters

The Ising model is a model for pairwise interactions between binary variables that has become popular in the psychological sciences. It has been first introduced as a theoretical model for the alignment between positive (+1) and negative (-1) atom spins. In many psychological applications, however, the Ising model is defined on the domain $\{0,1\}$ instead of the classical domain $\{-1,1\}$. While it is possible to transform the parameters of a given Ising model in one domain to obtain a statistically equivalent model in the other domain, the parameters in the two versions of the Ising model lend themselves to different interpretations and imply different dynamics, when studying the Ising model as a dynamical system. In this tutorial paper, we provide an accessible discussion of the interpretation of threshold and interaction parameters in the two domains and show how the dynamics of the Ising model depends on the choice of domain. Finally, we provide a transformation that allows to transform the parameters in an Ising model in one domain into a statistically equivalent Ising model in the other domain.

stat.ME↗

arXiv2020

Moderated Network Models

Pairwise network models such as the Gaussian Graphical Model (GGM) are a powerful and intuitive way to analyze dependencies in multivariate data. A key assumption of the GGM is that each pairwise interaction is independent of the values of all other variables. However, in psychological research this is often implausible. In this paper, we extend the GGM by allowing each pairwise interaction between two variables to be moderated by (a subset of) all other variables in the model, and thereby introduce a Moderated Network Model (MNM). We show how to construct the MNM and propose an L1-regularized nodewise regression approach to estimate it. We provide performance results in a simulation study and show that MNMs outperform the split-sample based methods Network Comparison Test (NCT) and Fused Graphical Lasso (FGL) in detecting moderation effects. Finally, we provide a fully reproducible tutorial on how to estimate MNMs with the R-package mgm and discuss possible issues with model misspecification.

stat.ME↗

arXiv2019

Intervention in undirected Ising graphs and the partition function

Undirected graphical models have many applications in such areas as machine learning, image processing, and, recently, psychology. Psychopathology in particular has received a lot of attention, where symptoms of disorders are assumed to influence each other. One of the most relevant questions practically is on which symptom (node) to intervene to have the most impact. Interventions in undirected graphical models is equal to conditioning, and so we have available the machinery with the Ising model to determine the best strategy to intervene. In order to perform such calculations the partition function is required, which is computationally difficult. Here we use a Curie-Weiss approach to approximate the partition function in applications of interventions. We show that when the connection weights in the graph are equal within each clique then we obtain exactly the correct partition function. And if the weights vary according to a sub-Gaussian distribution, then the approximation is exponentially close to the correct one. We confirm these results with simulations.

stat.ME↗