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Estimating psychopathological networks: be careful what you wish for
Sacha Epskamp, Joost Kruis, Maarten Marsman
TL;DR
Psychopathological network models are difficult to estimate because their parameter counts can exceed available sample sizes. The paper discusses and simulates how regularization assumptions shape estimated networks, finding that constraints improve estimation but sparse outputs do not establish a sparse underlying structure.
Problem
Psychological network models can contain more unknown parameters than available observations, making assumptions about the true structure necessary for estimation.
Method
The paper discusses alternative estimation assumptions and uses simulations with different true network structures to examine their effects on estimated Ising models.
Results
Commonly used psychological sample sizes produce poor Ising-model estimates without constraints, while LASSO and low-rank approximation impose different structural forms.
Takeaways & Limitations
Choosing an estimation method is consequential because it can substantially affect the estimated network and the conclusions drawn from it.
Takeaways & Limitations
Sparse or low-rank estimated structures cannot validate the corresponding assumptions about the true network, and alternative representations may remain statistically indistinguishable.
Abstract
from arXiv · showhide
Network models, in which psychopathological disorders are conceptualized as a complex interplay of psychological and biological components, have become increasingly popular in the recent psychopathological literature. These network models often contain significant numbers of unknown parameters, yet the sample sizes available in psychological research are limited. As such, general assumptions about the true network are introduced to reduce the number of free parameters. Incorporating these assumptions, however, means that the resulting network will lead to reflect the particular structure assumed by the estimation method---a crucial and often ignored aspect of psychopathological networks. For example, observing a sparse structure and simultaneously assuming a sparse structure does not imply that the true model is, in fact, sparse. To illustrate this point, we discuss recent literature and show the effect of the assumption of sparsity in three simulation studies.
Introduction
Psychological network models can contain more unknown parameters than available data, so estimation requires assumptions about the underlying structure. Assuming sparsity can produce a sparse estimate without establishing that the true network is sparse.
- Psychological network models may be high-dimensional, with more unknown parameters than available observations.
- Assuming a sparse true model permits methods that potentially return a sparse network structure.
- A sparse estimated network alone cannot establish that the underlying true model is sparse.
Network Psychometrics
Network psychometrics estimates high-dimensional psychological networks using models such as GGMs and Ising models. Regularization, especially LASSO, reduces estimation complexity by shrinking many edge parameters to zero and producing sparse, interpretable networks.
- Network psychometrics estimates large psychological network structures with many parameters, commonly using GGMs for continuous data and Ising models for binary data.Both belong to the Markov Random Field class and represent conditional dependencies as edges.
- A network with P nodes requires estimating P(P −1)/2 parameters to encode pairwise conditional relationships.These estimates can be unstable with relatively low sample sizes.
- LASSO penalizes absolute edge weights, shrinking estimates toward zero and often producing exactly zero edges.The resulting model is usually sparse, with relatively few nonzero parameters.
- LASSO commonly improves cross-validation performance by preventing overfitting and yields more interpretable models than nonregularized Ising models.
- The LASSO tuning parameter can be selected using criteria such as the Extended Bayesian Information Criterion.The methodology has been developed for both GGMs and Ising models and implemented in software.
Sparse Network Models of Psychopathology
Sparse symptom networks have been interpreted as evidence against interchangeable symptoms and in favor of active symptom relationships. The paper cautions that LASSO imposes sparsity, so sparse estimates alone cannot determine whether symptoms are truly noninterchangeable.
- Psychopathology networks often show strong clustering among symptoms representing the same disorder.
- Under a common-cause model, interchangeable symptoms can produce clustered networks that are sparse and have unequal numbers of connections per symptom.
- A sparse approximated network alone cannot establish that symptoms are not interchangeable.
- LASSO assumes a sparse true network and searches for relatively few edges and paths explaining node co-occurrence.
- LASSO may have low sensitivity but high specificity, so selected edges are likely true while some true edges remain undetected.
The Bet on Sparsity
The paper contrasts sparse and low-rank regularization as different structural assumptions that can each fail when mismatched with the true network. Simulations use a fully connected Curie-Weiss network and a random sparse network to illustrate these consequences.
- The Bet on Sparsity: The LASSO can retrieve the true structure only when that structure is sparse, an assumption termed the bet on sparsity.
- The Bet on Sparsity: A common-cause model with interchangeable indicators corresponds to an Ising model that is often dense and low rank.Conditioning on all other items leaves no pair conditionally independent when a common cause generates the co-occurrences.
- The Bet on Sparsity: Low-rank regularization generally produces dense networks, whereas LASSO produces networks with many exactly zero edge parameters.
- The Bet on Sparsity: Both LASSO and low-rank methods can lose their structural bet when the assumed form does not match the true network.
Estimating an Ising Model When the Truth Is Dense
The simulations show that estimation methods impose their structural assumptions on recovered Ising networks. When the true network is dense or generated by a latent-variable model, regularization can create misleading sparsity, while unregularized estimates can contain spurious edges.
- The Curie-Weiss truth is fully connected with equal edge strength, but unregularized estimation produces spurious edge-strength differences, including negative edges.The simulation used 1,000 observations and compared unregularized logistic regressions, LASSO, and a Rank 2 approximation.
- Using LASSO for a dense Curie-Weiss network still yields a sparse structure, so observed sparsity does not establish that symptoms are non-interchangeable.The resulting sparse graph could arise from the estimation assumption even when nodes represent interchangeable indicators of one latent trait.
- A sparse truth with 20% of edges set to 0.2 is captured well by LASSO, whereas unregularized and Rank 2 estimates produce many false-positive edges.The Rank 2 approximation retains spurious connections even at high sample sizes, although higher rank improves estimation.
- The MIRT simulation uses normally distributed latent variables, binary symptoms, and item discrimination parameters as network edges.The model includes shared bridge symptoms connecting dysthymia and GAD clusters, with item discriminations set mainly to 1 and selected shared-item factors set to 0.75.
- With 1,000 observations for 19 nodes, unregularized estimates still show many spurious strong connections, while LASSO recovers clustering but makes the dense truth much sparser.The dataset contains 22.2 observations per parameter; LASSO retrieves two bridging connections and one negative connection but can suggest unequal connection counts and strengths.
Different Estimation Techniques
The appropriate estimation technique depends on assumptions about the unknown true network, the desired specificity, and practical considerations. Because the true structure is unavailable in practice, method selection is consequential rather than automatic.
- Low-rank estimation is better suited to networks expected to be low rank, whereas LASSO is better suited to networks expected to be sparse.The examples support opposite choices because each method works best when its structural assumption matches the true network.
- The true network structure is unknown in real applications, so choosing between low-rank estimation and LASSO cannot be based on certainty about the data-generating structure.Practical considerations also influence the choice, and LASSO combined with EBIC model selection is described as relatively fast.
- LASSO should be preferred when high specificity is important, meaning researchers want to avoid estimating edges absent from the true model.This recommendation follows the method's focus on limiting false-positive edges.
Conclusion
Network estimation can produce poor or method-shaped structures when psychological samples are small, so estimated sparsity or density cannot by itself validate the assumed true network. The paper argues that estimator choice substantially affects both the recovered structure and the conclusions drawn from it.
- Conclusion: Common psychological sample sizes can yield poor Ising-model estimates without constraints on the parameter space.Large samples typically perform well regardless of estimation method, but smaller samples require constraints for better estimation.
- Conclusion: LASSO and low-rank methods impose different structural assumptions, producing sparse and dense low-rank networks, respectively.These outputs reflect the assumptions built into the estimation methods rather than necessarily the true data-generating structure.
- Conclusion: LASSO can return sparse networks even when the true network follows a Curie-Weiss structure, making observed sparsity weak evidence for a sparse truth.When the true structure is complicated and neither sparse nor low rank, regularization methods can partly fail even with relatively large samples.
- Conclusion: Statistically adequate network-model fit does not establish the network as the theoretical causal mechanism because latent-variable, network, and collider representations can be indistinguishable.A sparse network obtained with LASSO may also be represented by a multidimensional latent-variable model with residual correlations.
- Conclusion: Network models remain useful for visualizing relationships and selecting high-dimensional structures, but estimation method choice is consequential rather than trivial.LASSO can reduce false positives and illuminate strong dataset relationships, while its structural assumptions can shape subsequent conclusions.