Global identifiability of linear structural equation models

Drton, Mathias; Foygel, Rina; Sullivant, Seth

doi:10.1214/10-aos859

Cited by 55 publications

(84 citation statements)

References 18 publications

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“…15 Drton, Foygel, and Sullivant (2011) provide similar results to ours on the recovery of A. However, that paper assumes the unobserved heterogeneity is jointly normal and it assumes that contextual effects are absent.…”

Section: 2supporting

confidence: 70%

Linear Social Interactions Models

Blume

Brock

Durlauf

et al. 2013

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This paper provides a systematic analysis of identification in linear social interactions models. This is both a theoretical and an econometric exercise as the analysis is linked to a rigorously delineated model of interdependent decisions. We develop an incomplete information game that describes individual choices in the presence of social interactions. The equilibrium strategy profiles are linear. Standard models in the empirical social interactions literature are shown to be exact or approximate special cases of our general framework, which in turn provides a basis for understanding the microeconomic foundations of those models. We consider identification of both endogenous (peer) and contextual social effects under alternative assumptions on a priori information about network structure available to an analyst, and contrast the informational content of individual-level and aggregated data. Finally, we discuss potential ramifications for identification of endogenous group selection and differences between the information sets of analysts and agents.

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Section: 2supporting

confidence: 70%

Linear Social Interactions Models

Blume

Brock

Durlauf

et al. 2013

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“…(), Drton et al . (), Meshkat and Sullivant (), among many others. They used approaches in algebraic statistics such as Kruskal's Theorem (Kruskal, ) to study model identifiability.…”

Section: Discussionmentioning

confidence: 99%

“…The global identifiability in different contexts has been considered by Allman and Rhodes (2006), Drton et al (2011, Meshkat and Sullivant (2014), among many others. They used approaches in algebraic statistics such as Kruskal's Theorem (Kruskal, 1977) to study model identifiability.…”

Section: Discussionmentioning

confidence: 99%

“…First, using symbolic algebraic calculations as in Jones et al (2010), we propose a different technique, namely the Gröbner basis method originating from computational algebra. It has been used in various applications such as graphical models and causal inference (Garcia, 2004;Drton et al, 2011;Leung et al, 2016). However, there lacks a systematic introduction to the Gröbner basis method that is accessible to statisticians.…”

Section: Introductionmentioning

confidence: 99%

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Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Gröbner basis approach

et al. 2019

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Identifiability of statistical models is a fundamental regularity condition that is required for valid statistical inference. Investigation of model identifiability is mathematically challenging for complex models such as latent class models. Jones et al. used Goodman's technique to investigate the identifiability of latent class models with applications to diagnostic tests in the absence of a gold standard test. The tool they used was based on examining the singularity of the Jacobian or the Fisher information matrix, in order to obtain insights into local identifiability (ie, there exists a neighborhood of a parameter such that no other parameter in the neighborhood leads to the same probability distribution as the parameter). In this paper, we investigate a stronger condition: global identifiability (ie, no two parameters in the parameter space give rise to the same probability distribution), by introducing a powerful mathematical tool from computational algebra: the Gröbner basis. With several existing well‐known examples, we argue that the Gröbner basis method is easy to implement and powerful to study global identifiability of latent class models, and is an attractive alternative to the information matrix analysis by Rothenberg and the Jacobian analysis by Goodman and Jones et al.

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“…While observing correlations within the system is relatively easy, transitioning from observed correlations to a causal or mechanistic understanding is hard. After all, there can be many ways that the same activities emerge from distinct causal chains (Drton et al, 2011;Peters et al, 2017). Reaching a mechanistic level of understanding in the mammalian brain is incredibly hard as they contain countless neurons (e.g.…”

Section: Introductionmentioning

confidence: 99%

Inferring causal connectivity from pairwise recordings and optogenetics

Lepperød

Stöber

Hafting

et al. 2018

Preprint

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To study how the brain works, it is crucial to identify causal interactions between neurons, which is thought to require perturbations. However, when using optogenetics we typically perturb multiple neurons, producing a confound -any of the stimulated neurons can have affected the postsynaptic neuron. Here we show how this produces large biases, and how they can be reduced using the instrumental variable (IV) technique from econometrics. The interaction between stimulation and the absolute refractory period produces a weak, approximately random signal which can be exploited to estimate causal connectivity. When simulating integrate-and-fire neurons, we find that estimates from IV are better than naïve techniques (R 2 = 0.77 vs R 2 = 0.01). The difference is important as the estimates disagree when applied to experimental data from stimulated neurons with recorded spiking activity. Presented is a robust analysis framework for mapping out network connectivity based on causal neuron interactions.

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Global identifiability of linear structural equation models

Cited by 55 publications

References 18 publications

Linear Social Interactions Models

Linear Social Interactions Models

Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Gröbner basis approach

Inferring causal connectivity from pairwise recordings and optogenetics

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