Estimating Parameters of Structural Models Using Neural Networks

Wei, Yanhao; Jiang, Zhenling

doi:10.2139/ssrn.3496098

Cited by 8 publications

(10 citation statements)

References 43 publications

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“…For models with tractable likelihood, we performed the same model identification process using AIC (Akaike, 1998) that relies on likelihood computation, penalized by number of parameters, to quantify model fitness as a benchmark. We note that another common criterion, BIC (Wei and Jiang, 2022), performed more poorly than AIC in our case.The best fitting model is identified based on the lowest AIC score - a successful model recovery would indicate that the true model has the lowest AIC score compared to other models fit to that data. To construct the confusion matrix, we computed best AIC score proportions for all models, across all agents, for data sets simulated from each cognitive model (Fig: 5; see methods).…”

Section: Resultsmentioning

confidence: 60%

“…By specifying model equations, researchers can inject different theoretical assumptions into models, and, for most models, simulate synthetic data to make predictions and compare against observed behavior. Researchers can quantitatively arbitrate between different theories by comparing goodness of fit (Akaike, 1998, Wei and Jiang, 2022) across different models. Furthermore, by estimating model parameters that quantify underlying cognitive processes, researchers have been able to characterize important individual differences (e.g.…”

Section: Figurementioning

confidence: 99%

“…Here, we test a related, general approach that leverage advances in artificial neural networks (ANNs) to estimate parameters and perform model identification for models with and without tractable likelihood, entirely bypassing the likelihood estimation (or approximation) step. ANNs have been successfully used to fit intractable models in different fields, including weather models (Lenzi et al, 2023) and econometric models (Wei and Jiang, 2022), and more recently cognitive models of decision making Radev, Mertens, et al, 2020; Radev, Voss, et al, 2020. We develop similar approaches to specifically target the intractability estimation problem in the field of computational cognitive science, including both parameter estimation and model identification, and thoroughly test it in a challenging class of models where there are strong dependencies between trials (e.g.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Artificial neural networks for model identification and parameter estimation in computational cognitive models

Rmus,

Pan,

Xia

et al. 2023

Preprint

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Computational cognitive models have been used extensively to formalize cognitive processes. Model parameters offer a simple way to quantify individual differences in how humans process information. Similarly, model comparison allows researchers to identify which theories, embedded in different models, provide the best accounts of the data. Cognitive modeling uses statistical tools to quantitatively relate models to data that often rely on computing/estimating the likelihood of the data under the model. However, this likelihood is computationally intractable for a substantial number of models. These relevant models may embody reasonable theories of cognition, but are often under-explored due to the lack of tools required to relate them to data. We propose to fill this gap using artificial neural networks (ANNs) to map data directly onto model identity and parameters, bypassing the likelihood estimation. Our results show that we can adequately perform both parameter estimation and model identification using our new ANN approach, including for models that cannot be fit using traditional likelihood-based methods. Our new ANN approach will greatly broaden the class of cognitive models researchers can quantitatively consider.

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Section: Resultsmentioning

confidence: 60%

Section: Figurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Artificial neural networks for model identification and parameter estimation in computational cognitive models

Rmus,

Pan,

Xia

et al. 2023

Preprint

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show abstract

“…Finally, it is worth mentioning that other recent work has considered the combination of deep learning and some form of structural modeling (examples include Wei and Jiang, 2019;Igami, 2020;Kaji et al, 2020;Chen et al, 2021). Typically, the goal is estimation of a parametric structural model and deep learning methods are applied to learn the mapping of data to parameters.…”

Section: Structured Deep Learning For Parameter Functionsmentioning

confidence: 99%

Deep learning for individual heterogeneity: an automatic inference framework

Farrell¹,

Liang²,

Misra³

2021

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We develop methodology for estimation and inference using machine learning to enrich economic models. Our framework takes a standard economic model and recasts the parameters as fully flexible nonparametric functions, to capture the rich heterogeneity based on potentially high dimensional or complex observable characteristics. These "parameter functions" retain the interpretability, economic meaning, and discipline of classical parameters. In contrast to common implementations of machine learning in economics, these functions need not be predictions. We show that deep learning is particularly well-suited to structured modeling of heterogeneity in economics. First, we show how the network architecture can be easily designed to match the global structure of the economic model, delivering novel methodology that moves deep learning beyond prediction. Second, we prove convergence rates for the estimated parameter functions. These parameter functions are then the key input into the finite-dimensional parameter of inferential interest. We obtain valid inference based on a novel orthogonal score or influence function calculation that covers any second-stage parameter and any machine-learning-enriched model that uses a smooth per-observation loss function. No additional derivations are required and the score can be taken directly to data, using automatic differentiation if needed to obtain the components: the researcher need only define the original model and define the parameter of interest. A key insight is that we need not write down the influence function in order to evaluate it on the data. We apply this after deep learning, but our result can be used for any first-step estimator. Our framework covers, as special cases, well-known examples such as average treatment effects and partially linear models, but we also seamlessly deliver new results for such diverse examples as price elasticities, willingness-to-pay, and surplus measures in binary or multinomial choice models, average marginal and partial effects of continuous treatment variables, fractional outcome models, count data, heterogeneous production function components, and more. Across all these contexts inference can be made as automated as is currently available in special cases. We illustrate the utility of our framework with an application to a large scale advertising experiment for short-term loans. We show how economically meaningful estimates and inferences can be made that would be unavailable without our framework.

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“…Finally, it is worth mentioning that other recent work has considered the combination of deep learning and structural modeling. Typically, the goal is estimation of a parametric structural model and deep learning methods are applied to learn the mapping of data to parameters (Wei and Jiang, 2019;Kaji et al, 2020;Igami, 2020). Our focus, using deep learning to estimate individual-level heterogeneity, is quite different, and further, we give theoretical results on deep neural network estimation and subsequent inference which are not available in prior work.…”

Section: Deep Thoughtsmentioning

confidence: 99%

Deep Learning for Individual Heterogeneity: An Automatic Inference Framework

Farrell¹,

Liang²,

Misra³

2020

Preprint

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We propose a methodology for effectively modeling individual heterogeneity using deep learning while still retaining the interpretability and economic discipline of classical models. We pair a transparent, interpretable modeling structure with rich data environments and machine learning methods to estimate heterogeneous parameters based on potentially high dimensional or complex observable characteristics. Our framework is widely-applicable, covering numerous settings of economic interest. We recover, as special cases, well-known examples such as average treatment effects and parametric components of partially linear models. However, we also seamlessly deliver new results for diverse examples such as price elasticities, willingness-to-pay, and surplus measures in choice models, average marginal and partial effects of continuous treatment variables, fractional outcome models, count data, heterogeneous production function components, and more. Deep neural networks are particularly well-suited to structured modeling of heterogeneity in economics: we show how the network architecture can be easily designed to match the global structure of the economic model, giving novel methodology for deep learning as well as, more formally, improved rates of convergence. Our results on deep learning have consequences for other structured modeling environments and applications, such as for additive models or other varying coefficient models. Our inference results are based on an influence function we derive, which we show to be flexible enough to to encompass all settings with a single, unified calculation, removing any requirement for case-by-case derivations. The usefulness of the methodology in economics is shown in two empirical applications: we study the response of 410(k) participation rates to firm matching and the impact of prices on subscription choices for an online service. Extensions of the main ideas to instrumental variables and multinomial choices are shown.

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Estimating Parameters of Structural Models Using Neural Networks

Cited by 8 publications

References 43 publications

Artificial neural networks for model identification and parameter estimation in computational cognitive models

Artificial neural networks for model identification and parameter estimation in computational cognitive models

Deep learning for individual heterogeneity: an automatic inference framework

Deep Learning for Individual Heterogeneity: An Automatic Inference Framework

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