cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.12851289.v3
title: Nonparametric Maximum Likelihood Methods for Binary Response Models With Random Coefficients

description: The venerable method of maximum likelihood has found numerous recent applications in <i>nonparametric</i> estimation of regression and shape constrained densities. For mixture models the nonparametric maximum likelihood estimator (NPMLE) of Kiefer and Wolfowitz plays a central role in recent developments of empirical Bayes methods. The NPMLE has also been proposed by Cosslett as an estimation method for single index linear models for binary response with random coefficients. However, computational difficulties have hindered its application. Combining recent developments in computational geometry and convex optimization, we develop a new approach to computation for such models that dramatically increases their computational tractability. Consistency of the method is established for an expanded profile likelihood formulation. The methods are evaluated in simulation experiments, compared to the deconvolution methods of Gautier and Kitamura and illustrated in an application to modal choice for journey-to-work data in the Washington DC area. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.13373991
title: Minimax Efficient Random Experimental Design Strategies With Application to Model-Robust Design for Prediction

description: In game theory and statistical decision theory, a random (i.e., mixed) decision strategy often outperforms a deterministic strategy in minimax expected loss. As experimental design can be viewed as a game pitting the Statistician against Nature, the use of a random strategy to choose a design will often be beneficial. However, the topic of minimax-efficient random strategies for design selection is mostly unexplored, with consideration limited to Fisherian randomization of the allocation of a predetermined set of treatments to experimental units. Here, for the first time, novel and more flexible random design strategies are shown to have better properties than their deterministic counterparts in linear model estimation and prediction, including stronger bounds on both the expectation and survivor function of the loss distribution. Design strategies are considered for three important statistical problems: (i) parameter estimation in linear potential outcomes models, (ii) point prediction from a correct linear model, and (iii) global prediction from a linear model taking into account an <i>L</i><sub>2</sub>-class of possible model discrepancy functions. The new random design strategies proposed for (iii) give a finite bound on the expected loss, a dramatic improvement compared to existing deterministic exact designs for which the expected loss is unbounded. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.13373991.v2
title: Minimax Efficient Random Experimental Design Strategies With Application to Model-Robust Design for Prediction

description: In game theory and statistical decision theory, a random (i.e., mixed) decision strategy often outperforms a deterministic strategy in minimax expected loss. As experimental design can be viewed as a game pitting the Statistician against Nature, the use of a random strategy to choose a design will often be beneficial. However, the topic of minimax-efficient random strategies for design selection is mostly unexplored, with consideration limited to Fisherian randomization of the allocation of a predetermined set of treatments to experimental units. Here, for the first time, novel and more flexible random design strategies are shown to have better properties than their deterministic counterparts in linear model estimation and prediction, including stronger bounds on both the expectation and survivor function of the loss distribution. Design strategies are considered for three important statistical problems: (i) parameter estimation in linear potential outcomes models, (ii) point prediction from a correct linear model, and (iii) global prediction from a linear model taking into account an <i>L</i><sub>2</sub>-class of possible model discrepancy functions. The new random design strategies proposed for (iii) give a finite bound on the expected loss, a dramatic improvement compared to existing deterministic exact designs for which the expected loss is unbounded. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.13373991.v1
title: Minimax efficient random experimental design strategies with application to model-robust design for prediction

description: In game theory and statistical decision theory, a random (i.e. mixed) decision strategy often outperforms a deterministic strategy in minimax expected loss. As experimental design can be viewed as a game pitting the Statistician against Nature, the use of a random strategy to choose a design will often be beneficial. However, the topic of minimax-efficient random strategies for design selection is mostly unexplored, with consideration limited to Fisherian randomization of the allocation of a predetermined set of treatments to experimental units. Here, for the first time, novel and more flexible random design strategies are shown to have better properties than their deterministic counterparts in linear model estimation and prediction, including stronger bounds on both the expectation and survivor function of the loss distribution. Design strategies are considered for three important statistical problems: (i) parameter estimation in linear potential outcomes models, (ii) point prediction from a correct linear model, and (iii) global prediction from a linear model taking into account an <i>L</i> <sub>2</sub>-class of possible model discrepancy functions. The new random design strategies proposed for (iii) give a finite bound on the expected loss, a dramatic improvement compared to existing deterministic exact designs for which the expected loss is unbounded.
DOI: 10.6084/m9.figshare.12851331
title: Rare Feature Selection in High Dimensions

description: It is common in modern prediction problems for many predictor variables to be counts of rarely occurring events. This leads to design matrices in which many columns are highly sparse. The challenge posed by such “rare features” has received little attention despite its prevalence in diverse areas, ranging from natural language processing (e.g., rare words) to biology (e.g., rare species). We show, both theoretically and empirically, that not explicitly accounting for the rareness of features can greatly reduce the effectiveness of an analysis. We next propose a framework for aggregating rare features into denser features in a flexible manner that creates better predictors of the response. Our strategy leverages side information in the form of a tree that encodes feature similarity. We apply our method to data from TripAdvisor, in which we predict the numerical rating of a hotel based on the text of the associated review. Our method achieves high accuracy by making effective use of rare words; by contrast, the lasso is unable to identify highly predictive words if they are too rare. A companion R package, called rare, implements our new estimator, using the alternating direction method of multipliers. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.12851331.v2
title: Rare Feature Selection in High Dimensions

description: It is common in modern prediction problems for many predictor variables to be counts of rarely occurring events. This leads to design matrices in which many columns are highly sparse. The challenge posed by such “rare features” has received little attention despite its prevalence in diverse areas, ranging from natural language processing (e.g., rare words) to biology (e.g., rare species). We show, both theoretically and empirically, that not explicitly accounting for the rareness of features can greatly reduce the effectiveness of an analysis. We next propose a framework for aggregating rare features into denser features in a flexible manner that creates better predictors of the response. Our strategy leverages side information in the form of a tree that encodes feature similarity. We apply our method to data from TripAdvisor, in which we predict the numerical rating of a hotel based on the text of the associated review. Our method achieves high accuracy by making effective use of rare words; by contrast, the lasso is unable to identify highly predictive words if they are too rare. A companion R package, called rare, implements our new estimator, using the alternating direction method of multipliers. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.12931153
title: Bayesian Semiparametric Longitudinal Drift-Diffusion Mixed Models for Tone Learning in Adults

description: Understanding how adult humans learn nonnative speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions using longitudinal learning experiments under a multi-category decision making paradigm. Drift-diffusion processes are popular in such contexts for their ability to mimic underlying neural mechanisms. Motivated by these problems, we develop a novel Bayesian semiparametric inverse Gaussian drift-diffusion mixed model for multi-alternative decision making in longitudinal settings. We design a Markov chain Monte Carlo algorithm for posterior computation. We evaluate the method’s empirical performances through synthetic experiments. Applied to our motivating longitudinal tone learning study, the method provides novel insights into how the biologically interpretable model parameters evolve with learning, differ between input-response tone combinations, and differ between well and poorly performing adults. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.12931153.v1
title: Bayesian Semiparametric Longitudinal Drift-Diffusion Mixed Models for Tone Learning in Adults

description: Understanding how adult humans learn nonnative speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions using longitudinal learning experiments under a multi-category decision making paradigm. Drift-diffusion processes are popular in such contexts for their ability to mimic underlying neural mechanisms. Motivated by these problems, we develop a novel Bayesian semiparametric inverse Gaussian drift-diffusion mixed model for multi-alternative decision making in longitudinal settings. We design a Markov chain Monte Carlo algorithm for posterior computation. We evaluate the method’s empirical performances through synthetic experiments. Applied to our motivating longitudinal tone learning study, the method provides novel insights into how the biologically interpretable model parameters evolve with learning, differ between input-response tone combinations, and differ between well and poorly performing adults. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.12912705
title: Do School Districts Affect NYC House Prices? Identifying Border Differences Using a Bayesian Nonparametric Approach to Geographic Regression Discontinuity Designs

description: What is the premium on house price for a particular school district? To estimate this in New York City we use a novel implementation of a geographic regression discontinuity design (GeoRDD) built from Gaussian processes regression (kriging) to model spatial structure. With a GeoRDD, we specifically examine price differences along borders between “treatment” and “control” school districts. GeoRDDs extend RDDs to multivariate settings; location is the forcing variable and the border between school districts constitutes the discontinuity threshold. We first obtain a Bayesian posterior distribution of the price difference function, our nominal treatment effect, along the border. We then address nuances of having a functional estimand defined on a border with potentially intricate topology, particularly when defining and estimating causal estimands of the local average treatment effect (LATE). We test for nonzero LATE with a calibrated hypothesis test with good frequentist properties, which we further validate using a placebo test. Using our methodology, we identify substantial differences in price across several borders. In one case, a border separating Brooklyn and Queens, we estimate a statistically significant 20% higher price for a house on the more desirable side. We also find that geographic features can undermine some of these comparisons. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.12912705.v2
title: Do School Districts Affect NYC House Prices? Identifying Border Differences Using a Bayesian Nonparametric Approach to Geographic Regression Discontinuity Designs

description: What is the premium on house price for a particular school district? To estimate this in New York City we use a novel implementation of a geographic regression discontinuity design (GeoRDD) built from Gaussian processes regression (kriging) to model spatial structure. With a GeoRDD, we specifically examine price differences along borders between “treatment” and “control” school districts. GeoRDDs extend RDDs to multivariate settings; location is the forcing variable and the border between school districts constitutes the discontinuity threshold. We first obtain a Bayesian posterior distribution of the price difference function, our nominal treatment effect, along the border. We then address nuances of having a functional estimand defined on a border with potentially intricate topology, particularly when defining and estimating causal estimands of the local average treatment effect (LATE). We test for nonzero LATE with a calibrated hypothesis test with good frequentist properties, which we further validate using a placebo test. Using our methodology, we identify substantial differences in price across several borders. In one case, a border separating Brooklyn and Queens, we estimate a statistically significant 20% higher price for a house on the more desirable side. We also find that geographic features can undermine some of these comparisons. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.12912705.v1
title: Do School Districts Affect NYC House Prices? Identifying Border Differences Using a Bayesian Nonparametric Approach to Geographic Regression Discontinuity Designs.

description: What is the premium on house price for a particular school district? To estimate this in New York City we use a novel implementation of a Geographic Regression Discontinuity Design (GeoRDD) built from Gaussian processes regression (kriging) to model spatial structure. With a GeoRDD, we specifically examine price differences along borders between “treatment” and “control” school districts. GeoRDDs extend RDDs to multivariate settings; location is the forcing variable and the border between school districts constitutes the discontinuity threshold. We first obtain a Bayesian posterior distribution of the price difference function, our nominal treatment effect, along the border. We then address nuances of having a functional estimand defined on a border with potentially intricate topology, particularly when defining and estimating causal estimands of the local average treatment effect (LATE). We test for nonzero LATE with a calibrated hypothesis test with good frequentist properties, which we further validate using a placebo test. Using our methodology, we identify substantial differences in price across several borders. In one case, a border separating Brooklyn and Queens, we estimate a statistically significant 20% higher price for a house on the more desirable side. We also find that geographic features can undermine some of these comparisons.
DOI: 10.6084/m9.figshare.11903034
title: Principal component analysis of spatially indexed functions

description: We develop an expansion, similar in some respects to the Karhunen–Loève expansion, but which is more suitable for functional data indexed by spatial locations on a grid. Unlike the traditional Karhunen–Loève expansion, it takes into account the spatial dependence between the functions. By doing so, it provides a more efficient dimension reduction tool, both theoretically and in finite samples, for functional data with moderate spatial dependence. For such data, it also possesses other theoretical and practical advantages over the currently used approach. The paper develops complete asymptotic theory and estimation methodology. The performance of the method is examined by a simulation study and data analysis. The new tools are implemented in an R package.
DOI: 10.6084/m9.figshare.11903034.v2
title: Principal component analysis of spatially indexed functions

description: We develop an expansion, similar in some respects to the Karhunen–Loève expansion, but which is more suitable for functional data indexed by spatial locations on a grid. Unlike the traditional Karhunen–Loève expansion, it takes into account the spatial dependence between the functions. By doing so, it provides a more efficient dimension reduction tool, both theoretically and in finite samples, for functional data with moderate spatial dependence. For such data, it also possesses other theoretical and practical advantages over the currently used approach. The paper develops complete asymptotic theory and estimation methodology. The performance of the method is examined by a simulation study and data analysis. The new tools are implemented in an R package.
DOI: 10.6084/m9.figshare.11903034.v1
title: Principal Component Analysis of Spatially Indexed Functions

description: We develop an expansion, similar in some respects to the Karhunen–Loève expansion, but which is more suitable for functional data indexed by spatial locations on a grid. Unlike the traditional Karhunen–Loève expansion, it takes into account the spatial dependence between the functions. By doing so, it provides a more efficient dimension reduction tool, both theoretically and in finite samples, for functional data with moderate spatial dependence. For such data, it also possesses other theoretical and practical advantages over the currently used approach. The article develops complete asymptotic theory and estimation methodology. The performance of the method is examined by a simulation study and data analysis. The new tools are implemented in an R package. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.14156618
title: Asymptotics for EBLUPs: Nested Error Regression Models

description: In this paper we derive the asymptotic distribution of estimated best linear unbiased predictors (EBLUPs) of the random effects in a nested error regression model. Under very mild conditions which do not require the assumption of normality, we show that asymptotically the distribution of the EBLUPs as both the number of clusters and the cluster sizes diverge to infinity is the convolution of the true distribution of the random effects and a normal distribution. This result yields very simple asymptotic approximations to and estimators of the prediction mean squared error of EBLUPs, and then asymptotic prediction intervals for the unobserved random effects. We also derive a higher order approximation to the asymptotic mean squared error and provide a detailed theoretical and empirical comparison with the well-known analytical prediction mean squared error approximations and estimators proposed by Kackar & Harville (1984) and Prasad & Rao (1990). We show that our simple estimator of the predictor mean squared errors of EBLUPs works very well in practice when both the number of clusters and the cluster sizes are sufficiently large. Finally, we illustrate the use of the asymptotic prediction intervals with data on radon measurements of houses in Massachusetts and Arizona.
DOI: 10.6084/m9.figshare.14156618.v2
title: Asymptotics for EBLUPs: Nested Error Regression Models

description: In this paper we derive the asymptotic distribution of estimated best linear unbiased predictors (EBLUPs) of the random effects in a nested error regression model. Under very mild conditions which do not require the assumption of normality, we show that asymptotically the distribution of the EBLUPs as both the number of clusters and the cluster sizes diverge to infinity is the convolution of the true distribution of the random effects and a normal distribution. This result yields very simple asymptotic approximations to and estimators of the prediction mean squared error of EBLUPs, and then asymptotic prediction intervals for the unobserved random effects. We also derive a higher order approximation to the asymptotic mean squared error and provide a detailed theoretical and empirical comparison with the well-known analytical prediction mean squared error approximations and estimators proposed by Kackar & Harville (1984) and Prasad & Rao (1990). We show that our simple estimator of the predictor mean squared errors of EBLUPs works very well in practice when both the number of clusters and the cluster sizes are sufficiently large. Finally, we illustrate the use of the asymptotic prediction intervals with data on radon measurements of houses in Massachusetts and Arizona.
DOI: 10.6084/m9.figshare.12851463
title: Network Dependence Can Lead to Spurious Associations and Invalid Inference

description: Researchers across the health and social sciences generally assume that observations are independent, even while relying on convenience samples that draw subjects from one or a small number of communities, schools, hospitals, etc. A paradigmatic example of this is the Framingham Heart Study (FHS). Many of the limitations of such samples are well-known, but the issue of statistical dependence due to social network ties has not previously been addressed. We show that, along with anticonservative variance estimation, this can result in <i>spurious associations due to network dependence</i>. Using a statistical test that we adapted from one developed for spatial autocorrelation, we test for network dependence in several of the thousands of influential papers that have been published using FHS data. Results suggest that some of the many decades of research on coronary heart disease, other health outcomes, and peer influence using FHS data may suffer from spurious associations, error-prone point estimates, and anticonservative inference due to unacknowledged network dependence. These issues are not unique to the FHS; as researchers in psychology, medicine, and beyond grapple with replication failures, this unacknowledged source of invalid statistical inference should be part of the conversation.