arXiv subjects

Luke Miratrix

Publications and source records attributed to Luke Miratrix.

35 records · Page 2Linked to original sources

arXiv2019

Weak separation in mixture models and implications for principal stratification

Principal stratification is a widely used framework for addressing post-randomization complications. After using principal stratification to define causal effects of interest, researchers are increasingly turning to finite mixture models to estimate these quantities. Unfortunately, standard estimators of mixture parameters, like the MLE, are known to exhibit pathological behavior. We study this behavior in a simple but fundamental example, a two-component Gaussian mixture model in which only the component means and variances are unknown, and focus on the setting in which the components are weakly separated. In this case, we show that the asymptotic convergence rate of the MLE is quite poor, such as $O(n^{-1/6})$ or even $O(n^{-1/8})$. We then demonstrate via theoretical arguments as well as extensive simulations that, in finite samples, the MLE behaves like a threshold estimator, in the sense that the MLE can give strong evidence that the means are equal when the truth is otherwise. We also explore the behavior of the MLE when the MLE is non-zero, showing that it is difficult to estimate both the sign and magnitude of the means in this case. We provide diagnostics for all of these pathologies and apply these ideas to re-analyzing two randomized evaluations of job training programs, JOBS II and Job Corps. Our results suggest that the corresponding maximum likelihood estimates should be interpreted with caution in these cases.

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arXiv2019

Matching with Text Data: An Experimental Evaluation of Methods for Matching Documents and of Measuring Match Quality

Matching for causal inference is a well-studied problem, but standard methods fail when the units to match are text documents: the high-dimensional and rich nature of the data renders exact matching infeasible, causes propensity scores to produce incomparable matches, and makes assessing match quality difficult. In this paper, we characterize a framework for matching text documents that decomposes existing methods into: (1) the choice of text representation, and (2) the choice of distance metric. We investigate how different choices within this framework affect both the quantity and quality of matches identified through a systematic multifactor evaluation experiment using human subjects. Altogether we evaluate over 100 unique text matching methods along with 5 comparison methods taken from the literature. Our experimental results identify methods that generate matches with higher subjective match quality than current state-of-the-art techniques. We enhance the precision of these results by developing a predictive model to estimate the match quality of pairs of text documents as a function of our various distance scores. This model, which we find successfully mimics human judgment, also allows for approximate and unsupervised evaluation of new procedures. We then employ the identified best method to illustrate the utility of text matching in two applications. First, we engage with a substantive debate in the study of media bias by using text matching to control for topic selection when comparing news articles from thirteen news sources. We then show how conditioning on text data leads to more precise causal inferences in an observational study examining the effects of a medical intervention.

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arXiv2018

Randomization Tests that Condition on Non-Categorical Covariate Balance

A benefit of randomized experiments is that covariate distributions of treatment and control groups are balanced on average, resulting in simple unbiased estimators for treatment effects. However, it is possible that a particular randomization yields covariate imbalances that researchers want to address in the analysis stage through adjustment or other methods. Here we present a randomization test that conditions on covariate balance by only considering treatment assignments that are similar to the observed one in terms of covariate balance. Previous conditional randomization tests have only allowed for categorical covariates, while our randomization test allows for any type of covariate. Through extensive simulation studies, we find that our conditional randomization test is more powerful than unconditional randomization tests and other conditional tests. Furthermore, we find that our conditional randomization test is valid (1) unconditionally across levels of covariate balance, and (2) conditional on particular levels of covariate balance. Meanwhile, unconditional randomization tests are valid for (1) but not (2). Finally, we find that our conditional randomization test is similar to a randomization test that uses a model-adjusted test statistic.

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arXiv2018

A Nonparametric Bayesian Methodology for Regression Discontinuity Designs

One of the most popular methodologies for estimating the average treatment effect at the threshold in a regression discontinuity design is local linear regression (LLR), which places larger weight on units closer to the threshold. We propose a Gaussian process regression methodology that acts as a Bayesian analog to LLR for regression discontinuity designs. Our methodology provides a flexible fit for treatment and control responses by placing a general prior on the mean response functions. Furthermore, unlike LLR, our methodology can incorporate uncertainty in how units are weighted when estimating the treatment effect. We prove our method is consistent in estimating the average treatment effect at the threshold. Furthermore, we find via simulation that our method exhibits promising coverage, interval length, and mean squared error properties compared to standard LLR and state-of-the-art LLR methodologies. Finally, we explore the performance of our method on a real-world example by studying the impact of being a first-round draft pick on the performance and playing time of basketball players in the National Basketball Association.

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arXiv2018

A Bayesian Nonparametric Approach to Geographic Regression Discontinuity Designs: Do School Districts Affect NYC House Prices?

Most research on regression discontinuity designs (RDDs) has focused on univariate cases, where only those units with a "forcing" variable on one side of a threshold value receive a treatment. Geographical regression discontinuity designs (GeoRDDs) extend the RDD to multivariate settings with spatial forcing variables. We propose a framework for analysing GeoRDDs, which we implement using Gaussian process regression. This yields a Bayesian posterior distribution of the treatment effect at every point along the border. We address nuances of having a functional estimand defind on a border with potentially intricate topology, particularly when defining and estimating causal estimands of the local average treatment effect (LATE). The Bayesian estimate of the LATE can also be used as a test statistic in a hypothesis test with good frequentist properties, which we validate using simulations and placebo tests. We demonstrate our methodology with a dataset of property sales in New York City, to assess whether there is a discontinuity in housing prices at the border between two school district. We find a statistically significant difference in price across the border between the districts with $p$=0.002, and estimate a 20% higher price on average for a house on the more desirable side.

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arXiv2017

Prior matters: simple and general methods for evaluating and improving topic quality in topic modeling

Latent Dirichlet Allocation (LDA) models trained without stopword removal often produce topics with high posterior probabilities on uninformative words, obscuring the underlying corpus content. Even when canonical stopwords are manually removed, uninformative words common in that corpus will still dominate the most probable words in a topic. In this work, we first show how the standard topic quality measures of coherence and pointwise mutual information act counter-intuitively in the presence of common but irrelevant words, making it difficult to even quantitatively identify situations in which topics may be dominated by stopwords. We propose an additional topic quality metric that targets the stopword problem, and show that it, unlike the standard measures, correctly correlates with human judgements of quality. We also propose a simple-to-implement strategy for generating topics that are evaluated to be of much higher quality by both human assessment and our new metric. This approach, a collection of informative priors easily introduced into most LDA-style inference methods, automatically promotes terms with domain relevance and demotes domain-specific stop words. We demonstrate this approach's effectiveness in three very different domains: Department of Labor accident reports, online health forum posts, and NIPS abstracts. Overall we find that current practices thought to solve this problem do not do so adequately, and that our proposal offers a substantial improvement for those interested in interpreting their topics as objects in their own right.

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arXiv2017

Beyond the Sharp Null: Randomization Inference, Bounded Null Hypotheses, and Confidence Intervals for Maximum Effects

Fisherian randomization inference is often dismissed as testing an uninteresting and implausible hypothesis: the sharp null of no effects whatsoever. We show that this view is overly narrow. Many randomization tests are also valid under a more general "bounded" null hypothesis under which all effects are weakly negative (or positive), thus accommodating heterogenous effects. By inverting such tests we can form one-sided confidence intervals for the maximum (or minimum) effect. These properties hold for all effect-increasing test statistics, which include both common statistics such as the mean difference and uncommon ones such as Stephenson rank statistics. The latter's sensitivity to extreme effects permits detection of positive effects even when the average effect is negative. We argue that bounded nulls are often of substantive or theoretical interest, and illustrate with two applications: testing monotonicity in an IV analysis and inferring effect sizes in a small randomized experiment.

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arXiv2017

Bounding, an accessible method for estimating principal causal effects, examined and explained

Estimating treatment effects for subgroups defined by post-treatment behavior (i.e., estimating causal effects in a principal stratification framework) can be technically challenging and heavily reliant on strong assumptions. We investigate an alternative path: using bounds to identify ranges of possible effects that are consistent with the data. This simple approach relies on fewer assumptions and yet can result in policy-relevant findings. As we show, covariates can be used to substantially tighten bounds in a straightforward manner. Via simulation, we demonstrate which types of covariates are maximally beneficial. We conclude with an analysis of a multi-site experimental study of Early College High Schools. When examining the program's impact on students completing the ninth grade "on-track" for college, we find little impact for ECHS students who would otherwise attend a high quality high school, but substantial effects for those who would not. This suggests potential benefit in expanding these programs in areas primarily served by lower quality schools.

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arXiv2017

Decomposing Treatment Effect Variation

Understanding and characterizing treatment effect variation in randomized experiments has become essential for going beyond the "black box" of the average treatment effect. Nonetheless, traditional statistical approaches often ignore or assume away such variation. In the context of randomized experiments, this paper proposes a framework for decomposing overall treatment effect variation into a systematic component explained by observed covariates and a remaining idiosyncratic component. Our framework is fully randomization-based, with estimates of treatment effect variation that are entirely justified by the randomization itself. Our framework can also account for noncompliance, which is an important practical complication. We make several contributions. First, we show that randomization-based estimates of systematic variation are very similar in form to estimates from fully-interacted linear regression and two stage least squares. Second, we use these estimators to develop an omnibus test for systematic treatment effect variation, both with and without noncompliance. Third, we propose an $R^2$-like measure of treatment effect variation explained by covariates and, when applicable, noncompliance. Finally, we assess these methods via simulation studies and apply them to the Head Start Impact Study, a large-scale randomized experiment.

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arXiv2017

A conditional randomization test to account for covariate imbalance in randomized experiments

We consider the conditional randomization test as a way to account for covariate imbalance in randomized experiments. The test accounts for covariate imbalance by comparing the observed test statistic to the null distribution of the test statistic conditional on the observed covariate imbalance. We prove that the conditional randomization test has the correct significance level and introduce original notation to describe covariate balance more formally. Through simulation, we verify that conditional randomization tests behave like more traditional forms of covariate adjustmet but have the added benefit of having the correct conditional significance level. Finally, we apply the approach to a randomized product marketing experiment where covariate information was collected after randomization.

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arXiv2016

Conducting sparse feature selection on arbitrarily long phrases in text corpora with a focus on interpretability

We propose a general framework for topic-specific summarization of large text corpora, and illustrate how it can be used for analysis in two quite different contexts: an OSHA database of fatality and catastrophe reports (to facilitate surveillance for patterns in circumstances leading to injury or death) and legal decisions on workers' compensation claims (to explore relevant case law). Our summarization framework, built on sparse classification methods, is a compromise between simple word frequency based methods currently in wide use, and more heavyweight, model-intensive methods such as Latent Dirichlet Allocation (LDA). For a particular topic of interest (e.g., mental health disability, or chemical reactions), we regress a labeling of documents onto the high-dimensional counts of all the other words and phrases in the documents. The resulting small set of phrases found as predictive are then harvested as the summary. Using a branch-and-bound approach, this method can be extended to allow for phrases of arbitrary length, which allows for potentially rich summarization. We discuss how focus on the purpose of the summaries can inform choices of regularization parameters and model constraints. We evaluate this tool by comparing computational time and summary statistics of the resulting word lists to three other methods in the literature. We also present a new R package, textreg. Overall, we argue that sparse methods have much to offer text analysis, and is a branch of research that should be considered further in this context.

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arXiv2016

Principal Score Methods: Assumptions and Extensions

Researchers addressing post-treatment complications in randomized trials often turn to principal stratification to define relevant assumptions and quantities of interest. One approach for estimating causal effects in this framework is to use methods based on the "principal score," typically assuming that stratum membership is as-good-as-randomly assigned given a set of covariates. In this paper, we clarify the key assumption in this context, known as Principal Ignorability, and argue that versions of this assumption are quite strong in practice. We describe different estimation approaches and demonstrate that weighting-based methods are generally preferable to subgroup-based approaches that discretize the principal score. We then extend these ideas to the case of two-sided noncompliance and propose a natural framework for combining Principal Ignorability with exclusion restrictions and other assumptions. Finally, we apply these ideas to the Head Start Impact Study, a large-scale randomized evaluation of the Head Start program. Overall, we argue that, while principal score methods are useful tools, applied researchers should fully understand the relevant assumptions when using them in practice.

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arXiv2016

More Powerful Multiple Testing in Randomized Experiments with Non-Compliance

Two common concerns raised in analyses of randomized experiments are (i) appropriately handling issues of non-compliance, and (ii) appropriately adjusting for multiple tests (e.g., on multiple outcomes or subgroups). Although simple intention-to-treat (ITT) and Bonferroni methods are valid in terms of type I error, they can each lead to a substantial loss of power; when employing both simultaneously, the total loss may be severe. Alternatives exist to address each concern. Here we propose an analysis method for experiments involving both features that merges posterior predictive $p$-values for complier causal effects with randomization-based multiple comparisons adjustments; the results are valid familywise tests that are doubly advantageous: more powerful than both those based on standard ITT statistics and those using traditional multiple comparison adjustments. The operating characteristics and advantages of our method are demonstrated through a series of simulated experiments and an analysis of the United States Job Training Partnership Act (JTPA) Study, where our methods lead to different conclusions regarding the significance of estimated JTPA effects.

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arXiv2016

Posterior Predictive P-values with Fisher Randomization Tests in Noncompliance Settings: Test Statistics vs Discrepancy Variables

In randomized experiments with noncompliance, tests may focus on compliers rather than on the overall sample. Rubin (1998) put forth such a method, and argued that testing for the complier average causal effect and averaging permutation based p-values over the posterior distribution of the compliance status could increase power, as compared to general intent-to-treat tests. The general scheme is to repeatedly do a two-step process of imputing missing compliance statuses and conducting a permutation test with the completed data. In this paper, we explore this idea further, comparing the use of discrepancy measures, which depend on unknown but imputed parameters, to classical test statistics and exploring different approaches for imputing the unknown compliance statuses. We also examine consequences of model misspecification in the imputation step, and discuss to what extent this additional modeling undercuts the permutation test's model independence. We find that, especially for discrepancy measures, modeling choices can impact both power and validity. In particular, imputing missing compliance statuses assuming the null can radically reduce power, but not doing so can jeopardize validity. Fortunately, covariates predictive of compliance status can mitigate these results. Finally, we compare this overall approach to Bayesian model-based tests, that is tests that are directly derived from posterior credible intervals, under both correct and incorrect model specification. We find that adding the permutation step in an otherwise Bayesian approach improves robustness to model specification without substantial loss of power.

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arXiv2014

Randomization Inference for Treatment Effect Variation

Applied researchers are increasingly interested in whether and how treatment effects vary in randomized evaluations, especially variation not explained by observed covariates. We propose a model-free approach for testing for the presence of such unexplained variation. To use this randomization-based approach, we must address the fact that the average treatment effect, generally the object of interest in randomized experiments, actually acts as a nuisance parameter in this setting. We explore potential solutions and advocate for a method that guarantees valid tests in finite samples despite this nuisance. We also show how this method readily extends to testing for heterogeneity beyond a given model, which can be useful for assessing the sufficiency of a given scientific theory. We finally apply our method to the National Head Start Impact Study, a large-scale randomized evaluation of a Federal preschool program, finding that there is indeed significant unexplained treatment effect variation.

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arXiv2014

To Adjust or Not to Adjust? Sensitivity Analysis of M-Bias and Butterfly-Bias

"M-Bias," as it is called in the epidemiologic literature, is the bias introduced by conditioning on a pretreatment covariate due to a particular "M-Structure" between two latent factors, an observed treatment, an outcome, and a "collider." This potential source of bias, which can occur even when the treatment and the outcome are not confounded, has been a source of considerable controversy. We here present formulae for identifying under which circumstances biases are inflated or reduced. In particular, we show that the magnitude of M-Bias in linear structural equation models tends to be relatively small compared to confounding bias, suggesting that it is generally not a serious concern in many applied settings. These theoretical results are consistent with recent empirical findings from simulation studies. We also generalize the M-Bias setting (1) to allow for the correlation between the latent factors to be nonzero, and (2) to allow for the collider to be a confounder between the treatment and the outcome. These results demonstrate that mild deviations from the M-Structure tend to increase confounding bias more rapidly than M-Bias, suggesting that choosing to condition on any given covariate is generally the superior choice. As an application, we re-examine a controversial example between Professors Donald Rubin and Judea Pearl.

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arXiv2014

Concise comparative summaries (CCS) of large text corpora with a human experiment

In this paper we propose a general framework for topic-specific summarization of large text corpora and illustrate how it can be used for the analysis of news databases. Our framework, concise comparative summarization (CCS), is built on sparse classification methods. CCS is a lightweight and flexible tool that offers a compromise between simple word frequency based methods currently in wide use and more heavyweight, model-intensive methods such as latent Dirichlet allocation (LDA). We argue that sparse methods have much to offer for text analysis and hope CCS opens the door for a new branch of research in this important field. For a particular topic of interest (e.g., China or energy), CSS automatically labels documents as being either on- or off-topic (usually via keyword search), and then uses sparse classification methods to predict these labels with the high-dimensional counts of all the other words and phrases in the documents. The resulting small set of phrases found as predictive are then harvested as the summary. To validate our tool, we, using news articles from the New York Times international section, designed and conducted a human survey to compare the different summarizers with human understanding. We demonstrate our approach with two case studies, a media analysis of the framing of "Egypt" in the New York Times throughout the Arab Spring and an informal comparison of the New York Times' and Wall Street Journal's coverage of "energy." Overall, we find that the Lasso with $L^2$ normalization can be effectively and usefully used to summarize large corpora, regardless of document size.

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