Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting (AST)

We propose a locally efficient estimator for a class of semiparametric data combination problems. A leading estimand in this class is the average treatment effect on the treated (ATT). Data combination problems are related to, but distinct from, the class of missing data problems with data missing at random (of which the average treatment effect (ATE) estimand is a special case). Our estimator also possesses a double robustness property. Our procedure may be used to efficiently estimate, among other objects, the ATT, the two-sample instrumental variables model (TSIV), counterfactual distributions, poverty maps, and semiparametric difference-in-differences. In an empirical application, we use our procedure to characterize residual Black–White wage inequality after flexibly controlling for “premarket” differences in measured cognitive achievement. Supplementary materials for this article are available online.     

Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT

We propose inverse probability weighted estimators for the local average treatment effect (LATE) and the local average treatment effect for the treated (LATT) under instrumental variable assumptions with covariates. We show that these estimators are asymptotically normal and efficient. When the (binary) instrument satisfies one-sided noncompliance, we propose a Durbin–Wu–Hausman-type test of whether treatment assignment is unconfounded conditional on some observables. The test is based on the fact that under one-sided noncompliance LATT coincides with the average treatment effect for the treated (ATT). We conduct Monte Carlo simulations to demonstrate, among other things, that part of the theoretical efficiency gain afforded by unconfoundedness in estimating ATT survives pretesting. We illustrate the implementation of the test on data from training programs administered under the Job Training Partnership Act in the United States. This article has online supplementary material.     

Pseudo Panel Data Models With Cohort Interactive Effects

When genuine panel data samples are not available, repeated cross-sectional surveys can be used to form so-called pseudo panels. In this article, we investigate the properties of linear pseudo panel data estimators with fixed number of cohorts and time observations. We extend standard linear pseudo panel data setup to models with factor residuals by adapting the quasi-differencing approach developed for genuine panels. In a Monte Carlo study, we find that the proposed procedure has good finite sample properties in situations with endogeneity, cohort interactive effects, and near nonidentification. Finally, as an illustration the proposed method is applied to data from Ecuador to study labor supply elasticity. Supplementary materials for this article are available online.     

Exponential class of dynamic binary choice panel data models with fixed effects

ABSTRACT

This paper proposes an exponential class of dynamic binary choice panel data models for the analysis of short T (time dimension) large N (cross section dimension) panel data sets that allow for unobserved heterogeneity (fixed effects) to be arbitrarily correlated with the covariates. The paper derives moment conditions that are invariant to the fixed effects which are then used to identify and estimate the parameters of the model. Accordingly, generalized method of moments (GMM) estimators are proposed that are consistent and asymptotically normally distributed at the root-N rate. We also study the conditional likelihood approach and show that under exponential specification, it can identify the effect of state dependence but not the effects of other covariates. Monte Carlo experiments show satisfactory finite sample performance for the proposed estimators and investigate their robustness to misspecification.     

An alternative approach for compatibility of two discrete conditional distributions

ABSTRACT

Conditional specification of distributions is a developing area with increasing applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the compatibility of two conditional probability distributions under the finite discrete setup. A technique based on rank-based criterion is shown to be particularly convenient for identifying compatible distributions corresponding to complete conditional specification including the case with zeros.The proposed methods are illustrated with several examples.     

Prognostic score matching methods for estimating the average effect of a non-reversible binary time-dependent treatment on the survival function

In evaluating the benefit of a treatment on survival, it is often of interest to compare post-treatment survival with the survival function that would have been observed in the absence of treatment. In many practical settings, treatment is time-dependent in the sense that subjects typically begin follow-up untreated, with some going on to receive treatment at some later time point. In observational studies, treatment is not assigned at random and, therefore, may depend on various patient characteristics. We have developed semi-parametric matching methods to estimate the average treatment effect on the treated (ATT) with respect to survival probability and restricted mean survival time. Matching is based on a prognostic score which reflects each patient’s death hazard in the absence of treatment. Specifically, each treated patient is matched with multiple as-yet-untreated patients with similar prognostic scores. The matched sets do not need to be of equal size, since each matched control is weighted in order to preserve risk score balancing across treated and untreated groups. After matching, we estimate the ATT non-parametrically by contrasting pre- and post-treatment weighted Nelson–Aalen survival curves. A closed-form variance is proposed and shown to work well in simulation studies. The proposed methods are applied to national organ transplant registry data.

     

Landmark estimation of survival and treatment effects in observational studies

Clinical studies aimed at identifying effective treatments to reduce the risk of disease or death often require long term follow-up of participants in order to observe a sufficient number of events to precisely estimate the treatment effect. In such studies, observing the outcome of interest during follow-up may be difficult and high rates of censoring may be observed which often leads to reduced power when applying straightforward statistical methods developed for time-to-event data. Alternative methods have been proposed to take advantage of auxiliary information that may potentially improve efficiency when estimating marginal survival and improve power when testing for a treatment effect. Recently, Parast et al. (J Am Stat Assoc 109(505):384–394, 2014) proposed a landmark estimation procedure for the estimation of survival and treatment effects in a randomized clinical trial setting and demonstrated that significant gains in efficiency and power could be obtained by incorporating intermediate event information as well as baseline covariates. However, the procedure requires the assumption that the potential outcomes for each individual under treatment and control are independent of treatment group assignment which is unlikely to hold in an observational study setting. In this paper we develop the landmark estimation procedure for use in an observational setting. In particular, we incorporate inverse probability of treatment weights (IPTW) in the landmark estimation procedure to account for selection bias on observed baseline (pretreatment) covariates. We demonstrate that consistent estimates of survival and treatment effects can be obtained by using IPTW and that there is improved efficiency by using auxiliary intermediate event and baseline information. We compare our proposed estimates to those obtained using the Kaplan–Meier estimator, the original landmark estimation procedure, and the IPTW Kaplan–Meier estimator. We illustrate our resulting reduction in bias and gains in efficiency through a simulation study and apply our procedure to an AIDS dataset to examine the effect of previous antiretroviral therapy on survival.     

Immaculating the inconsistent estimator of slope parameter in measurement error model with replicated data

ABSTRACT

The measurement error model with replicated data on study as well as explanatory variables is considered. The measurement error variance associated with the explanatory variable is estimated using the complete data and the grouped data which is used for the construction of the consistent estimators of regression coefficient. These estimators are further used in constructing an almost unbiased estimator of regression coefficient. The large sample properties of these estimators are derived without assuming any distributional form of the measurement errors and the random error component under the setup of an ultrastructural model.     

On the Use of GLS Demeaning in Panel Unit Root Testing

One of the most well-known facts about unit root testing in time series is that the Dickey–Fuller (DF) test based on ordinary least squares (OLS) demeaned data suffers from low power, and that the use of generalized least squares (GLS) demeaning can lead to substantial power gains. Of course, this development has not gone unnoticed in the panel unit root literature. However, while the potential of using GLS demeaning is widely recognized, oddly enough, there are still no theoretical results available to facilitate a formal analysis of such demeaning in the panel data context. The present article can be seen as a reaction to this. The purpose is to evaluate the effect of GLS demeaning when used in conjuncture with the pooled OLS t-test for a unit root, resulting in a panel analog of the time series DF–GLS test. A key finding is that the success of GLS depend critically on the order in which the dependent variable is demeaned and first-differenced. If the variable is demeaned prior to taking first-differences, power is maximized by using GLS demeaning, whereas if the differencing is done first, then OLS demeaning is preferred. Furthermore, even if the former demeaning approach is used, such that GLS is preferred, the asymptotic distribution of the resulting test is independent of the tuning parameters that characterize the local alternative under which the demeaning performed. Hence, the demeaning can just as well be performed under the unit root null hypothesis. In this sense, GLS demeaning under the local alternative is redundant.     

Alternative diff-in-diffs estimators with several pretreatment periods

This paper deals with the identification of treatment effects using difference-in-differences estimators when several pretreatment periods are available. We define a family of identifying nonnested assumptions that lead to alternative difference-in-differences estimators. We show that the most usual difference-in-differences estimators imply equivalence conditions for the identifying nonnested assumptions. We further propose a model that can be used to test multiple equivalence conditions without imposing any of them. We conduct a Monte Carlo analysis and apply our approach to several recent papers to show its practical relevance.     

THE POTENTIAL FOR BIAS IN PRINCIPAL CAUSAL EFFECT ESTIMATION WHEN TREATMENT RECEIVED DEPENDS ON A KEY COVARIATE

Motivated by a potential-outcomes perspective, the idea of principal stratification has been widely recognized for its relevance in settings susceptible to posttreatment selection bias such as randomized clinical trials where treatment received can differ from treatment assigned. In one such setting, we address subtleties involved in inference for causal effects when using a key covariate to predict membership in latent principal strata. We show that when treatment received can differ from treatment assigned in both study arms, incorporating a stratum-predictive covariate can make estimates of the "complier average causal effect" (CACE) derive from observations in the two treatment arms with different covariate distributions. Adopting a Bayesian perspective and using Markov chain Monte Carlo for computation, we develop posterior checks that characterize the extent to which incorporating the pretreatment covariate endangers estimation of the CACE. We apply the method to analyze a clinical trial comparing two treatments for jaw fractures in which the study protocol allowed surgeons to overrule both possible randomized treatment assignments based on their clinical judgment and the data contained a key covariate (injury severity) predictive of treatment received.     

Clustering the mixed panel dataset using Gower's distance and k-prototypes algorithms

ABSTRACT

Panel datasets have been increasingly used in economics to analyze complex economic phenomena. Panel data is a two-dimensional array that combines cross-sectional and time series data. Through constructing a panel data matrix, the clustering method is applied to panel data analysis. This method solves the heterogeneity question of the dependent variable, which belongs to panel data, before the analysis. Clustering is a widely used statistical tool in determining subsets in a given dataset. In this article, we present that the mixed panel dataset is clustered by agglomerative hierarchical algorithms based on Gower's distance and by k-prototypes. The performance of these algorithms has been studied on panel data with mixed numerical and categorical features. The effectiveness of these algorithms is compared by using cluster accuracy. An experimental analysis is illustrated on a real dataset using Stata and R package software.     

Composite likelihood for aggregate data from clustered multistate processes under intermittent observation

Abstract

Markov processes offer a useful basis for modeling the progression of organisms through successive stages of their life cycle. When organisms are examined intermittently in developmental studies, likelihoods can be constructed based on the resulting panel data in terms of transition probability functions. In some settings however, organisms cannot be tracked individually due to a difficulty in identifying distinct individuals, and in such cases aggregate counts of the number of organisms in different stages of development are recorded at successive time points. We consider the setting in which such aggregate counts are available for each of a number of tanks in a developmental study. We develop methods which accommodate clustering of the transition rates within tanks using a marginal modeling approach followed by robust variance estimation, and through use of a random effects model. Composite likelihood is proposed as a basis of inference in both settings. An extension which incorporates mortality is also discussed. The proposed methods are shown to perform well in empirical studies and are applied in an illustrative example on the growth of the Arabidopsis thaliana plant.     

The SR Periodicals Miscellany

Abstract

Libraries play a crucial role in identifying, organizing, classifying, and delivering access to useful information at the point of need including information that is otherwise freely available online. A new classification system for free electronic resources called Scholarship, Persistence, Entity, Compatibility, and Convenience (SPECC) can help library personnel determine whether specific free electronic resources should be made available through their libraries. SPECC is not intended to be used as the only means of evaluating free electronic resources for collection development purposes, but SPECC does broadly categorize most free electronic resources and can save time and money.     

Structural Vector Autoregressions With Nonnormal Residuals

In structural vector autoregressive (SVAR) modeling, sometimes the identifying restrictions are insufficient for a unique specification of all shocks. In this paper it is pointed out that specific distributional assumptions can help in identifying the structural shocks. In particular, a mixture of normal distributions is considered as a possible model that can be used in this context. Our model setup enables us to test restrictions which are just-identifying in a standard SVAR framework. The results are illustrated using a U.S. macro data set and a system of U.S. and European interest rates.     

Bayesian Approach to Multicentre Sparse Data

In a 2 × 2 contingency table, when the sample size is small, there may be a number of cells that contain few or no observations, usually referred to as sparse data. In such cases, a common recommendation in the conventional frequentist methods is adding a small constant to every cell of the observed table to find the estimates of the unknown parameters. However, this approach is based on asymptotic properties of the estimates and may work poorly for small samples. An alternative approach would be to use Bayesian methods in order to provide better insight into the problem of sparse data coupled with fewer centers, which would otherwise be difficult to carry out the analysis. In this article, an attempt has been made to use hierarchical Bayesian model to a multicenter data on the effect of a surgical treatment with standard foot care among leprosy patients with posterior tibial nerve damage which is summarized as seven 2 × 2 tables. Monte Carlo Markov Chain (MCMC) techniques are applied in estimating the parameters of interest under sparse data setup.     

Comparing crossing hazard rate functions by joint modelling of survival and longitudinal data

Abstract

It is one of the important issues in survival analysis to compare two hazard rate functions to evaluate treatment effect. It is quite common that the two hazard rate functions cross each other at one or more unknown time points, representing temporal changes of the treatment effect. In certain applications, besides survival data, we also have related longitudinal data available regarding some time-dependent covariates. In such cases, a joint model that accommodates both types of data can allow us to infer the association between the survival and longitudinal data and to assess the treatment effect better. In this paper, we propose a modelling approach for comparing two crossing hazard rate functions by joint modelling survival and longitudinal data. Maximum likelihood estimation is used in estimating the parameters of the proposed joint model using the EM algorithm. Asymptotic properties of the maximum likelihood estimators are studied. To illustrate the virtues of the proposed method, we compare the performance of the proposed method with several existing methods in a simulation study. Our proposed method is also demonstrated using a real dataset obtained from an HIV clinical trial.     

Alternative transformations to eliminate fixed effects

In a panel data model with fixed individual effects, a number of alternative transformations are available to eliminate these effects such that the slope parameters can be estimated from ordinary least squares on transformed data. In this note we show that each transformation leads to algebraically the same estimator if the transformed data are used efficiently (i.e. if GLS is applied). If OLS is used, however, differences may occur and the routinely computed variances, even after degrees of freedom correction, are incorrect. In addition, it may matter whether “redundant” observations are used or not.     

The Discrete Normal Distribution

Abstract

The normal distribution has been playing a key role in stochastic modeling for a continuous setup. But its distribution function does not have an analytical form. Moreover, the distribution of a complex multicomponent system made of normal variates occasionally poses derivational difficulties. It may be worth exploring the possibility of developing a discrete version of the normal distribution so that the same can be used for modeling discrete data. Keeping in mind the above requirement we propose a discrete version of the continuous normal distribution. The Increasing Failure Rate property in the discrete setup has been ensured. Characterization results have also been made to establish a direct link between the discrete normal distribution and its continuous counterpart. The corresponding concept of a discrete approximator for the normal deviate has been suggested. An application of the discrete normal distributions for evaluating the reliability of complex systems has been elaborated as an alternative to simulation methods.     

Semiparametric Smooth Coefficient Stochastic Frontier Model With Panel Data

ABSTRACT

We investigate the semiparametric smooth coefficient stochastic frontier model for panel data in which the distribution of the composite error term is assumed to be of known form but depends on some environmental variables. We propose multi-step estimators for the smooth coefficient functions as well as the parameters of the distribution of the composite error term and obtain their asymptotic properties. The Monte Carlo study demonstrates that the proposed estimators perform well in finite samples. We also consider an application and perform model specification test, construct confidence intervals, and estimate efficiency scores that depend on some environmental variables. The application uses a panel data on 451 large U.S. firms to explore the effects of computerization on productivity. Results show that two popular parametric models used in the stochastic frontier literature are likely to be misspecified. Compared with the parametric estimates, our semiparametric model shows a positive and larger overall effect of computer capital on the productivity. The efficiency levels, however, were not much different among the models. Supplementary materials for this article are available online.