A unified analysis of regression adjustment in randomized experiments

Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand this phenomenon, we develop a unified comparison of the asymptotic variance of a class of linear regression-adjusted estimators. Our analysis is based on the classical theory for linear regression with heteroscedastic errors and thus does not assume that the postulated linear model is correct. For a completely randomized binary treatment, we provide sufficient conditions under which some regression-adjusted estimators are guaranteed to be more asymptotically efficient than others. We explore other settings such as general treatment assignment mechanisms and generalized linear models, and find that the variance dominance phenomenon no longer occurs.Comment: 17 pages, 1 figure, 2 table

Simultaneous Inference for Empirical Best Predictors With a Poverty Study in Small Areas

[Abstract]: Today, generalized linear mixed models (GLMM) are broadly used in many fields. However, the development of tools for performing simultaneous inference has been largely neglected in this domain. A framework for joint inference is indispensable to carry out statistically valid multiple comparisons of parameters of interest between all or several clusters. We therefore develop simultaneous confidence intervals and multiple testing procedures for empirical best predictors under GLMM. In addition, we implement our methodology to study widely employed examples of mixed models, that is, the unit-level binomial, the area-level Poisson-gamma and the area-level Poisson-lognormal mixed models. The asymptotic results are accompanied by extensive simulations. A case study on predicting poverty rates illustrates applicability and advantages of our simultaneous inference tools.The authors gratefully acknowledge the support from the Swiss National Science Foundation for the project 200021-192345. In addition, they acknowledge the support from the MINECO grants MTM2017-82724-R and MTM2014-52876-R, the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015 and Centro Singular de Investigación de Galicia ED431G/01), all of them through the ERDF. The computations were performed at the University of Geneva on the Baobab cluster.Xunta de Galicia; ED431C-2016-015Xunta de Galicia; ED431G/0

Simple bootstrap for linear mixed effects under model misspecification

[Abstract]: Linear mixed effects are considered excellent predictors of cluster-level parameters in various domains. However, previous research has demonstrated that their performance is affected by departures from model assumptions. Given the common occurrence of these departures in empirical studies, there is a need for inferential methods that are robust to misspecifications while remaining accessible and appealing to practitioners. Statistical tools have been developed for cluster-wise and simultaneous inference for mixed effects under distributional misspecifications, employing a user-friendly semiparametric random effect bootstrap. The merits and limitations of this approach are discussed in the general context of model misspecification. Theoretical analysis demonstrates the asymptotic consistency of the methods under general regularity conditions. Simulations show that the proposed intervals are robust to departures from modelling assumptions, including asymmetry and long tails in the distributions of errors and random effects, outperforming competitors in terms of empirical coverage probability. Finally, the methodology is applied to construct confidence intervals for household income across counties in the Spanish region of Galicia.The authors gratefully acknowledge support from the Swiss National Science Foundation, projects 200021-192345 and P2GEP2-195898, as well as from the Instituto Galego de Estatística who provided us with the data set. In addition, this research has been supported by MICINN grant PID2020-113578RB-I00, and by Xunta de Galicia (Grupos de Referencia Competitiva ED431C 2020/14), GAIN (Galician Innovation Agency) and the Regional Ministry of Economy, Employment and Industry grant COV20/00604 and Centro de investigación del Sistema universitario de Galicia ED431G 2019/01, all of them through ERDF. The computations were performed at the University of Geneva using Baobab and Yggdrasil HPC Service and using the computational facilities of the Advanced Computing Research Centre, University of Bristol.Xunta de Galicia; ED431C 2020/14Xunta de Galicia; ED431G 2019/01Switzerland. Swiss National Science Foundation; 200021-192345Switzerland. Swiss National Science Foundation; P2GEP2-195898Xunta de Galicia; COV20/0060

Simultaneous inference for linear mixed model parameters with an application to small area estimation

Open access financiado por Universite de Geneve (article funding)European Regional Development Fund[Abstract]: Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical tools for valid simultaneous inference for mixed parameters are rare. This is surprising because one often faces inferential problems beyond the pointwise examination of fixed or mixed parameters. For example, there is an interest in a comparative analysis of cluster-level parameters or subject-specific estimates in studies with repeated measurements. We discuss methods for simultaneous inference assuming a linear mixed model. Specifically, we develop simultaneous prediction intervals as well as multiple testing procedures for mixed parameters. They are useful for joint considerations or comparisons of cluster-level parameters. We employ a consistent bootstrap approximation of the distribution of max-type statistic to construct our tools. The numerical performance of the developed methodology is studied in simulation experiments and illustrated in a data example on household incomes in small areas.Swiss National Science Foundation; 200021-192345,Swiss National Science Foundation; P2GEP2_195898Xunta de Galicia; ED431C 2020/14Ministerio de Ciencia e Innovación; PID2020-113578RB-I00Galician Innovation Agency/ Ministerio de Economía, empleo e industria; COV20/00604Xunta de Galicia; ED431G2019/0

Simultaneous Inference for Empirical Best Predictors with a Poverty Study in Small Areas

Today, generalized linear mixed models are broadly used in many fields. However, the development of tools for performing simultaneous inference has been largely neglected in this domain. A framework for joint inference is indispensable to carry out statistically valid multiple comparisons of parameters of interest between all or several clusters. We therefore develop simultaneous confidence intervals and multiple testing procedures for empirical best predictors under generalized linear mixed models. In addition, we implement our methodology to study widely employed examples of mixed models, that is, the unit-level binomial, the area-level Poisson-gamma and the area-level Poisson-lognormal mixed models. The asymptotic results are accompanied by extensive simulations. A case study on predicting poverty rates illustrates applicability and advantages of our simultaneous inference tools.Comment: 46 pages, 20 figures; simulations and data analysis expanded, additional remarks adde

Simultaneous and post-selection inference for mixed parameters

This thesis primarily focuses on the development of statistically valid tools for simultaneous and post-selection inference for a mixed parameter under linear mixed models (LMM) and generalised LMM (GLMM) as well as the investigation of their performance in practice. First, we construct simultaneous confidence intervals for mixed parameters using the max-type statistic, which is readily applicable in the multiple testing procedure. We show that the cluster-wise inference is statistically invalid once we deal with joint statements and it may lead to completely erroneous conclusions. Second, we deal with the simultaneous inference for empirical best predictors in GLMM. Finally, we investigate the issue of post-selection inference for a mixed parameter using conditional Akaike information criterion as a model selection procedure. Within the framework of LMM, we develop a complete theory to construct confidence intervals for mixed parameters under three frameworks: nested and general models, as well as a misspecified setting