Corrected Standard Errors with Clustered Data

The use of cluster robust standard errors (CRSE) is common as data are often collected from units, such as cities, states or countries, with multiple observations per unit. There is considerable discussion of how best to estimate standard errors and confidence intervals when using CRSE (Harden 2011; Imbens and Kolesár 2016; MacKinnon and Webb 2017; Esarey and Menger 2019). Extensive simulations in this literature and here show that CRSE seriously underestimate coefficient standard errors and their associated confidence intervals, particularly with a small number of clusters and when there is little within cluster variation in the explanatory variables. These same simulations show that a method developed here provides more reliable estimates of coefficient standard errors. They underestimate confidence intervals for tests of individual and sets of coefficients in extreme conditions, but by far less than do CRSE. Simulations also show that this method produces more accurate standard error and confidence interval estimates than bootstrapping, which is often recommended as an alternative to CRSE.

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Practical and Effective Approaches to Dealing With Clustered Data

Political Science Research and Methods ◽

10.1017/psrm.2017.42 ◽

2018 ◽

Vol 7 (3) ◽

pp. 541-559 ◽

Cited By ~ 20

Author(s):

Justin Esarey ◽

Andrew Menger

Keyword(s):

Recent Work ◽

Clustered Data ◽

Standard Errors ◽

Data Sets ◽

Number Of Clusters ◽

Uncertainty Measures ◽

R Packages ◽

Robust Standard Errors

Cluster-robust standard errors (as implemented by the eponymous cluster option in Stata) can produce misleading inferences when the number of clusters G is small, even if the model is consistent and there are many observations in each cluster. Nevertheless, political scientists commonly employ this method in data sets with few clusters. The contributions of this paper are: (a) developing new and easy-to-use Stata and R packages that implement alternative uncertainty measures robust to small G, and (b) explaining and providing evidence for the advantages of these alternatives, especially cluster-adjusted t-statistics based on Ibragimov and Müller. To illustrate these advantages, we reanalyze recent work where results are based on cluster-robust standard errors.

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Confidence intervals for the common coefficient of variation of rainfall in Thailand

PeerJ ◽

10.7717/peerj.10004 ◽

2020 ◽

Vol 8 ◽

pp. e10004

Author(s):

Warisa Thangjai ◽

Sa-Aat Niwitpong ◽

Suparat Niwitpong

Keyword(s):

Standard Deviation ◽

Confidence Interval ◽

Confidence Intervals ◽

Coefficient Of Variation ◽

Daily Rainfall ◽

Moisture Index ◽

Interval Estimates ◽

The Common ◽

Log Normal ◽

Confidence Interval Estimates

The log-normal distribution is often used to analyze environmental data like daily rainfall amounts. The rainfall is of interest in Thailand because high variable climates can lead to periodic water stress and scarcity. The mean, standard deviation or coefficient of variation of the rainfall in the area is usually estimated. The climate moisture index is the ratio of plant water demand to precipitation. The climate moisture index should use the coefficient of variation instead of the standard deviation for comparison between areas with widely different means. The larger coefficient of variation indicates greater dispersion, whereas the lower coefficient of variation indicates the lower risk. The common coefficient of variation, is the weighted coefficients of variation based on k areas, presents the average daily rainfall. Therefore, the common coefficient of variation is used to describe overall water problems of k areas. In this paper, we propose four novel approaches for the confidence interval estimation of the common coefficient of variation of log-normal distributions based on the fiducial generalized confidence interval (FGCI), method of variance estimates recovery (MOVER), computational, and Bayesian approaches. A Monte Carlo simulation was used to evaluate the coverage probabilities and average lengths of the confidence intervals. In terms of coverage probability, the results show that the FGCI approach provided the best confidence interval estimates for most cases except for when the sample case was equal to six populations (k = 6) and the sample sizes were small (nI < 50), for which the MOVER confidence interval estimates were the best. The efficacies of the proposed approaches are illustrated with example using real-life daily rainfall datasets from regions of Thailand.

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Publication Bias in Meta-Analysis: Confidence Intervals for Rosenthal’s Fail-Safe Number

International Scholarly Research Notices ◽

10.1155/2014/825383 ◽

2014 ◽

Vol 2014 ◽

pp. 1-17 ◽

Cited By ~ 21

Author(s):

Konstantinos C. Fragkos ◽

Michail Tsagris ◽

Christos C. Frangos

Keyword(s):

Confidence Intervals ◽

Normal Approximation ◽

Meta Analysis ◽

Variance Estimator ◽

Nonparametric Bootstrap ◽

Interval Estimates ◽

Variance Estimators ◽

Lower Confidence ◽

Confidence Interval Estimates ◽

Fail Safe

The purpose of the present paper is to assess the efficacy of confidence intervals for Rosenthal’s fail-safe number. Although Rosenthal’s estimator is highly used by researchers, its statistical properties are largely unexplored. First of all, we developed statistical theory which allowed us to produce confidence intervals for Rosenthal’s fail-safe number. This was produced by discerning whether the number of studies analysed in a meta-analysis is fixed or random. Each case produces different variance estimators. For a given number of studies and a given distribution, we provided five variance estimators. Confidence intervals are examined with a normal approximation and a nonparametric bootstrap. The accuracy of the different confidence interval estimates was then tested by methods of simulation under different distributional assumptions. The half normal distribution variance estimator has the best probability coverage. Finally, we provide a table of lower confidence intervals for Rosenthal’s estimator.

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Understanding, Choosing, and Unifying Multilevel and Fixed Effect Approaches

Political Analysis ◽

10.1017/pan.2020.41 ◽

2020 ◽

pp. 1-20

Author(s):

Chad Hazlett ◽

Leonard Wainstein

Keyword(s):

Random Effects ◽

Fixed Effects ◽

Multilevel Models ◽

Standard Errors ◽

Point Estimate ◽

Fe Model ◽

Grouped Data ◽

Coefficient Estimates ◽

Political Science Education ◽

Robust Standard Errors

Abstract When working with grouped data, investigators may choose between “fixed effects” models (FE) with specialized (e.g., cluster-robust) standard errors, or “multilevel models” (MLMs) employing “random effects.” We review the claims given in published works regarding this choice, then clarify how these approaches work and compare by showing that: (i) random effects employed in MLMs are simply “regularized” fixed effects; (ii) unmodified MLMs are consequently susceptible to bias—but there is a longstanding remedy; and (iii) the “default” MLM standard errors rely on narrow assumptions that can lead to undercoverage in many settings. Our review of over 100 papers using MLM in political science, education, and sociology show that these “known” concerns have been widely ignored in practice. We describe how to debias MLM’s coefficient estimates, and provide an option to more flexibly estimate their standard errors. Most illuminating, once MLMs are adjusted in these two ways the point estimate and standard error for the target coefficient are exactly equal to those of the analogous FE model with cluster-robust standard errors. For investigators working with observational data and who are interested only in inference on the target coefficient, either approach is equally appropriate and preferable to uncorrected MLM.

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