scholarly journals Reflections on modern methods: demystifying robust standard errors for epidemiologists

2020 ◽  
Author(s):  
Mohammad Ali Mansournia ◽  
Maryam Nazemipour ◽  
Ashley I Naimi ◽  
Gary S Collins ◽  
Michael J Campbell
Keyword(s):  
Statistical Model ◽  
Regression Coefficient ◽  
Worked Examples ◽  
Standard Errors ◽  
Clinical Papers ◽  
Statistical Estimates ◽  
The Mean ◽  
Measure Of Uncertainty ◽  
Robust Standard Errors ◽  
Sample Estimate

Abstract All statistical estimates from data have uncertainty due to sampling variability. A standard error is one measure of uncertainty of a sample estimate (such as the mean of a set of observations or a regression coefficient). Standard errors are usually calculated based on assumptions underpinning the statistical model used in the estimation. However, there are situations in which some assumptions of the statistical model including the variance or covariance of the outcome across observations are violated, which leads to biased standard errors. One simple remedy is to userobust standard errors, which are robust to violations of certain assumptions of the statistical model. Robust standard errors are frequently used in clinical papers (e.g. to account for clustering of observations), although the underlying concepts behind robust standard errors and when to use them are often not well understood. In this paper, we demystify robust standard errors using several worked examples in simple situations in which model assumptions involving the variance or covariance of the outcome are misspecified. These are: (i) when the observed variances are different, (ii) when the variance specified in the model is wrong and (iii) when the assumption of independence is wrong.

Estimates and inferences in accounting panel data sets: comparing approaches

2017 ◽  
Vol 18 (3) ◽  
pp. 268-283
Author(s):  
Felix Canitz ◽  
Panagiotis Ballis-Papanastasiou ◽  
Christian Fieberg ◽  
Kerstin Lopatta ◽  
Armin Varmaz ◽  
...  
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Cross Section ◽  
Design Methodology ◽  
Estimation Methods ◽  
Standard Errors ◽  
Data Sets ◽  
Content Type ◽  
The Mean ◽  
Robust Standard Errors

Purpose The purpose of this paper is to review and evaluate the methods commonly used in accounting literature to correct for cointegrated data and data that are neither stationary nor cointegrated. Design/methodology/approach The authors conducted Monte Carlo simulations according to Baltagi et al. (2011), Petersen (2009) and Gow et al. (2010), to analyze how regression results are affected by the possible nonstationarity of the variables of interest. Findings The results of this study suggest that biases in regression estimates can be reduced and valid inferences can be obtained by using robust standard errors clustered by firm, clustered by firm and time or Fama–MacBeth t-statistics based on the mean and standard errors of the cross section of coefficients from time-series regressions. Originality/value The findings of this study are suited to guide future researchers regarding which estimation methods are the most reliable given the possible nonstationarity of the variables of interest.

Multi-Center Calibration of the Second Reference Material for Thromboplastin, Rabbit, Plain, Coded CRM 149R

1991 ◽  
Vol 65 (03) ◽  
pp. 263-267 ◽  
Author(s):  
A M H P van den Besselaar ◽  
R M Bertina
Keyword(s):  
Reference Material ◽  
Standard Error ◽  
Standard Errors ◽  
Sensitivity Index ◽  
Long Term Stability ◽  
Significant Bias ◽  
The Mean ◽  
The Relationship ◽  
International Sensitivity Index

SummaryIn a collaborative trial of eleven laboratories which was performed mainly within the framework of the European Community Bureau of Reference (BCR), a second reference material for thromboplastin, rabbit, plain, was calibrated against its predecessor RBT/79. This second reference material (coded CRM 149R) has a mean International Sensitivity Index (ISI) of 1.343 with a standard error of the mean of 0.035. The standard error of the ISI was determined by combination of the standard errors of the ISI of RBT/79 and the slope of the calibration line in this trial.The BCR reference material for thromboplastin, human, plain (coded BCT/099) was also included in this trial for assessment of the long-term stability of the relationship with RBT/79. The results indicated that this relationship has not changed over a period of 8 years. The interlaboratory variation of the slope of the relationship between CRM 149R and RBT/79 was significantly lower than the variation of the slope of the relationship between BCT/099 and RBT/79. In addition to the manual technique, a semi-automatic coagulometer according to Schnitger & Gross was used to determine prothrombin times with CRM 149R. The mean ISI of CRM 149R was not affected by replacement of the manual technique by this particular coagulometer.Two lyophilized plasmas were included in this trial. The mean slope of relationship between RBT/79 and CRM 149R based on the two lyophilized plasmas was the same as the corresponding slope based on fresh plasmas. Tlowever, the mean slope of relationship between RBT/79 and BCT/099 based on the two lyophilized plasmas was 4.9% higher than the mean slope based on fresh plasmas. Thus, the use of these lyophilized plasmas induced a small but significant bias in the slope of relationship between these thromboplastins of different species.

scholarly journals Understanding, Choosing, and Unifying Multilevel and Fixed Effect Approaches

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.

The analysis of the results of a rotation experiment on the use of straw and fertilizers

1953 ◽  
Vol 43 (1) ◽  
pp. 77-88 ◽  
Author(s):  
H. D. Patterson
Keyword(s):  
Present Experiment ◽  
Treatment Effects ◽  
Standard Errors ◽  
Methods Of Analysis ◽  
Seasonal Factors ◽  
Long Term Experiments ◽  
The Mean ◽  
Linear Regressions

An experiment, designed to test different ways of using straw with fertilizers, and involving a three course rotation of crops, was carried out at Rothamsted between 1933 and 1951. The methods of analysis developed for this experiment are described in the present paper and demonstrated using yields of potatoes.Treatment effects of interest are given by the mean yields over all years and the linear regressions of yield on time. These estimates are straightforward but the evaluation of their errors is complicated by the existence of correlations due to the recurrence of treatments on the same plots. Further complications are introduced when, as frequently happens in long-term experiments, treatment effects show real variation from year to year. A method is given for estimating standard errors which include a contribution from this variation.The various relationships between yields and the uncontrolled seasonal factors can also be examined; in the present experiment there is some indication that the effects of treatments on yields of potatoes are influenced by the dates of planting.In other circumstances the analysis requires modifications, some of which are briefly considered.

scholarly journals Discussion of Identification, Estimation and Approximation of Risk under Interventions that Depend on the Natural Value of Treatment Using Observational Data, by Jessica Young, Miguel Hernán, and James Robins

2014 ◽  
Vol 3 (1) ◽  
Author(s):  
Mark J. van der Laan ◽  
Alexander R. Luedtke ◽  
Iván Díaz
Keyword(s):  
Statistical Model ◽  
Observational Data ◽  
Robust Estimation ◽  
Statistical Estimation ◽  
Estimation Problem ◽  
Target Parameter ◽  
Adaptive Parameters ◽  
The Mean ◽  
Data Adaptive ◽  
Statistical Estimation Problem

AbstractYoung, Hernán, and Robins consider the mean outcome under a dynamic intervention that may rely on the natural value of treatment. They first identify this value with a statistical target parameter, and then show that this statistical target parameter can also be identified with a causal parameter which gives the mean outcome under a stochastic intervention. The authors then describe estimation strategies for these quantities. Here we augment the authors’ insightful discussion by sharing our experiences in situations where two causal questions lead to the same statistical estimand, or the newer problem that arises in the study of data adaptive parameters, where two statistical estimands can lead to the same estimation problem. Given a statistical estimation problem, we encourage others to always use a robust estimation framework where the data generating distribution truly belongs to the statistical model. We close with a discussion of a framework which has these properties.

scholarly journals Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Otávio Bartalotti
Keyword(s):  
Bias Correction ◽  
Asymptotic Theory ◽  
Regression Discontinuity ◽  
Traditional Approach ◽  
Standard Errors ◽  
Test Coverage ◽  
Regression Discontinuity Designs ◽  
The Common ◽  
Theoretical Results ◽  
Robust Standard Errors

AbstractIn regression discontinuity designs (RD), for a given bandwidth, researchers can estimate standard errors based on different variance formulas obtained under different asymptotic frameworks. In the traditional approach the bandwidth shrinks to zero as sample size increases; alternatively, the bandwidth could be treated as fixed. The main theoretical results for RD rely on the former, while most applications in the literature treat the estimates as parametric, implementing the usual heteroskedasticity-robust standard errors. This paper develops the “fixed-bandwidth” alternative asymptotic theory for RD designs, which sheds light on the connection between both approaches. I provide alternative formulas (approximations) for the bias and variance of common RD estimators, and conditions under which both approximations are equivalent. Simulations document the improvements in test coverage that fixed-bandwidth approximations achieve relative to traditional approximations, especially when there is local heteroskedasticity. Feasible estimators of fixed-bandwidth standard errors are easy to implement and are akin to treating RD estimators aslocallyparametric, validating the common empirical practice of using heteroskedasticity-robust standard errors in RD settings. Bias mitigation approaches are discussed and a novel bootstrap higher-order bias correction procedure based on the fixed bandwidth asymptotics is suggested.

scholarly journals The association between WASH, nutrition, and early childhood growth faltering in rural Cambodia: a cross-sectional risk factor analysis

2021 ◽  
Author(s):  
Amanda Justine Lai ◽  
Ramya Ambikapathi ◽  
Oliver Cumming ◽  
Krisna Seng ◽  
Irene Velez ◽  
...  
Keyword(s):  
Drinking Water ◽  
Regression Models ◽  
Water Source ◽  
Community Level ◽  
Standard Errors ◽  
Drinking Water Source ◽  
Household Level ◽  
Growth Outcomes ◽  
Growth Faltering ◽  
Robust Standard Errors

Background Inadequate nutrition in early life and exposure to sanitation-related enteric pathogens have been linked to poor growth outcomes in children. Despite rapid development in Cambodia, high prevalence of growth faltering and stunting persist among children. This study aimed to assess nutrition and WASH variables and their association with nutritional status of children under 24 months in rural Cambodia. Methods We conducted surveys in 491 villages across 55 rural communes in Cambodia in September 2016 to measure associations between child, household, and community-level risk factors for stunting and length-for-age z-score (LAZ). A primary survey measured child-level variables, including anthropometric measures and risk factors for growth faltering and stunting, for 4,036 children under 24 months of age from 3,877 households (approximately 8 households per village). A secondary survey of 5,341 households, including the same households from the primary survey and an additional 1,464 households (approximately 3 additional household per village) from the same villages, assessed village-level WASH variables to understand community water, sanitation, and hygiene (WASH) conditions that may influence child growth outcomes. For LAZ, we calculated bivariate and adjusted associations (as mean differences) with 95% confidence intervals using generalized estimating equations (GEEs) to fit linear regression models with robust standard errors. For stunting, we calculated unadjusted and adjusted prevalence ratios (PRs) with 95% confidence intervals using GEEs to fit Poisson regression models with robust standard errors. For all models assessing effects of household-level variables, we used GEEs to account for clustering at the village level. Findings After adjustment for potential confounders, presence of water and soap at a household's handwashing station was found to be significantly associated (p<0.05) with increased LAZ (adjusted mean difference in LAZ +0.10, 95% CI 0.03 to 0.16), and household use of an improved drinking water source was associated with less stunting in children compared to households that did not use an improved source of drinking water (aPR 0.81, 95% CI 0.66 to 0.98); breastfeeding and community-level access to an improved drinking water source were associated with a lower LAZ score (-0.16, 95% CI -0.27 to -0.05; -0.13, 95% CI -0.26 to 0.00). No other nutrition (i.e., dietary diversity, meal frequency) or sanitation variables (i.e., household's safe disposal of child stools, household-level sanitation, community-level sanitation) were measured to be associated with LAZ scores or stunting in children under 24 months of age.

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