Fixed Effects Of Group Research Articles

Efficient peer effects estimators with group effects

We study linear peer effect models where peers interact in groups and individual’s outcomes are linear in the group mean outcome and characteristics. We allow for unobserved random group effects as well as observed fixed group effects. The specification is in part motivated by the moment conditions imposed in Graham (2008). We show that these moment conditions can be cast in terms of a linear random group effects model and that they lead to a class of GMM estimators with parameters generally identified as long as there is sufficient variation in group size or group types. We also show that our class of GMM estimators contains a Quasi Maximum Likelihood estimator (QMLE) for the random group effects model, as well as the Wald estimator of Graham (2008) and the within estimator of Lee (2007) as special cases. Our identification results extend insights in Graham (2008) that show how assumptions about random group effects, variation in group size and certain forms of heteroscedasticity can be used to overcome the reflection problem in identifying peer effects. Our QMLE and GMM estimators accommodate additional covariates and are valid in situations with a large but finite number of different group sizes or types. Because our estimators are general moment based procedures, using instruments other than binary group indicators in estimation is straight forward. Our QMLE estimator accommodates group level covariates in the spirit of Mundlak and Chamberlain and offers an alternative to fixed effects specifications. This model feature significantly extends the applicability of Graham’s identification strategy to situations where group assignment may not be random but correlation of group level effects with peer effects can be controlled for with observable group level characteristics. Monte-Carlo simulations show that the bias of the QMLE estimator decreases with the number of groups and the variation in group size, and increases with group size. We also prove the consistency and asymptotic normality of the estimator under reasonable assumptions.

Exploring the performance of the GPSC method under several levels of outliers

The aim of this study is to evaluate the performance of the Groupwise Principal Sensitivity Components method which is a robust iterative procedure for fitting linear regression models with fixed group effects. A simulation study is carried out to assess its ability to detect multiple outliers located in the response variable (vertical outliers) or in the explanatory and response variable (high leverage outliers). Several levels of outliers are considered ranging from 5% to 45% within selected groups. The results suggest that the GPSC method is able to avoid the masking effect under low or moderate level of outliers -approximately below to 30%. Additionally, in almost all cases the GPSC method reports lower levels of false outlier detection under high leverage outliers.

Simultaneous Semiparametric Estimation of Clustering and Regression

ABSTRACT We investigate the parameter estimation of regression models with fixed group effects, when the group variable is missing while group-related variables are available. This problem involves clustering to infer the missing group variable based on the group-related variables, and regression to build a model on the target variable given the group and eventually some additional variables. Thus, this problem can be formulated as the joint distribution modeling of the target and of the group-related variables. The usual parameter estimation strategy for this joint model is a two-step approach starting by learning the group variable (clustering step) and then plugging in its estimator for fitting the regression model (regression step). However, this approach is suboptimal (providing in particular biased regression estimates) since it does not make use of the target variable for clustering. Thus, we advise the use of a simultaneous estimation approach of both clustering and regression, in a semiparametric framework. Numerical experiments illustrate the benefits of our proposition by considering wide ranges of distributions and regression models. The relevance of our new method is illustrated on real data dealing with problems associated with high blood pressure prevention. The proposed approach is implemented in the R package ClusPred available on CRAN. Supplementary materials containing the technical details and the R codes are available online.

Midshaft Fractures of the Clavicle: A Meta-analysis Comparing Surgical Fixation Using Anteroinferior Plating Versus Superior Plating

To compare the outcomes of clavicle fracture fixation using anteroinferior versus superior plate placement. We performed a meta-analysis of studies that have reported on outcomes after superior or anteroinferior plate fixation for acute midshaft clavicle fractures (Orthopaedic Trauma Association 15-B). A computerized literature search in the Pubmed, Scopus, and Cochrane Library databases was used to identify relevant articles. Only full text articles without language restrictions were evaluated. The inclusion criteria consisted of: (1) fracture of the midshaft clavicle; (2) surgery for acute fractures (within 1 month of the fracture); (3) adult patients (16 years of age and older); and (4) open reduction and internal fixation with plate application in either the anteroinferior or superior position. Studies were excluded if they did not specify plate location, evaluated multitrauma patients, investigated minimally invasive procedures, or studied operations for revision, nonunion, malunion, or infection. The primary measured outcomes were symptomatic hardware (implant prominence or irritation) and surgery for implant removal. The secondary outcomes were time to union, fracture union, nonunion, malunion, Disabilies of the Arm, Shoulder and Hand score, Constant score, and implant failure. Frequencies and proportions of cases were recorded for binary outcomes, whereas mean and standard deviations were recorded for continuous outcomes. Other summary statistics provided were used to impute mean and standard deviations under the assumption of normality when these were not reported. Continuous outcomes were compared between groups using linear mixed effects models, whereas binary outcomes were compared using mixed effects logistic regression models, including fixed group effects and random study effects. P-values less than 0.05 were considered statistically significant. All analyses were performed using SAS v. 9.4 (SAS Institute Inc, Cary, NC). A total of 1428 articles were identified among the 3 databases, of which 897 remained after removing duplicates. From that pool, 57 relevant studies were evaluated. Articles were excluded because of an inability to specify plate location (6), a subject pool not exclusively consisting of acute fractures (4) or midshaft fractures (2), a minimally invasive surgical approach (6), use of nonstandard plates (1), poor reporting of functional outcomes (2), and a duplicate group of patients (2). This left 34 articles to be used in the meta-analysis. Of these, 8 studies reported on patients with anteroinferior plating (N = 390) and 27 studies reported on patients with superior plating (N = 1104). No significant differences were found with respect to the functional shoulder scores (Disabilies of the Arm, Shoulder and Hand and Constant) between the 2 groups. There was no significant difference between each group for the probability of having a union (P = 0.41), malunion (P = 0.28), nonunion (0.29), or implant failure (P = 0.39). Patients in the superior plating group had a significantly higher probability of suffering from symptomatic hardware (0.17) as compared to patients in the anteroinferior plating group (0.08), (P = 0.005). In addition, the superior plating group had a significantly higher rate of surgery for implant removal (0.11 vs. 0.05), (P = 0.008). The findings of this investigation demonstrate that plating along the superior and anteroinferior aspects of the clavicle lead to similar operative outcomes with respect to union, nonunion, malunion, and implant failure, as well as similar functional outcomes scores. Plates applied to the superior aspect of the clavicle are associated with higher rates of symptomatic hardware and more frequent implant removal. Therapeutic Level III. See Instructions for Authors for a complete description of levels of evidence.

Outlier detection and robust estimation in linear regression models with fixed group effects

This work studies outlier detection and robust estimation with data that are naturally distributed into groups and which follow approximately a linear regression model with fixed group effects. For this, several methods are considered. First, the robust fitting method of Peña and Yohai [A fast procedure for outlier diagnostics in large regression problems. J Am Stat Assoc. 1999;94:434–445], called principal sensitivity components (PSC) method, is adapted to the grouped data structure and the mentioned model. The robust methods RDL1 of Hubert and Rousseeuw [Robust regression with both continuous and binary regressors. J Stat Plan Inference. 1997;57:153–163] and M-S of Maronna and Yohai [Robust regression with both continuous and categorical predictors. Journal of Statistical Planning and Inference 2000;89:197–214] are also considered. These three methods are compared in terms of their effectiveness in outlier detection and their robustness through simulations, considering several contamination scenarios and growing contamination levels. Results indicate that the adapted PSC procedure is able to detect a high percentage of true outliers and a small number of false outliers. It is appropriate when the contamination is in the error term or in the covariates, detecting also possibly masked high leverage points. Moreover, in simulations the final robust regression estimator preserved good efficiency under Normality while keeping good robustness properties.

Tax evasion and social interactions

The paper extends the standard tax evasion model by allowing for social interactions. In Manski's [Manski, C.F. (1993). Identification of Endogenous Social Effects: The Reflection Problem. Review of Economic Studies 60(3), 531–542.] nomenclature, our model takes into account endogenous interactions, i.e., social conformity effects, exogenous interactions, i.e., fairness effects, and correlated effects. Our model is tested using experimental data. Participants must decide how much income to report given individual and group tax rates and audit probabilities, and given a feedback on the other members' reporting behavior. Myopic and self-consistent expectations are considered in the analysis. In the latter case, the estimation is based on a two-limit simultaneous tobit with fixed group effects. A unique social equilibrium exists when the model satisfies coherency conditions. In line with Brock and Durlauf [Brock, W.A., Durlauf, S.N. (2001b). Interactions-Based Models, in J. Heckman and E. Leamer, eds., Handbook of Econometrics 5, Elsevier Science B.V., 3297–380.], the intrinsic nonlinearity between individual and group responses helps identify the model. Our results provide evidence of fairness effects but reject social conformity.

Tax Evasion and Social Interactions

The paper extends the standard tax evasion model by allowing for social interactions. In Manski's (1993) nomenclature, our model takes into account social conformity effects (i.e., endogenous interactions), fairness effects (i.e., exogenous interactions) and sorting effects (i.e., correlated effects). Our model is tested using experimental data. Participants must decide how much income to report given their tax rate and audit probability, and given those faced by the other members of their group as well as their mean reported income. The estimation is based on a two-limit simultaneous tobit with fixed group effects. A unique social equilibrium exists when the model satisfies coherency conditions. In line with Brock and Durlauf (2001b), the intrinsic nonlinearity between individual and group responses is sufficient to identify the model without imposing any exclusion restrictions. Our results are consistent with fairness effects but reject social conformity and correlated effects.