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.

scholarly journals ANALISIS PENGARUH UTANG BERBASIS BUNGA DAN PENDAPATAN NON-HALAL TERHADAP NILAI PERUSAHAAN EMITEN SAHAM SYARIAH

2018 ◽  
Vol 4 (2) ◽  
pp. 103
Author(s):  
Muhammad Adlan ◽  
Imron Mawardi
Keyword(s):  
Panel Data ◽  
Firm Value ◽  
Fixed Effects ◽  
Lower Portion ◽  
Standard Errors ◽  
Fixed Effects Models ◽  
Total Debt ◽  
Robust Standard Errors ◽  
Operating Revenue

This study aims to determine whether interest-based debt limitation and non-halal income limitation have significant effect on the firm value. Sharia stock issuers in Indonesia are obliged to pass several conditions set by the market regulator, some of them are limitations of the interest-based debt and non-halal income. This study assumes that the lower portion of interest-based debt and non-halal income, the more the investors will prefer the stocks, thus increasing the firm value. The subjects of this study are the companies listed on JII period 2013-2017. This study measures interest-based debt with ratio of interest-based debt devided by total debt, measures non-halal income with ratio of non-halal income divided by operating revenue, and measures the value of the firm with PBV. The analysis of this study using panel data regressions with fixed effects models with robust standard errors. The results shows that interest-based debt and non-halal income have no effects on the value of the firm, partially and simultaneously

scholarly journals The effects of misspecifying the random part of multilevel models

Methodology ◽  
2020 ◽  
Vol 16 (3) ◽  
pp. 224-240
Author(s):  
David M. LaHuis ◽  
Daniel R. Jenkins ◽  
Michael J. Hartman ◽  
Shotaro Hakoyama ◽  
Patrick C. Clark
Keyword(s):  
Effect Size ◽  
Fixed Effects ◽  
Multilevel Model ◽  
Multilevel Models ◽  
The Other ◽  
Standard Errors ◽  
Moderate Effect Size ◽  
Moderate Effect ◽  
Level 1 ◽  
Random Part

This paper examined the amount bias in standard errors for fixed effects when the random part of a multilevel model is misspecified. Study 1 examined the effects of misspecification for a model with one Level 1 predictor. Results indicated that misspecifying random slope variance as fixed had a moderate effect size on the standard errors of the fixed effects and had a greater effect than misspecifying fixed slopes as random. In Study 2, a second Level 1 predictor was added and allowed for the examination of the effects of misspecifying the slope variance of one predictor on the standard errors for the fixed effects of the other predictor. Results indicated that only the standard errors of coefficient relevant to that predictor were impacted and that the effect size for the bias could be considered moderate to large. These results suggest that researchers can use a piecemeal approach to testing multilevel models with random effects.

scholarly journals Fixed Effects Individual Slopes: Accounting and Testing for Heterogeneous Effects in Panel Data or Other Multilevel Models

2019 ◽  
Author(s):  
Tobias Rüttenauer ◽  
Volker Ludwig
Keyword(s):  
Panel Data ◽  
Fixed Effects ◽  
Multilevel Models ◽  
Preschool Education ◽  
Growth Curves ◽  
Individual Growth ◽  
Fe Model ◽  
Specification Tests ◽  
Practical Applications ◽  
Heterogeneous Effects

Fixed effects (FE) panel models have been used extensively in the past, as those models control for all stable heterogeneity between units. Still, the conventional FE estimator relies on the assumption of parallel trends between treated and untreated groups. It returns biased results in the presence of heterogeneous slopes or growth curves that are related to the parameter of interest (e.g., selection into treatment is based on individual growth of the outcome). In this study, we derive the bias in conventional FE models, and show that fixed effects individual slope (FEIS) models can overcome this problem. This is a more general version of the conventional FE model, which accounts for heterogeneous slopes or trends, thereby providing a powerful tool for panel data and other multilevel data in general. We propose two versions of the Hausman test that can be used to identify misspecification in FE models. The performance of the FEIS estimator and the specification tests is evaluated in a series of Monte Carlo experiments. Using the examples of the marital wage premium and returns to preschool education (Head Start), we demonstrate how taking heterogeneous effects into account can seriously change the conclusions drawn from conventional FE models. Thus, we propose to test for bias in FE models in practical applications and to apply FEIS if indicated by the specification tests.

scholarly journals Total Factor Productivity of Agricultural Firms in Vietnam and Its Relevant Determinants

Economies ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 4 ◽  
Author(s):  
Mai Huong Giang ◽  
Tran Dang Xuan ◽  
Bui Huy Trung ◽  
Mai Thanh Que
Keyword(s):  
Total Factor Productivity ◽  
Random Effects ◽  
Fixed Effects ◽  
Foreign Ownership ◽  
State Ownership ◽  
Sustainable Growth ◽  
Bank Loan ◽  
Fe Model ◽  
Factor Productivity ◽  
Agricultural Enterprises

In Vietnam, agriculture is a key sector that promotes economic growth and poverty reduction. Therefore, improving productivity in agriculture is indispensable to the sustainability of the country. This research examined productivity and its determinants from 420 enterprises operating in agriculture. Productivity was measured as the total factor productivity (TFP) obtained from fixed and random effects models. The determinants of TFP including size and age, share of state and foreign ownership, export, accessibility to Internet and bank loan of firms, controlled for year fixed effects, were analyzed. It was shown that 74.6% companies in the agricultural sector were small in size (<10<200 employees). Although the number of large firms (>300 employees) explained 10.6%, they had a remarkable and positive TFP (38.8%, p < 0.01), while both small and very small (<10, and <200 employees, respectively) had strikingly negative TFP values (−71.3% and −32.1%, respectively, p < 0.01), as compared to the medium sizes (<200<300 employees). It was also revealed that although foreign ownership was only 3.8% on average, it had a notably positive effect on TFP (55.0%, p < 0.01). In contrast, state ownership accounted for 30.7%, but it had a negative influence on TFP (−7.5%). The export contributed a negligible and statistically significant effect to TFP (2.6%), which might be attributed to a limited number of firms (4.5%) having mobility in agricultural export. 73% received a bank loan, and only 18.2% had access to the Internet, but both of them yielded remarkable TFP values (18.5%, p < 0.01 and 3.4%, p < 0.05 respectively). The Hausman test indicated that the fixed effects (FE) model was more effective than the random effects (RE) model to estimate the TFP. The findings of this study suggested that reform efforts should focus on improving the productivity of small agricultural enterprises. In addition, foreign investment, effective use of bank loan and Internet accessibility should be further enhanced. The results of this study may provide insights for policymakers who aim to improve the productivity in agricultural enterprises and thereby contribute to the sustainable growth of the country.

scholarly journals Fixed Effects Individual Slopes: Accounting and Testing for Heterogeneous Effects in Panel Data or Other Multilevel Models

2020 ◽  
pp. 004912412092621 ◽  
Author(s):  
Tobias Rüttenauer ◽  
Volker Ludwig
Keyword(s):  
Panel Data ◽  
Fixed Effects ◽  
Multilevel Models ◽  
Preschool Education ◽  
Growth Curves ◽  
Individual Growth ◽  
Fe Model ◽  
Specification Tests ◽  
Practical Applications ◽  
Heterogeneous Effects

Fixed effects (FE) panel models have been used extensively in the past, as those models control for all stable heterogeneity between units. Still, the conventional FE estimator relies on the assumption of parallel trends between treated and untreated groups. It returns biased results in the presence of heterogeneous slopes or growth curves that are related to the parameter of interest (e.g., selection into treatment is based on individual growth of the outcome). In this study, we derive the bias in conventional FE models and show that fixed effects individual slope (FEIS) models can overcome this problem. This is a more general version of the conventional FE model, which accounts for heterogeneous slopes or trends, thereby providing a powerful tool for panel data and other multilevel data in general. We propose two versions of the Hausman test that can be used to identify misspecification in FE models. The performance of the FEIS estimator and the specification tests is evaluated in a series of Monte Carlo experiments. Using the examples of the marital wage premium and returns to preschool education (Head Start), we demonstrate how taking heterogeneous effects into account can seriously change the conclusions drawn from conventional FE models. Thus, we propose to test for bias in FE models in practical applications and to apply FEIS if indicated by the specification tests.

Ideal Point Estimation with a Small Number of Votes: A Random-Effects Approach

2001 ◽  
Vol 9 (3) ◽  
pp. 192-210 ◽  
Author(s):  
Michael Bailey
Keyword(s):  
Monte Carlo ◽  
Random Effects ◽  
Bayesian Approach ◽  
Fixed Effects ◽  
Ideal Point ◽  
Point Estimation ◽  
Standard Errors ◽  
Fixed Effects Models ◽  
Ideal Points ◽  
Ideal Point Estimation

Many conventional ideal point estimation techniques are inappropriate when only a limited number of votes are available. This paper presents a covariate-based random-effects Bayesian approach that allows scholars to estimate ideal points based on fewer votes than required for fixed-effects models. Using covariates brings more information to bear on the estimation; using a Bayesian random-effects approach avoids incidental parameter problems. Among other things, the method allows us to estimate directly the effect of covariates such as party on preferences and to estimate standard errors for ideal points. Monte Carlo results, an empirical application, and a discussion of further applications demonstrate the usefulness of the method.

Correcting Fixed Effect Standard Errors When a Crossed Random Effect Was Ignored for Balanced and Unbalanced Designs

2019 ◽  
Vol 44 (4) ◽  
pp. 448-472
Author(s):  
Mark H. C. Lai
Keyword(s):  
Random Effects ◽  
Multilevel Models ◽  
Random Effect ◽  
Social Science Research ◽  
Hierarchical Structures ◽  
Generalized Least Squares ◽  
Fixed Effect ◽  
Standard Errors ◽  
Primary Study ◽  
Crossed Random Effects

Previous studies have detailed the consequence of ignoring a level of clustering in multilevel models with straightly hierarchical structures and have proposed methods to adjust for the fixed effect standard errors ( SEs). However, in behavioral and social science research, there are usually two or more crossed clustering levels, such as when students are cross-classified by schools and neighborhoods, yet it is not uncommon that researchers focus only on one level of clustering. Using the generalized least squares framework, in this study, we derive the bias in the fixed effect SE estimators when one crossed random effect is omitted. We then showed, using data from the Scotland Neighborhood Study, how one can correct for the SEs and obtain corrected statistical inference when a misspecified two-level model was used in a primary study, which is useful when evaluating observational studies or cluster randomized trials that ignored a crossed random effects or when conducting meta-analyses. In addition, our analytic results provide theoretical insights on how one can quantify imbalance with cross-classified data by the strength of association between the two-crossed random effects in a contingency table and how the degree of imbalance relates to the correction factor for the fixed effect SEs.

Adaptive Centering with Random Effects: An Alternative to the Fixed Effects Model for Studying Time-Varying Treatments in School Settings

2009 ◽  
Vol 4 (4) ◽  
pp. 468-491 ◽  
Author(s):  
Stephen W. Raudenbush
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Standard Errors ◽  
Time Varying ◽  
Fixed Effects Model ◽  
School Settings ◽  
Heterogeneity Of Treatment Effects ◽  
Multiple Levels ◽  
Computational Simplicity ◽  
The Impact

Fixed effects models are often useful in longitudinal studies when the goal is to assess the impact of teacher or school characteristics on student learning. In this article, I introduce an alternative procedure: adaptive centering with random effects. I show that this procedure can replicate the fixed effects analysis while offering several comparative advantages: the incorporation into standard errors of multiple levels of clustering; the modeling of heterogeneity of treatment effects; the estimation of effects of treatments at multiple levels; and computational simplicity. After illustrating these ideas in a simple setting, the article formulates a general linear model with adaptive centering and random effects and derives efficient estimates and standard errors. The results apply to studies that have an arbitrary number of nested and cross-classified factors such as time, students, classrooms, schools, districts, or states.

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