scholarly journals The Limits of Marginality

2021 ◽  
Author(s):  
Andrew Heathcote ◽  
Dora Matzke
Keyword(s):  
Model Selection ◽  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Order Term ◽  
Test Point ◽  
Linear Regression Models ◽  
Random Effects Models ◽  
Target Article ◽  
Fixed And Random Effects

AbstractThe “marginality principle” for linear regression models states that when a higher order term is included, its constituent terms must also be included. The target article relies on this principle for the fixed-effects part of linear mixed models of ANOVA designs and considers the implication that if extended to combined fixed-and-random-effects models, model selection tests specific to some fixed-effects ANOVA terms are not possible. We review the basis for this principle for fixed-effects models and delineate its limits. We then consider its extension to combined fixed-and-random-effects models. We conclude that we have been unable to find in the literature, including the target article, and have ourselves been unable to construct any satisfactory argument against the use of incomplete ANOVA models. The only basis we could find requires one to assume that it is not possible to test point-null hypotheses, something we disagree with, and which we believe is incompatible with the Bayesian model-selection methods that are the basis of the target article.

scholarly journals Within- and Between-cluster Effects in Generalized Linear Mixed Models: A Discussion of Approaches and the Xthybrid command

2017 ◽  
Vol 17 (1) ◽  
pp. 89-115 ◽  
Author(s):  
Reinhard Schunck ◽  
Francisco Perales
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Negative Binomial ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Consistent Estimation ◽  
Random Effects Models ◽  
Fixed Effects Models ◽  
Correlated Random Effects

One typically analyzes clustered data using random- or fixed-effects models. Fixed-effects models allow consistent estimation of the effects of level-one variables, even if there is unobserved heterogeneity at level two. However, these models cannot estimate the effects of level-two variables. Hybrid and correlated random-effects models are flexible modeling specifications that separate within-and between-cluster effects and allow for both consistent estimation of level-one effects and inclusion of level-two variables. In this article, we elaborate on the separation of within- and between-cluster effects in generalized linear mixed models. These models present a unifying framework for an entire class of models whose response variables follow a distribution from the exponential family (for example, linear, logit, probit, ordered probit and logit, Poisson, and negative binomial models). We introduce the user-written command xthybrid, a shell for the meglm command. xthybrid can fit a variety of hybrid and correlated random-effects models.

Meta-Analysis

1992 ◽  
Vol 17 (4) ◽  
pp. 279-296 ◽  
Author(s):  
Larry V. Hedges
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Meta Analysis ◽  
Statistical Significance ◽  
Fixed And Random Effects ◽  
Mean And Variance ◽  
The Mean ◽  
Combining Estimates ◽  
Effect Magnitude

The use of statistical methods to combine the results of independent empirical research studies (meta-analysis) has a long history. Meta-analytic work can be divided into two traditions: tests of the statistical significance of combined results and methods for combining estimates across studies. The principal classes of combined significance tests are reviewed, and the limitations of these tests are discussed. Fixed effects approaches treat the effect magnitude parameters to be estimated as a consequence of a model involving fixed but unknown constants. Random effects approaches treat effect magnitude parameters as if they were sampled from a universe of effects and attempt to estimate the mean and variance of the hyperpopulation of effects. Mixed models incorporate both fixed and random effects. Finally, areas of current research are summarized, including methods for handling missing data, models for publication selection, models to handle studies that are not independent, and distribution-free models for random effects.

scholarly journals Benefits of Bayesian Model Selection and Averaging for Mixed-Effects Modeling

2021 ◽  
Author(s):  
Daniel W. Heck ◽  
Florence Bockting
Keyword(s):  
Model Selection ◽  
Random Effects ◽  
Mixed Models ◽  
Bayesian Model ◽  
Fixed Effects ◽  
Bayes Factor ◽  
Mixed Effects ◽  
Bayes Factors ◽  
Mixed Effects Models ◽  
Within Subjects

Bayes factors allow researchers to test the effects of experimental manipulations in within-subjects designs using mixed-effects models. van Doorn et al. (2021) showed that such hypothesis tests can be performed by comparing different pairs of models which vary in the specification of the fixed- and random-effect structure for the within-subjects factor. To discuss the question of which of these model comparisons is most appropriate, van Doorn et al. used a case study to compare the corresponding Bayes factors. We argue that researchers should not only focus on pairwise comparisons of two nested models but rather use the Bayes factor for performing model selection among a larger set of mixed models that represent different auxiliary assumptions. In a standard one-factorial, repeated-measures design, the comparison should include four mixed-effects models: fixed-effects H0, fixed-effects H1, random-effects H0, and random-effects H1. Thereby, the Bayes factor enables testing both the average effect of condition and the heterogeneity of effect sizes across individuals. Bayesian model averaging provides an inclusion Bayes factor which quantifies the evidence for or against the presence of an effect of condition while taking model-selection uncertainty about the heterogeneity of individual effects into account. We present a simulation study showing that model selection among a larger set of mixed models performs well in recovering the true, data-generating model.

Bridging Methodological Divides Between Macro- and Microresearch: Endogeneity and Methods for Panel Data

2019 ◽  
Vol 46 (1) ◽  
pp. 70-99 ◽  
Author(s):  
Paul D. Bliese ◽  
Donald J. Schepker ◽  
Spenser M. Essman ◽  
Robert E. Ployhart
Keyword(s):  
Panel Data ◽  
Random Effects ◽  
Fixed Effects ◽  
Theory Development ◽  
Modeling Framework ◽  
Random Effects Models ◽  
Data Support ◽  
Fixed And Random Effects

Both macro- and micro-oriented researchers frequently use panel data where the outcome of interest is measured repeated times. Panel data support at least five different modeling frameworks (within, between, incremental/emergent, cross-level, and growth). Researchers from macro- and micro-oriented domains tend to differentially use the frameworks and also use different analytic tools and terminology when using the same modeling framework. These differences have the potential to inhibit cross-discipline communication. In this review, we explore how macro- and microresearchers approach panel data with a specific emphasis on the theoretical implications of choosing one framework versus another. We illustrate how fixed-effects and random-effects models differ and how they are similar, and we conduct a thorough review of 142 articles that used panel data in leading management journals in 2017. Ultimately, our review identifies ways that researchers can better employ fixed- and random-effects models, model time as a meaningful predictor or ensure unobserved time heterogeneity is controlled, and align hypotheses to analytic choice. In the end, our goal is to help facilitate communication and theory development between macro- and micro-oriented management researchers.

scholarly journals Effects of dutasteride on prostate cancer incidence: A systematic review and meta-analysis

2020 ◽  
Vol 11 (4) ◽  
pp. 7266-7270
Author(s):  
Gyeong-Eun Min ◽  
Haesoo Kim ◽  
Da Eun Lee ◽  
Kisok Kim
Keyword(s):  
Prostate Cancer ◽  
Random Effects ◽  
Fixed Effects ◽  
Meta Analysis ◽  
Adult Males ◽  
Fixed Effects Model ◽  
Random Effects Models ◽  
Benign Prostate Hypertrophy ◽  
Fixed And Random Effects ◽  
Meta Analyses

5-Alpha-reductase inhibitors (5-ARIs) are used in the treatment of benign prostate hypertrophy (BPH). 5-ARIs, such as finasteride and dutasteride, suppress the biosynthesis of dihydrotestosterone (DHT), a precursor of androgen, which is closely related to the incidence of prostate cancer (PCa). A previous meta-analysis demonstrated a relationship between finasteride use and the incidence of PCA. However, there have been no meta-analyses on the relationship between PCa and dutasteride alone. This meta-analysis was performed to examine the prevalence of PCa in adult males taking dutasteride. We searched PubMed for reports regarding PCa risk and dutasteride use. The study was conducted according to the PRISMA guidelines for systematic reviews and meta-analyses. The analytic hierarchy process (AHP) method was used to weight the studies. Odds ratios (ORs), 95% confidence intervals (CIs), and P-values were calculated using fixed- and random-effects models. A total of eight articles were included in the meta-analysis. The overall OR for both the fixed- and random-effects models was 0.669 and the 95% CI for the random-effects model (0.526–0.851; P = 0.006) was wider than that for the fixed effects model (0.548–0.817; P < 0.001). This study confirmed that the incidence of PCa was significantly reduced by taking dutasteride.

scholarly journals Association of bisphenol A with puberty timing: a meta-analysis

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hui Meng ◽  
Yunping Zhou ◽  
Yunxia Jiang
Keyword(s):  
Bisphenol A ◽  
Confidence Intervals ◽  
Random Effects ◽  
Strong Correlation ◽  
Fixed Effects ◽  
Meta Analysis ◽  
Random Effects Models ◽  
Study Heterogeneity ◽  
The Relationship ◽  
Prevalence Ratios

AbstractObjectivesThe results of existing studies on bisphenol A (BPA) and puberty timing did not reach a consensus. Thereby we performed this meta-analytic study to explore the association between BPA exposure in urine and puberty timing.MethodsMeta-analysis of the pooled odds ratios (OR), prevalence ratios (PR) or hazards ratios (HR) with 95% confidence intervals (CI) were calculated and estimated using fixed-effects or random-effects models based on between-study heterogeneity.ResultsA total of 10 studies involving 5621 subjects were finally included. The meta-analysis showed that BPA exposure was weakly associated with thelarche (PR: 0.96, 95% CI: 0.93–0.99), while no association was found between BPA exposure and menarche (HR: 0.99, 95% CI: 0.89–1.12; OR: 1.02, 95% CI: 0.73–1.43), and pubarche (OR: 1.00, 95% CI: 0.79–1.26; PR: 1.00, 95% CI: 0.95–1.05).ConclusionsThere was no strong correlation between BPA exposure and puberty timing. Further studies with large sample sizes are needed to verify the relationship between BPA and puberty timing.

scholarly journals P075 Travel or cheers? Examining the drivers and mechanisms of home court advantage in the 2020/2021 NBA regular season

2021 ◽  
Vol 2 (Supplement_1) ◽  
pp. A45-A45
Author(s):  
J Leota ◽  
D Hoffman ◽  
L Mascaro ◽  
M Czeisler ◽  
K Nash ◽  
...  
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Natural Experiment ◽  
National Basketball Association ◽  
Home Team ◽  
The Road ◽  
On The Road ◽  
The Impact ◽  
The Relationship

Abstract Introduction Home court advantage (HCA) in the National Basketball Association (NBA) is well-documented, yet the co-occurring drivers responsible for this advantage have proven difficult to examine in isolation. The Coronavirus disease (COVID-19) pandemic resulted in the elimination of crowds in ~50% of games during the 2020/2021 NBA season, whereas travel remained unchanged. Using this ‘natural experiment’, we investigated the impact of crowds and travel-related sleep and circadian disruption on NBA HCA. Methods 1080 games from the 2020/2021 NBA regular season were analyzed using mixed models (fixed effects: crowds, travel; random effects: team, opponent). Results In games with crowds, home teams won 58.65% of the time and outrebounded (M=2.28) and outscored (M=2.18) their opponents. In games without crowds, home teams won significantly less (50.60%, p = .01) and were outrebounded (M=-0.41, p &lt; .001) and outscored (M=-0.13, p &lt; .05) by their opponents. Further, the increase in home rebound margin fully mediated the relationship between crowds and home points margin (p &lt; .001). No significant sleep or circadian effects were observed. Discussion Taken together, these results suggest that HCA in the 2020/2021 NBA season was predominately driven by the presence of crowds and their influence on the effort exerted by the home team to rebound the ball. Moreover, we speculate that the strict NBA COVID-19 policies may have mitigated the travel-related sleep and circadian effects on the road team. These findings are of considerable significance to a domain wherein marginal gains can have immense competitive, financial, and even historical consequences.

scholarly journals The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 48-76
Author(s):  
Freddy Hernández ◽  
Viviana Giampaoli
Keyword(s):  
Weibull Distribution ◽  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Mixed Model ◽  
Random Effect ◽  
Estimation Procedure ◽  
Weibull Regression ◽  
Two Parameters ◽  
The Impact

Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of misspecification of the shape of the random effects in mixed models. Notably, these studies primarily concentrated their efforts on models with response variables that have normal, logistic and Poisson distributions, and the results were not conclusive. As such, we investigated the misspecification of the shape of the random effects in a Weibull regression mixed model with random intercepts in the two parameters of the Weibull distribution. Through an extensive simulation study considering six random effect distributions and assuming normality for the random effects in the estimation procedure, we found an impact of misspecification on the estimations of the fixed effects associated with the second parameter σ of the Weibull distribution. Additionally, the variance components of the model were also affected by the misspecification.

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