Interaction Effects in Linear and Generalized Linear Models: Examples and Applications Using Stata®

2019 ◽  
Author(s):  
Robert Kaufman
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Interaction Effects

scholarly journals Interpreting Interaction Effects in Generalized Linear Models of Nonlinear Probabilities and Counts

2021 ◽  
pp. 1-27
Author(s):  
Connor J. McCabe ◽  
Max A. Halvorson ◽  
Kevin M. King ◽  
Xiaolin Cao ◽  
Dale S. Kim
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Interaction Effects

scholarly journals Optimal Scaling of Interaction Effects in Generalized Linear Models

2009 ◽  
Vol 44 (1) ◽  
pp. 59-81 ◽  
Author(s):  
Joost van Rosmalen ◽  
Alex J. Koning ◽  
Patrick J. F. Groenen
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Interaction Effects ◽  
Optimal Scaling

scholarly journals modglm: An R package for testing, interpreting, and displaying interactions in generalized linear models of discrete data

2021 ◽  
Author(s):  
Connor McCabe ◽  
Max Andrew Halvorson ◽  
Kevin Michael King ◽  
Xiaolin Cao ◽  
Dale Sim Kim
Keyword(s):  
Open Source ◽  
Generalized Linear Models ◽  
Open Source Software ◽  
Interaction Effect ◽  
Software Package ◽  
Linear Models ◽  
R Package ◽  
Interaction Effects ◽  
Research Practice ◽  
Nonlinear Scale

Many researchers hope to examine interaction effects using generalized linear models (GLMs) to predict outcomes on nonlinear scales. For instance, logistic and Poisson GLMs are used to estimate associations between predictors and outcomes in nonlinear probability and count scales, respectively. However, we (McCabe et al., 2021; Halvorson et al., in press) and others (Ai & Norton, 2003; Mize, 2019; Norton, Wang, & Ai, 2004) have shown that testing and interpreting interaction effects on these scales is not straightforward. GLMs require the application of partial derivatives and/or discrete differences to compute and probe interaction effects appropriately when models are interpreted on their nonlinear scale. Currently available open-source software does not provide methods of computing these interaction effects on probability and count scales, reflecting a central limitation in applying these methods in research practice. Here, we introduce `modglm`, an R-based software package that accompanies our manuscript providing recommendations for computing interaction effects in nonlinear probability and counts (McCabe et al., 2021). This software produces the interaction effect between two variables in generalized linear models of probabilities and counts and provides additional statistics and plotting utilities for evaluating and describing this effect.

scholarly journals Interpreting interaction effects in generalized linear models of nonlinear probabilities and counts

2020 ◽  
Author(s):  
Connor McCabe ◽  
Max Andrew Halvorson ◽  
Kevin Michael King ◽  
Xiaolin Cao ◽  
Dale Sim Kim
Keyword(s):  
Generalized Linear Models ◽  
Logistic Model ◽  
Linear Models ◽  
Interaction Effects ◽  
Predictor Variables ◽  
Model Parameters ◽  
Marginal Effect ◽  
Psychology Research ◽  
Product Term ◽  
Traditional Approaches

Psychology research frequently involves the study of probabilities and counts. These are typically analyzed using generalized linear models (GLMs), which can produce these quantities via nonlinear transformation of model parameters. Interactions are central within many research applications of these models. To date, typical practice in evaluating interactions for probabilities or counts extends directly from linear approaches, in which evidence of an interaction effect is supported by using the product term coefficient between variables of interest. However, unlike linear models, interaction effects in GLMs describing probabilities and counts are not equal to product terms between predictor variables. Instead, interactions may be functions of the predictors of a model, requiring non-traditional approaches for interpreting these effects accurately. Here, we define interactions as change in a marginal effect of one variable as a function of change in another variable, and describe the use of partial derivatives and discrete differences for quantifying these effects. Using guidelines and simulated examples, we then use these approaches to describe how interaction effects should be estimated and interpreted for GLMs on probability and count scales. We conclude with an example using the Adolescent Brain Cognitive Development Study demonstrating how to correctly evaluate interaction effects in a logistic model.

Effect of Different Dentifrices, Bleaching with 35% Hydrogen Peroxide, and Red Wine on Surface Color and Roughness of Bovine Enamel

2020 ◽  
Vol 02 ◽  
Author(s):  
RM Garcia ◽  
WF Vieira-Junior ◽  
JD Theobaldo ◽  
NIP Pini ◽  
GM Ambrosano ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Generalized Linear Models ◽  
Repeated Measures ◽  
Red Wine ◽  
Linear Models ◽  
Artificial Saliva ◽  
Surface Color ◽  
Dental Bleaching ◽  
Surface Alteration ◽  
Bovine Enamel

Objective: To evaluate color and roughness of bovine enamel exposed to dentifrices, dental bleaching with 35% hydrogen peroxide (HP), and erosion/staining by red wine. Methods: Bovine enamel blocks were exposed to: artificial saliva (control), Oral-B Pro-Health (stannous fluoride with sodium fluoride, SF), Sensodyne Repair & Protect (bioactive glass, BG), Colgate Pro-Relief (arginine and calcium carbonate, AR), or Chitodent (chitosan, CHI). After toothpaste exposure, half (n=12) of the samples were bleached (35% HP), and the other half were not (n=12). The color (CIE L*a* b*, ΔE), surface roughness (Ra), and scanning electron microscopy were evaluated. Color and roughness were assessed at baseline, post-dentifrice and/or -dental bleaching, and after red wine. The data were subjected to analysis of variance (ANOVA) (ΔE) for repeated measures (Ra), followed by Tukey ́s test. The L*, a*, and b* values were analyzed by generalized linear models (a=0.05). Results: The HP promoted an increase in Ra values; however, the SF, BG, and AR did not enable this alteration. After red wine, all groups apart from SF (unbleached) showed increases in Ra values; SF and AR promoted decreases in L* values; AR demonstrated higher ΔE values, differing from the control; and CHI decreased the L* variation in the unbleached group. Conclusion: Dentifrices did not interfere with bleaching efficacy of 35% HP. However, dentifrices acted as a preventive agent against surface alteration from dental bleaching (BG, SF, and AR) or red wine (SF). Dentifrices can decrease (CHI) or increase (AR and SF) staining by red wine.

Economic burden of readmission due to postoperative cerebrospinal fluid leak in Chinese patients

2020 ◽  
Vol 9 (16) ◽  
pp. 1105-1115
Author(s):  
Shuqing Wu ◽  
Xin Cui ◽  
Shaoyu Zhang ◽  
Wenqi Tian ◽  
Jiazhen Liu ◽  
...  
Keyword(s):  
Cerebrospinal Fluid ◽  
Generalized Linear Models ◽  
Economic Burden ◽  
Linear Models ◽  
Chinese Patients ◽  
Cerebrospinal Fluid Leakage ◽  
Index Hospitalization ◽  
Real World Data ◽  
Factors Associated ◽  
Hospitalization Cost

Aim: This real-world data study investigated the economic burden and associated factors of readmissions for cerebrospinal fluid leakage (CSFL) post-cranial, transsphenoidal, or spinal index surgeries. Methods: Costs of CSFL readmissions and index hospitalizations during 2014–2018 were collected. Readmission cost was measured as absolute cost and as percentage of index hospitalization cost. Factors associated with readmission cost were explored using generalized linear models. Results: Readmission cost averaged US$2407–6106, 35–94% of index hospitalization cost. Pharmacy costs were the leading contributor. Generalized linear models showed transsphenoidal index surgery and surgical treatment for CSFL were associated with higher readmission costs. Conclusion: CSFL readmissions are a significant economic burden in China. Factors associated with higher readmission cost should be monitored.

Determination of Enzyme or Binding Constants Using Generalized Linear Models, with Particular Reference to Michaelis–Menten Models

1989 ◽  
Vol 78 (5) ◽  
pp. 413-416
Author(s):  
Gerald Van Belle ◽  
Sue Leurgans ◽  
Pat Friel ◽  
Sunwei Guo ◽  
Mark Yerby
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Binding Constants

scholarly journals Testing for treatment effect in covariate-adaptive randomized trials with generalized linear models and omitted covariates

2021 ◽  
pp. 096228022110082
Author(s):  
Yang Li ◽  
Wei Ma ◽  
Yichen Qin ◽  
Feifang Hu
Keyword(s):  
Generalized Linear Models ◽  
Treatment Effect ◽  
Linear Models ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
Asymptotic Results ◽  
Adaptive Randomization ◽  
Adjustment Method ◽  
Inflated Type

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two-sample t-test for treatment effect is typically conservative. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method.

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