Efficient estimation of variance components in nonparametric mixed-effects models with large samples

Helwig, Nathaniel E.

doi:10.1007/s11222-015-9610-5

Cited by 11 publications

(10 citation statements)

References 37 publications

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“…We fit the above model to the same three response variables (effective, genuine, and pleasant) using the same two-stage estimation procedure [29]. We used a cubic smoothing spline for the timing asymmetry effect function, and the three covariates were modeled as previously described, i.e., using a cubic smoothing spline for age and drinking, and a nominal smoothing spline for gender.…”

Section: Methodsmentioning

confidence: 99%

Dynamic properties of successful smiles

et al. 2017

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Facial expression of emotion is a foundational aspect of social interaction and nonverbal communication. In this study, we use a computer-animated 3D facial tool to investigate how dynamic properties of a smile are perceived. We created smile animations where we systematically manipulated the smile’s angle, extent, dental show, and dynamic symmetry. Then we asked a diverse sample of 802 participants to rate the smiles in terms of their effectiveness, genuineness, pleasantness, and perceived emotional intent. We define a “successful smile” as one that is rated effective, genuine, and pleasant in the colloquial sense of these words. We found that a successful smile can be expressed via a variety of different spatiotemporal trajectories, involving an intricate balance of mouth angle, smile extent, and dental show combined with dynamic symmetry. These findings have broad applications in a variety of areas, such as facial reanimation surgery, rehabilitation, computer graphics, and psychology.

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Section: Methodsmentioning

confidence: 99%

Dynamic properties of successful smiles

et al. 2017

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“…As alternatives to the monotonic model (abbreviated as MO), we considered simple linear (LIN) and categorical (CAT) regression, isotonic regression (ISO; Barlow et al , 1972; Robertson et al , 1988), penalized ordinal regression (OS; Gertheiss & Tutz, 2009; Gu, 2013), penalized ordinal regression with monotonicity constraint (OSMO; Helwig, 2017), as well as linear and cubic spline models (LS and CS; e.g., Gu, 2013; Helwig, 2016). The latter two are primarily designed for continuous responses but may still perform reasonably well for linear relationships or a sufficiently large number of predictor categories.…”

Section: Simulationsmentioning

confidence: 99%

Modelling monotonic effects of ordinal predictors in Bayesian regression models

Bürkner

Charpentier

2020

Brit J Math & Statis

116

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Ordinal predictors are commonly used in regression models. They are often incorrectly treated as either nominal or metric, thus under‐ or overestimating the information contained. Such practices may lead to worse inference and predictions compared to methods which are specifically designed for this purpose. We propose a new method for modelling ordinal predictors that applies in situations in which it is reasonable to assume their effects to be monotonic. The parameterization of such monotonic effects is realized in terms of a scale parameter b representing the direction and size of the effect and a simplex parameter bold-italicς modelling the normalized differences between categories. This ensures that predictions increase or decrease monotonically, while changes between adjacent categories may vary across categories. This formulation generalizes to interaction terms as well as multilevel structures. Monotonic effects may be applied not only to ordinal predictors, but also to other discrete variables for which a monotonic relationship is plausible. In simulation studies we show that the model is well calibrated and, if there is monotonicity present, exhibits predictive performance similar to or even better than other approaches designed to handle ordinal predictors. Using Stan, we developed a Bayesian estimation method for monotonic effects which allows us to incorporate prior information and to check the assumption of monotonicity. We have implemented this method in the R package brms, so that fitting monotonic effects in a fully Bayesian framework is now straightforward.

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“…We used the same simulation conditions as in Section 3.1 with one exception described in following. As underlying data generating processes, we considered the main effects and interaction models described in Section 3.1 in three different variations: 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 linear (LIN) and categorical (CAT) regression 3 , isotonic regression (ISO; Barlow et al, 1972;Robertson et al, 1988), penalized ordinal regression (OS; Gertheiss & Tutz, 2009;Gu, 2013), penalized ordinal regression with monotonicity constraint (OSMO; Helwig, 2017), as well as linear and cubic spline models (LS and CS; e.g., Gu, 2013;Helwig, 2016). The latter two are primarily designed for continuous responses but may still perform reasonably well for linear relationships or sufficiently large number of predictor categories.…”

Section: Comparison To Other Approachesmentioning

confidence: 99%

Modeling Monotonic Effects of Ordinal Predictors in Bayesian Regression Models

Bürkner¹,

Charpentier²

2018

Preprint

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Ordinal predictors are commonly used in regression models. They are often incorrectly treated as either nominal or metric, thus under- or overestimating the contained information. Such practices may lead to worse inference and predictions compared to methods which are specifically designed for this purpose. We propose a new method for modeling ordinal predictors that applies in situations in which it is reasonable to assume their effects to be monotonic. The parameterization of such monotonic effects is realized in terms of a scale parameter $b$ representing the direction and size of the effect and a simplex parameter $\zeta$ modeling the normalized differences between categories. This ensures that predictions increase or decrease monotonically, while changes between adjacent categories may vary across categories. This formulation generalizes to interaction terms as well as multilevel structures. Monotonic effects may not only be applied to ordinal predictors, but also to other discrete variables for which a monotonic relationship is plausible. In simulation studies, we show that the model is well calibrated and, in case of monotonicity, has similar or even better predictive performance than other approaches designed to handle ordinal predictors. Using Stan, we developed a Bayesian estimation method for monotonic effects, which allows to incorporate prior information and to check the assumption of monotonicity. We have implemented this method in the R package brms, so that fitting monotonic effects in a fully Bayesian framework is now straightforward.

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Efficient estimation of variance components in nonparametric mixed-effects models with large samples

Cited by 11 publications

References 37 publications

Dynamic properties of successful smiles

Dynamic properties of successful smiles

Modelling monotonic effects of ordinal predictors in Bayesian regression models

Modeling Monotonic Effects of Ordinal Predictors in Bayesian Regression Models

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