# Adaptive Regression for Modeling Nonlinear RelationshipsAdaptive Regression Modeling of Multivariate Continuous Outcomes

Adaptive Regression for Modeling Nonlinear Relationships: Adaptive Regression Modeling of... [This chapter formulates and demonstrates adaptive regression modeling of means and variances for repeatedly measured continuous outcomes treated as multivariate normal. Analyses are presented of dental measurements of the distance in mm from the center of the pituitary to the pterygomaxillary fissure in terms of the age and gender of the child while accounting for dependence of dental measurements for the same child. These are example analyses of data with no missing outcome values. Analyses are also presented of strength in terms of time and type of weightlifting program while accounting for dependence of strength measurements for the same subject. These are example analyses of data with missing outcome values. Analyses of these data sets use marginal models based on order 1 autoregressive (AR1) correlations and exchangeable correlations (EC) and estimated with maximum likelihood (ML) or generalized estimating equations (GEE). They also use transition models, with the current outcome value a function of prior outcome values, and general conditional models, with the current outcome value a function of other, past as well as prior, outcome values. The issue of moderation is addressed, that is, how the effect of a predictor on an outcome can change with values of a moderator variable. For example, how the effect of age on the child’s dental measurements can change with the gender of the child. Moderation analyses are commonly based on interactions, but can be more generally based on geometric combinations, that is, products of power transforms of primary predictors using possibly different powers.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Adaptive Regression for Modeling Nonlinear RelationshipsAdaptive Regression Modeling of Multivariate Continuous Outcomes

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-33944-3
Pages
63 –108
DOI
10.1007/978-3-319-33946-7_4
Publisher site
See Chapter on Publisher Site

### Abstract

[This chapter formulates and demonstrates adaptive regression modeling of means and variances for repeatedly measured continuous outcomes treated as multivariate normal. Analyses are presented of dental measurements of the distance in mm from the center of the pituitary to the pterygomaxillary fissure in terms of the age and gender of the child while accounting for dependence of dental measurements for the same child. These are example analyses of data with no missing outcome values. Analyses are also presented of strength in terms of time and type of weightlifting program while accounting for dependence of strength measurements for the same subject. These are example analyses of data with missing outcome values. Analyses of these data sets use marginal models based on order 1 autoregressive (AR1) correlations and exchangeable correlations (EC) and estimated with maximum likelihood (ML) or generalized estimating equations (GEE). They also use transition models, with the current outcome value a function of prior outcome values, and general conditional models, with the current outcome value a function of other, past as well as prior, outcome values. The issue of moderation is addressed, that is, how the effect of a predictor on an outcome can change with values of a moderator variable. For example, how the effect of age on the child’s dental measurements can change with the gender of the child. Moderation analyses are commonly based on interactions, but can be more generally based on geometric combinations, that is, products of power transforms of primary predictors using possibly different powers.]

Published: Sep 21, 2016

Keywords: Conditional Generative Model; Marginal Model; Dent Measurements; Prior Measurement Outcomes; Adaptive Transition Model

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