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Title: Projection pursuit regression versus generalized additive model for location scale and shape an application in health Authors:  Teresa Oliveira - Universidade Aberta (Portugal)
Luzia Mendes - University of Porto (Portugal)
Jose Pereira - Universidade do Porto (Portugal) [presenting]
Abstract: The relationship of periodontal probing depth (PPD) with age, high-density lipoproteins (HDL) and diabetic status (DS) was addressed using two different methods, the projection pursuit regression model (PPR) and the generalized additive model for location scale and shape (GAMLSS). The first is non-parametric and non-linear by nature, and the second is a distributional semi-parametric regression method. In the gamlss model was assumed a truncated exponential modified Gaussian distribution of PPD, with three distribution parameters $(\mu, \nu and \tau)$ to be modeled as a function of data. The results were similar, with both models yielding the same r squared (0.31), uncovering a curve shape relationship between PPD and HDL and DS, and their effects on the dependent variable are of the same sign, allowing for similar conclusions. From the user's perspective, the advantages of PPR over GAMLSS are that interactions between predictors do not need to be explained, and a probabilistic distribution for the dependent variable is not assumed a priori. Moreover, for a sufficiently large number of terms, it can approximate any continuous function in $\mathbb{R}_{p}$. However, the interpretation of the PPR is not as intuitive as GAMLSS models.