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My situation right now is that I have the mixed model with quadratic term but it doesn't perform very well. So I am wondering if I can apply loess or spline regression to the mixed model instead of the quadratic term. I just want to see the different.

P.s. this is what my code looks like: Model response = age age^2; Random intercept age age^2;

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What you are describing sounds like a Semiparametric Nonlinear Mixed Effects model. The model would be:

$y_i = b_i + f(age_i) + e_i$ where $b_i \sim N(0,\sigma_b^2)$, $e_i \sim N(0,R_i)$ for some covariance matrix $R_i$, and $f(age)$ is an unknown function that is estimated via a B-spline.

It is possible to fit such a model within the nlme package in R. One relevant reference for this would be:

Elmi, Ratcliffe, Parry, and Guo (2011), A B-spline Based Semiparametric Nonlinear Mixed Effects Model, Journal of Computational and Graphical Statistics.

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  • $\begingroup$ yi=bi+f(agei)+ei where bi∼N(0,σ2b), ei∼N(0,Ri), isn't that the same as non-linear model? What is the difference between Semiparametric Nonlinear M-E Model and Non-Linear M-E Model? $\endgroup$
    – Phume
    Commented Apr 11, 2015 at 3:51
  • $\begingroup$ Since $f(age)$ is unknown, it is estimated using some nonparametric technique. In the NLME model, we assume $f(age)$ is a parametric function. $\endgroup$
    – aphe
    Commented Apr 11, 2015 at 14:08

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