Dear List,

I apologise if this has been covered before, but I haven't been able to find an exact answer to my question and I am hoping someone can help or advise. I am fitting an lmer model and would like to know if there is evidence for curvature or not in the regression, and if there is curvature, to plot the predictions and see what it looks like. I had been using orthogonal polynomials (poly default), but I have realised that I get vastly different results, in terms of significance, depending on whether I use orthogonals or raw. I have the impression from reading about this that orthogonal ones are better for my case (ie model selection, but not to extract the equation), but I am not sure if that is correct, and if it means I can follow the orthogonal or the raw result. Model formula and model summaries are below for raw and orthogonal polynomals. The data 'looks' like there should be a linear but not quadratic effect.
Thank you in advance,

Rebecca Ross,
Dphil Candidate,
Oxford University

> summary(avalt2POLY)
Linear mixed model fit by REML
Formula: total_RO ~ poly(Av_alt, 2) + (1 | Block) + (1 | fam:Type)
   Data: F2dat
  AIC  BIC logLik deviance REMLdev
 2557 2580  -1273     2562    2545
Random effects:
 Groups   Name        Variance Std.Dev.
 fam:Type (Intercept)  28.621   5.3499
 Block    (Intercept)  14.759   3.8417
 Residual             111.788  10.5730
Number of obs: 329, groups: fam:Type, 194; Block, 5
Fixed effects:
                 Estimate Std. Error t value
(Intercept)        23.281      1.856  12.541
poly(Av_alt, 2)1  -82.333     12.776  -6.444
poly(Av_alt, 2)2   -3.875     12.781  -0.303
Correlation of Fixed Effects:
            (Intr) p(A_,2)1
ply(Av_,2)1  0.000
ply(Av_,2)2  0.000 -0.002
> summary(avalt2RAW)
Linear mixed model fit by REML
Formula: total_RO ~ Av_alt + I(Av_alt^2) + (1 | Block) + (1 | fam:Type)
   Data: F2dat
  AIC  BIC logLik deviance REMLdev
 2605 2627  -1296     2562    2593
Random effects:
 Groups   Name        Variance Std.Dev.
 fam:Type (Intercept)  28.621   5.3499
 Block    (Intercept)  14.759   3.8417
 Residual             111.788  10.5730
Number of obs: 329, groups: fam:Type, 194; Block, 5
Fixed effects:
              Estimate Std. Error t value
(Intercept)  3.709e+01  1.024e+01   3.623
Av_alt      -6.827e-03  1.444e-02  -0.473
I(Av_alt^2) -1.479e-06  4.877e-06  -0.303
Correlation of Fixed Effects:
            (Intr) Av_alt
Av_alt      -0.974
I(Av_alt^2)  0.950 -0.993



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