[R-sig-ME] non-linear slope in random regression model

[Thierry Onkelinx]

Dear David,

Polynomials are technically still a linear model since they result is in
linear combination of variable.

The only straightforward answer to you question is: it depends on the data.
If you have plenty data, then I'd go for model 1. If the data doesn't
require a second and 3th order polynomial, then their random effect
variance will be very small. And the model will be reduced to model 2.

Note than plenty data means a lot of different id AND a lot of months per
id. If you have only one year of data then random=~poly(month, 1)|ID is
about as complex as you can go.

A 3th order polynomial seems a bit odd to me to model seasonality. I'd
rather expect an even order. You might want to consider fitting month as a
factor in the fixed effects. Then you model the seasonality without
assumptions on the pattern.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2015-09-10 10:47 GMT+02:00 David Villegas Ríos <chirleu op gmail.com>:

> Hello,
> I'm fitting some random regression models to investigate variation over
> time of a response trait.
> The time variable is "month", and by fitting a random regression model I
> want to investigate variation in plasticity across individuals, i.e.,
> differences in the "slope" between trait and time across individuals.
>
> The relationship between the response trait and month is non-linear.
> Basically, it describes a seasonal cycle.
>
> I have considered two model candidates:
>
> *Model 1*: fitting a polynomial of month in the fixed effects part to
> describe the non-linearity and get the population mean effect of month, and
> then a random slope using again the polynomial for month, to ge the
> individual differences.
>
> trait~poly(month,3),random=~poly(month,3)|ID
>
>
> *Model 2*: fitting a polynomial of month in the fixed effect part to
> describe the non-linearity, and then the individual-specific deviation from
> the fixed-effect means is modelled as a funtion of month (linear), assuming
> that the non-linearity is already accounted for with the fixed effect.
>
> trait~poly(month,3),random=~month|ID
>
> *My question is*:
> Is it neccesary to include the non-linearity in the random part if it was
> already included in the fixed-effects part?
>
> The idea of fitting model 2 comes from the following reference (page 488):
>
> Dingemanse, N. J., Barber, I., Wright, J., & Brommer, J. E. (2012).
> Quantitative genetics of behavioural reaction norms: genetic correlations
> between personality and behavioural plasticity vary across stickleback
> populations.*Journal of evolutionary biology*, *25*(3), 485-496.
>
>
> Thank you.
>
> David
>
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