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

[David Villegas Ríos]

Thanks Thierry and Alastair.

I do have a lot of IDs (~290) but not so many month per ID (a mean of 10).

So from your comments I conclude that if I run model 2, or as suggested by
Thierry this equivalent model, in which month is a factor in the fixed
part...

trait~as.factor(month),random=~month|ID

...and I get significant between individual differences in the slope of the
random effect, the conclusion is that individuals differ in their
non-linear (as described by factor(month) or poly(month,3) in the fixed
part) relationship between trait and month. Right?

If this is correct then I would not upgrade to a higher order random slope
to keep things simple!

Best,

David




2015-09-10 11:08 GMT+02:00 Thierry Onkelinx <thierry.onkelinx at inbo.be>:

> 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 at 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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>>
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>
>

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