Konteks :
Bayangkan Anda memiliki studi longitudinal yang mengukur variabel dependen (DV) sekali seminggu selama 20 minggu pada 200 peserta. Meskipun saya tertarik pada umumnya, DV yang saya pikirkan termasuk kinerja pekerjaan setelah perekrutan atau berbagai tindakan kesejahteraan setelah intervensi psikologi klinis.
Saya tahu bahwa pemodelan multilevel dapat digunakan untuk memodelkan hubungan antara waktu dan DV. Anda juga dapat mengizinkan koefisien (mis. Intersep, kemiringan, dll.) Bervariasi antar individu dan memperkirakan nilai tertentu untuk peserta. Tetapi bagaimana jika saat memeriksa data secara visual Anda menemukan bahwa hubungan antara waktu dan DV adalah salah satu dari yang berikut:
- berbeda dalam bentuk fungsional (mungkin ada yang linier dan ada yang eksponensial atau ada yang diskontinuitas)
- berbeda dalam varian kesalahan (beberapa individu lebih mudah berubah dari satu titik waktu ke titik berikutnya)
Pertanyaan :
- Apa yang akan menjadi cara yang baik untuk mendekati pemodelan data seperti ini?
- Secara khusus, pendekatan apa yang baik dalam mengidentifikasi berbagai jenis hubungan, dan mengelompokkan individu sehubungan dengan jenis mereka?
- Implementasi apa yang ada dalam R untuk analisis tersebut?
- Apakah ada referensi tentang cara melakukan ini: buku teks atau aplikasi yang sebenarnya?
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I'd recommend taking a look at a couple of papers by Heping Zhang using adaptive splines for modeling longitudinal data:
In addition, see the MASAL page for software including an R package.
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It looks to me like Growth Mixture Models might have potential to allow you to examine your error variance. (PDF here). (I'm not sure what multiplicative heteroscedastic models are, but I will definitely have to check them out).
Latent group based trajectory models have become really popular lately in criminology. But many people simply take for granted that groups actually exist, and some astute research has pointed out that you will find groups even in random data. Also to note Nagin's group based modelling approach does not allow you to assess your error (and honestly I have never seen a model that would look anything like a discontinuity).
Although it would be difficult with 20 time points, for exploratory purposes creating simple heuristics to identify patterns could be helpful (e.g. always low or always high, coefficient of variation). I'm envisioning sparklines in a spreadsheet or parallel coordinates plots but I doubt they would be helpful (I honestly have not ever seen a parallel coordinate plot that is very enlightening).
Good luck
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Four years after asking this question, I've learnt a few things, so perhaps I should add a few ideas.
I think Bayesian hierarchical modelling provides a flexible approach to this problem.
Software: Tools like jags, stan, WinBugs, and so on potentially combined with their respective R interface packages (e.g., rjags, rstan) make it easier to specify such models.
Varying within person error: Bayesian models make it easy to specify the within person error variance as a random factor that varies between people.
For example, you could model scoresy on participants i=1,...,n at time points j=1,...J as
Thus the standard deviation of each person might be modelled as a gamma distribution. I have found this to be an important parameter in many psychological domains where people vary in how much they vary over time.
Latent classes of curves: I have not explored this idea as much yet, but it is relatively straight forward to specify two or more possible data generating functions for each individual and then let the Bayesian model choose the most likely model for a given individual. Thus, you would typically get posterior probabilities for each individual regarding which functional form describes the individuals data.
As a sketch of an idea for a model, you could have something like the following:
Wherexij is time and λ(1)ij represents expected values for a three parameter exponential model and λ(2)ij represents expected values for a quadratic model. πi represents the probability that model will choose λ(1)ij .
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John Fox has a great appendix available on-line using nlme to look at longitudinal data. It may be useful for you:
http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-mixed-models.pdf
There's a lot of great stuff there (and Fox' books are generally quite good!).
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