linear model with both within subject correlation and cross sectional

[ronen]

shalom,

I have data in the following way:

about 30 groups are followed for about 40 months.

Each month we observe Y_it (group i on time t)  which is unique to each group

and X_t which change only in time t but common to all groups.

The mixed linear model is:

Y_it = beta_i*X_t + u_i + gamma_i*v_t + e_it

where:

 beta_i  - is the fixed effect coefficient of X on group i

u_i    - is a random intercept of group i (could also change it to a fixed effect of group)

v_t  - is a random effect/noise of time t

gamma_i - is the specific effect of v_t on group i

We assume u_i,v_t and e_it are all normal and independent

Therefore covariance of y_it and y_jt (given X) is gamma_i*gamma_j*sigma(v_t)^2

How do I model such a depence in R (lme or lmer)?

I thought to use random effect for the u_i and repeated measures for the v_i ? 

But I am not sure how.

Thank you!

Ronen

 

   

[amit gal]

Sounds like the kind of data I need for my PhD :-)

As a reference, I recommend Andrew Gelmans' book on hierarchical regression models - I found it highly instructive and clear (and he uses R, but recommends using bayesian approach to estimate such models. he does, however give examples of using lmer)

I haven't used that for a long time now, but I would guess you'd do something like this:

lmer( y~((1+v)|g+x*g)) where g is the grouping variable

maybe you need to split it into

lmer( y~ 1|g +v|g + x*g)

I hope I'm not completely off target here. so take this with a grain of salt

Amit

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[ronen]

thank u Amit!

I dont have the book - but i will inquier about it

I was probably not clear enough!

I have one observation from each group on each time point (n~30*40)

so group is like a subject which is followed for T time points

The observed variables are: Y,X,group,time

v is a random noise on time t

perhapse you ment:  "time|g"

but this is not the case. this will give an identical covariance between any Y_it and Y_jt (givan X)

In my model the covariance should be specific for exh i and j (=gamma_i*gamma_j*var(v))

but similar on all time points.

It means group/subject i will usualy respond more/less strongly than group j

to the random noises on time t

Thats why random effect is not good here.

I should use repeated - but I am not sure how to specify the type of covariance.

   

Do you have an idea?

Thank you

Ronen

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[amit gal]

That was clear. :)

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[amit gal]

I'm not sure if i understand this fully. But am driving so will look at it later

On May 18, 2015 11:11 AM, "ronen" <rfl...@gmail.com> wrote:

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[Moran Koren]

Why not using panel data methods? such as vector auto-regressions and such?

[ronen]

Thank u Moran,

I think random effects and repeated measures are panel data methods. no?

I assume there is no auto-correlation here (this could be tested later)

The main issue is the cross sectional dependence created by unmeasured common shocks

on time t.

I think there is no ready ready made procedure for this...

Ronen

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