[R-sig-ME] Fwd: syntax equation of random intercepts and slopes model

[Ben Bolker]

That looks about right. You didn't specify the variance of e_ij in
your description, and you didn't say explicitly that the u_ and e_
values are Normally distributed ...

On Thu, May 17, 2018 at 2:27 PM, Juan Pablo Edwards Molina

Sorry, I edited the lmer function...
============================================
Dear list,
I fitted a linear mixed effects models to a set of 41 field trials
with plot-level assessments of x,y, for estimating the linear
regression coefficients β_0 and β_1
res1 <- lmer(y ~ x+ (x|trial), data=mydata, REML=F)
W_ij= (β_0 + u_0i)+ (β_1+ u_1i) x_ij + e_ij
where j subscript represents the j-plot within i-trial, both for y or
x. β0 and β1 are the population average intercept and slope; u0i and
u1i are the effect of the i-trial on the intercept and the slope,
respectively, considered as random variables (with mean 0 and
variances τ_u0 and τ_u1 a )
I´m not sure if I´m in the right path... I would really appreciate any guidance.
Juan Edwards
National Institute of Agriculture Technology - Argentina
_______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

[Juan Pablo Edwards Molina]

Thanks prof. Bolker,
Do you mean this?

u_i∼N(0,τ^2) e_ij∼N(0,v_i)

Juan
Juan

Post by Ben Bolker
That looks about right. You didn't specify the variance of e_ij in
your description, and you didn't say explicitly that the u_ and e_
values are Normally distributed ...
On Thu, May 17, 2018 at 2:27 PM, Juan Pablo Edwards Molina

Sorry, I edited the lmer function...
============================================
Dear list,
I fitted a linear mixed effects models to a set of 41 field trials
with plot-level assessments of x,y, for estimating the linear
regression coefficients β_0 and β_1
res1 <- lmer(y ~ x+ (x|trial), data=mydata, REML=F)
W_ij= (β_0 + u_0i)+ (β_1+ u_1i) x_ij + e_ij
where j subscript represents the j-plot within i-trial, both for y or
x. β0 and β1 are the population average intercept and slope; u0i and
u1i are the effect of the i-trial on the intercept and the slope,
respectively, considered as random variables (with mean 0 and
variances τ_u0 and τ_u1 a )
I´m not sure if I´m in the right path... I would really appreciate any guidance.
Juan Edwards
National Institute of Agriculture Technology - Argentina
_______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

[Viechtbauer, Wolfgang (SP)]

It should be:

u_0i ~ N(0, τ^2_0)
u_1i ~ N(0, τ^2_1)
e_ij ~ N(0, sigma^2)

and it is also worth mentioning that the model allows for correlation between u_0i and u_1i. So, technically, the assumption is:

[u_0i] ~ MVN([0], [τ^2_0 rho*τ_0*τ_1])
[u_1i] ([0] [ τ^2_1 ])

And if one wants to be really explicit, we assume that u_0i and e_ij are independent and u_1i and e_ij are independent.

Best,
Wolfgang

-----Original Message-----
From: R-sig-mixed-models [mailto:r-sig-mixed-models-***@r-project.org] On Behalf Of Juan Pablo Edwards Molina
Sent: Friday, 18 May, 2018 1:34
To: Ben Bolker
Cc: R SIG Mixed Models
Subject: Re: [R-sig-ME] Fwd: syntax equation of random intercepts and slopes model

Thanks prof. Bolker,
Do you mean this?

u_i∼N(0,τ^2) e_ij∼N(0,v_i)

Juan
Juan

Post by Ben Bolker
That looks about right. You didn't specify the variance of e_ij in
your description, and you didn't say explicitly that the u_ and e_
values are Normally distributed ...
On Thu, May 17, 2018 at 2:27 PM, Juan Pablo Edwards Molina

Sorry, I edited the lmer function...
============================================
Dear list,
I fitted a linear mixed effects models to a set of 41 field trials
with plot-level assessments of x,y, for estimating the linear
regression coefficients β_0 and β_1
res1 <- lmer(y ~ x+ (x|trial), data=mydata, REML=F)
W_ij= (β_0 + u_0i)+ (β_1+ u_1i) x_ij + e_ij
where j subscript represents the j-plot within i-trial, both for y or
x. β0 and β1 are the population average intercept and slope; u0i and
u1i are the effect of the i-trial on the intercept and the slope,
respectively, considered as random variables (with mean 0 and
variances τ_u0 and τ_u1 a )
I´m not sure if I´m in the right path... I would really appreciate any guidance.
Juan Edwards
National Institute of Agriculture Technology - Argentina

[Viechtbauer, Wolfgang (SP)]

Yes, that's the same model.

Best,
Wolfgang

-----Original Message-----
From: Juan Pablo Edwards Molina [mailto:***@gmail.com]
Sent: Friday, 18 May, 2018 15:42
To: Viechtbauer, Wolfgang (SP)
Cc: R SIG Mixed Models
Subject: Re: [R-sig-ME] Fwd: syntax equation of random intercepts and slopes model

Excellent!

Is it the case of your example tutorial in
http://www.metafor-project.org/doku.php/tips:two_stage_analysis#mixed-effects_model_approach
?

Thanks Wolfgang!

Juan Edwards

Juan

2018-05-18 10:27 GMT-03:00 Viechtbauer, Wolfgang (SP)

Post by Viechtbauer, Wolfgang (SP)
u_0i ~ N(0, τ^2_0)
u_1i ~ N(0, τ^2_1)
e_ij ~ N(0, sigma^2)
[u_0i] ~ MVN([0], [τ^2_0 rho*τ_0*τ_1])
[u_1i] ([0] [ τ^2_1 ])
And if one wants to be really explicit, we assume that u_0i and e_ij are independent and u_1i and e_ij are independent.
Best,
Wolfgang
-----Original Message-----
Sent: Friday, 18 May, 2018 1:34
To: Ben Bolker
Cc: R SIG Mixed Models
Subject: Re: [R-sig-ME] Fwd: syntax equation of random intercepts and slopes model
Thanks prof. Bolker,
Do you mean this?
u_i∼N(0,τ^2) e_ij∼N(0,v_i)
Juan
Juan

Post by Ben Bolker
That looks about right. You didn't specify the variance of e_ij in
your description, and you didn't say explicitly that the u_ and e_
values are Normally distributed ...
On Thu, May 17, 2018 at 2:27 PM, Juan Pablo Edwards Molina

Sorry, I edited the lmer function...
============================================
Dear list,
I fitted a linear mixed effects models to a set of 41 field trials
with plot-level assessments of x,y, for estimating the linear
regression coefficients β_0 and β_1
res1 <- lmer(y ~ x+ (x|trial), data=mydata, REML=F)
W_ij= (β_0 + u_0i)+ (β_1+ u_1i) x_ij + e_ij
where j subscript represents the j-plot within i-trial, both for y or
x. β0 and β1 are the population average intercept and slope; u0i and
u1i are the effect of the i-trial on the intercept and the slope,
respectively, considered as random variables (with mean 0 and
variances τ_u0 and τ_u1 a )
I´m not sure if I´m in the right path... I would really appreciate any guidance.
Juan Edwards
National Institute of Agriculture Technology - Argentina