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

[Viechtbauer, Wolfgang (SP)]

Yes, that's the same model.

Best,
Wolfgang

-----Original Message-----
From: Juan Pablo Edwards Molina [mailto:edwardsmolina at 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)
<wolfgang.viechtbauer at maastrichtuniversity.nl>:
> 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-bounces at 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
>
> 2018-05-17 16:57 GMT-03:00 Ben Bolker <bbolker at gmail.com>:
>> 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
>> <edwardsmolina at gmail.com> wrote:
>>> 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)
>>>
>>> I wish to write the model equation for its publication, so this is my first try:
>>>
>>> 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