It should be:
u_0i ~ N(0, ?^2_0)
u_1i ~ N(0, ?^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], [?^2_0 rho*?_0*?_1])
[u_1i] ([0] [ ?^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,?^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 ?_0 and ?_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= (?_0 + u_0i)+ (?_1+ u_1i) x_ij + e_ij
where j subscript represents the j-plot within i-trial, both for y or
x. ?0 and ?1 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 ?_u0 and ?_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