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

[Juan Pablo Edwards Molina]

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, random = ~ x | trial , data=mydata)

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