# Have I correctly specified my model in glmer ?

#### Cynderella

##### New Member
The following multilevel logistic model with one explanatory variable at level 1 (individual level) and one explanatory variable at level 2 (group level) :

$$\text{logit}(p_{ij})=\pi_{0j}+\pi_{1j}x_{ij}\ldots (1)$$
$$\pi_{0j}=\gamma_{00}+\gamma_{01}z_j+u_{0j}\ldots (2)$$
$$\pi_{1j}=\gamma_{10}+\gamma_{11}z_j+u_{1j}\ldots (3)$$

where , the group-level residuals $$u_{0j}$$ and $$u_{1j}$$ are assumed to have a multivariate normal distribution with expectation zero . The variance of the residual errors $$u_{0j}$$ is specified as $$\sigma^2_0$$ , and the variance of the residual errors $$u_{1j}$$ is specified as $$\sigma^2_1$$ .

Substituting equation (2) and (3) in equation (1) yields ,

$$\text{logit}(p_{ij})=\gamma_{00}+\gamma_{10}x_{ij}+\gamma_{01}z_j+\gamma_{11}x_{ij}z_j+u_{0j}+u_{1j}x_{ij}\ldots (4)$$

Now I want to specify the formula in glmer . So I wrote

Code:
m1 <- glmer(Y~X*Z+(X|group),data=dat,family=binomial)
where "group" is the grouping variable that tells R who's in which .

Is this correct formula to fit the model in equation (4) ? I have scoured Google and I am still confused about the formula . It will be very helpful if anyone could explain the notation .

Many thanks! Regards .