I am fitting a shared parameter model where I have a binary $Y_2$ and a continuous $Y_1$, and I am using random effects in the mean structure to model them jointly
$$f(Y_1,Y_2)=\int f(Y_1,Y_2,b)\,\mathrm d b=\int f(Y_1|b)f(Y_2|b)f(b)\,\mathrm d b$$
where the mean structure for each
$$E[Y_1|b]=X^t\beta +b$$ $$E[Y_2|b]=\Phi(X^t\beta+b)$$
where $Y_1$ is normal and $Y_2$ is Bernoulli.
I am using the EM algorithm to solve for this, and it is increasing the $\log$ likelihood monotonically but the log-likelihood is very negative $(-20100)$ in the beginning and is increasing slowly. I am using the marginal linear and glm coefficient estimates (not considering the shared random effects b) as starting points.
What could be causing the large negative likelihood and if it converges at a negative log likelihood is there something wrong with my model?