Yes. See the following paper which is available on the website:
van Lier, P.A.C., Muthén, B., van der Sar, R.M. & Crijnen, A.A.M. (2004). Preventing disruptive behavior in elementary schoolchildren: Impact of a universal classroom-based intervention. In Journal of Consulting and Clinical Psychology, 72, 467-478.
For a sample of size (i), I have five(t=5) binary response variables, Y(it), and each binary response variable is a function of a vector (four of them) of scenario-dependent covariates X(it) and scenario-independent covariates Z(i). In other words, Y(it)= f[X(it),Z(i)]. Additionally, Y’s are collected from a sequence of 5 question that were asked to respondent in survey, that is there is no time difference between Y’s except that they came in a sequence ( i.e. NO growth model)and therefore they may share some auto-correlation.
I want to estimate a latent class (logit) model. Can I use Mplus to estimate this? Could you suggest me one example. I use version 4.1
Yes, you can use Mplus to do such a LCA. You would have direct effects of x and z on the items - those effects could even differ across classes. And you could, if you need to, include a factor in the model to account for the "auto-correlation" you mention. The version 5 UG which you find on our web site has several examples.