When there are more than one dependent variable which are correlated and both of them are dependent upon the same set of independent variables, then we can use the method of multivariate regression which allows multiple dependent variables provided assumptions of linear regression are satisfied. The method can be tested using statistical software packages like SPSS or others.

Structural equation modeling (SEM) in Amos SPSS software or Multivariate regression analysis is appropriate.

I like to handle all model parts at the same time (i.e factor and predictor models simultaneous). For this you should consider a structural equation model. In my opinion the easiest program to work with is Mplus (www.statmodel.com). It is designed for models involving the kind of path relationships among observed and latent variables shown in your model figure. Mplus has a simple interface language, powerful optimization engine for conducting analyses and a hefty set of examples in the user's guide (http://www.statmodel.com/download/usersguide/MplusUserGuideVer_8.pdf), and it is capable of handling also other outcome measurement scales beyond the continuous (e.g. various nominal and ordinal types as well as counts and survival times). There is a free demo available, but it is restricted to a limited set of variables that can be included in the model (http://www.statmodel.com/demo.shtml).

Thanks everyone for your great and informative responses