Testing is a commonly used approach to ensure the quality of software, of which model-based testing is a hot topic to test GUI programs such as Android applications (apps). Existing approaches mainly either dynamically construct a model that only contains the GUI information, or build a model in the view of code that may fail to describe the changes of GUI widgets during runtime. Besides, most of these models do not support back stack that is a particular mechanism of Android. Therefore, this paper proposes a model LATTE that is constructed dynamically with consideration of the view information in the widgets as well as the back stack, to describe the transition between GUI widgets. We also propose a label set to link the elements of the LATTE model to program snippets. The user can define a subset of the label set as a target for the testing requirements that need to cover some specific parts of the code. To avoid the state explosion problem during model construction, we introduce a definition "state similarity" to balance the model accuracy and analysis cost. Based on this model, a target directed test generation method is presented to generate event sequences to effectively cover the target. The experiments on several real-world apps indicate that the generated test cases based on LATTE can reach a high coverage, and with the model we can generate the event sequences to cover a given target with short event sequences.