I was watching this video (https://www.youtube.com/watch?v=Wy-WmY6x4tg) and the presenter mentions (@ 8:10) that in a Multi-State Model, the user is required to specify number of "States" within the model and which "Transitions" between these States are "Valid":
Based on this diagram, I can understand that for the Multi-State Model to work, (obviously) the user must specify how many States are in the model, but I am not sure why it is necessary for the user to specify which Transitions are "Valid". In the above example, there are 3 States - The First State can transition to the Second State or the Third State, the Second State can only transition to the Third State, and the Third State is an "absorbing" State (i.e. no transitions are allowed).
This transition structure has been codified into the generator matrix "Q" - but I still do not understand why this transition structure is necessary. For example, suppose we assume a model in which "any state can be reached from any state" - but based on the observed data, there is only evidence of certain transitions happening (e.g. like the above diagram): When it came time to estimate the entries of the Q Matrix, wouldn't the entries corresponding to transitions between states that was never observed in the data be estimated as 0 (regardless if they were codified as "valid transitions" into the transition structure) ? Why can't we just say that all transitions are valid and then all transitions that never happen in the data would be estimated 0?
Thus, if the Q matrix is specified as in the diagram - or if the Q matrix is specified in such a way, such that there are no 0's : For the same observed data, wouldn't the estimated values of the entries in both matrix specifications be identical?