I'm fitting a set of length-of-stay data by a model of mixture of exponentials. I've been following the example on page 436 in MASS (5th Ed.). However, I have a couple of questions while following this example.
What if we don't know how many components there are in the model in advance. Is there any established method to determine the number of components from a set of data? I'm aware that the usual likelihood ratio test is not appropriate in this case due to the possibility that the ML could occur at the boundry of the parameter space.
Secondly, the example in MASS uses a Q-Q plot to informally assess GOF. I was wondering if there are some more formal statistical tests for this purpose.
I appologise for asking questions that are slightly out-of-topic.
Many thanks.
Kevin
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