I did a bootstrap analysis on model {phi(sex*plot),p(plot)}, these are the summed results:
Statistical Summary of Numerical Variables
(Number of Observations = 100)
95% Confidence Interval
Variable Mean Standard Error Lower Upper
---------- --------------- -------------- --------------- ---------------
DEVIANCE 4122.271 10.1302 4102.415 4142.126
so.. c-hat= 4276.1013 / 4122.271 = 1.0373
Correct
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Ordened deviance method:
When i rank all 100 bootstrapped deviances, my observed deviance falls between the 93th and the 94th bootstrapped deviance.
Should my observered devaince fall in the tail (say the last 5%) of the expected deviances or just the other way around?
So, you have some evidence for lack of fit. If the model fit perfectly, you'd anticipate that 50% of the simulated deviances would fall above the observed value, and 50% would fall below.
So, looking at the rank ordering of the deviances gives you some evidence of whether or not there is lack of fit (and even gives you a P-value if you're so inclined), while the c-hat is the 'adjustment' you need to acccount for this lack of fit when deriving AIC vaues or other metrics for model selection.
In fact, this
is discussed on p. 23-25 of the GOF chapter. Specifically, on p. 24, the use of the ranked decviances, and the estimation of c-hat, are both specifically accounted for.