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We must specify the number of simulations and a 'seed' or starting value for the random number generator.
The defaults are 100 simulations (which is low-- you probably want more) and 0 (which takes the computer clock time to get a starting value).
By "significantly" here I do not necessarily mean "at some arbitrary p value", but rather more subjectively "enough to matter in terms of bias, precision, confidence interval coverage, etc".
These are standardized residuals, so if we think in terms of standard normal deviates we would expect the residuals to vary between about -2 and 2 under a fitting model.
All of the goodness of fit methods for count data are based on various notions of "discrepancy" between what the model predicts and what the data say.
The trick is to to determine if discrepancy is large enough to conclude that the data and the model disagree "significantly".
We have created the equivalent MARK model and saved the MARK project here. You will see in the results browser the single model Phi(g*t)p(t) and the identical deviance value (the AIC values differ because of different parameter counting).
If you right click and select "output in Notepad" you will see the saved log likelihood, deviance and c-hat statistics that RMark produced.
It is implemented (here for the Dipper example) from the Tests pull down menu Users can select optional c-hat, df and deviance output, or just deviance.