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Is it OK to use HL to judge the goodness-of-fit of a Logistic Regression when the data is a time series correlated from one period to another? I know that HL assumes independence of events, but I wonder what can be done when your data is not independent. Can I still use HL because data is rarely perfectly independent anyway? Or should I definitely use a different goodness-of-fit test?

Does it make any difference that my model is looking at the time series just as data points? ie the equation just takes inputs from independent variables but does not take into account past values.

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I hope someone who knows more will answer your actual question.

Until then, it bears noting that Hosmer-Lemeshow is not a good test. Briefly, its results are very sensitive to minor changes that should not matter at all -- how ties are dealt with and cutpoints are defined, and how many groups are used (ten is traditional, but shouldn't matter).

People, including Hosmer and Lemeshow, have been writing about this for a while -- see Hosmer, D. W., Hosmer, T., Le Cessie, S. & Lemeshow, S. A Comparison of Goodness-of-Fit Tests for the Logistic Regression Model. Statist. Med. 16, 965–980 (1997). and Allison, P. Measures of Fit for Logistic Regression. in SAS Global Forum 2014 (2014). at http://www.statisticalhorizons.com/wp-content/uploads/GOFForLogisticRegression-Paper.pdf. Paul Alison also has a lovely post summarizing this, Why I Don’t Trust the Hosmer-Lemeshow Test for Logistic Regression.

I don't believe there's a widely-accepted substitute for the H-L test; there's a literature, not a solution. The above references point to some possibilities.

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