st: goodness-of-fit stats with MI data

[Ryan Wells <rs_wells@yahoo.com>]

I am trying to figure out how to conduct a relevant 
goodness-of-fit test(s) in Stata after conducting a logistic regression 
model for a multiply imputed dataset.

White, Royston and Wood (2011) say that goodness-of-fit test statistics 
should not be combined using Rubin's rules. I know about the Wald-like 
"mi test" Stata command, as well as the implementation of R-squared for regression analysis (following Harel, 2009) in the ssc-downloadable command mibeta. I am also aware that there are proposed alternatives (not using Rubin's standard pooling rules) for a pooled likelihood ratio test statistic and a pooled chi-square test 
statistic (with associated p-values) that are applicable in a multiply 
imputed framework, although to my knowledge these are not implemented in Stata. (If there is a user command for these somewhere, I'd like to 
hear about it.) In my application (analyzing ELS education data from 
NCES), I would have used a BIC or AIC in a non-imputed setting.

What is the recommended procedure to conduct and report a model 
goodness-of-fit test for logistic regression analysis when using mi data in Stata? Thanks.

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