I am trying to interpret the coefficients presented in the output of a GLM fractional logit model I ran with multiply imputed data. My dependent variable is a share ranging from 0 to 1. Referring to this very helpful response by Maarten Buis a few years ago (https://www.statalist.org/forums/for...interpretation), I tried to obtain Odds Ratios (by adding the options eform base) and Average Marginal Effects (with mimrgns, dydx(w_remarried) post). However, Stata always provides values that are identical to the coefficient in the first model.
How to interpret the coefficient in the first model? How to obtain Odds Ratios and AMEs in fractional logit models in the mi-setting?
Code:
. mi estimate, post: glm share_joint w_remarried [pweight=xrwght], family(binomial) link(logit) vce(robust) nolog
Multiple-imputation estimates Imputations = 5
Generalized linear models Number of obs = 19,044
Average RVI = 0.0162
Largest FMI = 0.0294
DF adjustment: Large sample DF: min = 4,768.54
avg = 312,430.96
max = 620,093.37
Model F test: Equal FMI F( 1, 4768.5) = 264.94
Within VCE type: Robust Prob > F = 0.0000
------------------------------------------------------------------------------
share_joint | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
w_remarried | -1.013089 .0622403 -16.28 0.000 -1.135109 -.8910692
_cons | .5556401 .0181894 30.55 0.000 .5199895 .5912906
------------------------------------------------------------------------------
. mi estimate, post: glm share_joint w_remarried [pweight=xrwght], family(binomial) link(logit) vce(robust) nolog eform base
Multiple-imputation estimates Imputations = 5
Generalized linear models Number of obs = 19,044
Average RVI = 0.0162
Largest FMI = 0.0294
DF adjustment: Large sample DF: min = 4,768.54
avg = 312,430.96
max = 620,093.37
Model F test: Equal FMI F( 1, 4768.5) = 264.94
Within VCE type: Robust Prob > F = 0.0000
------------------------------------------------------------------------------
share_joint | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
w_remarried | -1.013089 .0622403 -16.28 0.000 -1.135109 -.8910692
_cons | .5556401 .0181894 30.55 0.000 .5199895 .5912906
------------------------------------------------------------------------------
. mimrgns, dydx(w_remarried) post
Multiple-imputation estimates Imputations = 5
Average marginal effects Number of obs = 19,044
Average RVI = 0.0298
Largest FMI = 0.0294
DF adjustment: Large sample DF: min = 4,768.54
avg = 4,768.54
Within VCE type: Delta-method max = 4,768.54
Expression : Linear prediction, predict(xb)
dy/dx w.r.t. : w_remarried
------------------------------------------------------------------------------
| dy/dx Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
w_remarried | -1.013089 .0622403 -16.28 0.000 -1.135109 -.8910692
------------------------------------------------------------------------------Many thanks,
Theresa
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