Hi;
I am using multiple imputation for a logistic regression problem I have. The response and one of my varbale is fully observed and am trying select the set of model which best describe the data. I am using the likelihood ratio test statistics proposed by Meng & Rubin (1992), and am getting negative differences in the pooled likelihood for some of the models.
If I fit the different models to each of the data sets, the most complex model has the lowest deviance, but when I use the pooled coefficients this is not necessarily the case. This leads for some model to a negative value in the mean of d_{L} resulting in a negative value in D_{L}. Is this common?
An example of my output is given below. d'0(1) = 427.0232 d'1(1) = 518.6282
d'0(2) = 425.6645 d'1(2) = 518.6282
d'0(3) = 436.4400
d'1(3) = 518.6282
d'0(g) is the deviance of the most complex model for imputation g. d'1(g) is the deviance of the model incorporating only the fully observed variable in imputation g.
Below is the likelihood from the pooled coefficients: d_L(1) = 521.2215 d_L(1) = 518.6282
d_L(2) = 638.0552 d_L(2) = 518.6282
d_L(3) = 494.4705
d_L(3) = 518.6282
Notice that for the simpler model the likelihood is always the same given that the variables is fully observed, but for the pooled data the most complex model sometimes has a higher likelihood.
Thanks for your help.
Vumani Dlamini Central Statistical Office Swaziland
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