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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