[R] firth's penalized likelihood bias reduction approach

[Yue]

hi all,

I have a binary data set and am now confronted with a "separation" issue. I
have two predictors, mood (neutral and sad) and game type (fair and
non-fair). By "separation", I mean that in the non-fair game, whereas 20%
(4/20) of sad-mood participants presented a positive response (coded as 1)
in the non-fair game, none of neutral-mood participants did so (0/20). Thus,
if drawing a 2x2 (mood x response, in the non-fair game) table, there was an
empty cell. I've learned that I can use Firth's penalized likelihood method
for bias reduction, which could be achieved using R packages "brglm" or
"logistf". However, I found the packages only deal with non-clustered data,
which is not the case for my data. I included game type as a within-subject
variable and mood as a between-subject variable, and I am interested in
their interaction. So, when involving the interaction term as a predictor, I
also need to control for within-subject correlation. Has anyone experience a
similar problem and how you solved it? or, any suggestion would be very much
appreciated!!! Thanks very much!!

Best,
Yue

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