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I have run poisson regression in SPSS (Generalized Linear Model), where BMI is my IV and length of stay (LOS) in hospital for certain disease is my DV (and it's a count variable).

When I run poisson, I get a heavily overdispersed model, where Deviance over DF is approximately 8. enter image description here

How can i deal with this problem using the options of "generalized linear model" dialouge?

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    $\begingroup$ Length of stay definitely is not a count variable! It's just a rounded duration. Perhaps, then, attempting to model this with a Poisson distribution is inappropriate. $\endgroup$
    – whuber ♦
    Commented Oct 14, 2023 at 16:13
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    $\begingroup$ @whuber I agree. Furthermore, I've seen many LOS distributions for inpatients and rarely do they appear to be Poisson-distributed. Much more often I find that the vast majority of patients stay less than 3 days. If they stay more than 3 days then there is a quickly flattening tail that follows characterizing substantial uncertainty in the LOS conditioned on staying more than just a few days. Zeta distributions tend to fit well, although I'm open to suggestions. $\endgroup$
    – Galen
    Commented Oct 14, 2023 at 22:09
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    $\begingroup$ Anything with units (like duration in units of time) won't be Poisson even if you discretize it. What happens when you change units? You get over or under dispersion. Theres other issues I could raise but "avoid count distribution models on data that have units" is a good starting place. $\endgroup$
    – Glen_b
    Commented Oct 14, 2023 at 22:52

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As @whuber points out in a comment, length of stay is not a count variable. Yes, you have a number of days that has to be a non-negative integer, but that's just because LOS is usually measured in days. It could be measured in hours or even minutes! You could certainly have a stay of 0.5 days or whatever.

Often, LOS is censored. If it is, then you want some sort of time to event model. The most common is Cox proportional hazards, but there are others. If there is no censoring, then you can treat it as continuous. There's a lot of material on LOS as a DV, you can search for it, both here and in books, etc.

As an aside, if you did have an overdispersed count measure, then the usual solution would be negative binomial regression (count models are very commonly overdispersed).

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