Interpret/transform coefficients and 95% CI of meglm with gamma distribution

[Manqing Liu]

Hi,

The outcome in my model is cost and we set the distribution to be gamma distribution. I am not sure how to transform the model output to the ones that are easier to interpret.

The model looks like this:

meglm cost i.type x1 x2 x3 || id:, family(gamma) link(log)

I'm interested in figuring out how does the cost change with 1 unit change of hospital type (type = 1 if type A, and type = 0 if type B). I tried adding eform to exponentiate the coefficients but they still look very small to me. Any idea?

Thanks!

[Clyde Schechter]

The gamma family is not really relevant to interpreting the coefficients in the way you want. What matters is the log link. Your instinct to use the -eform- option was correct: the exponentiated coefficient represents the ratio of the type A expected cost to the type B expected cost. If the result looks smaller than you expected, it isn't the fault of using the gamma family. Nor is it a matter of the scale (unit of measurement) of the cost variable, as exp(coefficient) gives a ratio, and is therefore dimensionless.

Further investigation of the discrepancy between your results and your expectations might include any of the following:

1. Checking whether the model is reasonably well fit to the data.
2. Checking whether the data are incorrect in some way (e.g. not properly sampled or inaccurately ascertained, corrupted during data management, large parts of the data excluded from the model).
3. Modifying your expectations.

[Manqing Liu]

Thanks for the clarifications!