Stats
Continuous variables in a logistic regression model (February 9, 2005).
I got a question by email that asked, in a rather indirect way, how to interpret the odds
ratio estimate for a continuous variable in a logistic regression model. It turns out that
the odds ratio represents a change in the estimated odds of the outcome when the continuous
variable increases by one unit. See
for a more detailed discussion of this interpretation.
I failed to mention in that web page how important the measurement scale is in this
situation. If you use grams as a unit of weight rather than kilograms, then you will be
estimating a relative change in odds per gram change in weight, which is often so small that
it is difficult to make sense out of it.
Here's an example computed from the bf.sav file that I use in several of my training
classes:
The dependent variable is exclusive breast feeding at discharge, and birth weight in grams
has a highly significant effect on the outcome (p=0.005). But notice that the estimated odds
ratio is very close to 1. It turns out that the estimated odds of exclusive breast feeding at
discharge increase by 0.2% for every increase in birth weight by one gram. This is rather
hard to interpret.
If you refit the model using birth weight in kilograms, you get the same p-value, but now
the odds ratio is much easier to interpret.
The odds of exclusive breast feeding at discharge increase six fold when the birth weight
increases by one kilogram.
You need to be a bit cautious about these findings because the research study was
restricted to pre-term births, but clearly the interpretation is much easier using kilograms
rather than grams.
In theory, you could convert from one odds ratio to the other by raising 1.002 to the
1,000 power, but this calculation is difficult to perform and is subject to rounding error. A
better way to make the conversion would be to take the log odds ratio (0.002) and mulitply
that by 1,000 and then exponentiate the result. Even then, you would have considerable
rounding error because of the way SPSS displays the log odds ratio.
07/08/2008.
Category: Logistic regression
