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I have been reading the odds tutorial on UCLA's stats page. And I am trying to figure out if my interpretation of the results below is correct. Based upon looking at the data the results seem to hold true. 

Variables to Predict Submit or Cancel (1,0)
DummyServiceA: Binary
DummyServiceB: Binary
DummyServiceC: Binary
AT_START: Continous
ID_SEQ: Continous
TOT: Continous

Logistic Regression Results 
exp(cbind(OR = coef(mymodel), confint(mymodel)))
                                OR      2.5     97.5      
DummyServiceA               0.3994   0.3215   0.4982   
DummyServiceB               6.5028   5.1442   8.2549   
DummyServiceC               0.2928   0.239    0.3604   
AT_START                    0.9986   0.9984   0.9987   
ID_SEQ                      0.949    0.94     0.9579   
TOT                         0.9992   0.9984   0.9998
  • Odds of Submit are 60% lower if ServiceA is selected instead of ServiceB or ServiceC
  • Odds of Submit are 550% higher if ServiceB is selected instead of ServiceA or ServiceC
  • Odds of Submit are 71% lower if ServiceC is selected instead of ServiceA or ServiceB
  • For every unit increase in AT_START there is 0% change in odds for Submit
  • 5% decrease in odds of Submit for every unit increase in ID_SEQ
  • For every unit increase in TOT there is 0% change in odds for Submit
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  • $\begingroup$ Note that interpretation of the coefficients for categorical variables depends on how you've coded them, which you don't say. The default for R's glm is the dummy coding described by @Maarten; unless you remove the intercept term (by putting -1 in the formula), in which case sum-to-zero coding is used. It's very important to be clear about this before you use the model. $\endgroup$
    – Scortchi ♦
    Commented Sep 23, 2014 at 8:51

1 Answer 1

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Indicator (dummy) variables typically compare one service with a reference service (D?). So, someone using service A would have a 60% higher odds (of death, being married, entering the hospital wearing a pink tutu, ...) than someone using service D.

I would change the unit of AT_START and TOT. The effects of both variables are statistically significant, but the unit is probably too small to give you meaningfull odds ratios. For example, if they are measured in euros, I would divide that variable by 1000, so it now measures whatever it measures in 1000s of euros.

I would center the continuous variables and also report the baseline odds. This is a convenient writing trick to remind the readers about the difference between odds and probabilities. You just start with one or two sentences discussing the baseline odds. For example if you centered all continuous variables at the mean and the baseline odds is .4, then you could write something like "For a person who uses service D and with average values on AT_START, ID_SEQ, and TOT the odds of death is .4, that is, we expect to find .4 dead persons for ever living person with those characteristics."

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    $\begingroup$ (+1) I usually prefer not to centre - after all the average predictor values in a sample aren't always especially meaningful or memorable - but often find it handy to use an origin close to the observations - degrees hotter than room temperature, years older than 18. $\endgroup$
    – Scortchi ♦
    Commented Sep 23, 2014 at 9:01

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