I have data on student graduation (1 = graduated, 0 = not graduated), as well as student gender and whether or not they were diagnosed with a disorder (categorical variable where it can be none, mild, moderate, or severe).

Using R studio to analyze data and get Odds Ratios:

outputx<- svyglm(GRADUATE~GENDER+DISORDER,  family = quasibinomial, data=SCHOOL, design = SWSCHOOL, maxit=100)

This provides the following:

                OR     2.5%    97.5%    P
(intercept)    0.01     0.007  0.0317   < 2.2e-16  
GENDERFemale   4.31     2.08   16.61    <001269
DISORDERMild   0.84     0.33    2.26    0.604
DISORDERMed    1.18     0.954   3.18    0.085
DISORDERSev    0.48     0.234   0.91    0.048  

I don't understand how the odds relate to the reference group for the independent variables.

Is it saying people who graduate are 4.31 more likely to be female compared to people who did not graduate?

Or is it saying people who are female are 4.31 more likely to graduate compared to males?

Ditto for the disorder variable - what does the 0.48 mean in relation to the reference group for "no disorder" here? It seems like it has no interpretation.


2 Answers 2


It's saying that the odds of females graduating is 4.31 higher than the odds of males, holding constant disorder. That doesn't mean females are 4.31 times more likely to graduate, but it does mean females are more likely to graduate. You can think of it as that among females, the ratio of the number who graduate to the number who don't graduate is 4.31 times higher than it is among males.

Odds ratios are notoriously challenging to interpret, and, given that all your variables are categorical, you could fit another model, like a binomial model with an identity link (just by setting family = quasibiomial(link = "identity") and start = rep(.15, 5)), which would allow you to interpret the coefficients as the difference in the probability of graduating.

For DISORDERSev, the value of 0.48 means that the odds of graduating for those with severe disorder is 0.48 the odds for those with no disorder, indicating that those with severe disorder are less likely to graduate than those with no disorder. The reference category is no disorder.


This link may be helpful for you: https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-how-do-i-interpret-odds-ratios-in-logistic-regression/

Typically, odds ratios are interpreted as scalars that represent the increased/decreased likelihood of association to the response variable. Your first interpretation is correct, with a slight modification: holding all other factors constant, the odds of females graduating is 4.31 more times that of males.

In other words, it depends on the way the model is specified.

It's harder to assess the odds ratios for insignificant covariates (in your case - mild and severe). However, for the severe condition, given that p < 0.05, we could say that the odds of students with severe disabilities graduating is only 0.48 times, or approximately half that of the odds of students without disabilities graduating.

Hope that was helpful.

  • 1
    $\begingroup$ Note that their results table is already in odds ratios, so no exponentiation is needed. Also, "0.48 times, or approximately half as likely" interprets the odds ratio as if it were a risk ratio, which it is not. $\endgroup$
    – Noah
    Commented May 28, 2020 at 8:24
  • 1
    $\begingroup$ The reference category is 'no disorder', so .48 compares students with severe disorder to those with no disorder. It's not simply "without severe disorder" because of the students with mild disorder. I'm not sure how you interpreted my answer as not referring to a binary predictor or outcome. I don't use any language that would suggest a continuous variable. $\endgroup$
    – Noah
    Commented Jun 12, 2020 at 18:37
  • $\begingroup$ I see what you're saying regarding the reference group. However, where in the code is the reference group specified? The odds.ratio function has no mention of it either, so I thought the reference group would be specified as variable = 0: cran.r-project.org/web/packages/questionr/questionr $\endgroup$ Commented Jun 12, 2020 at 19:00
  • 1
    $\begingroup$ The OP says that there are four levels of the disorder variable, and there are three odds ratios for disorder, so the fourth category (which the OP lists as "none") is the reference category. The odds.ratio function just exponentiates the estimated logistic regression coefficients. It doesn't know whether those coefficients came from a categorical variable or not, so the documentation won't mention that. $\endgroup$
    – Noah
    Commented Jun 12, 2020 at 19:05
  • $\begingroup$ Got it, that makes sense. Modified my answer again! $\endgroup$ Commented Jun 12, 2020 at 19:08

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