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I am trying to interpret the output of a logistic regression with categorical and continuous variables. I am a bit struggling to get the concept of "other values fixed / other variables constant".

As far as I know, I am always comparing to the reference group (when variables are categorical). However, I have BMI continuous. So are my interpretations correct?

The reference group is people with "high school" education, "good" self-assessment, age "<18" and "no" medication intake and a BMI of (hypothetically) "0" or a any "fixed" value?

  1. People in the reference category have a chance to pass of (e^-0.73) 0.47.
  2. When people have a PhD and good self-assessment, age <18, no medication intake (BMI fixed value), their chance to pass increases by about (e^1.46) 4.32.
  3. When they have a PhD and are aged 18-25, their chance increases by about (e^1.465+1.03) 12.12 compared to the chance of people with high school, good self-assessment, age <18, no medication intake and BMI constant.

So is BMI hypothetically 0 or at a (any) fixed value?

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    $\begingroup$ Should the data be provided as text, not as an image? $\endgroup$ Commented Feb 5 at 4:55
  • $\begingroup$ you mean I should copy/paste the results of the logistic regression instead of inserting an image? I thought the formatting would be better when I use an image directly. $\endgroup$
    – Gustav
    Commented Feb 5 at 16:18

2 Answers 2

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Your first bullet is right for a person with a BMI of 0. Of course, no one has such a BMI. (That's assuming BMI wasn't centered or scaled).

In your second and third bullets, you left out "by a factor of" (but, look at the conditions: No one can have a PhD and be under 18. Even Terry Tao didn't get his PhD until age 21.

As an aside, categorizing age is a bad idea, use age in years, if you have it. Also, age and education are ordinal and you seem to be ignoring that.

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  • $\begingroup$ "Also, age and education are ordinal and you seem to be ignoring that." How did you mean that? How can I ignore the ordinal character of a variable in logistic regression? $\endgroup$
    – Gustav
    Commented Feb 4 at 11:44
  • $\begingroup$ I just got confused because here (stats.oarc.ucla.edu/other/mult-pkg/faq/general/…) it says "The coefficient for math says that, holding female and reading at a fixed value, we will see 13% increase in the odds of getting into an honors class for a one-unit increase in math score since exp(.1229589) = 1.13." so reading is here continuous and they write about holding it fixed instead of 0? $\endgroup$
    – Gustav
    Commented Feb 4 at 11:46
  • $\begingroup$ I see the issues with age <18 and PhD - thank you. Unfortuntaley, I only have age as categories. $\endgroup$
    – Gustav
    Commented Feb 4 at 11:47
  • $\begingroup$ You ignore it by not accounting for it. That is, you are treating age and education as if they were nominal, not ordinal. But ordinal indpendent variables are tricky. For your second comment, they are talking about an increase, your first bullet gave an amount. $\endgroup$
    – Peter Flom
    Commented Feb 4 at 11:48
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    $\begingroup$ Ruth Lawrence gained a PhD in 1989 - more precisely a DPhil (Oxon) - at age 17. $\endgroup$
    – Henry
    Commented Feb 5 at 12:44
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Programming suggestions:

  • Remove the asterisks from the output as this represents bad statistical practice
  • Don’t use long-winded function calls in formulas as this messes up all the later model output
  • I don’t worry about which reference level was chosen when a model is fitted but rather specify that when I ask for estimates. The rms package makes this easy, and gives lots of other customized output specifically for logistic regression:
dd <- datadist(mydata); options(datadist=‘ddist’)
f <- lrm(y ~ x1 + x2 + rcs(bmi, 4), data=mydata)
summary(f, x1=‘High School’, bmi=c(25, 35))

This will use High School as the reference category for getting odds ratios for x1 and use a range of 25-35 for getting an odds ratio for the continuous variable bmi. Defaults would have been to use quantiles.

See RMS for more and especially note partial effect plots, which are typically better than single point estimates.

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  • $\begingroup$ the asterisks are bad practice? Never heard of that but see them very often, however, thank you for the hint. The definition of range for bmi is a cool thing of RMS! $\endgroup$
    – Gustav
    Commented Feb 5 at 16:26
  • $\begingroup$ Very many statisticians have criticized R for showing asterisks by default. They perpetuate the terrible practice of having arbitrary thresholds for 'significance'. $\endgroup$ Commented Feb 6 at 0:12

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