Using direct method

[Charlie]

Dear QCA expert,

Most of my data is qualitative so I am using the direct assignment method for most of my conditions. I do nevertheless have one condition based on numerical data. I therefore want to use the direct method for this condition.

I have been using the approach laid out by Ragin in his Redesigning Social Inquiry book. However, I got stuck just before being able to set the degree of membership. I am finding this passage impossible to understand: degree of membership = exp(log odds)/[1+exp(log odds)]. I am really unsure about what I need to do with the data I have so far scaled etc. In case it helps I am attaching the table I am using. 

Thanks a lot in advance for your help!

Charlie

[Ingo Rohlfing]

Dear Charlie,

with the formula, you are taking a deep dive into the mechanics of direct calibration. I think this is not necessary for empirical research where you simply want to directly calibrate a variable. At a minimum, you only need to specify the points of full exclusion, the crossover point and the point of full inclusion. Is there a specific reason why you read up on the statistics of direct calibration?

Regards

Ingo

[Adrian Dușa]

On Tuesday, January 27, 2026 at 11:50:23 PM UTC+2:

[...]

with the formula, you are taking a deep dive into the mechanics of direct calibration. I think this is not necessary for empirical research where you simply want to directly calibrate a variable. At a minimum, you only need to specify the points of full exclusion, the crossover point and the point of full inclusion. Is there a specific reason why you read up on the statistics of direct calibration?

Indeed.

For a step by step tutorial on how to use the direct method, please see section 4.2.2 on the Direct method, the “s-shape” functions:

https://dusadrian.github.io/QCAbook/calibration.html#s-shape

And, if you really are interested in understanding the logistic formula, the next section 4.2.3 might help:

https://dusadrian.github.io/QCAbook/calibration.html#logistic

Hope this helps,

Adrian 

[Kalihputro Fachriansyah]

Hello Charlie,

The practical troubleshooting has already been answered above, so I’d like to add a few reflections from my own experience, as I also found Ragin’s explanation confusing at first.

1. The first helpful idea for me was understanding odds in a fuzzy‑set context. Odds express how much a case is “in” a set compared to how much it is “out”. Odds equal to 1 mean a case is equally in and out (a 50/50 situation), which corresponds to a membership score of 0.5, also known as the crossover point. In this situation the log of the odds is zero, which is the centre point of the verbal labels that Ragin describes.

2. What is easy to miss in the book is that the log‑odds values shown in Table 5.1 are only an illustration of the mathematical transformation for nine verbal labels. These values are not derived from any empirical data, nor are they required for calibration. They simply show how verbal distinctions like “mostly in” or “more out than in” can be located on a log‑odds scale. In fact, when Ragin applies the direct method in Table 5.2, the only log‑odds values he actually needs are the ones for full membership and full nonmembership. These two values are the anchors used to compute the scalars that convert deviations from the crossover into log‑odds.

3. Once the chosen log‑odds values are set, they can be turned into odds by using the exponential function. For example, a log‑odds value of 5 corresponds to odds of roughly 148, which simply expresses a very strong degree of membership.

4. After that, the fuzzy‑set membership score is obtained by applying the logistic transformation (a formula that you've been asking). In plain language, this is a mathematical way to map any log‑odds value into the 0–1 range. It ensures that log‑odds equal to zero give a membership of 0.5, and that positive or negative values are compressed smoothly toward 1 or 0.

I have attached an Excel file that shows an example of the calculation using five verbal labels, in case it is helpful for anyone working through the same steps. However, I opt to use Prof Adrian's QCA R package of calibrate() for practicality.

Best regards,
Kalihputro
IOE, University College London