An Introduction to Multilevel Modeling Techniques by Heck Ronald H.; Thomas Scott L.;

Author:Heck, Ronald H.; Thomas, Scott L.;
Language: eng
Format: epub
Publisher: Taylor & Francis Group
Published: 2020-06-15T00:00:00+00:00

Logit Link Function

For proportions and dichotomous data, common link functions are the logit link or probit link function. The logit link function, which is the canonical link function for the binomial distribution, is most often used because it represents a fairly easy transformation of the expected scores of by using the natural logarithm1 (ln) of the probability of each event occurring:

, (6.4)

where the logit coefficient η is the log of the odds of the event coded = 1 occurring. Therefore, although the predicted value for the transformed outcome can take on any real value, the probability = 1 will always lie between 0 and 1.

We can also use the log odds coefficient to estimate the probability y = 1. For example, if the proportion of students who receive a degree is 0.80 and the proportion who does not is 0.20, we can express this as follows:

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