In some cases of attribute gauge, there is a continuous variable (reference value) behind the attribute-type decision. In the recent literature, a fixed effect logit model is used for gauge study. In this paper, the random effect concept is applied to the problem. Two different alternatives are studied, the random intercept and the random intercept–random slope model. The random effect concept enables us to characterise the operators in general and to estimate the conditional probabilities of misclassification. Different estimation methods are proposed and compared through simulation. The theoretically less correct, but computationally much simpler estimation method using a fixed effect model proved to be only a slightly less effective than the estimation using a mixed effect model. Copyright © 2011 John Wiley & Sons, Ltd.