A simulation study of statistical tests in logistic measurement error models

Measurement error models in logistic regression have been subject to much research during the last 10–15 years. In this work, we will focus on statistical testing in these models. We will compare the measurement error likelihood ratio test with a Wald-type test based on the so-called regression calibration method with both asymptotic- and bootstrap standard errors, and the score test, in some finite sample situations. We find that all tests perform approximately equally with regard to empirical power. With regard to the empirical test size, the Wald-type test based on the asymptotic standard error was too conservative, whereas the Wald-type test based on a trimmed boostrap standard error performed quite unstably. In summary, we will recommend the use of likelihood ratio tests or score tests in logistic measurement error situations.