An improved test of latent-variable model misspecification in structural measurement error models for group testing data.

We consider structural measurement error models for group testing data. Likelihood inference based on structural measurement error models requires one to specify a model for the latent true predictors. Inappropriate specification of this model can lead to erroneous inference. We propose a new method tailored to detect latent-variable model misspecification in structural measurement error models for group testing data. Compared with the existing diagnostic methods developed for the same purpose, our method shows vast improvement in the power to detect latent-variable model misspecification in group testing design. We illustrate the implementation and performance of the proposed method via simulation and application to a real data example.