Mutual Information Reliability for Latent Class Analysis

Latent class models are powerful tools in psychological and educational measurement. These models classify individuals into subgroups based on a set of manifest variables, assisting decision making in a diagnostic system. In this article, based on information theory, the authors propose a mutual information reliability (MIR) coefficient that summaries the measurement quality of latent class models, where the latent variables being measured are categorical. The proposed coefficient is analogous to a version of reliability coefficient for item response theory models and meets the general concept of measurement reliability in the Standards for Educational and Psychological Testing. The proposed coefficient can also be viewed as an extension of the McFadden’s pseudo R-square coefficient, which evaluates the goodness-of-fit of logistic regression model, to latent class models. Thanks to several information-theoretic inequalities, the MIR coefficient is unitless, lies between 0 and 1, and receives good interpretation from a measurement point of view. The coefficient can be applied to both fixed and computerized adaptive testing designs. The performance of the MIR coefficient is demonstrated by simulated examples.

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Different latent class models were used and evaluated for assessing the accuracy of campylobacter diagnostic tests: overcoming imperfect reference standards?

Epidemiology and Infection ◽

10.1017/s0950268818001723 ◽

2018 ◽

Vol 146 (12) ◽

pp. 1556-1564 ◽

Cited By ~ 2

Author(s):

J. Asselineau ◽

A. Paye ◽

E. Bessède ◽

P. Perez ◽

C. Proust-Lima

Keyword(s):

Diagnostic Accuracy ◽

Diagnostic Tests ◽

Goodness Of Fit ◽

Latent Class ◽

Latent Class Models ◽

Reference Standard ◽

Promising Alternative ◽

Data Sparseness ◽

Campylobacter Infection ◽

Class Models

AbstractIn the absence of perfect reference standard, classical techniques result in biased diagnostic accuracy and prevalence estimates. By statistically defining the true disease status, latent class models (LCM) constitute a promising alternative. However, LCM is a complex method which relies on parametric assumptions, including usually a conditional independence between tests and might suffer from data sparseness. We carefully applied LCMs to assess new campylobacter infection detection tests for which bacteriological culture is an imperfect reference standard. Five diagnostic tests (culture, polymerase chain reaction and three immunoenzymatic tests) of campylobacter infection were collected in 623 patients from Bordeaux and Lyon Hospitals, France. Their diagnostic accuracy were estimated with standard and extended LCMs with a thorough examination of models goodness-of-fit. The model including a residual dependence specific to the immunoenzymatic tests best complied with LCM assumptions. Asymptotic results of goodness-of-fit statistics were substantially impaired by data sparseness and empirical distributions were preferred. Results confirmed moderate sensitivity of the culture and high performances of immunoenzymatic tests. LCMs can be used to estimate diagnostic tests accuracy in the absence of perfect reference standard. However, their implementation and assessment require specific attention due to data sparseness and limitations of existing software.

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