Measurement Models with Binary Indicators: A Tutorial for the Assessment of Antenatal Care Quality

Abstract Background: Confirmatory Factor Analysis (CFA) is a methodology classically used to relate continuous (observed) indicators to latent variables through a measurement model. Estimation approaches have been proposed to deal with situations in which the indicators do not follow a multivariate normal distribution, particularly when they are asymmetric, ordinal or binary. Bayesian Confirmatory Factor Analysis (BCFA), which includes prior distributions for model parameters, has been used for such setups. Literature about CFA and BCFA for binary indicators is still scarce even though several applications in Epidemiology and Public Health could benefit from its use. Objective: To systematize and discuss the main characteristics and computational implementation of the CFA and BCFA with binary indicators in R and Mplus software for the measurement of antenatal care quality in Primary Health Care (PHC) in Brazil. Methods: Data from the external evaluation of the Brazilian National Program for the Improvement of Access to and Quality of Primary Health Care (PMAQ-AB) were used to assess the quality of antenatal care (construct). Ten binary (adequate/inadequate) indicators (items) were used in the measurement model considering the frequentist and Bayesian CFA. Results: CFA results (standardized and unstandardized estimates, goodness-of-fit statistics and factor scores) were provided in R and Mplus. Reliability measures, however, are not readily available in Mplus. Estimates from CFA and BCFA were close using noninformative priors. Sensitivy analyses for priors specification do not indicate substantial changes in the results. Conclusions: Measurement models with binary indicators, under both frequentist and Bayesian frameworks, should be considered more often as they can be applied in several health analyses for definition of constructs or latent variables. We provided a detailed tutorial, with recommendations and illustration of its use, that enhances the description of the characteristics of a population that can not be directly observed and/or are measured by a set of several indicators, such as quality of health care.