Inferential implications of normalizing binomial proportions in a structural equation model: A simulation study...

Area of Science:

• Statistics
• Biostatistics
• Veterinary Epidemiology

Background:

• Structural Equation Models (SEM) often lack explicit handling for binomial outcome variables.
• This necessitates using normal approximations of empirical proportions, which can impact health-related outcome inferences.
• The study addresses the inferential implications of these approximations in SEM.

Purpose of the Study:

• To assess the inferential implications of specifying binomial variables as empirical proportions in SEM.
• To compare model performance when binomial outcomes are treated as binomial versus proportional predictors/outcomes.
• To evaluate the practical utility of these SEM strategies in a beef feedlot health context.

Main Methods:

• A simulation study was conducted using generated data on body weight, morbidity count, and average daily gain.
• Two SEMs were fitted: Model 1 (binomial outcome, proportional predictor) and Model 2 (proportional outcome and predictor).
• A proof-of-concept data application on beef feedlot morbidity (BRD) was performed using SEM extensions.

Main Results:

• Model 1 demonstrated accurate structural parameter estimation and adequate confidence interval coverage.
• Model 2 showed poor coverage for morbidity-related parameters, indicating model misspecification.
• Both models had sufficient power for parameter detection, and Model 2 showed potential for mediation analysis despite interpretability issues.

Conclusions:

• Normal approximation of binomial disease outcomes in SEM is a viable strategy for mediation inference and prediction.
• While Model 1 (binomial outcome, proportional predictor) offers better interpretability and coverage, Model 2 (proportional outcome and predictor) may be necessary for testing mediation.
• Careful consideration of model specification is crucial for accurate interpretation of SEM results involving binomial outcomes.