An Instrumental Variable Estimator for Mixed Indicators: Analytic Derivatives and Alternative Parameterizations.

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• The model-implied instrumental variable (MIIV) estimation framework has seen significant methodological development over three decades.
• Prior work established MIIV for continuous and ordered categorical endogenous variables, and introduced generalized method of moments estimators.

Purpose of the Study:

• To advance the MIIV estimation framework by introducing novel analytical and methodological contributions.
• To extend the applicability of MIIV to a broader range of data types and model specifications within SEM.

Main Methods:

• Derivation of analytic derivatives for the PIV estimator using matrix calculus.
• Extension of the PIV estimator to handle mixtures of binary, ordinal, and continuous variables.
• Generalization of the PIV model to incorporate intercepts and means, and inputting known threshold values for ordinal variables.

Main Results:

• The paper presents a generalized PIV model capable of estimating means, variances, and covariances for underlying variables in SEM.
• An empirical example demonstrates the application to a mixture of continuous and ordinal variables with fixed thresholds.
• A simulation study compares the novel estimator's performance against the WLSMV estimator.

Conclusions:

• The developed PIV estimator offers a versatile and robust method for SEM analyses involving mixed-type variables.
• This methodological advancement expands the utility of instrumental variable approaches in statistical modeling.
• The findings suggest the novel estimator is a viable alternative to existing methods like WLSMV for complex data structures.