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Structural Equation Modeling: Applications Using Mplus by Xiaoqian Wang, Jichuan Wang

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Appendix 2.D Calculating Probabilities Using PROBIT Regression Coefficients

Let us define U an observed binary indicator, y* the unobserved continuous response variable; img the latent construct variable or factor, underlying y* ; img is factor loading, and img is measurement error.

(2.15) equation

(2.16) equation

where img is a threshold, the probability of having U = 1 is:

(2.17) equation

For this function either the PROBIT function or LOGITSTIC function can be the appropriate link function to relate the observed variable y to factor img. Mplus uses LOGIT link for ML estimators and PROBIT link for WLS estimators. The default estimator for modeling categorical outcomes is WLSMV, thus the default link function is PROBIT. In Mplus ...

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