Structural Equation Modeling: Applications Using Mplus

Appendix 2.D Calculating Probabilities Using PROBIT Regression Coefficients

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

(2.15)

(2.16)

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

(2.17)

For this function either the PROBIT function or LOGITSTIC function can be the appropriate link function to relate the observed variable y to factor . 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 ...