Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 14CALCULATING PROBABILITIES FROM PROBITREGRESSION COEFFICIENTSFollowing is a description of how to translate probit regressioncoefficients to probability values. For a treatment of probit regressionfor binary and ordered categorical (ordinal) variables, see Agresti (1996,2002).For a binary dependent variable, the probit regression model expressesthe probability of u given x as,P (u = 1 | x) = F (a + b*x)= F (-t + b*x),where F is the standard normal distribution function, a is the probitregression intercept, b is the probit regression slope, t is the probitthreshold where t = -a, and P (u = 0 | x) = 1 – P (u = 1 | x).Following is an output excerpt that shows the results from the probitregression of a binary variable u on the covariate age:Estimates S.E. Est./S.E.uONage 0.055 0.001 43.075Thresholdsu$1 3.581 0.062 57.866Using the formula shown above, the probability of u = 1 for age = 62 iscomputed as follows:P (u = 1 | x = 62) = F (-3.581 + 0.055*62)= F (-0.171).Using the z table, the value -0.171 corresponds to a probability ofapproximately 0.43. This means that the probability of u = 1 at age 62 is0.43.For an ordered categorical (ordinal) dependent variable with threecategories, the probit regression model expresses the probability of u440