Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 14log odds (x 0 +1) = a + b*(x 0 + 1) = a + b*x 0 + b,such that the increase from x 0 to x 0 + 1 in the log odds is b. Thecorresponding odds increase is exp (b). For example, consider thecontinuous covariate age with a logistic regression coefficient of .75 fora dependent variable of being depressed (u = 1) or not being depressed(u = 0). This means that for an increase of one year of age the log oddsof being depressed versus not being depressed increases by .75. Thecorresponding odds increase is 2.12.For a binary covariate x scored as 0 and 1, the log odds for u = 1 versusu = 0 are,log odds (x = 0) = a + b*0,log odds (x = 1) = a + b*1,such that the increase in the log odds is b as above. Given themathematical rule that log y – log z is equal to log (y / z), the differencein the two log odds,b = log odds (x = 1) – log odds (x = 0)= log [odds (x = 1) / odds (x = 0)],is the log odds ratio for u = 1 versus u = 0 when comparing x = 1 to x =0. For example, consider the binary covariate gender (1 = female, 0 =male) with a logistic regression coefficient of 1.0 for a dependentvariable of being depressed (u = 1) or not being depressed (u = 0). Thismeans that the log odds for females is 1.0 higher than the log odds formales for being depressed versus not being depressed. Thecorresponding odds ratio is 2.72, that is the odds for being depressedversus not being depressed is 2.72 times larger for females than formales.In the case of a binary dependent variable, it is customary to let the firstcategory u = 0 be the reference category as is done in (1). When adependent variable has more than two categories, it is customary to letthe last category be the reference category as is done below. For anunordered categorical (nominal) variable with more than two categoriesR, the probability expression in (1) generalizes to the followingmultinomial logistic regression,442