In ordered logit, an underlying probability The coefficients and threshold points are score for an observation of being in the ith estimated using maximum likelihood In the response category is estimated as a linear parameterization of SPSS, no constant function of the independent variables and appears because its effect is absorbed into a set of threshold points(also called cut the threshold The SPSS output provides single values for The probability of observing response ategory i corresponds to the probability that the estimated linear function, plus each X variable) are the main items of random error, is within the range of the interests in the ordered logit table. (One of threshold points estimated for that the advantages using Stata is that odds ratios are available) Pr(response category for the jth When b=0. x has no effect on y. the outcome=)=Pr(-1<b, X,+ b2X2+ effect of x increases as the absolute value bkxk+u ski) of b increases. There are not separate b One estimates the coefficients b,, b2,.b, coefficients for each of the outcomes(or ne minus the number of outcomes as we along with threshold points k,, k2,..., KH-1 have seen in multinomial logistic here i is the number of possible response categories of the dependent variable. All of regression in which we considered logistic this is a direct generalization of the binary gression with a nominal dependent ariable) logistic model5 9 • In ordered logit, an underlying probability score for an observation of being in the ith response category is estimated as a linear function of the independent variables and a set of threshold points (also called cut points). • The probability of observing response category i corresponds to the probability that the estimated linear function, plus random error, is within the range of the threshold points estimated for that response. 10 • Pr(response category for the jth outcome = i) = Pr(ki-1 <b1X1j + b2X2j + … + bkXkj + uj ≤ ki) • One estimates the coefficients b1, b2, … bk along with threshold points k1, k2, …, ki-1, where i is the number of possible response categories of the dependent variable. All of this is a direct generalization of the binary logistic model. 6 11 • The coefficients and threshold points are estimated using maximum likelihood. In the parameterization of SPSS, no constant appears because its effect is absorbed into the threshold points. • The SPSS output provides single values for the b coefficients. The b coefficients (one for each X variable) are the main items of interests in the ordered logit table. (One of the advantages using Stata is that odds ratios are available) 12 • When b = 0, X has no effect on Y. The effect of X increases as the absolute value of b increases. There are not separate b coefficients for each of the outcomes (or one minus the number of outcomes as we have seen in multinomial logistic regression in which we considered logistic regression with a nominal dependent variable)