* This program is for replicating Table 6.4 in the WandB textbook. set more 1 use happy gen rfaminc = faminc replace rfaminc = faminc/1.020356234 if year == 85 replace rfaminc = faminc/1.019083969 if year == 86 replace rfaminc = faminc/1.021628499 if year == 87 replace rfaminc = faminc/1.034351145 if year == 88 replace rfaminc = faminc/1.063613232 if year == 89 replace rfaminc = faminc/1.091603053 if year == 90 replace rfaminc = faminc/1.132315522 if year == 91 replace rfaminc = faminc/1.176844784 if year == 92 replace rfaminc = faminc/1.218829517 if year == 93 replace rfaminc = faminc/1.251908397 if year == 94 replace rfaminc = faminc/1.272264631 if year == 95 replace rfaminc = faminc/1.288804071 if year == 96 replace rfaminc = faminc/1.312977099 if year == 97 gen hap4 = happy recode hap4 0/5 = 1 6/7=2 8=3 9/10=4 gen age = 1900+year-gebjahr gen agesq = age^2 tab hap4 gen rlinc = log(rfaminc) * Reproducing the first column of Table 6.4 - the ordered logit ologit hap4 age agesq health rlinc unemp * The odds ratio form of the equation with accompanying Brant test o * of the Single Index (Parallel Regressions) Assumption. If the null hypothesis of * Parallel Regressions is rejected we should go to the generalized * ordered logit model that is estimated in gologit or gologit2. In * the case of the Happy data the null hypothesis of the Single Index * is rejected. Use generalized ordered logit model which is reported below. ologit hap4 age agesq health rlinc unemp, or brant, detail * Using the glogit2 command for estimating the generalized ordered logit model * This routine was authored by Richard Williams. See Williams_gologit2.pdf gologit2 hap4 age agesq health rlinc unemp * The odds ratio form of the equation gologit2 hap4 age agesq health rlinc unemp, or * Now for the computation of the Likelihood Ratio test of the Single Index hypothesis. * From the Ordered Logit model above we have a log likelihood value of -5680.0843. * This is the restricted model that imposes the Single Index assumption. * From the above Generalized Ordered Logit model we obtain the log likelihood * value of -5667.3121. This represents the fit of the unrestricted model because * we are not imposing the Single Index assumption. Then the likelihood ratio * statistic is -2log(lambda) = -2(logl(restricted model) - logl(unrestricted model)) * = -2(-5680.0843 -(-5667.3121)) = -2(-12.7722) = 25.5444. * The number of degrees of freedom of the chi-square test is 18 - 8 = 10 * where the number of parameters in the unrestricted model (gologit2) is 18 * while the number of parameters in the restricted model (ologit) is 7. * It follows that the p-value associated with the observered statistic of * 25.5444 is 0.004404 < 0.05. Therefore we reject the null hypothesis of a * Single Index. You can use the EXCEL function chisq.dist.rt to obtain * this probability value. Therefore, we see that the Brant and * Likelihood Ratio tests give the same result. The generalized ordered logit model * (gologit2) is to be preferred. That is, the Generalized Ordered Logit model, in this * case, is to be preferred over the Stanard (Single Index) Ordered Logit model.