Interpreting Multinomial Logistic Regression Results: Sociology Example, Study notes of Sociology

Download Interpreting Multinomial Logistic Regression Results: Sociology Example and more Study notes Sociology in PDF only on Docsity! Sociology multinomial logit • interpreting multinomial logistic regressions; • recovering equations/comparisons not estimated • probability computations The data for this exercise comes for the 1991 General Social Survey. The categorical dependent variable occ is coded as follows: occ=0 if a workers occupation is laborer, operative or craft; occ=1 if occupation is clerical, sales, or service; occ=2 if occupation is managerial, technical, or professional. The independent variables are : educ is years of schooling; age is age in years; sexx is coded 1 male, 0 female; rural is coded 1 if grew up in rural area, 0 otherwise. 1. tab occ occ | Freq. Percent Cum. ------------+----------------------------------- 0 | 172 27.17 27.17 1 | 248 39.18 66.35 2 | 213 33.65 100.00 ------------+----------------------------------- Total | 633 100.00 Let’s begin with the null model with no regressors: 2. mlogit occ,base(0) Iteration 0: log likelihood = -688.49317 Multinomial regression Number of obs = 633 LR chi2(0) = 0.00 Prob > chi2 = . Log likelihood = -688.49317 Pseudo R2 = 0.0000 ------------------------------------------------------------------------------ occ | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- 1 | _cons | .3659343 .0992281 3.688 0.000 .1714508 .5604177 ---------+-------------------------------------------------------------------- 2 | _cons | .2137977 .1025124 2.086 0.037 .0128771 .4147183 ------------------------------------------------------------------------------ (Outcome occ==0 is the comparison group) The coefficients above are on the logodds scale. In particular, they are the log odds of being in occupation 1 versus 0 and 2 versus 0. Hence, they should equal the following: and the same for category 2: ln(231/172)=.2137977. docsity.com Now let’s add education to the model: 3. mlogit occ educ,base(0) Iteration 0: log likelihood = -688.49317 Iteration 1: log likelihood = -578.97699 Iteration 2: log likelihood = -568.79391 Iteration 3: log likelihood = -568.46166 Iteration 4: log likelihood = -568.4611 Multinomial regression Number of obs = 633 LR chi2(2) = 240.06 Prob > chi2 = 0.0000 Log likelihood = -568.4611 Pseudo R2 = 0.1743 ------------------------------------------------------------------------------ occ | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- 1 | educ | .2175129 .0495753 4.388 0.000 .120347 .3146788 _cons | -2.341483 .6221847 -3.763 0.000 -3.560943 -1.122024 ---------+-------------------------------------------------------------------- 2 | educ | .7404903 .0630034 11.753 0.000 .6170059 .8639747 _cons | -9.937645 .8608307 -11.544 0.000 -11.62484 -8.250448 ------------------------------------------------------------------------------ (Outcome occ==0 is the comparison group) To get the coefficients on the odds ratio scale we just add the option ,rrr like so: 4. mlogit occ educ,base(0) rrr Iteration 0: log likelihood = -688.49317 Iteration 1: log likelihood = -578.97699 Iteration 2: log likelihood = -568.79391 Iteration 3: log likelihood = -568.46166 Iteration 4: log likelihood = -568.4611 Multinomial regression Number of obs = 633 LR chi2(2) = 240.06 Prob > chi2 = 0.0000 Log likelihood = -568.4611 Pseudo R2 = 0.1743 ------------------------------------------------------------------------------ occ | RRR Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- 1 | educ | 1.242981 .0616212 4.388 0.000 1.127888 1.369819 ---------+-------------------------------------------------------------------- 2 | educ | 2.096963 .1321158 11.753 0.000 1.853371 2.372572 ------------------------------------------------------------------------------ (Outcome occ==0 is the comparison group) docsity.com