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From |
"Luis Ortiz" <luis.ortiz@upf.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Coefficients of mlogit and predicted probabilities as generated by prtab and prgen |

Date |
Fri, 17 Jul 2009 13:35:42 +0200 |

Hi, I am puzzling from what I judge as diverging results (different sign) of interaction terms in a multinomial logit model and predicted probabilities, as generated through prtab and shown graphically through prgen and graph. I am doing research on the returns of human capital investment in terms of occupational attainment. For some theoretical reasons, my dependent variable (occup_att_2, see below) is built as follows: 1. Managers 2. Professionals 3. Associate Professionals 4. Clerks, 5. Lower service and other occupations ?Clerks? is my reference category in the dependent variable. I have applied a multinomial logit model to the sample of one of my national cases of study. My data set is the result of merging different cross-sectional surveys corresponding to eight different years; I am using labour force surveys for up to eight years. Since I am especially interested in looking at the TREND in the returns of human capital investment, I have made interactions of the variable ?year? (capturing the different years included in the data) and educational attainment. Here, I present the results of one my models. I have excluded the coefficients corresponding to other indep vars I'm not so interested in. . xi: mlogit occup_att_2 i.tert_ed*year_3 sex_2 mstatus_2 age national_2_2 national_2_3 tenure per > m_2_2 perm_2_3, b(4) nolog i.tert_ed _Itert_ed_1-5 (naturally coded; _Itert_ed_3 omitted) i.tert~d*year_3 _IterXyear__# (coded as above) Multinomial logistic regression Number of obs = 525579 LR chi2(68) = 432135.20 Prob > chi2 = 0.0000 Log likelihood = -414328.03 Pseudo R2 = 0.3427 ---------------------------------------------------------------------------- -- occup_att_2 | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+-------------------------------------------------------------- -- Managers | _Itert_ed_1 | .8369161 .1164738 7.19 0.000 .6086317 1.065201 _Itert_ed_2 | -.5057224 .1448549 -3.49 0.000 -.7896329 -.221812 _Itert_ed_4 | -.1405644 .1441132 -0.98 0.329 -.4230211 .1418922 _Itert_ed_5 | .4043363 .1040787 3.88 0.000 .2003458 .6083269 year_3 | .0006106 .009962 0.06 0.951 -.0189145 .0201357 _IterXyear~1 | .024218 .0122985 1.97 0.049 .0001133 .0483227 _IterXyear~2 | .033616 .0151505 2.22 0.026 .0039216 .0633103 _IterXyear~4 | -.0013059 .0143873 -0.09 0.928 -.0295046 .0268927 _IterXyear~5 | .000611 .0112359 0.05 0.957 -.0214109 .0226329 _cons | -3.208653 .0965292 -33.24 0.000 -3.397847 -3.019459 -------------+-------------------------------------------------------------- -- Profession~s | _Itert_ed_1 | 3.870921 .1599636 24.20 0.000 3.557398 4.184444 _Itert_ed_2 | -.5270488 .1966783 -2.68 0.007 -.9125312 -.1415665 _Itert_ed_4 | -.3029058 .2470132 -1.23 0.220 -.7870428 .1812312 _Itert_ed_5 | -2.130236 .24443 -8.72 0.000 -2.60931 -1.651162 year_3 | -.0705025 .0171069 -4.12 0.000 -.1040313 -.0369736 _IterXyear~1 | .058865 .0177997 3.31 0.001 .0239782 .0937517 _IterXyear~2 | .1749493 .021033 8.32 0.000 .1337253 .2161732 _IterXyear~4 | .0403727 .0249201 1.62 0.105 -.0084698 .0892152 _IterXyear~5 | .0838841 .0262562 3.19 0.001 .0324228 .1353453 _cons | -3.485732 .1563276 -22.30 0.000 -3.792128 -3.179335 -------------+-------------------------------------------------------------- -- Associate ~s | _Itert_ed_1 | .5250349 .088949 5.90 0.000 .3506981 .6993717 _Itert_ed_2 | .2204853 .0970563 2.27 0.023 .0302584 .4107123 _Itert_ed_4 | .219423 .1074958 2.04 0.041 .0087351 .4301109 _Itert_ed_5 | -.2276642 .0876818 -2.60 0.009 -.3995174 -.0558111 year_3 | .0345487 .0073366 4.71 0.000 .0201691 .0489282 _IterXyear~1 | .0072084 .0093549 0.77 0.441 -.0111268 .0255436 _IterXyear~2 | .0260399 .0102047 2.55 0.011 .0060391 .0460406 _IterXyear~4 | -.0186982 .0106685 -1.75 0.080 -.0396081 .0022117 _IterXyear~5 | -.0133634 .0093698 -1.43 0.154 -.0317279 .0050011 _cons | -.8378662 .0728109 -11.51 0.000 -.980573 -.6951594 -------------+-------------------------------------------------------------- -- Low servic~r | _Itert_ed_1 | -.6625195 .0883424 -7.50 0.000 -.8356674 -.4893716 _Itert_ed_2 | .7419491 .0849377 8.74 0.000 .5754743 .9084238 _Itert_ed_4 | 2.149201 .0871306 24.67 0.000 1.978429 2.319974 _Itert_ed_5 | 2.418502 .0701088 34.50 0.000 2.281091 2.555912 year_3 | .0643842 .0063551 10.13 0.000 .0519284 .07684 _IterXyear~1 | -.0171698 .0091566 -1.88 0.061 -.0351165 .0007769 _IterXyear~2 | -.0339005 .0089674 -3.78 0.000 -.0514763 -.0163247 _IterXyear~4 | -.1356851 .0087742 -15.46 0.000 -.1528822 -.1184881 _IterXyear~5 | -.0473144 .0075397 -6.28 0.000 -.0620919 -.0325369 _cons | .2592752 .0623827 4.16 0.000 .1370073 .3815432 ---------------------------------------------------------------------------- -- (occup_att_2==Clerks is the base outcome) As you see, the coefficient of the interaction of time (year_3) and the dummy variable corresponding to the highest educational attainment (university degree) has a positive sign for the category 'Professionals' in the dependent variable. A university degree not only seems to increase the likelihood of being in this category, vis-à-vis the category of reference, but also that time seems to have an effect increasing this likelihood (versus the likelihood of increasing the possibility of finding yourself in the reference category (?Clerks?). For the sake of presenting graphically this trend, a) I have run another multinomial logistic model excluding interactions of time and educational attainment dummies. Please, note that I have JUST excluded the interactions of time and educational attainment from the previous model; apart from that, both models are identical. b) I have used the prgen command to generate the predicted probabilities corresponding to the variable 'year_3' time when the dummy variable corresponding to university degree (_Itert_ed_1) is 1, the other dummies corresponding to other educational attainment levels are 0 and (by default) the rest of independent variables are kept to the mean; prgen year_3, x(_Itert_ed_1=1 _Itert_ed_2=0 _Itert_ed_4=0 _Itert_ed_5=0) f(6) t(13) gen(univ) and c) I have generated graph by means of... graph twoway (scatter univp1 univp2 univp3 univp5 univp4 univx, connect(l l l l l) xtitle(University) ytitle(probability)) Now, the trend devised by the graph (not show here) reveals a DECLINING expected probability of being 'Professional' when you have a university degree. It corresponds to the decreasing predicted probabilities which appear when I run the prtab command as follows prtab _Itert_ed_1 year_3, x(_Itert_ed_2=0 _Itert_ed_4=0 _Itert_ed_5=0) ...I just show the predicted probabilities for the category 'Professionals' in the dependent variable mlogit: Predicted probabilities for occup_att_2 Predicted probability of outcome 2 (Professionals) -------------------------------------------------------------------------- tert_ed== | year_3 1 | 6 7 8 9 10 11 12 13 ----------+--------------------------------------------------------------- 0 | 0.0248 0.0240 0.0232 0.0225 0.0217 0.0210 0.0203 0.0197 1 | 0.6741 0.6662 0.6580 0.6498 0.6414 0.6329 0.6242 0.6155 -------------------------------------------------------------------------- Now my question comes. I do not understand that such decreasing probabilities appear when the interaction of year_3 and _Itert_ed_1 has shown before (initial model) to be positive. How could I interpret this discordance? How is it possible? As suggested in the guidelines of Statalist, I have looked for help in the Statalist itself, but I'm afraid I'm stuck with this problem. I would very much appreciate your help on this. In any case, my apologies for the query, if it results too long, and my gratitude for your attention, if you have reached this point. -.-.-.-.-.-.-.- Luis Ortiz Profesor Agregado Departament de Ciencies Polítiques i Socials Universitat Pompeu Fabra Ramon Trias Fargas, 25-27 08005 Barcelona Phone: +34-93-5422368 Fax: +34-93-5422372 http://www.upf.edu/dcpis/ http://sociodemo.upf.edu/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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