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# Statistics for Sociologists III SOC 362

UW

GPA 3.77

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This 6 page Class Notes was uploaded by Deron Effertz on Thursday September 17, 2015. The Class Notes belongs to SOC 362 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/205179/soc-362-university-of-wisconsin-madison in Sociology at University of Wisconsin - Madison.

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Date Created: 09/17/15

smut 352 mltmemal legxt mteeptetmg mh1t1neme1 1eg1et1t tegteemnt tetevetmg equatxansca vpaxxsans nut eetmetee yxababxlxty canvputatxans The eete tee th1e exexcxse met tee the 1991 senete1 same shtvey The teteget1te1 eeyeneent vet1et1e ace 1t teeee et fallcws ace 0 1f e wethete etthy en 1t 1etet tme et teett ace 1 1f etthyetmn 1t t1et1te1 ee1ee et eemte ace 2 1f etthyetmn 1t managexxa tethmte1 et yxafessxanal The meeyeneent vet1et1et ete eeht 1t yeett cf schaalxng ege 1t ege 1n yeete texx 1t teeee 1 male 11 female thee1 1t teeee 1 1f gteu up 1n thee1 etee a ethemee 1 teh etc etc 1 Fteq yettent chm Letvt hegm mth the he made mth he tegtettett 2 melt etheee1u 1tetet1en a 1eg Jxkelxhccd regs 17 hh1t1neme1 tegtetemn uhmtet cf ete m 1 th121a1 a an ye t gt th12 Leg Jxkelxhccd regs 17 yeeh e 2 a noun etc 1 cef ste tt 1 rgt1z1 1m cnf Interval 1 1 tent 1 man man 3 ass a nun 171mg 560077 2 1 ene 1 2137177 11125121 2 use a 117 a12s771 11171 Outcaan etc 11 1t the campaxxsan gtehw 1he teettmehte eheve are eh the lagedds ete1e 1h pattxmlat they are the 1th adds es hem 11 ecmpatxm 1 versus a and 2 versus a heme they shauld equal the fellewmg 114 248 1117 3559343 172 2137977 and the me in categety 2 1111231172 m let39s add edeeetleh te the model ln 111 312mm 1 Q d n 0 a2 322 u a neeglt gee edeeheeeml Iteratxun av leg Jxkelxhuud rags A9317 Iteratxun 139 leg Jxkelxhuud 7578 97699 I e en le 11kg ee 5 6166 le ks heltlnemlel eegeeeelen Number 2 eh LR man no 06 179 gt W2 a noun Leg Jxkelxhuud esas ml Beetle x2 0 ms eee Cuef Std ee 1 17gtle 95quot lt1an Interval l l eeee 2175129 M95753 a ass a one 1203M 31A 7SS eene 72 mass 2218A7 es 762 a one es sansas 7 2202A 2 l eeee mourn moms ll 75 a one 6170059 s6397A7 eene es ssms senssm ell sun 0 one ell msa es 2snus Outcame eee a le the eemeeeleen geeeey Tu get the eeemelelte eh the ewe eetle eeele we just add the egtleh ue lxke ee 4 weglt gee eduuybasew quote Iteratxun av leg Jxkelxhuud rags A9317 Iteratxun 139 leg Jxkelxhuud 7578 97699 Iteratxun 239 leg Jxkelxhuud esas 7939 Iteratxun 239 leg Jxkelxhuud esas A6166 Iteratxun av leg Jxkelxhuud esas ml heltlnemlel eegeeeelen Number e2 eh 633 LR man no 06 179 gt W2 a noun Leg Jxkelxhuud esas ml Seudu x2 0 ms eee m Std ee 1 17gtle 95quot lt1an Interval l eeee l 2A2981 0616212 a ass a one l l27sss l 369819 2 l l 2 096963 ls2llss ll 75 a one l ssssn 2 272572 Outcame eee a le the eemeeeleen geeeey 1he retereretstreh er the eees tatxu 1s analogous te ugxstn regressan Elmme t est Dry 1 expt 2175129 1 2129s1 she 51m1a21y ter esteeery thsh eeeh1ee 12 n9 ter eseh ehe yesr 1 re e 1h sehee11he Recovenhg coefnmehcs not esnmced whet 1 the etteet et ehe addxtxuna yesr et sehee11he eh the eees et heme 1h accupatxun 2 rsther thsh 17 T1115 campatxsun wss het estmstee heesese accupatxun a wss husm es the hsse esteeery st111 we esh recover the relevant eeettmehts trem these thst were reeertee abuve For exse1e seeeese we wsht the campatxsun et accupatxun 2 te accupatxun 1 takan the 1stter es the hsse campatxsun esteeery Then we have 1n m 7 a1 32 7 mm heme 1t ehe addxtxuna yesr et sehee11he xncteases the ugudds et eee 2 xnstead et a by um she xncteases the ugudds et 1 xnsbead et a by 2175 the1 1t rheresses the ugudds et 2 verses 1 takan eee 1 es the hsse esteeer by 4 217 5229 z 7 l 274047 2175 5229 ete thst thrs 1s 1dentxca txu ter esteeery 2 te the eees s ery Tu get the eees rstre we jest take expt 52 the hsse estee 29 saw u asxde trem reeherhe ettut te the tatxu er the eees rs tatxu t ty 1 trem the r tessxun abuve wrth a s 2 n91 2 1h s smulat fashxu s11 the retereeets e cueffxcxmts trem s m1t1hems1 teqtessxun thst takes 1 es the hsse esteeery esh he reeeveree trem the rese1ts abuve hs sh exerciSE h shehm she be te dc th1s se thst yen get the fallavu39ng results 5 h1e91t eee eeeehssem Jog hkehhocd em 9217 Jog hkehhocd em 97699 Jog hkehhocd eseg 7991 Iterathon 3 log hkehhocd eseg met 1 etathon A Jog hkehhocd eseg m1 Iterathon a he1t1eee1e1 regressm number i ehs e 1 mm 2m as 17th gt m2 a noun Log hkehhcod eseg m1 udo 2 a 1m ess Coef std rr r mu ssh Conf Interval a ehes 7 2175129 msvs VA 3322 a am 7 31mm 7 12am cons 2 mm e221w 3 m a mm 1 122024 3 seam ehes 5229774 051m 10 1s a mm 42211237 e237711 cons 77 sse1e1 Mamas V10 25 a nun es 1mm rs 1mm Outcome see 1 1s the nonpathson greey Note that the education coefficient for the comparison of occupation 0 to occupation 1 is identical in magnitude but opposite in sign to the education coefficient for the comparison of occ 1 to occ 0 Now that you know how to recover coefficients and odds ratios by hand here s a command that does it automatically and covers all possibilities 6 listcoef educ mlogit N 633 Factor Change in the Odds of occ Variable educ sd 27166amp Odds comparing Group 1 Group 2 b 2 Pgtz eAb eAbSth 1 2 052298 10169 0000 05928 0 2415 1 0 021751 4388 0000 12430 1 8056 2 1 052298 10169 0000 16870 4 1403 2 0 074049 11753 0000 20970 74758 0 1 021751 4388 0000 08045 0 5538 0 2 074049 11753 0000 04769 0 1338 Probability interpretations How about computing the probability of being in each occupation for a gi en value of schooling To o this ask stata to compute the probabilities with the following command 7 predict p0 p1 p2 Now to get these for each year way destroys your original data of schooling value I did the following which by the fil 8 collapse mean p0 p1 p2byeduc Then I summed the probabilities for each vlaue of educ 9gen summpp0 p1 p2 10 list educ p0 p1 p2 summp educ p0 pl 2 summ p 1 3 08438 01559 00004 1 2 4 08127 01866 00008 1 3 5 07768 02217 00015 1 4 6 07359 02611 00030 1 5 7 06899 0 3042 00059 1 6 8 06385 03499 00115 1 7 9 05817 03963 00220 1 8 10 05192 04396 00412 1 9 11 04506 04743 00751 1 10 12 03763 04923 01314 1 11 13 02977 04842 02181 1 12 14 02194 04435 03371 1 13 15 01485 03731 04784 1 14 16 00919 02871 06210 1 15 17 00525 02038 07437 1 16 18 00281 01358 08360 1 17 19 00144 00866 08990 1 18 20 00072 00536 09392 1 Notice that for each value of education the probabilities as given by summp sum to Here39s eh exemje es umyutxng the pzubabxlxtxes I an u in me as edulzl yeeee expe994 74052du5 A d 16 Z 2 M 1 expe234 1175201145 expe9947405mm mm 15 67544 6210 108772 eh exeeheee ye shuuld try te umpuba A me as the hthez pzubabxlxtxes et me hthez 1eve1e es eduhetmh te make me ya hm hrm uete thet the effect as e hhe yen hhehge 1h eeheen heth 1h rmtwetnm 2 dePaAds ah the vejue es ethem just lxke the bxnizy me end he due tn the fact hehnheee smhtmh es eeheenhg he ah the pzubahxlxty as eey mg thet we start seem Thus he thet the pzubibxlxtxes ere e sociology 362 properties of least squares fit 1 regress hrwage edyr Source 1 SS df MS Number of obs 515 F 1 513 9772 Model 1 198006338 1 198006338 Prob gt F a 00000 Residual 1 103948996 513 202629622 Risquared 01600 Adj Risquared 01584 Total 1 12374963 514 240758035 Root MSE 45014 hrwage 1 Coef Std Err t Pgt1t1 95 Conf Interval edyrs 1 823475 0833033 9885 0000 6598174 9871327 icons 1 71774601 1116715 71589 0113 73968497 4192961 the next command creates Vector of residuals 2 predict rsdihatresidua the next command creates Vector of fitted y hats 3 predict wageihat mean sum of fitted yhats sum of observed y39s therefore mean of yhats of y s sum of residuals is zero therefore mean of residuals is zero summ wageihat rsdihat hrwage 4 Variable 1 Obs Mean Std Dev Min Max Wageihat 1 515 9088874 1962718 48132 1304795 rsdihat 1 515 684e09 4497059 8051 1624595 1 515 9088874 490671 335 2629 hrwage independent variable xedyrs has zero correlation with residuals the fitted yhats has zero correlation with residua regressor x and yhats have same correlation with dependent variable y 5 correlate hrwage edyrs wageihat rsdihat obs515 hrwage edyrs wageihat rsdihat hrwage1 10000 edyrs1 04000 10000 wageihat1 04000 10000 10000 rsdihat1 09165 00000 00000 10000 Note the correlation of 9165 between the dependent variable hrwge and the residuals rsdihat Here s where it comes from R24216 1 R21 1684 ll R2 v8 9165 The sense it makes is this If the correlation between the dependent variable and the independent variable is the s uare root f Risquared then t e correlation of the dependent variable and the residual must be the square root leRisquared

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