Table Of ContentSeries Number 07-031
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..
SAGEUNIVERSITYPAPERS
Series: Qu&ntitative Appliòations
irílbéSpciàI Qcinces
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Serieá Edito; MichaelS LewisBeck,UmverSilyof/owa
MOBILITY
Editorial Consultants
! Richard A Berk, Sociofog% University of California, Los Angeles
William D Berry, Political Science, Flonda Stato University
Kénneth A Bollen, Sociology, University of North Carolina. Chapel Hill
Linda B Bourque, Public Health, University of California, Los Angeles
Jacques A Hagenaars, Social Sciences, Tilburg University
:
Sally Jackson, Communications, UniversityofArizona
Richard M Jaeger, Education, University of North Carolina, Greensboro
Gary King, Department of Government, Harvard University
Roger E Kirk, Psychology, Baylor University
Helena Chmura Kraemer, Psychiatry and Behavioral Sciences, Stanford MICHAEL HOUT
University
Peter Marsden, Sociology, Harvard University Uni.v ersi. ty of Arizona
Helmut Norpoth, Political Science, SUN Y Stony Brook
Frenk L Schmidt, Management and Organization, UniversIty of Iowa
Herbert Welsberg, Political Science, The Ohio State University
Publisher
Sara Miller McCune, Sage Publicdtions, Inc
INSTRUCTIONS TO POTENTIAL CONTRIBUTORS
For guidelines on submission of a monograph proposal to this senes, please wnte
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Michaei S Lewis-Beck, Editor
Sage QASS Series
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DepartmentofPoliticalScience k SAGE PUBLICATIONS
Iowa CitJiÀ 52242 The international Professional Publishers
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Camden-Carrot! Librcü5
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Copyright © 1983 by Sage Publications, Jnc.
CONTENTS
rifAneoc lrwlom rrrdi igtioinhnrgt gs,b fyrore ros ambenyr yv t ahenmdey .ep iaNunnbfosol ,irp smhaerelatert .ico otfnr o tshntiioscr abogoreo kma nmedc arhyeat rnbieiecv araell, p sriyonsdcteulumcde, idwn ogitr h puohtuiotl itpzoeecrdom piiynss iianongny, Series Editor's Introductiofi 5
i . Analyzing Mobility Tables 7
For information address: The Basics 8
Sources ofMobilitY Data 10
ElementarY Operations i i
Publicatìons, Inc.
2455 Teller Road f Tests Applied to the Mobility Table 13
®SAGE
Newbury Park, California 91320 Odds Ratios 16
E-mail:
[email protected]
Mobility RatioS 16
SAGE Publications Ltd.
6 Bonhill Street 2. IndeVendefle ìn Parts of the Table 18
London EC2A 4PU
United Kingdom QuasiPerfect Mobility Defined 19
A LogLinear Model of Quasi-Perfect Mobility 19
SAGE Publications India Pvt. Ltd.
M-32 Market QuasiPerfect Mobility Results 21
Greater Kailash I Barriers to Mobility at the Top and Bottom: The Corners
New Delhi 110 048 India Model 23
Printed in the United States of America Symmetrical Associaton 25
3. social Distalict Models 27
International Standard Book Number Constrained Diagonals Models 27
O-8039-2056-3
Status BarTiers and Crossings Parameters 31
Library of Congress Catalog Card No. L.C. 83-060605 Mobility Models in Logit Form 34
4. Topological Models 37
The FenthermanH5er Model ofMobility to First
00 01 02 13 12 11 10 9 8 Occupations 38
Issues in Revising Models: Fit and Parsimony 41
Indeterminacy of Topological Models 46
WUadnhaipevntee rdsci it(tydi nePgpa epane dru sinneirgvi eeosrns ti itttyhle e p aasntpdye liren, cmlpuladeneau staehl e u upssaeep det)hr: e n upmrobpeer.r -Ofonrem o.f Rtheem foelmlobweirn gto f ocrimtea ttsh ec aSn abgee 5. SUcnailfeodr mM oAdseslosc oiaf tAiosns oc5i2a tion 51
Generalizations of Uniform Association 54
C(s1eA)r i:e ISsv aeogrnsee . Qn,u Gan. tiRta.,t iv&e NAoprpploitcha,t iHon. s( 1in9 7t6h)e. ASoncailayls iSsc ioefn vcaersi,a Nncoe. 0(S7-a0g0e1 U). nBiveevresriltyy PHailples,r MAAnnoaadllyyessliilssi ooff5 6AA ssssoocciiaattiioonn iwni tthhe t hUe. SD. iDagaotan al 5D8e leted 60
OR
similar Parameters Under Different Models 63
So(a2ng) QeI.v uearnsetinta, tiGv.e RA.,p p&l iNcaotiropnost hi,n Hth. e1 9S7o6c.i aAl nSacliyesnicse os,f vsearrïieasn cneo.. S0a7g-0e 0U1.n iBveervseitryly P Hapilelrs ,s eCriAes: EAq Cuoivmalpeanrti sMono d0eflMs_oRbeilpirtiys ein 6B6a itain and Denmark 66
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6. New Developments 68
Latent Structures of Mobility 69
ISntfaeturrsi,n gA uCtloansso mStyru catnudre T frraoinmin Mg oinb iOlictyc uPpaatuteornnasj M72o bility 76
7. Applicaj5 of Mobility Tables to Family and Religion 80
Occupations of Husbajds and Wives 80
Religious Assortative Marriage 82 Series Editor's Introduction
Religious Socialization 85
8. ConcJuj0 87 Mobility Tables by Michael Hout reviews all of the most widely
used methods for analyzing cross-classified data on occupational
References 88 origins and destinations. It should not be thought, however, that the
About the Author 93 volume is of use only to sociologists, or to a subset of sociologists at
that. As Professor Hout notes at the beginning and then expands on
near the end, the models and methods of mobility analysis can be used
in a wide variety of contexts. What distinguishes mobility tables is the
identity between row and column categories. Since this feature is often
found, the material reviewed and explained by Rout should find ready
application in a number of settings and disciplines..
Chapter introduces the basic ideas and tests designed to show
1
whether or not there is perfect mobility (which there seldom is). Chapter
2 considers certain kinds of partial mobility, as when there is limited
mobility in the very top or bottom categories. These models are special
cases of a more general model, which is developed in Chapter 3. The
material in this chapter assumes ordered categories, but it is important
to note that not all analyses of mobility tables require this assumption.
Chapter 4 covers a still more general model, one that incorporates
rather complex conditions of mobility and stability. In Chapter 5, the
focus changes slightly to that of socioeconomic achievement. The
methods used in this analysis and the assumptions on which it is based
differ from those of mobility research, as Hout makes clear at the outset.
Chapter 6 then dicusses some very recent papers to show the reader
the direction in which work on mobility tables is headed. Finally,
Chapter 7 shows by example how the method of mobility tables can
be applied to other areas.
Throughout the volume, care is taken to point out similarities and
differences among models. To further that goal each model is applied
to data on mobility from father's occupation to son's first occupation
from Featherman and Hauser's 1973 study of the American labor force.
Since it is expected that many readers will attempt to reproduce the
results in the book as a means of understanding the models, results are
presented in enough detail that interested researchers can validate their
efforts. Although the book does not contain detailed instructions for
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especially problceommaptiuct ecra sperso. grams, computing advice is rendered in MOBILITY TABLES
apauePdrpB ilesienecc,ca aebuM isoleioft b yosi tfloui tifdyt set hntTehts aom braloeentusdh g oshrdhe 5osy euebaltdr ecly uhobceenir dds a. cntho evi mecropangoferi tnaaennsdt ovbfo emlcuaomubseiel itofyof r tr heaes e Wawriicddhee
MICHAEL HOUT
-Richard G. Niemi University of Arizona
Series CO-Editor
t. ANALYZING MOBILITY TABLES
Social mobility is one of the most studied topics in social science.
Interest in intergenerational mobility goes back to Marx and Weber,
yet new findings and analytical developments come faster and more
furiously in this field than in any other in sociology. This intense activity
is warranted by mobility's place in our understanding of social stratifi-
cation. Because the structure of intergenerational mobility gauges
the persistence of material advantage from one generation to the next,
answers to fundamental questions about opportunity, class, and
privilege depend on the correct specification of that structure. To
appreciate this point, compare the variety of conclusions about oppor-
tunity in capitalist society reached by Lipset and Bendix (1959: 57-60),
Lenski (1966: 411-415), Blau and Duncan (1967: 432-441), Wright and
Perrone (1977), Featherman and ilauser (1978: 481-495), Brieger
(1981), and Rout (forthcoming).
Many methodological developments have advanced the study of
mobility in the past fifteen years. Some of these advances are quite
technical. While I have tried to keep technical detail to a minimum, at
least a nodding familiarity with recent developments in the analysis of
cross-classified data is necessary before some models can be appre-
ciated. Fienberg (1980), Knoke and Burke (1980), and Clogg (forth-
cming-) are good introductory sources. On the other hand, the reader
need not be up on the latest in latent structure models, quasi-uniform
AUTHOR'S NOTE: ¡have benefited greatly from the comments of Cl Word C. Clogg,
Otis Dudley Duncan, Robert M. Hauser, and Michael E Sobe? on drafts of this book.
Thanks to each of them for their he/p and advice. lam also grateful toJo Migliara, who
typed and retyped my manuscript, and io Sherry Cooksey. for her carefuiproofreading.
The original research reported here was paid for by the University of Arizona.
7
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awsisllo bciea tiinotnro mduocdeedls ,a so nr etwhe mlikaete. riWalh. en these models are relevant, they pressme locomotive firemen, aircraft mechanics, telephone repair
mawpioptnnDlieocesgavsrte ialotpohnhpes m dcaearinefnf t usc bsoiienvo entarh epoedp f sl iitpneuad dCt yhth o oa afpn amtanelyory bs7sii.sql i.ut yaT rqheue i tcamkblolyed .ep laSss ospm troee s oentnohtneedrm foiineb litldhitsiys- micno eanCn s,o didmaisentptdiaan trcitaoot bofcit1ll a i1tsafys n dpwdeo itsdtehiicte ittO ihomfenl a ckooefd rtisnr)eg, n tpdhrseo ioàrre dtriueerp etlsoic oamfti opannas aotg fse tpumrdeeivetis o piusus ta ssn touthtdheiemesr
is an impoaflt goal, 0parabi1ity is of paramount importance. In
The Basics such instances the 0erridg concern should be to replicate the coding
of 0thers as closely as 0ssible (e.g., Baron, 1980).
Occupational mobility tables Five occupational categories will be used in most of the examples
daomorOltrecasfheso conctfetbuhc keiimniuprreilrn aipa aetsotgtayydiuic oto biictbnsotnaju oee n bap cv sliuaatseca ' sstas hrie ia irotatfdaesnharnb e aoetasllohcf te sf.hteo ateaieerTrtsr i nr iwdhg as teeiwt rhcni psamicoo;tlne iem roonkt pshtsfamehoo ettds eni ioco on 'lonsmapantm cset cee ocrum rsoirmc nroirorrgp dnooetnioi idnnsw nmiose tng- arlevotcsi s. gta lc oiaogriscTns i rfuasso k hsvpibowonefaalcy coeriti einii.woa oaapgelbTnrne c lmul .rhioe asepen Fosor.i so bni ptAmrmtishshlo ioetipeit c asny oedot c,tr cse ccsnccstocioatosuourt nitmpdupun 'saisoasamn ,ttufft igiii oaobtroo hlsnnunnlttey . ot iabtHuInh nsi doleett iOheipmdtmaygien sg ofo,c r oirb5sean1y rt oam 9 t ohssGo7l tecek2rturhsi h).ego .sed aAaoicmnittnc e fse uBaeshsipwnn-.or a adiw tTtet h aisxdhoei anee ntimhs smatce iparyap nelrrotoeaee euTst dlggcia tuioohtalfsinrOfanoeie,es Un rssseaset nihnovçtftidefho,iPtn i,mh so tab eiamrnsbeeind gOtnafow ii lnnoryctesh laksyetaeit _ nnse s u gdttotehs ohjfpefd ereftd iei h(e fcssseisiuaetvn iemlde ntF y-aaGeai nat gtaoiiancufo llaicdrdyn tae tes sn hceg1e rasopvpo trreerPooiefgefelcs tos eeema rneeainoendtrdsse -.
toionr Atcchuufirtrserr erem nnstote nlooeocccgcctiruunappgpaa hott.ii rooiMnng ioinissb iiainlnnitttedyrr a gfgreeonnmeer ravfataatitirohoinaenabral'lsl e m ,mo oacosbcb iuiliniplti aytmyt.i .oo Msnt o otbofi lstihutyeb jfeerxoctam'ms ffpiirrlesstts apreer saornrSa ytehda ti ns htahree saemaceh ocrodmerb. iTnhatei ocnel los fo of rtihgei nt aabnlde. gdievset itnhaet icoonu.n Ltse ot fi
oepoTdDmtfbgca ihaeifomctecaiflcurto.ettoaih,pi ern uboomeas1asinnd t9lleamiait s7o st r 7yocusnoyo )a scao.c fttt colae c fE ub mbfgucde pvloapOoee eatrdatsebnitcate.eigi ic oifltsooliuhin. tnnr piymaiseaMea l dlnu sat d io sunoataitsiamnnn tttblla d ayebte ll sshcce a i reaoTrrseag n ddirUodcet eeulfab e.d e Scncssecs.ea. t t o uTcidte(ndeCodU hxgaetdieipo.etodseSnils r odois.a is iune i nc itDmass n o v ( htdeiafcahlsuepanol reat giraad oas oegrmDbsogt ceimld eefcoaeliapua,rbsec ter,aplnaa g e1ratt doer it9 toemeon ci8ftondcuf1oae n uu)mirLn(.lsc p Ft ta btOtha heitbeotoeovaaior fno etn ar hort n,n dLh efcaae aer11oullcmb 92ycric47r,ocssa0a4e7iuirn0ost1n)'-es .0n t - ULUoppwppeeerrr NNNOteLanUnmUuaCatOf lUuaaIl PFCSPSCrrartaooteorc11ftapseeei1SftcsS)itsSaCePSiittToO OeWm5nfr)talSfo5s,ll rlS0S ko . e tnrrhseSaoet lnraua frxfleai etoadtiu lr ìng
tghoeroCierrsei ttaiecrreai aln aofont rdw speelrlla edgcemtvineagltoi cap nec doa.n pcTpehrreno spc,r riilatietterhi aen uusmedb ebry o mf oosctc ruespeaatriochnearls c matiex- Lower Manual CCSOerrparaevffrtitascSmte1i vfweelneso,, r kCoOetfhrlseS rt TUCtl0fl
tcWahcïamnaethvt epeiseglgloeseooc t,ri rifgyoiotea ehrstcee"e om c srnrcheeaolsonafmesut saslidm rdccob ehs ofntelmuao"rtnt ou dmirscnae oucro milsmfeut bs dtahd ienneeasues c m aidbtlpoh eoes ettrth hh spsaoo knanwfit solt l wereteoordhmn f pic c tuedreooanri-dfpffc fetomoesa smlrnfoleeoadb enrro niet lf mswi (tckteyhloei.a legnrslrk .e.se, a d evTnes aean.hna wlgeldyFsr o sc aorisetvskrhhn eeeiasrsremurs sxte,s.o -, : Farm OLLFFMaaapbbnremooIrarr eeettianrrvssb e,,ao snor. edtmhr s,fear arnar nuc'ft oaumcfr atiOunnracgignc esUr sP t
Figure 1 Five.CatOßofl'
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oninraidtgieoixnn tia hraeen drtho edw esssa tmainnead t( iaoj tn tl heje.a sWct oahlsue mnfa nir s aa;n sd ft hj ieas roethc etch uenp uasmatimobneea,r lo orfi gpine rasnodn sd ewsittih Çjgç5 OccupationT AbBy LSEo tn 's First Occupation
ciuit mohsenemi s siofucdobaberinrjnlee eicd dtt ssihuis neitbni nmjl eagtchatuetiesinrms hsdi seai coarvtegriei oogirnmnyinsa m.sli mooabfpn itoldher e.t adTtneahtsb etli fendo.ai rsTt timihonenacysnt )iya.o r neTo sbhf peetesthwece iec acellmea nclso lesmsdli lfeosiiln cbsb ai eltwetcioo aha nuinbc sdiehen FOuapctcphueepria'sNt ioonn mlat NonUim,p4pa1en4ru al NoLnmoS5wao2ne1nru ' sa lO ccMuUpap3anp0tuie2oar ln MLoanw6u4ea3rl Far4r0a T2,o9t2al0
sdcTrteleahasptisutOsosi snirc ft"acyiomtna ifssgotouie nobbnsnioj l,ea icmctlcoyltayusr s pakssasmtsot a imutooiupmbneswi a"plolai o ttryrvhdot aelaryrrtinai g atmbiv bnlaoelsersb i aialbientsal, de ki .tme hd emTenahso itbsidcn iriliaofseft s,ie sobor-neacr nsdlda,t sposrwfsiaoofncirmemwtideca. erb.drI eylnys Mse otmaeorraiobcgdbihil inieltseroy,s.f LuFTLpaooorwptwmaeeelr r r MNMoaannnumuaaall f lual 4,777415290064891 2,596932651444748 2,284675452741641 3711,,,,397662510715863 ¡28,2213436027858 124649,,,,,200695081533620
ttvtuMhhoweneernoie cgtubesoiiinnninrmlr tgsiertt p ayhlatlan heinstcsmeetdifa dto tyc du(ro wDmeson sifuestit shitdnm ni catauedonatedbani oanuti,al tntcit .1stea oy 9mtr i6iinos6pgt n;ati an t Batusown so ra druaeneo ydlpdaff otatt oenihtdonnh,a en etds1ds rta9ho'sis7tnuie ap5spao s) tpo.c iv rocinFienuno s omplsster.haeo nsteeTbci xoiehdtlan hieattm eoytipa n pc prt loohbeemebrr,y r lo mseepcselmaot,ao tmtcb stieitiiobsrulr nciidnttnu yhi mieb oanseift-gs.- : goOefafaf tTokomrhlrtaose n tbrotdeiol ichMtcoyaal ovtlaiebenlc io lbtig Getduyerae netS a ahttt uo eodBorney r.mm i otNaaofio ntbnhtyi ala iibnmtty l eso 1a ib9emsi 4alte9irht l eyyya eGnseatfderuf. nod LeAriteri sapsl a lsba reSrgyte oe ia-cGnsnicadldaale lsSpeBseu 'csenro nvd(nd1eetCiy9nx5 mt'(s 4NPi )nO (Osv1rtBe9ausX5-dtC2Yiy-),
icftolaarlsiT csUaiifzb.ieSelde.s . fmIaM etghnoie svrt2e' ss0e xoataconmc u6pep4lxea astymi eoianpnr l setb h yioos sf f o banaog 'esom kfi ionrrb estfi1 lef9irut7 yl3tl o-. ttiaTtmbhhlieese . c tdiaTvibaihllgeiiasö. nnt aaolbc lcceue lplcsar toiaosrsne- bE1a9les8im0s).e , nwtahrYic ho pgaetrhaetiros ndsa ta on intergenerational mobility on a regular
Sources of Mobility Data The 1ementary procedures used to analyze any cross_classification
are useful starting places in the analysis ofulobility tables. Perhaps the
bt(Dfshuuoueanrtp t cdMcapdeee l.iooren r nmsesTtt uch ihestenmine otd dteonsaUir b rtgteao.ioSelc fi n.ctt t iyPaehon Breena dt ub teaMieroroet faunaa M sDuarecc l.ad ohomvB m fiiCl nodeat bh u utLiher flr.r eia eto nCyFanmdn eeta an arPOlsestyhuou tsnierspsiv rosu mec tDloyo apafsult aln ideoro cltanef tn oe yddmSf D uteRhdrumevaon tebbdacyeeea rrcnoisten)n n M oa1nmfn9i. a6dotHlh2 b c ieain(e luu inltsn1asye9dub r7eso)a3,.rsr mopItcahterfn eoe nidp ssst eatei trngcnhecuetteleessse nr .tcm gottoahemTelgneunhea emte rrardy aonri toyw sitou opt rotn eifprprbrletecoeulfrew rtecfnairle otto naitpnwoogtesan e rgwtc shoee fifeasont hsrtrl a iaaonigcnbwn redorfo sol rpos w scewcr_sorea cc lcppoeuloaertnmu5r rtcdc5arnoe egi flndetuiphtC samee bagra ncytesides s 0 tni.o5ho stu tfeaTri tg stifh htbelweoetsuh w ottteeiaf o orbpsmcnerlea e trssl.Toc c eTrfuoae nblfafdat bleaeteprligs eeotte rInio2s.--
oafs itnhdei vi1d9u7a0l sC. ensus collected data on prior inotcrcaugpeanteiroantsio noaf la m soabmilpitlye noaf titohnes gfoivre ne acohri gciant egoocrcyu poaft ioorni.g inT;h teh ei nifmloawg e pies rocfe nltaabgoers flroewcoinrdg othuet
lmsiocomebAneisln eisot ytrtaeh. tceeors r' dsvosi tuianrlc Ierne dcooifa rndmaso psboyillsiistte ymi sd saa. ptRai ooingse oetfhrfei'sn gm(1 s9atur5rd3iya) g aoenf a irlneytcseoirsrg doe nfs eemrcaatitroiroinan gaoelf dfsTliuohsbwtersriitebna guna ttriieioan lnta o vl soaotfrh iaeloa trirgoigginevi nedansim fffdoeoernrseg tni ecnoaeaccsthc iou bnped taewotsicteoicennunsap tiiiaonnt infobl;on ow.tt hh Tae i nhndiefm looaUwgu.et Sfa .l noisddw ao otfafuo trlsf alhpoboawowrr-.
ticular occupational categories.
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TABLE 2 TABLE 3
Inflow and Outflow Percentages for Mobility from Father's Indexes of Dissimilarity Between Pairs of Origins (below the
Occupation to Son's First Occupation diagonal) and Destinations (above the diagonal) for Mobility
from Father's Occupation to Son's First Occupation
Son 's Occupation
Occupation
Father's Upper Lower Upper Lower
Occupation Noninanual Nonmanual Manual Manual Farm Total Upper Lower Upper Lower
Occupation Nonmanual Nonmanual Manual Manual Farm
Inflow Percentages
Upper Nonmanual 34.5 17.6 11.5 8.1 1.8 14.7 Upper Nonmanual - .169 .310 .353 .483
Lower Nonmanual 17.7 17.7 9.7 8.8 2.1 11.3 Lower Nonmanual .163 - .155 .192 .688
Upper Manual 19.5 21.9 32.6 21.1 4.8 20.5 Upper Manual .308 .200 - .158 .640
Lower Manual 18.4 30.8 29.4 41.8 10.5 30.1 Lower Manual .384 .276 .157 .607
Farm 10.0 12.0 16.8 20.2 80.9 23.4 Farm .499 .407 .367 .354 -
Total 100.0 100.0 100.0 100.0 100.0 100.0
Outflow Percentages
proportions for lower thanual occupations and those for farm occu-
Upper Nonmanual 48.4 17.8 10.3 22.0 1.4 100.0
Lower Nonmanual 32.1 23.3 11.3 31.2 2.1 100.0 pation is:
Upper Manual 19.5 15.9 20.9 41.0 2.6 100.0
Ls=.l26-.O88+.l52-.O77+.128.O95+.554-.346r.354
Lower Manual 12.6 15.2 12.8 55.4 3.9 100.0
Farm 8.8 7.7 9.5 34.6 39.4 100.0
Total 20.6 14.9 13.2 40.0 11.4 100.0 The index of dissimilarity measures the proportion of cases that would
have to be reclassified in order to make the two sets of outflow pro-
portions identical. Table 3 presents the index of dissimilarity for each
Inflow and outflow percentages are informative at a very low le»el
pair of origins and destinations.
of analysis. While they provide some information about the process of
social stratification, other processes related to the relative supply and
demand of labor power from different strata also influence the inflow Tests Applied to the Mobility Table
x2
and outflow patterns. For example, the high fertility offarmers coupled
with a decrease in the proportion of the U.S. labor force in farming Another elementary operation in common use is the x2 test. The
contributes to the unbalanced inflow/outflow pattern for farm occu- test of the null hypothesis of no association is routine in the analysis of
pations. While only 39.4 percent of farmers' sons follow their fathers cross-classified data, and it is certainly germane to the analysis of
into farming, 80.9 percent of farmers in 1973 have farm origins. One of mobility tables. In fact, the model of statistical independence that
the objectives of the statistical modeling techniques to be covered in underlies the x2 test has a substantive interpretation in the context of
this book is to control for extraneous forces like the redistribution of mobility table analysis.
the demand for labor in the U.S. (or other) economy, and differential Suppose that the distribution of origins is fixed by the labor demand
conditions faced by the fathers and by differential fertility among
fertility.
Another elementary operation is the calculation of the index of dis- origins. Suppose further that the distribution of destinations is fixed
similarity between the outflow proportions for two origins or between by the demand for different types of labor within the national economy.
the inflow proportions for two destinations. The index of dissimilarity If sons or daughters are randomly assigned to destinations subject only
is the sum of positive differences between two proportional distribu- to these two constraints on the marginal distributions, mobility is
tions. For example, the index of dissimilarity between the outflow perfect in the sense that the odds on arriving at any one destination are
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Freqnencies Expected UTnAdBeLr EM 4o del of Perfect Mobility J(oR l-a r1g)2e dseagmrepelse so ft hfriese sdtoamtis tiifc t hies dnuisltl rhibyuptoetdh easpisp riso txriume a(twelhye raes Rx 2e qwuaitlhs
from Father's Occupation to Son's First Occupation the number of rows [and columns} in the table). lt is quite common to
Son's Occupation find references to equation 2 às "ehi-square" itself. But although this
Father's Upper Lower Upper Lower statistic is distributed approximately as x2 when the null hypothesis is
Occupation Nonmanual Nonmanual Manual Manual Farm Total true and the sample is large, the formula for the x2 distribution is
different. Thus I will designate the statistic in equation 2 as X2. Another
LUUoppwppeeerrr MNNoaonnnummaala nnuuaall 468604411...035294 436330458...632672 325389846...489500 11,,619360370...004003 243563642...271885 224,,,209582360 stitoantiss tiisc tchoamt mis odnilsytr iubsuetde da sa pwperlol:x imately as x2 under the same assump-
Lower Manual 1,236.36 893.58 791.07 2,399.15 682.84 6,003
Farm 957.70 692.18 612.78 1,858.41 528.94 4,650 L2 = 2 f1 log (f1/F) [3]
Total 4,101 2,964 2,624 7,958 2,265 19,912
where log is the natural logarithm function. L2 is quite different from
completely determined by the marginal distribution of destinations: Xo2f firne ecdoommp uift atthieo nn,u bllu th yitp tootohe issi sd iisst rtirbuuet eadn da s ifx 2th we istha m(Rp le- i1s) 2l adregger. ees
DoWfe hssettanint iamsttiioocbanilsl i itanyrd eies pinpedenerdfpeeencntc,de ee iansc tho o frfteo onwr i cgoailnfl seo.du Tttfhhleois w mi so pwdeerhcly eo ntfht paee gfreafsme ciistl itmahreo mbsaiälmidteyel,. tbees tIl fao rtfgh eethr n etu hmlla onhd ytephlo eo thfc eopsreirsre fsoepfco tp nmedrifonebgcit l ivmtaylo ucbeoi lniostnyis titssh efoa lfxs 2ce ,a dlbcisouttlrhai tbiXun2tg ia oXnn2d. aLSn2o d wt hLile2l
making the index of dissimilarity zero for each pair of origins (and for and comparing their values to the percentile value in a tabulation of the
ehcaoacvluhem ppnar)ie.r c Tioshef ledyre esfttohinree a,t siaothmnese ) .x 2p Orotfe pscoto ruitsri osienn,a vnlo okd eeidsmt rptiobir uidctieaotle nmr mionib nieelia tcywh h taerbtohlwee r w(ooilrrl Xwb2oe tdhfai siglt rrteioba utreteirjo etnch.t a tnIhf ethX 2ne uanllnu hdmy bLp2eo rt ahirenes tihlsee so stf a tpbhelaernf, e wcthte e mr enojeubcmitl ibttyhe;er inifnu X lt2lh heay nxpd2o Lttha2b easlreies,
antotrti btuhete do btsoe rsvaemd ppliantgte ernrr oorf. deviations from perfect mobility can be of perfect mobility. If the number in the table lies between X2 and L2
calTcuhlea tfiiorsnt sotfe pfr eiqn utehnec ixe2s teesxtp efocrte tdh eu mndoedre lp eorff epcetr fmecotb miliotyb.i liTtyh isis ethxe- (oau trLca2or emi s eoi unpttocrsoosmdibuelc)ee, dbth uneto btte esactsa uiass eicn hidet ecctkae nrom nb ien Xda2te eco.o r mtop omseadke inatno i nsudbetsetarmntiinvaetley
pectteesdt : frequency is the same as would normally be calculated for a and statistically interpretable components (X2 cannot). In fact, L2 is a
superior statistic; X2 is carried because it is so familiar. When these
r ntn/N procedures are followed for the mobility data in Table 1, we find that
[I] X2 r 7166.77 and L2 r 6170.13 with 16 degrees of freedom. With 16
where N is total sample size and n and n1 are origin and destination dsoe gtrheee sn uolfl fhryepedoothmes, itsh oef 9p5etrhf epcet rcmeonbtiilleit yo fis threej exc2t eddi sbtryi bau htiuogne ims a2r6g.3in0.,
marginaIs, respectively. All that is special is the interpretation of the Another index of fit is the index of dissimilarity between observed
model of independence (no association) as a model of perfect mobility. and expected frequencies. While the index of dissimilarity does not
Expected frequencies for the U.S. data are in Table 4. test the null hypothesis of perfect mobility (or any other null hy-
The second step in the usual x2 test is to compare these expected pothesis), its interpretation as the proportion of cases misclassified by
frequencies with the observed frequencies according to the formula: the model is appealing. The index of dissimilarity between the observed
frequencies in Table I and the expected frequencies in Table 4 is .201.
x2 = - F1J)2/F1J Thus the model of perfect mobility misclassifies one-fifth of the cases
[2]
in Table I.
j;
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r
16
17
Odds Ratios
TABLES
Odds Ratios for Basic Set of 2 X 2 Subtables from Table I
A not-so-elementary operation that will be important later on is the
calculation of odds ratios for adjacent rows and columns. For a 2 X 2 origins Destinations Compared
contingency table, the association in the table can be measured by the Compared 5.4 4.3 3:2 2:1
odds ratio (or cross-products ratio):
5:4 1.964 .836 1.300 1.098
a f11f22/f12f21 4:3 1.122 2.725 .707 .944
- [4] 3:2 1.489 .639 2.203 1.106
or some transformation (e.g., the natural logarithm) of a (see Goodman, 2:1 .722 1.464 .847 15.954
¡969a, 1969b, 1979a; Davis, ¡974; Fienberg, 1980). a greater than ¡.0
oianfsd stoihcceai ta(etRsio n-a . ¡pT)2oh soei dtaidvsses oraacstiiasootisco ifnao tirion t nha; e R a2 X Xl e Rs2s tsatubhblatena bc al¡en.0s bfieon red xipcpaarietressss oeadf anidne jgateacrtemivnset Gfrelaqsuse n(1c9y5 4f)o,r ththea mt coeblill ittoy rthaeti of refqour ecneclly i ,ejx ipse tchteed r autniod eorf tthhee ombosdeervl eodf
rows and columns of the full table (Goodman, 1979a). The order of perfect mobility:
rows and columns is a substantive decision that affects the odds ratios. RJ=fj/Fj
Goodman (1979a) refers to these 2 X 2 subtables as the "basic set" of [6]
smuabttiaobnl.e sT. hAusll tthhee (Rot her¡ )p2 oosdsdibsl er astuiobss toabf ltehse cfoonrmta:i n redundant infor- Although the R are useful for exploratory analysis (e.g., Hauser, ¡979),
R3 is more commonly used as a measure of the association between
ff1+,+ origins and destinations. Unfortunately, Ru does not measure the
f [5] strength of association.
twdpomofhodnbionblifheeeoroif r s c iegf dNcttfeteanc rhohhearretioo veslleeauepelti ii edr ninrnserrcad o oti gcq lec t otriap.ur haotd dmrfaeoantBdaeg enrhlsofdnnderi ursiadz ct ssnetfottoeej te oeh g. rwfd l. daretos ¡ hmItt h.omdAb0hinewmemodya)e ronn.ss iet o ysrl t i iclehdTtfuo rn haoa aeembnbh eretrt ltseee eli n hoeoa ct g o"uehdmqbasaoorf mee is uponrtgop l aieeter bUemedhrusaf neesretotr.tbtfa. "Sreel roeao n . osNocof snyatme tdifrhf lo stc d ltaeohnm 2p thtet id ofeoeeaooroaa feXnr nmb lsrdfliatal sesssir ir2so l.o cicaeo ui svdtgoc ttross yhsieidomeamuchae.lend lb ito p oarioTa,tawo spatbalfthsi .nra bhino paeil teliTn nir teteiit eep gnn hrysia rif a m a nsaeneTmtait qct pmc antmewutolahob dripadniefmeonl lll e es libl am eoab ylSoisbs(ssebl f. o aei itatsnmuNb layihuisims ismt oaoialey tttidttpfr aahtp.ii uey eslcabbeoi l Tìp eetll.jrtr r eecae ehdtrtiT oabn ihv cfsamhnld1bioaa eraet.syitrne-0. sl (oltwoaTddroiGiansofiefoyh tf snoinTtdTrfteohtpeeh o enihh.eeaerniedm eese nr aTmt fewn(dhotise ahxtinI eaernc opet9tomecrntesnu p7e ron,tonsiore3 rnmgttto aai1b)ih ds bv,rtl9omi oe e. lue6fon itordbo. t5taT of aby itd,b A shwbdlj taeleishrya1iessltoaocfe,9 tsysft tc tB 6oiteio-hmiohio9rcawaslbesenea bito j .bia iun; e trbo mmiteh TtacsiHina c o lttohomn.taiiiain tidohobuddsyTua en ias e slrihloisterDinnesg te a f trmyitttur cti,nohathi ec ehnoro naea al1aemca lb l tl9 t aaom r ii7otdfelsnfboaari8 obai etsb sts,aiy(rsi heqsllt l1ets 1erriopru f9r ttive9,lcuyeaeb 6et7eeinlt roiu7c9 adlitprc ir :ott,t an soeiisifsqeo9t ogu1air ibtsu3ntn9sg oa eoco-a8sr gsma9drte1 nn erhbi7wr )stteose.be )iim t iss qtlstwalBcaayytwl ues o tnhs eiaeeetneemttycdosds e meea otue mpincoeutlftorpoe fl h seanai ittsoses arhhatb se oiristeintacciido sh ft groa e rameiaiaifltaxolnsn .essy otp f mssstbae iFbae oomtndhaoibcuiccasd alrdtalriiiensvebeetaeaerdtyddxsye--l,-.
ginal effects, systematic association, and errors (both measurement and
sampling errors). The creators of the mobility ratio saw it as the ratio
Mobility Ratios
of systematic association to marginal effects They did not recognize
.
the existence or importance of errors.
of Bpeefroferec t mmovoibnigli toyn, tI ow mouoldde lsl ikthe atto a rdei smpoosree coof mthpele txo pthica no fth me omboilditeyl be Dacecseppittae btlhee m pereasseunrecse ooff aesrsroocri ainti othne bneutwmeeerna toorri,g imnso abnildit yd ersattiinoast imonasy
ratios. Invented by Goldhamer and popularized by Rogoff (1953) and if errors are insignificant relative to systematic association and if the
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n
18
19
marginal effects estimated under the model of perfect mobility are
unbiased estimates of the true marginal effects. These conditions seldom 1965, 1972a; Pullum, 1975) and a model that allows for symmetrical
hold for real data. barriers to mobility.
The third objection is that, in practice, a researcher has no way of Quasi-Perfect Mobility Defined
assessing the relative importance of error and systematic interaction
without reference to a model that fits the data. Once a model that fits is To analyze tables with an excess of cases along the diagonal, several
found, the mobility ratio is not needed; the association is better de- people (Blumen et al., 1955; Goodman, 1961, 1965, 1969a, 1969b;
scribed by the parameters of the model. White, 1963) proposed models that distinguish mobility from imito-
Hope (1981) defends the mobility ratio on the grounds that it always bility. Consider Goodman's version. According to this model, the
has the same value for a given table, while alternatives derive their observed pattern of mobility is the outcome of two separate processes.
value from the specific model fit. But it is the very insensitivity of the The first process-the immobility part-allocates a certain proportion
mobility ratio that is the problem. No matter what model is correct for of people ("stayers") to destinations that are the same as their origins.
a given mobility table, the mobility ratio is always the same. Therefore, The second process-the mobility part-resembles perfect mobility
it gives at best an imperfect clue as to the structure of association in the because it allocates the remainder of the population to destinations
table (Hauser, 1979). Worse, it is often misleading. The mobility ratio without regard to their origins. Some ofthe people allocated according
should not be interpreted as a measure of association. to this process may end up where they started; for them origin and
destination are the same-just as they are for the stayers. The difference
between these people and stayers is that while "stayers" do not leave
their origin status because of forces not accounted for by the model,
2. INDfl'ENDENCE IN PARTS OF TIIF TABLE the others aTrive by chance-just as the destinations of the movers are
arrived at by chance.
As discussed in the section onx2 tests in Chapter 1, the modelofperfect Goodman's model is a refinement of the mover-stayer model devised
.-. mobility does not describe the U.S. mobility data in Table 1. 1 now by Blumen et al. (1955). The original mover-stayer model divided the
move on to more complex models. The models to be considered specify population according to their destinations. All people whose destina-
perfect mobility for some combinations of origins -and destinations but tions were the same as their origins were classified as stayers. According
barriers to mobility for others. Within the zones of perfect mobility, to this mover-stayer model, the only people allocated by chance are
destinations are statistically independent of origins, but significant the people whose origins and destinations are different; perfect mobility
association exists elsewhere in the table. Much of the recent literature is specified as conditional on the fact of movement. While Goodman's
i on social mobility has addressed this very issue: the existence of perfect model of quasi-perfect mobility (QPM) shares many concerns with the
!I mobility between some occupational categories and the nature of the mover-stayer model and its extensions (Singer and Spilerman, 1974,
: barriers between others (e.g., Hauser, 1978, 1979; Breiger, 1981). ¡976), Goodman's treatment is more internally consistent-and more
! The first place to look for barriers to mobility is along the diagonal consistent with other mobility models. In the mover-stayer model, only
of the mobility table. The differences between observed and expected stayers are immobile. Under QPM, some nonstayers are immobile by
frequencies for the U.S. data showed more immobility than is expected chance. They are allocated to a destination identical to their origin on
under the model of perfect mobility. This feature is common. Mobility the basis of perfect mobility. Otherwise there would be an imper-
studies have repeatedly shown "excess" immobility of this sort (e.g., missible association between origins and destinations for this group,
Lipset and Bendix, ¡959; Blau and Duncan, 1967; Featherman and which is supposed to be perfectly mobile (by definition, perfect mobility
Hauser, i978). Goodman's (1961, 1965, 1968, 1969a, 1969b, 1972a) exists only when origins and destinations are independent).
model of quasi-perfect mobility addresses the immobility issue, and
it will be considered first. Generalizations of the model of quasi-perfect
mobility that include off-diagonal constraints on upward or downward A Log-Linear Model of Quasi-Perfect Mobility
mbaorbriielirtsy tow imll oablsioli tbye act otnhsei deexrterde.m Tesh eosfe tihnec lsutdateu sa hmieordaerlc hthya (tG aolloodwms afonr, To Hdaov isnog, sthpeec infoietda titohne mofo dloegl -vlienrebaarl lym, oI dwelisll ins oiwn treoxdpurecsesd .i t Tfohrem malolys.t
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