the social class structure of occupational mobility (breiger r., 1981)

7/29/2019 The Social Class Structure of Occupational Mobility (Breiger R., 1981)

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The Social Class Structure of Occupational MobilityAuthor(s): Ronald L. BreigerReviewed work(s):Source: American Journal of Sociology, Vol. 87, No. 3 (Nov., 1981), pp. 578-611Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/2778935 .

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The SocialClassStructurefOccupationalMobility1RonaldL. BreigerCornellUniversity

Thispaperprovidesnanalytical rameworkithinwhich ypothesesof class structurere broughto beardirectlyn theformulationfmodelsfortheoccupationalmobility able.The proper ggregationofrows nd columnssportrayeds thefundamentalheoreticalssueinmobilityableanalysis, ather han s an exogenousgiven"to bedecidedupon prior o the constructionfexplicitmodels.Homoge-neityof mobilitywithin nd between lasses, class hierarchy,ndtangible oundedness re the central hemes. hese themes re im-plementedn oglinearmodels ndapplied nthe nalysis f arge 17-category) ntergenerationalobility ables. Four such tables fromthe studies f Blau and Duncan and ofFeatherman ndHauserarefittedcceptably. even falsifiableypothesesboutthe social classstructure foccupationalmobilityre identifiednd assessed com-parativelywithin henewframework.A "social class" makesup thetotality fthose lasssituationswithinwhichndividual nd generationalmobilitys easyandtypical. Weber 1922) 1978,p. 302]

Ananomaly haracterizeshepresenttate ofsocialmobilityesearch. ntheonehand,following oodman's 1972) articulation f a generalmulti-plicativemodel or ross-classifiedata,someof hemost nnovativemodelsand most ophisticatedata analyses fcontemporaryociology ave beenformulatedo deal with the specifics f the occupationalmobility able(Baron 1980; Clogg 1981; Duncan 1979; Feathermannd Hauser 1978;Goldthorpe980;Goodman 979c;Hauser1979;Hope 1980b).On theotherhand, esearchnthis rearemainsargelytheoretical. here s a persistenttendency,ncreasinglycknowledgedy mobility esearchershemselves,for heempirical nalyses o talkpast the earlier nd classical heoretical1 RobertM. Hauser and David L. Feathermangenerously rovided the data from heirstudy (Featherman nd Hauser 1975, 1978) on which table 1 of thispaper is based. Igratefully cknowledge he detailed and productivecommentsof Harrison C. White,JohnF. Padgett,and Michael J. Mandel on four arlier rafts f thispaper, and the sug-gestions f JamesN. Baron, Clifford . Clogg, Otis Dudley Duncan, Robert M. Hauser,David Karen, David A. Lax, and Lauri L. Perman.Financial supportwas providedundergrantsSER76-17502 and SES80-08658 from he National Science Foundation.Requestsfor eprints hould be sent to Ronald L. Breiger, epartment fSociology,Cornell Uni-versity, thaca, New York 14853.??) 1981by The University fChicago. All rights eserved0002-9602/82/8703-0003$01.50578 AJS Volume 87 Number 3


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Social Class Structurestatements f Marx, Weber, nd Sorokin Aberg1979; Charvat, inhart,andVercernik 978;Garniernd Hazelrigg 976; Goldthorpe 980;Horan1974; see also Giddens 1973; Parkin 1979; Wright1979). Occasionallycritics eem content o castigate increasedmethodologicalophistication,[employed]o thedetrimentf ociological hought" Bertaux 976, . 394;Coser 1975), thereby dvancingneither ctivity.This paper attemptsconstructiveeformulation.Socialmobility nalysts o nottakesocial classes eriously:hat s theproblem. s nthe andmarkontributionfFeathermannd Hauser 1978),mobilitynalysts aveconsistentlyapproached hemobility ablewithoutstrong theoretical resuppositionsbout affinitiesmong occupationalstrata.Like Blau and Duncan, they] ave worked nductively"Feather-man and Hauser 1978,p. 140, mphasis upplied; ee also Clogg 1981] ndthe discussionnn. 6 below).My aim n thispaper s to develop n opera-tional onceptualizationf ocial class structure hich nables his onceptto be brought o bear directlyntheformulationfmodels or heoccupa-tionalmobility able.The explicit oal here s a theoreticallynformedonceptf socialclassstructures,hat s, "one [providing]or reconstructionfdata" (Merton1968,p. 144), and not theconstructionr reconstructionfterminology.My usageoftheterm class" ismuch loser o Weber's oncept f"socialclasses" more ully laborated elow) han o thevarious lassformulationsofMarx. It is not incompatible ith the latter nd may well providemeansofspecifyingheir mpirical onsequences. onetheless,hecoreofmy approach s social class as "the totality f . . class situationswithinwhich . . generational obilitys easyand typical,"with lass situationsdefined s "typicalprobabilit[ies]f . . gaining position n life" Weber[1922]1978,p. 302) andreportednoccupationalmobility ables.

My starting oint s therecognitionhat "the problem f the existenceofdistinctlass boundaries' . . is notonewhich an be settled n abstracto"(Giddens 973, . 110). argue hat dentificationfthe ocialclass bound-aries of occupationalmobility equires methods hat focus ttentionnturn nvarious ubsets f theentire mobility]able" (Goodman1968,p.1093). The general oglinearmodel of Goodman e.g., 1968, 1969,1972,1974, 1979c) provides herichest ontext ordeveloping pecificmodels.Thenewframeworkeveloped ere s formally special ase ofGoodman'sgeneralmodel.However, t addresses he conceptual roblem osed suc-cinctly y Vanneman 1977,p. 786): "The advances ntroduced yGood-man . . only ncrease he importance f selecting he appropriate ate-gorizationchemen thefirst lace. In stratificationesearch, or nstance,whatcategories o constitutehe empirical lassesof modern ociety,ndhowdoes thecompositionftheseclasses shift ccording o institutionalcontext rnational etting?"

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American ournal f SociologyThe followingection f this paper offers formulationf social class

that specifies ow to studyoccupationalmobility ables. point out itsaffinities ith nd departuresrom everal cceptedviewpoints. he newframeworks offeredn theform f three nterrelatedheses.Each thesismay also be read as a criterionor n acceptablemodelof the mobilitytable. The sectionheaded"Implementation"akesup eachthesis n turn;a model hatmeets hese riterias proposed orhighly isaggregatedi.e.,large)tables.My indebtednesso Hauser 1979) is made clearthere, s arethetangible ncompatibilitiesn our approaches.n the"Data Analysis"section he new frameworks brought o bear on 17-categoryntergenera-tionalmobilityables;four uch ables rom he tudies fBlau and Duncan(1967) and Featherman nd Hauser (1978) are fitted cceptably. evenfalsifiable ypotheses bout the social class structure f occupationalmobility re identifiednd comparativelyssessedwithin hisframework.THEORETICAL ISSUESA StatementftheProblemThe mostcrucialrespect n which heorists nd empirical nalystshavetalkedpast one anothermaybe statedas follows:Theredoesnotexistmodel fthemobilityable hat akes heproper umbernd compositionfoccupationalategoriess an explicitheoreticalecision. his lack of atten-tionnotwithstanding,heproper umberndcompositionf socialclasses,ranging rom wo classesto "an almost ndlessmultiplicityf class situa-tions" see Giddens1973,p. 48), is perhaps he most central roblem obe addressed y any theory f social class.Empirical esearchersave turned wayfrom etailed,highly isaggre-gated mobilityables.The aggregationfmobility ata, allegedly prior"to theconstructionf models and certainly rior o theconstructionfexplicitmodels),s thenormmong ocialmobilitynalysts. auser 1979),for xample,ums cross herows nd columnsfa 17-categoryable con-taining 89= 17X 17 cells)to obtain five-categoryersioncontaining25 cells), t which ointheclaimshebeginso applyhisnewmodel.But Iclaimthatthe reductionftheoriginal able to the smaller ersion, orwhich ncompleteustifications provided FeathermanndHauser 1978,p. 29) other hanthestraightforwardbservationhat"we wereunabletospecify esignmatrices or 17X 17 mobility ablesto our satisfaction"(1978, p. 181), constitutes crucial heoretical ecision,which s no lessimportantorbeing n implicit ecision.22Similarly,Goldthorpe, lewellyn, nd Payne combine ategories f a 36-categoryableso as toproduce seven-categoryersion, nd thenconfine heir xplicitmodeling ffortsto thesmaller able (Goldthorpe 980, pp. 38-42, 94-120). They explaintheir eduction580


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Social Class StructureCombining articular ategoriesf a variable an lead to thedeletion fparameters hat would otherwise e necessary Goodman 1973; Duncan1975), rto the nsertionfparametershatwould therwisee unnecessary,or to no change n the parameters Goodman 1979a, p. 1087; see alsoAllison1980). Even if a model s correctlypecified ora five-categorymobility able for xample), hisfact lone carries o implicationhatthemodelfits say) the 17-categoryable fromwhich hesmaller newas con-structed, r vice versa.3 he ubiquitous roclivityfempirical esearchersfor ombiningategoriesi.e., producingmaller ersions fa given able)in the absence of any consistent rameworkf sociological heory voids

confrontinghis ssue nd turningtto advantage. ndeed,Duncan's 1979,p. 801) recent esults suggest hat an importantimitation f previousanalyses as beentheuse oftoo highly ggregated ersions" fthemobilitytable; in particular, he "substantive lausibility" f certainmodelswasenhancedwhenDuncanapplied hem oan eight-categoryather han o afive-categoryersion fthe ame table.ThreeThesesonSocialClassStructuresUntil he1950s, ociologicalheoriesfthe ggregationfmobilityhanceswere nseparable rom heories f social class. The attempt o pull theseconcerns parthas falteredGoldthorpe 980,p. 38). It is nowtime tobring ocial class back n to an empirical onceptualizationfoccupationalmobility.histaskrequireshefocused eorientationf heoryndmethods,and the disavowalboth ofmethodswhose elaborate esthetics bscureempirical roblemsnd oftheorieswithno referento existing ata. Theessentialsftheframeworkpropose re offeredelow ntheformfthreeinterrelatedheses.

THE AGGREGATION THESIS: Withreferenceo a mobility able, socialof thegiven36 categories o thederived even,which hey hen erm classes," byreferenceto "the available evidence" ofcomparabilityn a varietyofcriteria Goldthorpe1980,p. 39). The problem ftranslatinghese ssorted riteria ntoa single artition foccupa-tionsmay be highlighted ynoting hat,even fthe 36 categorieswerefully ankordered(a more estrictivessumptionhan the one the authors ctuallyuse), the number fwaysto partition hem ntoa seven-category ersion hat preserves he orderingwouldbe inexcess of 1.6 million. Goldthorpe nd his co-workers re among the most thoughtfulresearchers ho have considered roblems f the aggregation f occupational categorieswithout, owever, ormulatingxplicitmodelsfor uch aggregation.3 "The fact that the methodspresented n this series of articles by Goodman] can beappliedwheneach variable canhave any givennumber fcategories oes not t all implythat theresultsobtainedwith thesemethodswill be unaffectedy thenumber fcate-goriesused witheach variable" (Goodman 1979a, p. 1089, original mphasis).A similarproblem exists with respectto finite tate Markov chain models (Kemeny and Snell1960; Bartholomew 967, p. 18) and with respectto the latent structuremodels of themobility able of Clogg 1981).

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American ournal fSociologyclass tructures a single artitionfoccupational ategoriesmposed imul-taneously norigins rows f thetable)anddestinationscolumns).THE INTERNAL HOMOGENEITY THESIS: Mobility romnyoccupation oany other s explained y the social class structure. pecifically:he de-pendence f destinationn origin the association frows and columns)is always erowithin he subtableformed y crossingheoccupationsnanyclass A and those n anyclass B (whereA and B mayalso index hesameclass).

THE CLASS HIERARCHY THESIS: Classes reordered ith especto typicalmobility hances. nterclassmobilitys governed y a smallnumber fparameterstating hedependencefclassofdestination nclassoforigin.The aggregationhesis erveswellto indicate hepresent isjunctione-tween heorynd methods.Manyotherwisencompatibleheories f classhave as a goal theprovision f claimsabout the aggregationfdefinitesocialcollectivities,or xample,Weber'spostulationffour ocialclasses,one ofwhich-thepropertylessntelligentsia-is omposed ftechnicians,civil ervants,nd "variouskinds fwhite-collarmployees"Weber 1922]1978,p. 305). However, o loglinearmodels fthemobilityable exist tpresent or he ggregationfthe ocialcollectivitiesndexed ythetable'srows nd columns.nstead,manyofthedistinctive ontributionsflog-linear modelsto sociological nalysis e.g., Goodman1965, 1968, 1969,1972, 1979b;Hauser 1979; see also Bishop, Fienberg,nd Holland 1975,pp. 206-10, 20-24;Pullum1975;White 963)result romhe dentificationofvarioushomogeneousetsofcells nterioro thecross-classification,ndtheconditioningf "structural" ffectsn theassignmentf cells to suchregions.As Baron (1980, p. 817) pointsout,thesecontributionstand nsharpcontrast o the usual treatmentf the table as a conceptual ndstatistical hole by equating he tructuralfectswith herow ndcolumnmarginals). iven he extensiveearch o identifyhomogeneous"egions,it is remarkablehat no loglinearmobilitymodelhas beenformulatedortheaggregatesf cells nduced ya simultaneousartitionftherows ndcolumns f a table.4In marked ontrast o this ack of attention n thepart of empiricalanalysts,t is preciselyhisform faggregationhat s mostrelevant o4These brief emarkswill be understoodmorefully ythe reader nconjunctionwith thediscussion f models 1) and (2) presentedn the "Implementation" ectionbelow. Out-side theframework floglinearmodels,various analystshave investigated ertaincon-sequencesof simultaneous artitions f a table's rows and columns; however, ee n. 5belowand relateddiscussion n the text. RobertHauser has pointedout to me that theunpublished issertationfBeland (1978) anticipatesmuch thesameidea as the aggrega-tion thesisof thispaper,as implementedn model 1) to be presented elow. Withrefer-ence to Beland, Hauser employsthis criterion a single partitionof categories ppliedsimultaneously o a table's rows nd columns)to "measure the nformationost n aggre-gatingthedata" (Hauser 1979, p. 450; Featherman nd Hauser 1978, pp. 180-84).582


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Social Class Structuretheorists f social mobility. o Sorokin [1927] 1959, pp. 439-40), forexample,t appeared natural hat here recleavagesnot o much etweenoccupational roups n the narrow ense of the word, s betweenbiggersocial subdivisions oing n along the inesofthe affine'nd 'non-affine'occupational ubdivisions.... These differences,eing einforcedydiffer-ences ntheeconomic tatus f uchclasses, reate basis forwhat sstyledas the present lass-differentiation,ith ts satellites n the form f ..class antagonismnd class friction."The "affine" ccupational ubdivisionsfSorokin re the socialclasses"ofMax Weber [1922] 1978, pp. 302-7, 926-39). Besideshis well-knowndifferentiationf "class" from status" and "party," Weber also dis-tinguishedsocial classes"from lassesbasedonpurely conomic riteria.Social class is a distinctiveoncept orWeberbecause such classes can bedefined nly nthebasis of n analytical ggregationfmobilityhances.

A social lass, nWeber's ense, s formedfa cluster fclass ituationswhichre inked ogetheryvirtue f thefact hat heynvolve ommonmobilityhances, ither ithin hecareer f ndividualsr across hegen-erations.... AsWeber imselfoints ut, henotionf social lass'comesmuch loser o thatof statusgroup' handoes the conceptionfpurelyeconomiclass althoughs with conomiclass ituations,ndividuals hoare nthe ame ocial lassarenotnecessarilyonsciousf thefact).Thenotion f ocial lass s mportantecause . [withoutt] t s possibleodis-tinguishnalmostndlessmultiplicityf lass ituations.ut "social lass"exists nlywhen hese lass ituationsluster ogethernsuch way s tocreate commonexus f ocial nterchange. . [Giddens 973, . 48]

The thesis f nternal omogeneity.-Themgibuity f the last sentencequotedabove reveals he nsufficiencyf the aggregationhesis, f t is un-coupledfrom he other wotheses, o accountfor ocialmobility. ertainanalystshavepartitionedows nd columns fmobility ables,either yad hoc procedures r by theuse of clusteringlgorithmsBlau and Duncan1967, p. 58-67; Hope 1972;Vanneman 977).Laumann 1966,pp. 89-104;Laumann and Guttman 966) has defined social class as "a subsetofapopulation etermined ypartitioning. . accordingo such associationalrelationshipss . . . kinship, riendship,nd common esidence," nd hasidentifiedccupational lusters n the basis of coordinates esulting romsmallest-spacenalyses.However, ll theseprocedures avoid the questionofhowmany classes exist n a society" Vanneman1977, p. 788).5 The5 In the same vein, none of these analysts addressesthequestion of the statisticalfitofhis partitionmodel to the data,which s a persistent oncern fthepresent aper.Johnson(1980,pp. 67-70) provides usefuldiscussion f Hope's "contingency ierarchies"modelin thisregard.The goodness-of-fitriterion pplied in Laumann's (1966, 1973) smallest-space analysesdoes not pertainto the aggregation foccupational ategories ntolargerunits.

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American ournal fSociologyproblems that, "while theremay be an indefinite ultiplicityf cross-cuttingnterests reatedbydifferential arket apacities, here re only,inanygiven ociety, limited umber f lasses" Giddens 973, p. 105-6).What s the theoreticalropertyfa social classstructurehatallowstherelativelynambiguousdentificationf "a limited umber f classes"?It is inhis answer o this rucial uestion hat therecent heory f Gid-dens 1973) arrives, ircuitously,ack at theposition fBlau and Duncan.After iscussing hisposition, indicatewhy abandon t in favor f thethesis f nternal omogeneity."A consistent atternof disproportionatelyow movements etweenoccupational roups s all that s meantby a classboundary ere" BlauandDuncan 1967,p. 60). Likewise, orGiddens 1973,p. 107):

By the . . term"mediatetructuration"]refer o thefactors hichinterveneetweenheexistencefcertain ivenmarketapacitiesnd theformationf classes s identifiableocialgroupings,hat s to say whichoperates "overall" onnectinginks etweenhemarketn theone handandstructuredystemsf classrelationsn the other. . Themediatestructurationfclassrelationshipssgovernedbove llby thedistributionofmobilityhances hich ertain ithin given ociety . . In general,hegreater egree f"closure" fmobilityhances-bothntergenerationallyandwithinhe areer fthe ndividual-the ore his acilitatesheforma-tion f dentifiablelasses.In brief,he pproach fGiddens,ike hat fBlau andDuncan,proposesonly n internal efinitionfsocialclasses,not a concept f classstructureor of globalmobility egime.or thesewriters,lasses reessentiallyocio-metric cliques"defined o thatmobilityhances either n average, rincomparison ith xpected alues under hypothesisf"perfectmobility")arehigherwithin hecliquesthanbetweenhem.The approaches f Blau and Duncan (1967, pp. 58-67) and Giddens

(1973, pp. 99-117) cannot be called "explanations" f mobility mongoccupationalategories; lau and Duncanareclear bout t. Anexplanationwould ead to thereproductionf theobserved ata on detailedmobilitybetween ach pair of occupations. uch an explanation remains o begivenby theanalystwhocan provide he nformation,nd workout thetechniques, hereby ariablesmaybe partialled ut of a typicalmobilitytable to thepointwhere ntergenerationalonstraintsn [occupational]destination avebeeneliminated"Hope 1980a,p. 10). My contentionsthat n explanationsprovided ytheconditionalndependencefoccupa-tionalorigins nd destinations ithin ach class and within ach pair ofclasses.The "variables which hould]be partialled ut" are themarginaldistributionsf an explicitly ypothesizedocial classstructure,s definedinthethesis n aggregation.66Comparethis criterion f internalhomogeneitywhichassumes the aggregation hesisof this paper) with the criterion f conditional ndependence pplied in models oflatent584


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Social Class StructureStatedpositively,he elf-consistentelation f ocialclasses ndoccupa-tionalmobilityakesthefollowingorm, ccording othe nternal omoge-neitythesis.Occupationaldestination epends on origin nlywhen thepartitionf occupational ategoriesntoclasses s ignored.his is the ensein which ccupationalmobilitymaybe saidtobe "explained y" the ocialclass structure.Or,statednegatively,heunits fanalysis or ccupationalmobilityresocialclasses.The researcher ho gnores heseunits onfronts rich ndvariegated ableau in whichoccupationalmobility and inheritance) sstronger ith espect o certain airsofoccupationshan thers.n general,

the arger hetablethemore ifficultt stovisualize hismosaic s a wholeand to interpretts structured attern of mobility and inheritance).Analysis f the mosaicmay thengive way to conventions f routine rtappreciation; hus: "It mustbe emphasized hatthere s certainly everanythingvenapproaching omplete losure"ofmobility hances n ad-vancedcapitalist ocietiesGiddens1973,p. 107).The proper artition foccupational ategoriesntosocialclasses, hen,is onewhich atisfieshe globalcriterionf nternal omogeneity.f thereis no suchpartition or given ableof mobilityhances, heapproach fthispaperclearly ails. f there s morethanone suchpartition,hisap-proachdegenerateso theextent hat the variouspartitions remutuallyinconsistentsee n. 9 below).Theclasshierarchyhesis.-Thediscussion o farhas emphasizedn ex-tremelytrong efinitionf social class whichgoes beyond partition foccupationalategoriesorequire hat hepartitionnduce globalmobilityregime. tillmissings any stipulationf an orderingmong heclasses ntheir rovision fmobility hances, o that"thepicture . . which merges... is onemarked utby a hierarchyfbroadoccupationalategories achstructure. oudon (1973, 1975) and othershave proposed, nd Clogg (1981) has formu-lated and implemented,atent structuremodels of the occupational mobility able. InClogg's models, class" is the termgivento each of thet latentcomponent ables (eachof size R X R, given R occupationalcategories) ntowhich the originalR X R table isdecomposed.Then thehypothesis s that "withinthetth atent class the manifest ari-ables . . . aremutuallyndependent" Goodman 1974,p. 215). In contrast, n thispaper"class" refers o a tangiblegrouping f occupational ategories-not to an arrayof atentR X R tables of mputedmobility ounts. The approachof Clogg (1979, 1981) and thatof thepresentpaper each yield substantive nsightsnot obtainable by use of theotherapproach.The class conceptof thispaper, n contrast o the class conceptof atent truc-turemodels,has therelative dvantages of a) capturing he usage ofSorokin nd Weber,(b) allowingthe propernumber nd composition f occupationalcategories o be takenas an explicit nd falsifiableheoretical ecision, c) leading o models hatfit argemobilitytables, d) avoiding he dentificationroblems iscussed n Clogg 1981), and (e) avoidingrecourseto a substantive ociologicalconceptualization n whichclasses are viewed asrelevant or ociological nalysis only s "inherentlynobservable" ntities Clogg 1981).The benefits f Clogg's 1981) approachfollow rom is provision fexplicitmodelswhichgeneralize nd resolvetheclassic mover-stayeristinction f mobility able analysis.

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American ournal fSociologyrepresenting differentositionn the scale ofmaterial nd nonmaterialbenefits"Parkin1971,p. 24).Such a stipulation s providedby the thesison class hierarchy. histhesis elates xpresslyo a reduced-formablehaving ne row nd columnfor achclass.Thus,a necessary reconditions that nternal omogeneityactuallyprevails. atisfactionf the criterionf nternal omogeneityn-suresthat mobility mong lasses is notconfounded ithmobility mongoccupations.This preconditionfurtherlaborated elow n the subsectionheaded "Combining ategories")distinguisheshe reduced-formablesstudyfrom he reduced-formablesof others see n. 2 above and relateddiscussionnthe text).Modelshave been proposed nd implementedo exploit he assumptionofordinality or he rows nd/or olumns fa table Clogg 1980; Duncan1979; Goodman1972, 1979b; evine 1972;Simon 1974); these models refundamentallynterrelatedGoodman1979c). f a mobility able containsa largenumber foccupational ategories, owever, he assumption f anordering f rows nd/or olumns ecomesproblematic,othconceptually(because of the increasing revalence f "horizontalmobility"Blau andDuncan 1967,p. 117]) and practicallysince here reR! possible rderingsamongR occupational ategories). or thesereasons, arguethatthe ap-propriate omainof applicabilityfmodelsforordered ategoriess notthe occupational categories ut the classes of such categoriesdentifiedwithin heframeworkresentedbove.Duality.-Taken together,he threethesespostulate dual structurefor heoccupationalmobilityable. What s soughts a single artitionfoccupational ategories, ppliedsimultaneouslyo the rowsand columnsof a mobility able. Internally,he rowsand columns f each subtableresultingrom hispartitionreunordered, ithno dependencefdestina-tionon origin. xternally,he classesare orderedwithrespect o typicalmobility hances, lass of destination epending ifferentiallyn class oforigin.IMPLEMENTATIONCriterionA modelshouldfit ts data. In theprecedingection have consistentlyidentifieds one component f "explanation" he abilityof a model toreproduce he observed ountsofdetailedmobility etween achpair ofoccupations. his criterions notwidely cceptedby empirical nalysts fmobility ables.7Withrare xceptionsGoldthorpe980, p. 104-8;Hauser7For a briefbut cogent discussionof "why a high evel of fitshould be demanded ofmathematicalmodels of mobility rocesses," ee Hope (1976, p. 728).586


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Social Class Structure1979,pp. 445-47) theirmodels roduce ignificantackof fit o thehighlyaggregatedableson which hey etto work. viewthisproblems arisingfrom he ackof a frameworkor ggregationuch as the oneproposednthe previous ection, nd the correspondingack of applicability f theexistingmodels o largetables.Seeking modelthatmaintains idelityothe detailed ellfrequencies,nowdescribe rocedureso implementachofthe three hesesnturn.NotationConsidern R X R tableofobserved ounts ij(i = 1, . ., R; j = 1, .R) and fitted ountsFij under specifiedmodel;R is thenumber foccU-pational ategories. s in theprevious ection,we supposefor ubstantivereasons hatthetable shighly isaggregatedR large).Thissuppositionsnot, however, equired orthepurely ormal evelopment. s usual,therowsrepresentccupational riginse.g., "father's ccupation") nd thecolumns epresentestinationse.g.,"respondent'sirstob").Models

The aggregationhesis.-This callsfor partition ftheR occupationalcategoriesntoc classes.Simultaneouspplication f thispartitionorowsandcolumns fthetableresultsn a partition fthecells the i,) intorect-angular ubtablesk (k = 1, .. , c2).Thethesis f nternalomogeneity.-Thisosits hattheobserved ssocia-tionof origins nd destinationss spurious; bsenceof associationquasiindependence)s specified etween rigins nd destinations ithineach oftherectangularubtablesk (compareGoodman 972, . 689; Hauser1979,p. 419). Consider he simplestoglinearmodel atisfyinghis hesis:Fij-= a3iYjk for (i, j) E Sk , (1)subject o theusualnormalizationfparametersHauser 1979,p. 417).Formally,model 1) is a specialcase bothofHauser's 1979) model seealso Goodman1972, 1979b,p. 810) and of the newmodel 2) presentedbelow.Neither fthe attermodels Hauser's model nd model 2] ofthispaper) however,mplies heother.Comparison fmodel 1) with he attertwomodelswillthereforeerve ohighlighthedistinctive eaturesmple-mented n the newapproach.Hauser 1979) partitionshecellsof table nto levels,"but heimposesno further estrictioneither n theory r in practice; ee Hauser 1978,1979; Feathermannd Hauser 1978; Baron 1980; Goldthorpe 980) thatthe evelsmust onstituteectangularubtables ormed y application fasingle artition o the rows nd columns f thetable. n Hauser'smodel,

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American ournal fSociologythe cells grouped ogethernto any subset "level") may in principle edrawn rom nywheren the table. Hauser (1979,pp. 416-17) emphasizesthat, for his]model o be informative,he allocation f nteractionevelsacross ellsof the tablemustform meaningfulattern.... I have foundit difficulto interpret odelswhere he number f nteractionarametersis largerelative o the number f categoriesn the occupational lassifica-tion." n practice, pecifyingn informativeefinitionf"meaningfulat-tern"may eadto "a bootstrap peration" FeathermanndHauser 1978,p. 145).The aim ofHauser FeathermanndHauser1978,p. 140) snota modelincorporatingocial classes; that is thegoal of the present aper. Sincetheories f socialclass typicallyoncern heaggregationfcategoriesndtheir elationaltructureWright 979,pp. 3-18) rather hanthe aggrega-tion of cells nterior o themobility able,a modelfor heaggregationfcategoriess desirable.Model (1) is formally restrictedpecialcase cfHauser'smodel, herestrictioneing hatthe partition fcellssatisfies heaggregationhesis.This criterion equires he analyst to postulate an assignment f eachcategoryn the tableto a social class (R assignmentsre requiredn all),instead f requiring ostulation fan assignmentfeach cell in the tableto a higher evelofaggregationR2 assignmentsre requirednHauser'smodel).As inHauser'smoregeneralmodel, achexpected requencys theproduct fan overall ffecta), a roweffect,3i), column ffect,yj), ndan interaction ffect6k). The overalleffects the averageof the fittedcounts their eometric ean).The column nd roweffectseflect eaturesofthe overalldistributionsfrespondentsnd their athersrespectively)into occupational ategories, onditioned pon the model's interactionspecification.he interactionffectstherebeingone sucheffect or achaggregatefcells dentifiedytheresearcher,here hese ggregates arti-tionthe table's cells) correspondo the "relativedensities" fmobilitywithin achrespectiveggregateHauser 1979;Baron1980,p. 818).Clearly,hefit fmodel 1) to argemobilityables s (essentially)lwaysmuchworse hanthefitofHauser's moregeneralmodel.This is becausethegeneral lexibilityffordedheanalystofdrawing ellsfrom nywhereinthetable nto levels" s sharplyurtailed ythe ggregationhesis. hecorollaryf thegeneral lexibility,owever,s thedanger f a haphazardanduninterpretableggregationfcellsthatHauserwarns gainst.It follows hatsomecrucialgeneralizationr loosening fmodel 1) isdesirable-a loosening hat avoids potentially rbitrary ggregationsfcells.I willnowarguefor differenteneralizationfmodel 1) fromhe oneprovided yHauser.The new model 2) exploits hesimplevirtue fthe588


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Social Class Structureaggregationhesis: levels"continueoberestrictedotherectangularub-tables Sk) formedrom partitionfoccupations. ach such subtablehasits own row and column ffects. systematicncorporationfthese ub-table effects,hileretaininghe partition ftheR occupational ategoriesintoc classes, s consistent ith hetheme f thispaperthatsocialclassesare the ource f"meaningfulatterns" fmobilityhances. hus,considerthe model Fij = a#iyjYkBikrjk for (i, ) e Sk X (2)subject o the normalizationsfmodel 1) and, naddition,

HifiBik = Hyjrjik = 1over ll i (all ) inthekth ubtable.These newparametersnsure hefit ftherow and columnmarginals f eachrespectiveubtable, husreflectingfeaturesftheoriginnd destination istributionshatarespecifico eachsocialclass.Model (2) is thusthe hypothesis f simplerow-columnndependencewithin ach subtable. For any particular ubtable,the expectedvalues(Fij) producedby model 2) are identical o the expectedvalues (F*ij)resultingrom ittingimple ow-columnndependenceo that ubtable:F*ij = a*f*iey*j for (i, j) ( Sk (2')

The equivalence f 2) and (2') is givenby:a* = Xak (3a)i3i = i3iBik for i e Sk (3b)y*i = Yjijk for j e Sk . (3c)

Thus,a* is theaverage geometricmean) ofthe fitted alues in thekthsubtable, is the average geometric ean) of the fitted alues n thefull(R X R) table, and ak iS theirratio.Similarly,*i is the effectf rowwithin he kth ubtable, i is the effect f row in thefull R X R) table,and B,k is their atio.Further iscussionsprovidednAppendix .Formally,model 2) is clearly ess parsimonious hanmodel 1): con-siderablymoredegrees ffreedomrerequiredofit headditional aram-eters ik and Fjk (see App. A). This relative ack ofparsimonyn theformalmodel s countered y theadherence f model 2) to the centralthemes fthispaper. The aggregationriterions satisfied y model 2),as is thecriterion finternal omogeneityi.e., model 2]mandates hatallodds ratioswithin ny ubtablek havethevalue ofunity). t isunlikelythatmodel 1) can be applied uccessfullyo largetables; model 2) is itsnaturalgeneralization ithin he conceptual rameworkortrayed ere.Moreover, hedegrees ffreedomxpended n fitting odel 2) are associ-589


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American ournalfSociologyatedwithobserved ounts fmobilityo and/or romocialclasses;thesecountsmay themselves e modeledexplicitlyn reduced-formobilitytables see table4 andrelated iscussion elow).Analysts fmobility ables oftendistinguishmobility the set of cellsfij, i 5? j) from immobility"the set ofcellsfii on the table'sprincipaldiagonal), onfiningheir xplicitmodels o theformeretofcells.Withinthe generaloglinearmodel, t is straightforwardGoodman1965; Bishopet al. 1975)to buildthis dditional estrictionntomodel 2), andI assumeit in the applications eported elow(see App. A forfurtheretails onobtaining itted alues).

Thethesis n classhierarchy.-GivenpartitionftheR categoriesntoc classesthatsatisfies he internal omogeneityriterion,nemay thenexamine hepattern fmobilitymong he classes. Further iscussionsprovided elow n thesubsection eaded"Combining ategories.") uchexaminationallsfor epresentationftheR X R tablebya reduced-formc X c tablecontainingne row nd column or ach class.Thehierarchyriterion andateshat he lasses omposinghis educed-form able re orderedndthat hedependencefdestinationlassonclassoforiginsgovernedya smallnumber fparameterseflectinghis rder-ing. I will mplementhis criteriony meansof theuniformssociationmodel fDuncan 1979;Goodman 979b, p.811-12)and"Formulation "ofSimon 1974;Duncan 1979;Goodman 979b, p. 810-11).TESTING HYPOTHESES OF CLASS STRUCTURE: DATA ANALYSISMobility ableanalysis equires n explicit nd falsifiableommitmentsto thepartitionfoccupational ategoriesntotangibleocial classes.Thisis theparadigmaticmplicationfmodel ramework2). Heretoforentestedcommitmentsbound s tothe socialclassstructurefoccupationalmobil-ity, incenon-MarxistheoriesHoran1978)as well s "Marxist heory . .[have]direct mplicationsor the relationshipetweenoccupations ndclassesas positionswithin hesocialstructure"Wright 979,p. 117; seealso Vanneman1977]on therecastingfsocial classhypothesess parti-tions foccupationalategories).The data analysispresentedn thissection s nonstandardn severalrespectswhich re anticipated ere.First,highly isaggregated17-cate-gory)mobilityables are employed,ndfour uchtablesfrom hestudiesof Blau and Duncan (1967) and Featherman ndHauser 1978) arefittedacceptablyby a particular ypothesis, ppliedundermodel (2) of theprevious ection. econd, nd most mportant,evenfalsifiableypothesesabout the socialclass structurefoccupationalmobilityre identifiedndcomparativelyssessedwithin hisframework.hird, n aggregatedight-590


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Social Class Structurecategorymobility able is fitted cceptablyby a model postulatingnordering fclasses n their rovision f nterclassmobility hances.Thesethree opics re treatedn the subsections elow,which akeup (in turn)the three heses ropoundednthispaper.The primary ocusofthedata analysisreported ere s a 17-categoryintergenerationalobilityablebased on theOccupational hanges n aGenerationOCG-II) supplemento the March 1973 Current opulationSurvey,underthe direction f Featherman nd Hauser (1975, 1978).Table 1 (a moredetailedversion ftableE.1 in Featherman nd Hauser[1978, . 531],whichwas kindly rovided y theauthors) eportsmobilityfrom ather's ccupationo son's first ull-timeccupation.8he fit feachhypothesis ill lsobe assessedwith especto three dditional 7-categorytablesofmobility ata arising rom eathermannd Hauser's 1978)studyandfromOCG-I" (Blau and Duncan1967).TheAggregationhesisHere I briefly eview ixhypothesesnd indicate ources or ach in theliterature n occupationalmobility. hen I developmyownhypothesis.(The details feachhypothesis-thats,of eachhypothesizedartitionfoccupationalategories-are rovidednApp.B).The conventionalriadH1).-Blau andDuncan 1967,p. 59) suggestheexistence f three lasses"partitioned ytwosemipermeablelass bound-ariesthat imitdownwardmobility etween enerationss well as withinlifetimeareers, hough heypermit pwardmobility." hese classes aretheconventionalriad: white ollar,bluecollar, nd farm.Thispartitionofthe 17OCG categories Blau and Duncan 1967,p. 58) is repeated nAppendix . The Blau-Duncanhypothesisrosefromxploratorynalysisofthreemobilityables.Within heframeworkfmodel 2), I will scertainits goodness ffit o the detailedmobility ata.TheproletarianizationypothesisH2).-Arguingthat owerwhite-collarworkersre coming ncreasinglyo resemblemanualworkers ithrespectto theirmobilityhances,Vanneman 1977,pp. 793-98) suggests three-classpartitionifferingrom lau andDuncan's nthat lericalworkersregroupednside heworkinglass,notwithwhite-collarccupations. ccord-ing to Vanneman 1977, p. 804): "The pattern f results s convincing.8More precisely: able 1 is a classification f son's first ull-timeivilian occupationbyfather's or otherfamilyhead's) occupation at son's sixteenth irthday, he sons beingAmericanmen aged 20-64 in March 1973. The reported requencies re based on a com-plex samplingdesign and have beenweighted o estimatepopulationcountswhilecom-pensating or ertain ypesofnonresponse, s detailed n Featherman nd Hauser (1978,p. 150, and App. B). The weighted ata of table 1 have been rounded o integer aluesfrom he unrounded ata (kindly rovidedbyFeatherman nd Hauser) that analyzed.

591


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17/35

Social Class StructureUtilizing wo differentperational efinitionsf similarity,wo differentstatisticalmeasures f association, wo differentategorizationchemes,andtwodifferenteographic ases,the analysis as supported single on-clusion.The lower-whiteollar workers]re clusteredwith theworkingclassas predicted y the proletarianizationypothesis." ike mostoftheotherwriters onsidered ere,Vanneman id notexplore hegoodness ffit fhishypothesisodata.The occupational lite hypothesisH3).-Hope (1972, pp. 173-79) pro-poses differentodificationftheBlau-Duncan artition. ope's "overallpicture s one of a three-classociety oppedby an elite" (1972, p. 178).Specifically, ope separatesself-employedrofessionalsrom he otheroccupationsn Blau and Duncan's white-collarlass. Blau and Duncan(1967, p. 72) had previouslycknowledged hat "the self-employedro-fessionalss a whole onstitute distinct conomic liten our ociety...."The differenceetweenBlau and Duncan's partition hypothesis ) andHope's (hypothesis ) arose fromdifferencesn theirexploratoryata-analytic rocedures; onfirmatorynalysis fthe tatistical it feither ar-titionwas not undertaken.Hypothesesf occupationaltrataH4, H5, H6).-Several mobilityableanalysts ombine ategoriesf17-categoryablestoproduce maller ablesas a preludeo their xplicitmodeling fforts,nd notdueto an overt on-cernwith ocial class structure. onetheless,he questionnaturallyrisesas to whether he subtables Sk) identified y thesepartitions xhibithomogeneitynternally. his questionwville addressedherewithin heframeworkfmodel 2). I consider hefive-categoryartitionfFeathermanandHauser 1978,p. 28; designateds H4 here nd inApp. B); the nine-category artition fPullum 1975,p. 116; designatedH5); and the 12-category artitionfFeathermanndHauser 1978,p. 181; designated 6).

The class-autonomyypothesisH7).-I now propose modificationfHope's partition H3). The additional istinctions imposewithin wo ofthe classeshe identifiedeflectypothesizedariationsnthe occupationalautonomy ccorded o workers nthebasis oftheir mployment.There s a broadconsensus n the nsufficiencyftheconventional hite-collar and blue-collar ategories o account for mobility atterns.Thenecessary riterion ordistinguishingatterns f mobilitynternal o thesesegmentss referredo variously s the entrepreneurial/nonentrepreneurialdistinctionCarlsson1958,pp. 144-46),the bureaucratic/nonbureaucraticsetting f obs and the attendant possibilities or elf-directionnd self-employment"Featherman ndHauser 1978,p. 32; Laumann 1973, . 81),the degreeof role circumscriptionue to "rationalprinciples xplicitlyformulated"Blau and Duncan 1967,p. 73), and the relative ontrol verthe laborprocess xercised yworkersn variousclass locations Wright593


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American ournal f Sociology1978, p. 64-67).Whathasbeenmissings an explicitmodel fclassbound-ariesbywhich ccupationalutonomymay be broughto beardirectlynan explanationfdetailedmobilitylows.Withthiscriterions thegoal, propose subdivisionf Hope's white-collar egmentnto hree lasses II, III, IV), and I distinguishhree lasses(V, VI, VII) withinhis blue-collaregment. he resulting ypothesizedpartitions as followsnumbersn parenthesesefer o the categories ftable 1):

I. Proprietaryrofessionals1)II. Salariedmiddlelass 2,3, 4)III. Small mployers5)IV. Routinizedhite-collarorkers6, 7)V. Semi-autonomousraftsmen9, 10)VI. Manufacturingorkers8, 13,14)VII. Archaic orkinglass 11,12,15)VIII. Agriculturallass 16,17)

As inHope's hypothesisH3), self-employedrofessionalsredeemed oconstitutedistinctlass I), as areall agriculturalccupationsclassVIII).Within he white-collaregment ostulated y Hope (H3), I insistondistinguishingroprietorshipf a business rom alariedemployment.nnational amples uchas those onsideredn thispaper,proprietorsclassIII) for he mostpartownthetypesof modest stablishmentBlau andDuncan 1967,p. 72) often ssociatedwith the "traditional" ettybour-geoisie Wright 978,p. 39). I subdivide alariedwhite-collarccupationsaccordingothedegree f utonomy ypicallyxercisedytheirncumbents.The salariedmiddle lass (II) includes ccupationsengineer, ealthad-ministrator,nd insurance gentprovideexamples)whose incumbents,although mployees,xercise onsiderableontrol ver the conditions ftheirwork nd the mannern which t is accomplishedcompareWright1978,p. 81). In contrast,outinized hite-collarmployeesclass V) suchas banktellers,mailcarriers,nd salesclerks ave sucha smalldegree fcontrol ver theirwork ituationss toprohibitbyhypothesis)heir n-clusionwith therwhite-collarorkerscompareVanneman 977).Withinthe conventional lue-collar egment, he progressive ureau-cratization f manual work n themanufacturingndustry FeathermanandHauser1978,p. 32) andthehigh atesofunionizationnd other ormsofclassorganizationhereWright 978, . 172)relative o other ndustrieslead me to grouptogetherin classVI) all jobs in manufacturingcraft,operative,nd laborer) nd to distinguishhemfrom ognate ccupationsin other ndustriescompareTolbert,Horan,and Beck 1980).The craftworkersn theseother ndustriese.g., carpenters,ypesetters,elevisionmechanics) harerelatively onbureaucraticettingsnd "have at leasta594


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Social Class Structurelimited ormf utonomyntheirmmediateabour rocess" Wright 978,p. 81). I distinguishhemclass V) from heclass VII) of ow-levelmanualoccupations xistingn largepart prior o theriseof ndustrialapitalismand still argely utside ts immediate cope (e.g., meat cutters, xceptmanufacturing;rounds eepers; ractical urses).The Thesis on InternalHomogeneityEach of the sevenhypotheses as appliedto the data oftable1 by fittingmodel 2) ofthe ection eaded Implementation,"mployingachhypoth-esis n turn o induce herequisite artition. he question osed here, oreach hypothesis,s thedegree o which t identifiesn exhaustive et ofregionswithin hetable nsucha manner hateach region orms unifiedfield nternally.In thenext subsection will assess the claim thattheclasses re orderedn their rovision f nterclassmobilityhances.)Results ppear nthefirst olumn ftable 2,which eportshe ikelihoodratiogoodness-of-fittatisticG2)for achofthe even pplicationsfmodel(2) to thedata oftable1.The reader houldbear in mindthat each ofthe sevenhypotheses asformulatedy a researcheror a research eam)withconsiderableriorknowledge f thedetailed nteractiontructuref themobility able understudy. n threecases (Hi, H2, H3) the hypotheses esulted rom airlymechanical xploratoryearchprocedures.n the case ofH7, I had ex-tensive riorknowledge f the detailed nteractionsftable1. The readeris thereforencouraged o view thefindingsf the first olumn f table 2as indices f fit, ather hanas formal estsof goodness ffit see Bishop

TABLE 2TEST STATISTICS FOR SEVEN HYPOTHESES ON FOUR 17-CATEGORYINTERGENERATIONAL MOBILITY TABLES

FirstJob FirstJob CurrentJob CurrentJob1973 1962 1973 1962Hypothesis df (1) (2) (3) (4)Hi ...................... 180 407.8 336.7 371.1 323.0H2 ...................... 180 405.8 358.6 329.7 321.1H3 ...................... 154 361.5 300.9 327.3 282.3H4 ...................... 128 279.7 244.9 238.6 207.3H5 ..................... 55 158.4 146.4 116.8 86.2H6 ....19..... ... 19 127.2 97.9 58.8 47.7H7 ..................... 69 76.9 81.7 87.6 80.5

SOURCES.-Col. is table1of his aper; ol. 3 adapted rom eathermanndHauser 1978, . 535), ols.2and4 adaptedfrom lau andDuncan 1967, p.496 and497).NOTE.-Each hypothesis asfitted ndermodel 2). Reported ere re the degrees ffreedomdf) andlikelihood atiogoodness-of-fitG2) tatistics esultingrom he testof eachhypothesisn each 17-categorytable.

595


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American ournal fSociologyet al. [1975,p. 311]for n elaboration f thisdistinction;n the"extremerarity" fformal ypothesisests nthe ocial ciences, eeLeamer 1978]).The fit fhypothesis 7 to the data of table1 is acceptable y conven-tional standards.Under the convenientmyththat the hypothesiswasformulated ithnopriorknowledgefthedata,theprobabilityssociatedwith goodness-of-fittatisticG2) f 76.9on 69df s .24.By wayofcom-parison,noneoftheotherhypothesesits hedata evenat the 001level.The twohypothesesH5 andH6) withewer han 9dfdonotfit ppreciablybetter han hefirstourHl through 4). Neither anneman's orHope'sproposedmodificationH2 and H3, respectively) f the Blau-DuncanhypothesisHi) resultsn a substantiallymproved it o thedata withintheframeworkf model 2).9Fittedvaluesto table 1,underhypothesis 7 appliedvia model 2), arereportedntable3.10Because ofthe danger hathypothesis 7 fits diosyncraticeatures ftable1, testedtsfit as well s thefit fthe ixother ypotheses)nthreeadditional 7-categoryablesof ntergenerationalobility: ata obtainedin 1962 on mobility o firstob (Blau and Duncan 1967,table J2.2) anddata obtained n 1973 and 1962 on mobility o respondent'scurrentoccupation" Featherman nd Hauser 1978,table E.5; Blau and Duncan1967, table J2.1). Both the Blau-Duncanand the Featherman-Hauserstudies mployeddentical 7-categoryccupational ivisions."Resultsofthese ests ppear nthesecond, hird,nd fourth olumns ftable2.9Any partition Ha) contains nother artitionHb) if (Ha) n (Hb) = (Hb); that is, if allthe class boundaries f Ha) are preservedn (Hb). For example,Hope's partition H3) iscontained n Blau and Duncan's (Hi), differingnly n its refinementfBlau and Dun-can's "white collar" into self-employed rofessionals nd others (see App. B). Hope'srefinementf the Blau-Duncan hypothesis eads to a reduction n G2 of 46.3 (=407.8 -361.5) at the expenseof 26 (= 180 - 154) df see thefirstolumnof table2), which s amarginally ignificantmprovementn fit. Similarassessmentsmay be constructed orall otherpairs of hypotheses elated n such a way thatonehypothesis ontains he other.This statement risesfrom he observation hat model 2) under partition b includes heparameters f model 2) underpartitionHa if Ha containsHb; therefore,hese oglinearmodels re hierarchicaln the sense of Goodman 1970).10Cells in rows1 and 5 and cols. 1 and 5; cells [6,7], 9,10], 16,17] nd their ransposes;and diagonal cells 1, 5, 6, 7, 9, 10, 16, and 17 are fitted xactlyunderhypothesis 7; seeApp. A. The other iagonalcells report implied r mputed iagonalcounts" see Duncan1979, p. 800; Goodman 1972). The 204 remainingells are here fittedwith 69 df (G2=76.9; see table 2). These 204 cellscontain13,892ofthe19,913 ases.11 rior o analysis, eportedellcounts n tableJ2.1 Blau andDuncan 1967,p. 496) wereweighted ya constant o as toyield n adjustedtable sumof10,533 which s the djustedsumreported orthis table in Featherman nd Hauser [1978,p. 534]). A similar djust-ment was applied to table J2.2 (Blau and Duncan 1967, p. 497). See Featherman ndHauser (1978, pp. 511-14) fora discussion fweighting nd samplingvariability s ap-plied to the OCG-I and OCG-II studies.On the comparability f the definitionsf"firstjob" employed n the two studies, ee Featherman nd Hauser (1978, pp. 23-24).

596


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22/35

American ournal fSociologyHypothesis 7 is seento fit achofthefour 7-categoryables.On69 df,the probabilitiesssociatedwith ikelihoodatiovalues of 76.9, 81.7,87.6,and 80.5 are 24, 14, 06, and .16, respectively.hese findingsuggest hat(H7) doesfit diosyncraticeatures f table 1, but they demonstratetsacceptable it o eachofthe other ables as well. n contrast, oneof theother ixhypothesesrovides satisfactoryit othese 7-categoryables.12Interpretation.-A odelof the mobilityable musteliminate he nflu-ence of origin nd destination istributionsn the observedpatternofmobility.Modelsdiffern their onceptualizationf thistask.The standard baseline model of statistical ndependence "perfect

mobility"), or xample,dentifieshe origin nd destination istributionswith herow nd columnmarginalsfthe entire X R table.Suppose hismodelhad fit he data oftable 1. Among he mplicationsf sucha findingwouldbe that theoddsof becomingsay) a proprietornstead f a laborerwere dentical orrespondents riginatingn each occupational ategory,net of the abovementioned arginal istributions.The perfectmobilitymodelmaybe interpreteds the specialcase ofmodel 2) in which he analyst upposes hat there re no social classes(c = 1; see App. A). Classes are conceptualizeds those features f thesocial structure hich llowtheperfectmobilitymodelto obtainsimul-taneouslywithin ach subtableresultingrom partition foccupationalcategories. ather han mploy ncreasinglylaboratemodels f ssociationfor hetable s a whole, hegoalhere s to elaborate ocial tructureo that"perfectmobility"ctuallyholds.Given he acceptable it fthemodeled ounts ftable 3 to the observedcounts f table1,and theunacceptable it f theperfectmobilitymodel,"3we learn hatthe attermodel onfoundsatterns foccupationalmobilitywith heeffectsfmobilityo and from ocial classes.We learnthat,netof theclass-specific arginals,he associationwithin able1 is not statis-tically ignificantP = .24). This is the sensein whichthe social classstructure ostulatedby hypothesis 7 explains he observed ountsoftable1.Combining ategories.-Untilhispoint, have refused o reduce theinitial 7X 17tabletoa table ofsmaller ize.Suppose hatwenowreduceit to size 8 X 8, by combiningategoriesntotheeight lassespositedbyhypothesis 7. The result s a tablereportingbserved ounts fmobilitywithinnd between he ocialclasses.This reduced-formable, onstructedfromhedata oftable1,is providedntable4 (upper anel).1412Of he ixother ypotheses,hebestfitsprovidedyH5 applied o the1962data onmobilityo currentob:df= 55,G2= 86.2, = .005.13On256= (17 - 1)2 df, hemodelf ndependenceppliedo table yields 2 7,808.2.Related ommentsppearnn. 15below.14 The unroundedataon which able1 s based seen. 8 above)were mployedor hispurpose.598


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Social Class StructureGiventhatwe have establishedheconditionalndependenceforigins

and destinationsor hefull 17 X 17) table,weare n a positiono nterpretthereduced-formable (table 4) in a newway. Althought is a tableofobservedounts fmobility ithinndbetween lasses, t s alsosomethingelse. t is a matrix fclass-specific arginals hose nfluence as removedinorder o fit hemodel ftable3.15 Each countntheupper aneloftableTABLE 4

INTERCLASS MOBILITY TO FIRST JOB, 1973, WITH FITTED COUNTS FOR MODEL M6AND Row EFFECTS PARAMETERS (b) FOR THREE MODELSSON'S CLASS (First Job)

I II III IV V VI VII VIIIOBSERVED COUNTS

Father's class:I ......... 25 137 3 35 16 22 24 3II .... .. 29 1,222 17 467 191 324 368 38III. 19 308 33 194 86 160 167 26IV ....... 9 388 6 291 99 216 229 23V ........ 13 488 11 408 490 538 676 84VI 1 9. .. 19 558 4 542 259 1,464 739 98VII ........ 16 460 14 584 325 853 1,283 163VIII ........ 14 395 13 344 328 822 902 1,832FITTED COUNTS, MODEL M6

Father's class:I .......... 7 129.4 1.8 48.9 15.8 23.4 19.0 1.5II .. 4.... 31.4 762.3 13.6 458.1 186.8 348.6 357.1 36.4III... 12.4 311.2 5.7 199.8 84.2 162.3 171.9 18.1IV.... 14.8 378.1 7.1 250.9 107.5 210.8 226.9 24.3V 15.4 468.7 10.5 440.7 244.7 524.5 672.0 85.7VI. ... 18.9 566.0 12.5 516.3 259.3 596.2 752.6 94.6VII .14.1 480.1 12.0 565.9 323.1 844.5 1,211.7 173.1VIII . 12.1 400.7 9.8 451.4 252.0 643.8 902.9 126.1

Row EFFECTS PARAMETERS (b,)Model:M2 1.52 1.27 1.13 1.10 .93 .89 .83 .60M5. ... 1.43 1.11 1.09 1.07 .90 .91 .82 .80M6 1.42 1.12 1.09 1.07 .90 .91 .81 .82

SOURCE.-Table 1 of this paper.15A formal ecomposition f ssociation n the17 X 17 table underlies heseobservations;it is sketchedhere for he nterested eader.One arrayof class-specific arginals s givenbytheupperpanel oftable 4; these re the umsofthe ubtables k into which he 17 X 17table has previously een partitioned nderhypothesisH7. Under the model of ndepen-dence, hismarginal rray exhibits 9 = (8 - 1)2 df.A second rrayof class-specificmar-ginals s the 17 X 8 table reporting heoccupational origins f respondentsn each class;theseare therow marginals f the subtables k. Under ndependence, his marginal rrayexhibits 12 = (17 - 1)(8 - 1) df.The final rrayof class-specificmarginals s the 8 X 17tablereportingheclass origins f respondentsn each occupation also 112 df); these are

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American ournal fSociology4 is, by definition,he sumofone of the 64 subtablesk resultingrom ureight-class ypothesis.) herefore,model hatfits hereduced-formclassX class) table of countswillsimultaneouslynd by definitionitcertainmarginals hatwerenetted out to produce the model that adequatelycharacterizes he initiallygiven (17 X 17) table. Moreover to place aremark fKeithHope's within he frameworkfthepresent aper), "weshould lways beginby fitting he nteractionsproduct erms) nd onlylaterfit hemain terms"Hope 1980a,p. 9).We nowturn, herefore,o the reduced orm8 X 8) tableof nterclassmobility.The Class Hierarchy hesisFor expositoryurposes discuss hefit ffivemodels o the data of table4;these ivemodels re theones reatednDuncan 1979). Results rereportedintable5.The modelof ndependencer "perfectmobility" modelMl of table 5)isthe tandard aseline.ComparingtsG2value 6,672.4) o theG2 btainedin testingndependencen thefull 17 X 17) table see n. 13), we observethat 85% (=6,672.4/7,808.2) of the association mong the occupationalcategories f table 1 is due to the association f class of originwith lassofdestinationsee related ommentsn n. 15above).ComparingMl to the modelof"quasi-perfect obility" independenceforoff-diagonalells; model M3 of table 5), we observe he substantialtendency or lass of destination o be thesame as class of origin.Each of the remaining odels mposes n assumption s to the ordering

TABLE 5TEST STATISTICS FOR SIX MODELS FITTED TO TABLE 4

Model df G2IndependenceMl) .. .................................... 49 6,672.4Row effectsM2) 42 2,821.3Quasi independence, iagonalomitted M3) ......... ........ 41 886.2Uniformssociation,diagonalomittedM4) 40 168.4Row effects,iagonalomitted M5) .................... .... 34 100.1Row effects, iagonaland three ther ellsomitted*M6) 31 39.5

*Theother ells re VIII, IV), (VIII, V), and (VIII, VI) (see text).the olumnmarginalsf he ubtablesSk.Observe hat49+ (112 - 49) + (112 - 49) = 175,thedegrees f freedom sed up in testingmodel 2) when thediagonalcells (fi) as wellas theoff-diagonalells ft,) re estimated irectly. here are256 = (17- 1)2 df associatedwith hemodelof ndependence or hefull R X R) table, nd 256 - 175= 81 = (R -C)2thenumber fdf eftbymodel 2) (see App. A; here,R = 17 and c = 8).600


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Social Class Structureof he ocialclasses.Duncan's"uniformssociation"modelM4) introducesa single dditional arameter,,which has an obvious onceptual nalogytotheregressionoefficient,ince tgoverns he hift fthedestination is-tributionhatoccursforeach 'step' of the ordered rigin lassification"(Duncan 1979,p. 797; see also Goodman1979b).Model M4 thereforee-quires hattherows nd columns fthe table be ordereddenticallyndinthe"correct"way."6 his model eads to a substantialmprovementverM3 at the additional xpense f ust 1df.Still, he modeldoes not charac-terize he data.Models M2 andM5 assumeonly hatdestinationscols.ofthe table) areordered;herowsneednotbe.These models equire set ofparameters,i,onefor ach row henceDuncan's term, roweffects"models).The gapsbetween djacentcolumns re assumedequal (Simon 1974,p. 972), butthesegaps (governed ythebi) areallowed odifferetween ows.Each biis defined etofthetable's rowand columnmarginal ffects,nd is inter-pretable s the conditionalddsratioofmobilityoanyclass , relative oclass + 1, given riginsnclass (Simon1974).ModelsM2 andM5 differonly nthatrow ffectsor he attermodel respecifiedxclusivelyor heoff-diagonalells.Model M5 (roweffects, iagonalomitted) s the best-fitting odelofthoseconsidered o far.Moreover, xamination f the standardized ellresidualsBishop t al. 1975, p. 136-41)resultingromhefit fthismodelindicated hat ts ack offit s duealmost ntirely o its ackof fit n threecells, achofwhichnvolvesmobilitvut of theagriculturallass i.e.,rowVIII). 17In order o confirmhat the ackof fit fmodelM5 results lmost x-clusively romts lack offit o these three ells, row ffectsmodel wasfitted nceagaintothetable4 data. This time he three ells dentifiednnote 17 (as well as thecells on themaindiagonal, s inmodelM5) were16 Fitted counts formodel M4 were obtained by the trial-and-errorearch method ofDuncan (1979,pp. 797-98). The estimated alue of b (6 = 1.070) was computed o threedecimalplaces.A moregeneraldiscussion ftheestimation f expectedfrequencies nderthis modeland the othersdiscussedbelow is providedby Goodman (1979b,pp. 817-18,1979c). n thisregard hereader's ttentions also called to thecomprehensiveomputerprogram fHaberman 1979, pp. 571-85) that "can be used to computemaximum ikeli-hood estimates or ny log-linearmodel."17 Specifically, he observedmobility rom gricultural ccupations to routinizedwhite-collaroccupations cell [VIII, IV]) was substantially ess than thatpredictedby modelM5, whiletheobservedmobility fagriculturalworkers ntosemi-autonomous raft obs(cell [VIII, V]) and intomanufacturingobs (cell [VIII, VI]) was substantially reaterthan themodel'spredictions. lau and Duncan (1967, pp. 51, 79) suggest that "farmlaborer" erves s an "entry"occupation oryoungworkersmost of whom] annotcom-pete effectivelyorwhite-collarositions, nd [who] hus move ntomanual work."

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American ournal fSociologytreated s structuraleros Bishopet al. 1975,pp. 140-41).18 his model sdesignatedM6 here nd in table5. Witha goodness-of-fitest statistic f39.5 on 31 df, herow ffects odelM6 fits hedata acceptably y conven-tional standards P = .14). Fittedcountsobtainedfrom hismodelarereportedn thesecondpanelof table4. The biparameters stimated romthis model normedmultiplicativelyo unity), s well as those resultingfromM2 andM5, appearat the bottom ftable4.Interpretation.-Theitof modelM6 provides upport orthemodel'sassumptionhat social class destinationsre ordered niformlyfrom toVIII as listedntable4 andpreviouslynthetext)."9 he modelmposes oassumptionbouttheorderingf lassorigins,owever,nd nthis ightt sinterestingo examine he row ffect arametersthebi).Themodel peci-fies for xample) hat,netoftherow nd columnmarginalffectsftable4, theson ofa self-employedrofessionals 1.42 timesmore ikely bi =1.42)to havea firstob in class I than nclass II (and,more enerally,hathe s 1.42n imesmoreikely o havea firstob inclassj than nclassj + n).We can define hemobility ifferentialestowed ponsonsoriginatinginclass , relative o thosewhobegin ife ntheadjacentclass + 1,as theratiobilbi+,.For themodel hatfitsM6), the argestmobility ifferentialis for ons of self-employedrofessionalsclass I) relative o thoseofthesalariedmiddle lass class I). This differentials 1.27 =b1/b2 1.42/1.12;see the ast ineoftable4). The second argest ifferentials the onespan-ning he collar ine b4/b5 1.07/0.90 1.19).The thirdargests the onebetweenmanufacturingnd "preindustrial" ork b6/b7 .91/.81 1.12).Each of the remainingifferentialsetween djacentclasses s less than1.03.18 FittedcountsformodelsM5 and M6 were obtainedby use ofthe terativeproceduredevisedby Duncan (1979, p. 798). This procedureyields "impliedor imputed"fittedcounts Duncan 1979,p. 800) evenfor ells treated s structural eros.19 Correspondingly,he assumption hatoccupationaldestinations re ordereduniformlyfor heungroupedategories17-categoryevel) is not ustainedby thesedata, subject to(a) the nfinitesimalroportionfpossibleorderingsofwhich here re 17! = 3.56 X 1014in all) investigated y thiswriter,nd (b) the modeling ontext f table 5. (More generalframeworks,ot considered ere, representedn Goodman 1979c] nd in Clogg[1980]).For example,modelM5 appliedto the table 1 data yields G2of1,588.4on 223df.Withthe rows nd columns f table 1 permuted o accordwith Duncan's socioeconomicndexof occupations see Featherman nd Hauser 1978,p. 28), modelM5 yields G2of2,018.8or2,033.5 depending n howthe tie between ategories 1 and 13 on Duncan's index sresolved),also on 223df. For this and a relatedreason (the increasingprevalenceof"horizontalmobility" s larger tables are considered Blau and Duncan 1967,p. 117]),I have arguedthat the appropriatedomain ofapplicability f modelsforordered ate-gories s not the occupational ategoriesbut the classesof such categories dentified yapplication ftheaggregationnd internal omogeneityriteria.

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Social Class StructureThe findingf a highmobility ifferentialor onsofself-employedro-

fessionalss thestrongestlassdifferenceppearingnthesedata conflictswithBaron'sconclusion1980,p. 835)that themajor ontrast.. appearsto involve tightly ovenmental' rwhite-collarector, n theonehand,and all other ccupationalituses-highly ifferentiatedmong hemselves-on the other."Strictcomparisonsre unwarranted,owever.Baron'sexamination f the correspondenceetweenRogoff'sndianapolis tudyandcontemporaryobilityrends tthenationalevel mployed differentaggregationfoccupationsnd a differentodelingrameworkromhoseemployed ere, ndhisaggregationas not ntended osatisfy hecriterionof nternal omogeneityevelopednthispaper.These data bearout the "elite" standing f the sonsofself-employedprofessionalsseediscussionbove ofHope's hypothesis 3), ifthe readeriswillingo apply heterm elite" to a classwith nevenhigherropensity"not to fall" thanwouldhave beenthe case ifthebiparameters ad in-creaseduniformlyithclass of origin i.e., ifmodelM4 had providedsatisfactoryit; ee related ommentsnM4 and M5 inDuncan [1979,p.799]).20The partitionppliedhere H7) shareswithHope's thepostulationofself-employedrofessionalss a distinct lass,but it specifies morehighly ifferentiatedocialclassstructure. oreover, ypothesis 7 satis-fies hecriterionf nternal omogeneitysee table 2), which s central othemodelingrameworkevelopednthispaper.Thisdiscussion froweffectsb_)has beenconfinedo parameterssti-matedfromhemodel M6) thatfits hedata. Thesebiparametersrevir-tually dentical o thoseestimated rommodelM5 (compare he ast twolines ftable4). Therefore,ur nterpretationftheb, snot ltered y theadditional xclusion f three ells n row VIII thatdefines hedifferencebetween hemodelthat fits he data (M6) and Duncan's modelof "roweffects,iagonal mitted"M5).Summary.-Themajorresultof thedata analysisof thispaper is thedemonstrationfa dualitywithrespect o interclassmobility nd occupa-tionalmobility.Within hesubtables Sk) defined ysocial classpartition(H7), occupational rigins nd destinationsre independenttable 2).Mobility etween he classes table 4) is characterizedy thedifferentialdependencefdestinationlass on origin lassunder heassumption hatdestinationlassesare ordered niformly. odels thatincorporate heseclaimsmaintain idelityo thedetailed attern f cellfrequencies.20 The mobility ifferentialetween lass I and class II estimated rommodelM4, whichprovides an unsatisfactory itto the data, is 1.07 (see n. 16). Model M6 estimates hismobility ifferentials 1.27 (see text).

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American ournal fSociologyCONCLUSIONThe occupationalmobility able has servedas an anvil for sociologicalcraftworkince hedayswhenblacksmithsutnumberedocial cientistsnthe Americanabor force. he historyfsociological echnique onsistsnno smalldegree f mplements oned nd fashionedt this nvil see, e.g.,Bibby 1975; Blau and Duncan 1967; Boudon 1973; Featherman ndHauser 1978; Goodman 969; Pullum1975). The present aper arosefromtherecognitionhatsociologists ave remained eluctant, hroughouthishistorical eriod, o forge he texturefthematerial n which hey et towork.Theyhave not addressed xplicitlyheproblemhat "changes roma finer o a coarser lassificationorviceversa)can affectll the measuresof association fwhichweknow" Goodman nd Kruskal1954,p. 737).The clear act hat theres no finalolution o theproblem f hebreadthandheterogeneityfcategoriesn a classificationfoccupations" Duncan1968,p. 682; compare uncan 1975)doesnot icense ociologistso ignorethe qually learfact hat in a classcomposedotally ftheaffineccupa-tionalgroups, .g., of differentroups funskilled nd semiskilledabor,there ppears nd exists communityf nterests. . considerablyifferentfromthat] f another lass composed otally f other ffineccupationalgroups.... Thusfar hepartisans ftheclassstrugglemayhavea basisfortheir ctivityndpropaganda" Sorokin 927,pp. 439-40).This paperhas offered frameworkor ggregatingccupational ate-goriesnto ffinesocial)classes.The aggregationfrows nd columns asbeenportrayed ere s thefundamentalheoreticalssue nmobilityableanalysis, ather han as an exogenous given"to be decidedupon prior othe constructionf explicitmodels. Internal intraclass nd interclasshomogeneity,lass hierarchy,nd tangibleboundedness re the centralprinciples laborated,mplemented,ndapplied odatawithinhisframe-work.I have argued hatthisframeworkeadsto thehoning fexistingech-niquestoproducemodels hatfit argemobilityables.Falsifiable ommit-mentswhich ddress heproblem fthestructuringfoccupationswithintangible ocialclasses re essential or heanalysis fmobility ithin hisframework.he proper artition foccupationsnto social classes s onewhich atisfieshe criterionf nternal omogeneityithin ach classandbetween achpairofclasses see tables1, 2, and3). The appropriate ayto combine ccupational ategories,ccordingo thisframework,s to ag-gregate ccupations ithinhe amesocialclass seethereduced-formable4). In this way,the definitionf classes s taken to be theoreticallyndmethodologicallyrior o thestudy fmobility atterns etweenhem.The detailed eaturesf arge ables anand should e exploitedoassess604


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Social Class Structurethe goodness f fit f explicit ypothesesbout aggregation. he formula-tion fvarioushypothesesf nterest ould all for heuse ofdifferentetsof nitial ategories han the 17 OCG categories mployed ere.The OCGcategories re indicative, owever, f the possible directions orfuturework.Consider, or xample, hepartition f55 industriesnto "core"and"periphery"ectors ecently roposed y Tolbert,Horan, nd Beck (1980)andhypothesizedoprovide ppropriatenitsofanalysis or hestudy flabor market tructureamongotherphenomena).Within heframeworkdevelopedn thispaper,thedisaggregationf mobility ablesbydetailedindustryode wouldallowtheformulationnd testing fhypothesesfa"dual" or a more laborate segmented"abormarket ccording o whichlaborpoolstend obe distinct nd insulated rom ne another hrough hepresenceof separate seniority adders. Applicationof the frameworkdeveloped ere o "internal" abormarketsintragenerationalob mobilitywithin singlenstitutionr a small et of related" nstitutions)lsoseemspromising,wing o the necessity or ggregating etailed ob titles ntolarger,nternallyomogeneousategories eflectingypicalmobilityhances(Rosenbaum 979; Spilerman 977).21There s no shortage fhypotheses.What has been ackinghas beenanoperational onceptof social class structures.Withsuch a concept,hy-potheses an be broughto bear directlyn theformulationfmodels ortheoccupationalmobilityable.APPENDIX A: SOME PRACTICALITIES OF MODEL FITTINGThisAppendixreatsmodels 1) and (2) of the"Implementation"ection,andpresupposeshenotation sed there. he othermodels iscussednthispaper see table 5) are treated xtensivelylsew,-hereDuncan 1979; Good-man1972,1979c;Simon1974).Obtaining ittedValuesModel (1) is a specialcase of Hauser's 1979) model.Fittedvalues undermodel (1) may therefore e obtained by the procedure he outlines (1979,pp. 418-19). Without gain or loss of nformation, epresent he given R X Rtable of observed counts as a three-dimensional rray X = {Xijk} of sizeR X R X c2defined s:

Xijk = fij f r (i, j) e Sko otherwise,21 The frameworkfthispaperalso has relevance ormodels f ocialnetworks; ee Breiger(1981) and Holland and Leinhardt 1981).

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American ournal fSociologywhere signifieshe treatmentf a cell as a structuralero Bishopet al.1975, . 59). Let P (father's ccupationalategory), (respondent'sccupa-tional ategory),nd C (the subtablesk) representhe variables ndexed,respectively,yi, , and k. Following onventionalotation,n which hehighest-orderarginal onfigurationsitted nder givenhierarchicalog-linearmodel re isted na series fparenthesesBishopet al. 1975,p. 66),expected aluesformodel 1) areproduced yfitting arginal onfigura-tions P)(S)(C) ofthethree-dimensionalarray compareHauser 1979,p. 419).Fittedvaluesfor he new model 2), then, esult rom ittingmarginalconfigurationsPC)(SC) of the amethree-dimensionalrray see eq. [2] nthetext).Fittedvaluesformodel 2) can also be obtained rom n identical ro-cedure see eq. [2']). Considernturn achof the ubtablesk (k = 1, ...c2). For each subtable,fit themodelof row-columnndependence. heequivalence f thisprocedureor btaining itted alues and theprocedureof theprecedingaragraphsgivenby eq. [3] nthe text.As in theapplications eportedn the text, nemay chooseto confinethe explicitmodelto off-diagonalells cells ij such that # ). In thatcase, constrain he definitionf the three-dimensionalrrayto includeXijk = q for = j, and proceed s above. In the case ofmodel 2), thisproceduresidentical o fittingherow-columnndependence odel oeachsubtablenot ontainingellsonthediagonal ftheR X R table, ndfittingthe model of quasi independence oroff-diagonalells ("quasi-perfectmobility") o each subtablecontainingomecellson thediagonaloftheR X R table.DegreesofFreedomCalculation fdegrees ffreedomor he womodelssstraightforwardsee,e.g., Bishopet al. 1975, pp. 114-22).Model (1) requires itting maineffect,R - 1)nonredundantow arameters,R - 1)nonredundantolumnparameters,nd c - 1)2nonredundantubtable arameters.he numberfdegrees ffreedomssociatedwithmodel 1) willthereforen general eR- 1 - 2(R - 1) - (c - 1)2 = (R - 1)2 - (c 1)2; compare auser 1979,p. 418). Ifmodel 1) is confinedo off-diagonalells, herewill ngeneral e(R2-R) --1-2(R-1) -(c-1)2 = R(R-3)-c(c-2) degrees offreedom.Model (2) posits ndependence ithin achof the subtables k (thoughclearly otnecessarily ithin hefullR X R table).Thismodel equireshefit f main ffector heR X R table, 2 1nonredundantubtable aram-eters, (R - c) nonredundantowparameters,nd c(R - c) nonredundantcolumn arameters. odel 2) isthereforengeneralssociatedwith 2 1 -606


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Social Class Structure(C2 -1)-2c(R - c) = (R -C))2 degrees ffreedom.f model 2) is confinedtooff-diagonalells, s it is inthe text, tsassociatednumber fdegrees ffreedoms in general R - C)2- V, whereV equals R less thenumber fclassescontaining ewer hanthree ccupational ategories. onsider, orexample, he number f degrees f freedomssociated withthe test ofhypothesisH7) on a 17-categoryable.The hypothesisosits ight lasses,of which ive ontain ewer hanthree ccupational ategories. ereR =17, c = 8,V = 17 - 5, and thenumber fdegrees ffreedoms 17 - 8)2 -(17 - 5) = 69 (see the ast rowof table 2).Both models 1) and (2) aregeneralizationsfrow-columnndependence(or ofquasi independenceor ff-diagonalells), nd model 2) is a general-ization fmodel 1). In the pecial ase n which he nalyst upposes hereare no social classes c = 1), one obtainsfrom oth modelsthemodelofsimple ow-columnndependence ith R - 1)2 degrees ffreedom,rthemodelof quasi independence oroff-diagonalells with R - 1)2 - R de-grees f freedom.

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Social Class StructureREFERENCESAberg, . 1979."Social Mobility nd Class Structuration." ctaSociologica 2(3):247-71.Allison,P. D. 1980."AnalyzingCollapsed Contingency ables withoutActuallyCollaps-ing." American ociologicalReview 5 (February):123-30.Baron, J. N. 1980. "Indianapolis and Beyond: A StructuralModel of OccupationalMobility crossGenerations."American ournal fSociology 5 (January):815-39.Bartholomew, . J. 1967. StochasticModels,forocial Processes.New York: Wiley.Beland, Frangois.1978."La Reductionde categories ans les tableauxde contingence:eshypotheses 'independanceregionale." Ph.D. dissertation. epartmentof Sociology,Universit6 aval.Bertaux,Daniel. 1976."An AssessmentfGarnier ndHazelrigg'sPaper on Intergenera-tionalMobility n France." American ournal fSociology 2 (September):388-98.Bibby, J. 1975. "MethodsforMeasuringMobility."Quality ndQuantity (February):

107-36.Bishop,YvonneM. M., StephenE. Fienberg, nd Paul W. Holland. 1975.DiscreteMulti-variateAnalysis: Theorynd Practice.Cambridge,Mass.: MIT Press.Blau, Peter M., and Otis Dudley Duncan. 1967. The AmericanOccupational tructure.New York: Wiley.Boudon,Raymond. 1973. MathematicaltructuresfSocial Mobility.New York: Elsevier.--. 1975. "A Model for heAnalysisofMobilityTables." Pp. 511-29 in QuantitativeSociology:nternational erspectivesnMathematicalndStatisticalModeling, ditedbyH. M. Blalock,A. Aganbegian,F. M. Borodkin,Raymond Boudon, and V. Capecchi.New York: Academic Press.Breiger,Ronald L. 1981. "Commenton Holland and Leinhardt 1981)." Journalof theAmerican tatisticalA.ssociation6 (March): 51-53.Carlsson,Gbsta. 1958. Social Mobility nd Class Structure.und: Gleerup.Charvat, F., J. Linhart, nd J. Vercernik. 978. "Some Remarkson theApplicationofMobilityApproach n a SocialistSociety." Pp. 159-71 n Social Mobilityn ComparativePerspective,dited by WlodzimierzWesolowski,K. M. Slomczynski, nd B. W. Mach.Warsaw:PolishAcademyofSciences.Clogg, Clifford . 1979. MeasuringUnderemployment:emographicndicators or theUnited tates.New York: Academic Press.--. 1980."Some Models for heAnalysis fAssociation n Multi-WayCross-Classifica-tions Having Ordered Categories." Paper presentedat the annual meeting of theAmerican tatisticalAssociation,Houston.--. 1981. "Latent StructureModels ofMobility."AmericanJournalof Sociology 6(January): 36-68.Coser, L. A. 1975. "PresidentialAddress: Two Methods in Search of a Substance."American ociological eview 0 (December): 691-700.Duncan, OtisDudley. 1968. "Social StratificationndMobility:Problemsnthe Measure-mentof Trend." Pp. 675-719 in ndicators fSocial Change, ditedbyEleanorBernertSheldon and WilbertE. Moore. New York: RussellSage.--. 1975. "Partitioning olytomousVariables in MultiwayContingency nalysis."Social ScienceResearch (December): 167-82.--. 1979. "How DestinationDepends onOriginntheOccupationalMobilityTable."American ournal fSociology 4 (January):793-803.Featherman,David L., and RobertM. Hauser. 1975. "Design for Replicate StudyofSocialMobility n theUnitedStates." Pp. 219-52 inSocial IndicatorModels, ditedbyKennethC. Land and Seymour pilerman.New York: Russell Sage.--. 1978. Opportunitynd Change.New York: Academic Press.Garnier,M., and L. E. Hazelrigg.1976."Reply toDaniel Bertaux'sAssessment."Ameri-canJournal fSociology 2 (September):398-408.Giddens,Anthony. 973.The Class StructureftheAdvanced ocieties.NewYork: Harper& Row.Goldthorpe, ohnH., in collaborationwithCatrionaLlewellyn nd Clive Payne. 1980.Social Mobilitynd Class Structuren ModernBritain.Oxford:Clarendon.

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the social class structure of occupational mobility (breiger r., 1981)

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