The Strengths and Limitations of the Statistical Modeling of Complex Social Phenomenon: Focusing on SEM, Path Analysis, or Multiple Regression Models

Transcription

1 Th Strngths and Limitations of th Statistical Modling of Complx Social Phnomnon: Focusing on SEM, Path Analysis, or Multipl Rgrssion Modls Jihy Jon Abstract This papr analyzs th concptual framwork of thr statistical mthods, multipl rgrssion, path analysis, and structural quation modls. Whn stablishing rsarch modl of th statistical modling of complx social phnomnon, it is important to know th strngths and limitations of thr statistical modls. This study xplord th charactr, strngth, and limitation of ach modling and suggstd som stratgis for accurat xplaining or prdicting th causal rlationships among variabls. Espcially, on th studying of dprssion or mntal halth, th common mistaks of rsarch modling wr discussd. Kywords Multipl rgrssion, path analysis, structural quation modls, statistical modling, social and psychological phnomnon. I. INTRODUCTION ESEARCHERS us statistical mthods for invstigating R rlationships among variabls. In rcnt yars, thr hav bn a larg numbr of publications using SEM, path analysis, or multipl rgrssion modls, which contribut to th growth of quantitativ rsarchs. Howvr, ach of th mthods has still limitations and strngths and rsarchrs should considr thm whn using a statistical modl of complx social phnomnon in thir rsarchs. Somtims, th limitations of statistical modling ar not discussd or ignord by rsarchrs [1]. Whn stablishing a rsarch modl, rsarchrs should considr th purpos of rsarch, th availability and charactrs of givn data, th tim, cost, and ability of rsarchr and so on. It is important to us a statistical modl carfully with rspcts to limitations and strngths for an accurat xplaining or prdicting th causal rlationships among variabls. Th corrct undrstanding on statistical modling and appropriat using of mthods will lad to th corrct intrprtation of rsults, th bttr application to policy chang and th contribution to acadmic fild. Thrfor, in this papr, th concptual framwork of thr statistical mthods: multipl rgrssion, path analysis, and structural quation modls will b rviwd and th advantags and disadvantags of ach approach will b discussd. II. REGRESSION ANALYSIS Rgrssion analysis is a statistical mthod to invstigat rlationships btwn mor than on indpndnt variabls and only on dpndnt variabl. If th indpndnt variabl is on, J. Jon is with th Division of Policy Dvlopmnt and Rsarch, Kora Disabld Popl s Dvlopmnt Institut, Soul, ,Rpublic of Kora (phon: ; fax: ; -mail: ikwwjh@koddi.or.kr) it is simpl rgrssion. But, in social scinc, it is rar that having only on indpndnt variabl (prdictor) to prdict a social phnomnon. So, most rsarchrs us multipl rgrssion analysis. In past tns of yars, rsarchrs hav usd this multipl rgrssion analysis as a powrful tool bcaus it allows to modl statistically th rlationship btwn dpndnt variabl and a st of indpndnt variabl. Linar rgrssion is usd with continuous dpndnt variabls, whil logistic rgrssion is usd with dichotomous variabls. Both rgrssions allow for th assssmnt of whthr indpndnt variabls such as ag, gndr, ducation, attitud, bhavior ar associatd with dpndnt variabls (outcom/critrion) whil controlling for th outcoms ovrlapping associations with othr variabls. A. Common Purposs of Rgrssion Analysis Th purposs of rgrssion analysis ar idntifid by following: (1) figuring out indpndnt variabl influncing on dpndnt variabl, (2) providing rlationship btwn indpndnt variabl and dpndnt variabl (in othr words, whn on unit of indpndnt variabls chang, a rsarchr can know th amount of changs in dpndnt variabl), (3) stimating th dpndnt variabls according to th changs of a st of indpndnt variabls. In sum, whn th goal is to undrstand (including prdicting and xplaining) th causal influnc on a population outcom, rgrssion analysis can b a powrful tool. B. Prdiction and Explanation Prdiction and xplanation ar cntral concpt of scintific rsarch. Pdhazur (1997) statd that th potntial powr and addd complxity of rgrssion analysis ar bst rsrvd for ithr prdicting outcoms or xplaining rlationships. Prdiction only rquirs a corrlation but xplanation rquir mor [2]. In prdictiv rsarch, practical application is main mphasis, whil in xplanatory rsarch, undrstanding phnomna is th main mphasis. Thrfor, to distinguish thm is important to th us of rgrssion analysis and to th prdiction of rsults. For xampl, if prcivd discrimination of thnical minority wr highly corrlatd with th dprssion lvl, th prcivd racial discrimination would b a valid mans of prdicting dprssion. Howvr, in th analysis of data, it is not simpl to rport th prdiction. For xampl, if having a rligion wr highly corrlatd with th dprssion lvl, it would b valid to trat such indx as a usful prdictor of dprssion lvl. Thn, 1634

2 is it possibl to considr rligion as a caus of dprssion? Or as a policy suggstion in discussion, should it b statd that govrnmnt forc popl to hav rligion for th improvmnt of mntal halth of national population? Mayb, th answr is No. Thrfor, w hav to b carful to optimiz prdiction of critria and should b carful whn intrprting and discussing about rsarch findings. C. Rol of Thory Multipl rgrssion analysis is usd for two diffrnt aims of rsarch: prdiction and xplanation. Explanation is inconcivabl without thory bcaus it is in ordr to undrstand th procss lading to critrion. Also, in prdiction, thory is th bst guid for slcting critria and prdictors as wll as for dvloping masurs of such variabls. Prdictors should b slctd as a rsult of thortical considration [2]. It is not possibl to dcid whthr and how to control for a variabl without formulating a causal modl about th procss by which th indpndnt variabl affct th dpndnt variabl. Hr, th modl rflcts thory about th rlations among th variabls bing studid. D. Considration in Rgrssion Analysis: Limitations and Solutions 1) Analysis of Varianc In th rgrssion analysis, w can s th rport of analysis of varianc, showing th approximat prcntag of prdictor s account for critrion (dpndnt variabl). For xampl, th prdictors account for 60% of th varianc of critrion variabl (whn R 2 is.60). Mor prdictors ar inputtd, highr R 2 ar prsntd. Evn, whn adding statistically non-significant variabls into quation, th R 2 may incras. So, a rsarchr cannot tll th importanc of an indpndnt variabl by only using th incrmnt of R 2. Pdhazar (1997) statd that such an incrmnt would not b viwd as trivial [2]. This problm can b rducd by choosing appropriat slction mthod for thir rsarchs. This issu will b discussd in dtails latr. 2) Statistical Significanc From th output of paramtr stimats, a rsarchr can figur out if th hypothsis is accptd or rjctd. Using alpha =.05, if th probability is smallr than.05, usually it mans that th prdictor variabl is statistically significant. In rsult, th rgrssion quation can b also rportd as following: Y= A + B*X1 + C*X2 + D*X3 (X1, X2, and X3 ar indpndnt variabls, Y is dpndnt variabl). Hr, bcaus som of dpndnt variabls ar corrlatd ach othr, it is possibl that th variabl that was shown to b a statistically non-significant can turn out to b a statistically significant whn anothr variabl(s) ar dltd from th quation. So, making a st of indpndnt variabls in modl is vry important. Through dlting or adding variabls, th total rgrssion quation can chang. This problm also can b rducd by choosing appropriat slction mthod for thir rsarchs. 3) Prdictor Slction Bcaus many of th variabls ar intr-corrlatd, prdictor slction is most important procss in rgrssion analysis. Practical considrations in th slction of spcific prdictors may b various, dpnding on th circumstanc of th rsarch, rsarch intrst or aims, rsourcs, and fram of rfrnc tc. Thr ar various slction procdurs for yilding th bst rgrssion quation; all possibl rgrssions, forward slction, backward limination, stpwis slction, and block-wis slction. (3-1) All Possibl Rgrssion Bst subst of prdictors may procd by calculating all possibl rgrssion quations. Th limitation of this mthod is that a rsarchr should xamin vry larg numbr of quations: 2 K. Whn dciding on which is th bst quation among 2 K quations, maningfulnss should b primary considration rathr than a statistically significant incrmnt in R 2. For xampl, if thr wr two quations, th quation 1 composd of prdictor A and B with 0.58 (R 2 ) and quation 2 composd of prdictors A, B, and C with.62 (R 2 ). Th diffrnc of 4% as th incrmnt in R 2 should b considrd carfully. Th choic of bst quation to prdict a critrion dpnds on th maningfulnss of th variabl and tst rsult of statistical significanc corrsponding to alpha valu. (3-2) Forward Slction Th prdictor that has th highst corrlation with critrion is ntrd first into th quation. Th nxt prdictor is th on that has highst partial corrlation with critrion aftr partialing out th prdictor that is alrady in th quation. Also, at that tim, Sig T for th prdictors is xamind if th probability is lss than.05 (dfault PIN, probability of F-to-ntr). Th third prdictor to ntr is th on that has highst partial corrlation with critrion aftr partialing out th first two prdictors. Whn th all valus of Sig T rport xcd th dfault PIN, th analysis is trminatd. Hr, rsarchr can control th lvl of dfault PIN. If th PIN=.10, mor prdictors ar includd into th rgrssion quation. Th limitation of Forward Slction is that prdictors ar lockd in th ordr in which thy wr introducd into th quation. So, th prdictor alrady in quation cannot b dltd at latr stag although thr is a chang in slctd prdictor s corrlation with critrion by th combind contribution of prdictors introducd at latr stag. (3-3) Stpwis Slction In forward slction, although th prdictors in quation at arly stag los its usfulnss upon introduction of additional prdictor, th prdictors ar includd in quation at latr stag. Howvr, in stpwis slction, such prdictors ar dltd at latr stag. So, th substs of significant variabls ar diffrnt in ach stp: a prdictor that was shown as th bst can turn out to b worst whn th othr prdictors ar in th quation. Thn, a rsarchr should considr R 2 changs in ach quation, co-linarity (bcaus it is possibl that of two qual prdictors, on may b slctd and th othr may not b slctd du to a slight diffrnc in R 2 ), and Sig. valu at.05 lvl. But a rsarch has to still dcid whthr it is worthwhil to rtain it in th quation. Th final dcision dpnds on rsarchr s rsponsibility to stimat th usfulnss of a prdictor. 1635

3 (3-4) Backward Elimination: This mthod starts with th squard multipl corrlation of th critrion with all prdictors. Thn, prdictors ar scrutinizd on at a tim. Stp by stp, in th opposit way of forward slction, dlting a prdictor from quation is conductd. Th analysis is trminatd whn th dltion is judgd to produc a maningful rduction in R 2. (3-5) Block-Wis Slction: Prdictors ar groupd in blocks, basd on thortical considrations. Bginning with th first block, a Stpwis slction is applid and prdictors of first block compt for ntry into quation. Thn, Stpwis Slction is applid to th prdictors in scond block, with th rstriction that prdictors slctd at first stag rmain in th quation. So, if thr is a prdictor of scond block which has co-linarity problm with a prdictor of first block that is alrady in th quation, th prdictor will not b slctd. Th procdur is rpatd until prdictors from last block ar considrd. It is clar that whthr a prdictor ntrs into th quation or not dpnds on th ordr of ntry assignd to th block. Variabls blonging to a block assignd arlir ordr of ntry hav a bttr chanc to b slctd. In Block-wis Slction, Forward Slction may b applid to ach block, instad of Stpwis Slction. Hr, no slction is applid to th prdictors within a block. This combination of forcing som blocks into th quation and doing Block-wis Slction is usful in social and psychological scinc. For xampl, whn bing intrstd in dprssion as a critrion, th block-wis slction follows: 1) forc into th quation th dmographic information 2) forc into th quation disability-rlatd charactrs 3) do a Stpwis Slction to th various strssors (.g. lif tim discrimination xprinc, vryday discrimination xprincs and so on). Such a schm is rasonabl and usful bcaus rsarchr can not whthr th strssor variabls incras th prdictiv powr. On thing important is that it is dsignd to provid information for prdictiv, not xplanatory purpos. For xampl, that discrimination xprinc dos not incras th lvl of dprssion dos not man that discrimination xprinc is not an important dtrminr of dprssion. In sum, th slctd prdictors in quation may b diffrnt, dpnding on th slction mthod usd. Although prdictors A and B ar slctd in quation by all possibl rgrssion mthod, prdictr A and C ar slctd in quation by forward slction mthod. What is bst rgrssion quation dpnds on th slction mthod usd in analysis. Also, th ordr of ntr into quation is crucial in rgrssion analysis. Th corrct ordr may b th on that mts th spcific nds of th rsarchr. Howvr, a rsarchr nds to distinguish btwn xplanation and prdiction and should b carful to intrprt th rsults. Pdhazur (1997) statd thr is nothing wrong with any ordring of indpndnt variabls as long as th rsarchr dos not us th rsults for xplanatory purpos [2]. 4) Varianc Partitioning Varianc partitioning is on of various mthods in th pursuit of xplanations. Varianc partitioning mans th attmpts to partition R 2 into portions attributabl to diffrnt indpndnt variabls or to diffrnt sts of indpndnt variabls. Th problm is that th proportion of varianc incrmntd by a givn variabls dpnds on its ordr of ntry into quation, xcpt whn th indpndnt variabls ar not intrcorrlatd. This situation occurrd whn th prdictors ar intrcorrlatd and th notion of indpndnt contribution to varianc has no maning [2]-[4]. Goldbrgr (1991) assrtd that high R 2 is not vidnc in favor of th modl and criticizd mpirical rsarch rports xprssing I hav high R 2 so my thory is good[5]. Lwis-Bck and Skalaban (1991) statd that in ordr to s th ffct of X on a critrion, a rsarch should consult th rlvant slop stimat (b) instad of R 2. Howvr, many rsarchrs did not considr this problm dply and usd varianc partitioning in social scincs for dtrmining th rlativ importanc of indpndnt variabls [6]. Incrmntal partitioning of varianc was popularizd by Cohn and Cohn (1983) and commonly calld as hirarchical rgrssion analysis: th proportion of varianc accountd by all th indpndnt variabls ar partitiond incrmntally [7]. Th incrmntd proportion at ach stp is xprssd. By th way, th ordr of ntry into rgrssion analysis is crucial hr. For xampl, whatvr th corrlation btwn A and B, if A is ntrd first into th analysis, th varianc in critrion will includ th xplanatory powr it has by virtu of its corrlation with B. In ordr words, th shard xplanatory powr of A and B is allocatd xclusivly to A whn it is ntrd into rgrssion analysis. Thrfor, such an analysis should not b intndd to providing information about rlativ importanc of variabls, but rathr about th ffct of a variabl aftr having controlld for anothr variabl. (4-1) Lssons from Inappropriat us of Varianc Partitioning Incrmntal partitioning of varianc is usd frquntly in various rsarchs, oftn inappropriatly [2]. Th knowldg about th proportion of varianc incrmntd by blocks of variabls ntrd in a givn squnc shds no light on th spcific causal modl bcaus svral othr possibl modls of causation ar mor tnabl. Somtims, th combination of variabls in a block is additional difficultis. For xampl, it is not asy to dcid if th variabl of conomic activity blongs to th block of prsonal lmnts or th block of social lmnts. Dtrmination of th ordr of ntry into th rgrssion analysis should b basd on thortical considrations. In th absnc of a modl about th rlations among th variabls, no maningful dcision about th ordr of ntry of variabls into th analysis can b mad. Thr is an xampl of wrong xprssion: Two hirarchical multipl rgrssions wr prformd to invstigat this qustion. In th first rgrssion, th block of th four social comptncy variabls was ntrd in th first stp, followd in th scond stp by th block of four parntal bond variabls. In th scond rgrssion, this ordr of ntry was rvrsd, with parntal bonds ntrd first and social comptncis ntrd scond [8]. Pdhazur (1997) criticizd 1636

4 that this analysis is not consistnt with thory statd arlir that parntal bonds affct social comptncis [2]. Thrfor, only scond analysis should hav bn carrid out and its rsults intrprtd. Whn a block occurrd at th nd of th block-wis rgrssion analysis, its variancs ar rlativly small. Thrfor, incrmntal partitioning of varianc is not valid to dtrmin th indpndnt variabls rlativ ffcts on a dpndnt variabl. Thr is a common wrong xprssion : Th data ar prsntd in th form of a usfulnss analysis which xamins th rlativ abilitis of procdural and distributiv justic to xplain th varianc in th critrion variabls dpnding on which prdictor is ntrd first into th rgrssion quation [9]. 5) Dos Rgrssion Analysis Guarant th Causal Rlationship btwn Variabls? Rgrssion analyss rval rlationships among variabls, but do not imply that th rlationship to b causal. A strong rlationship btwn variabls could stm from many othr causs including th influnc of othr unmasurd variabls. For xampl, if popl with disabilitis ar found to b dprssd by disability discrimination xprincs, on may ask whthr this is du to th discrimination itslf or instad to a prxisting opprssion (.g. intrnalizd opprssion). This is on of th fundamntal limitations of rgrssion analysis, which rfr to fail for distinguishing btwn charactristics that wr mrly associatd with and occurrd bfor th discrimination xprinc (prxisting lmnt which may influnc on th rlationship btwn discrimination xprinc and dprssion) and thos for which vidnc of causality had bn (risk factor such as discrimination xprinc). Thr is anothr xampl. Prcivd discrimination xprincs might rsult in loss of control, lowr sns of control might rsult in prcption of mor discrimination, or thr could b a circularrlation btwn ths variabls. In ordr words, th rsult of rgrssion analysis dos not guarant th causal rlationship btwn indpndnt and dpndnt variabls. Just th rgrssion analysis can provid vidncs which hlp radrs to draw causal implications. In this situation, rsarchrs usd to choos on of following two stratgis: on is to us languag carfully to avoid claim for causation and th othr is to tak rfug in th claim that thy ar studying only association and not causation. According to Ruttr (2007), rsarchrs can avoid causal claims mploying corrlational trms such as association, prdictors, risk, or corrlation. Rsarchrs may count on radrs to draw causal implications on thir own [10]. In addition, for protcting ffcting from prxisting lmnts, a rsarchrs can mak a control groups which involvs random assignmnt of units to intrvntion or non-intrvntion (control group) conditions. Also, having validity is a important, as th sam dsign may contribut to mor or lss valid infrncs undr diffrnt circumstancs. Whn building validity of rsarch infrnc involvs ruling out altrnativ xplanations or rival hypothss. Also, Thory-basd rgrssion analysis stratgis also can hlp dvlop causal vidnc from corrlational data. Without thory, rsarchr cannot choos on maningful modl from tnd of modl which hav good modl fit. Whatvr th modl is, SEM, mdiating modl, or path analysis modl, all rsarch modls should b basd on thory. All ths activitis may contribut to th appropriat us of rgrssion analysis. 6) Masurmnt Error Bcaus th dpndnt variabl is on in rgrssion analysis, masurmnt rror occurs. Usually, a rsarchr maks dpndnt variabl by using of MEAN of a st of variabls. Espcially, whn stimating abstract concpts such as slf-concpt, dprssion lvls, or slf-stm, masurmnt rror occurs and influnc on th prdicting powr of rgrssion quations. Whn using SEM, th problm of masurmnt rror can b rducd. 7) Assumptions of Rgrssion Analysis Thr ar 4 assumptions: 1) linarity of th phnomnon masurd 2) constant varianc of th rror trms 3) indpndnc of th rror trms 4) normality of th rror trm distribution All assumptions should b tstd by chcking partial rgrssion plot, or by comparing null plot and rsidual plot. A rsarchr can idntify outlir from th plots too. Howvr, ths assumptions ar not satisfid, th rsults will provid wrong xplanation and prdiction. 8) Co-linarity or Multi-co-linarity This mans high rlation btwn indpndnt variabls and may driv into rducing th prdicting powr of ach indpndnt variabl and incrasing th prdicting powr of shard portion of indpndnt variabls to varianc. Thrfor, a rsarchr should stimat th lvl of co-linarity or multi-co-linarity, and s if it is problmatic or not. Thr ar a coupl of solutions: 1) dlting on variabl if th corrlation is vry high 2) If highly corrlatd two variabls ar important in modl, a rsarchr cannot tll th rlativ importanc among two, and should rport th rsult only for th purpos of prdicting, not xplaining. 3) Corrlation analysis is ncssary to s th rlationship btwn ach indpndnt variabl and dpndnt variabl. 9) Sampl Siz Th dgr of ovrstimation of R is affctd by th ratio of th numbr of prdictors to th sampl siz. Som rsarchrs rcommnd th ratio1:30 [2]. Howvr, to dtrmin sampl siz, statistical powr analysis is prfrabl. If th sampl siz is small, thr is a problm in gnralizing th rsults. III. PATH ANALYSIS Path analysis is a mthod for studying dirct and indirct ffcts. Path analysis is intndd not to discovr causs but to shd light on th tnability of th causal modl formulatd by a rsarchr. So, th aim of path analysis is an xplanation, not a prdiction. Of cours, th rsarchr should considr th thory or knowldg rlatd to what s/h wants to study. Path analysis can b considrd as on of SEMs which is composd of all 1637

5 obsrvd variabls, not using latnt variabls. 1 a b hand, is th part of th ffct of th indpndnt variabl that is mdiatd or transmittd by anothr variabl. And th total ffct is dfind as th sum of dirct and indirct ffcts. Dpnding on th causal modl, a variabl may or may not hav a dirct ffct on anothr variabl. 3 4 B S.52 A Fig. 1 An xampl of path analysis Fig. 1 is an xampl of path analysis. Th corrlation btwn xognous variabls is dpictd by a curvd arrow, indicating that th rsarchr dos not conciv of on variabl bing a caus of th othr. Th rlation btwn xognous variabls rmains unanalyzd. Variabl 1 and 2 is takn as a caus of 3. Variabl 3 is takn as a dpndnt on variabl 1 and 2 and as on of th indpndnt variabls with rspct to variabl 4. Bcaus it is almost nvr possibl to account for total varianc of variabls, rsiduals xprssd as a and b ar introducd to rprsnt ffcts of variabls not includd in th modl. A. Th Advantag of Path Analysis 1) Simultanous Analysis of Complx Modl Path analysis allows analyzing th rlationship btwn dpndnt variabls as wll as btwn indpndnt variabls and dpndnt variabls from on tim analysis. In path analysis, path cofficint is calculatd. It indicats th dirct ffct of a variabl hypothsizd as a caus of a variabl takn as an ffct. For xampl, P32 mans th dirct ffct of variabl 2 on variabl 3. Actually, th path cofficint is th standardizd rgrssion cofficints (bta) obtaind in multipl rgrssion analysis. In th multipl rgrssion analysis, dpndnt variabl is rgrssd in a singl analysis on all indpndnt variabls. Howvr, in path analysis, mor than on rgrssion analysis may b calld for. In th path analysis of Fig. 1, two path analyss ar calld for: from path analysis1, P31 and P32 ar obtaind by rgrssing variabl 3 on 1, and 2, and from path analysis2, P41 P42 and P43 ar obtaind by rgrssing variabl 4 on 1, 2and 3. 2) Dcomposition of Corrlations Anothr advantag of path analysis is that it affords th dcomposition of corrlations among variabls, thrby nhancing th intrprtation of rlations as wll as th pattrn of th ffcts of on variabl on anothr. From th path analysis, rsarchr can show th total ffct, th dirct ffct and indirct ffct via mdiation. In th analysis of causal modls, a distinction is mad btwn th dirct and indirct ffcts of indpndnt variabls on dpndnt variabls. A dirct ffct is dfind as th part of its ffct that is not mdiatd, or transmittd, by othr variabls. An indirct ffct, on th othr Fig. 2 Dirct ffct and indirct ffct Also, a variabl may hav mor than on indirct ffct on anothr variabl. Th us of path cofficints producs th corrlation matrix and plays an important rol in assssing th validity of a givn causal modl. Fig. 2 shows th dirct ffct and indirct ffct. Th dirct ffct of B on A is.30 and th indirct ffct of B on A via S is.31(=.52*.60). So, th total ffct is.61(= ). Somtims, it has bn oftn suggstd that path cofficints can b calculatd by carrying out rpatd multipl rgrssion analyss on appropriat substs of variabls [11]. It is partly tru but, if indpndnt variabls ar not corrlatd at all, this modl cannot b analyzd by multipl rgrssions and nds to dfin th corrct corrlation matrix by path analysis. B. Th Disadvantags of Path Analysis Although path analysis is usful tool for analyzing multipl causalitis, thr ar still svral problms. Such problms as th rquirmnts of linarity and homognity of variancs or th us of prdictor variabls that ar masurd with rrors ar commonly citd. Th following shorting comings ar rarly discussd in th us of path analysis [12]. 1) Limitation on Assumptions Th path analysis has th following assumptions. 1) Rlations among variabls in th modl ar linar, additiv, and causal. 2) Each rsidual is not corrlatd with variabls that prcd it in th modl. 3) Thr is on way causal flow. That is rciprocal causation btwn variabls is ruld out. 4) Th variabls ar masurd on an intrval scal. 5) Th variabls ar masurd without rror. All ths assumptions ar hard to b satisfid in social scinc. Thrfor, th assumptions itslf ar limitations. This issu will b discussd in nxt SEM sction. 2) Co-linarity Issu This is common problm in path analysis as wll as rgrssion analysis. Co-linarity occurs whn indpndnt variabls ar corrlatd highly, and influnc on th stimation of path cofficints to b lss accurat and mak rrors. Whn co-linarity incras, th ability to dtct a significant ffct is rducd and path cofficint bcoms lss accurat. Myrs (1990) suggstd that all VIF (Varianc Inflation Factor) should b lss than 10 [13]. Also, it is suggstd that all 1638

6 R-squir should b smallr than th R-squar of th complt modl [12]. 3) Maning of Modl fit Finding a significant fit of a path modl to a data st dos not dmonstrat that rlationships among variabls ar causal, bcaus causation may b mad by xtrnal lmnts to th statistical procss of path analysis. Also, rsarchrs may slip into a postriori approach to path analysis by adding or dropping variabls until a fit that maximizs th proportion of varianc xplaind is found. 4) Sampl Siz and Catgorical Variabls Us of catgorical variabls, non-random sampling, and small sampl siz prvnts th varianc-covarianc structur of th sampl from matching th varianc-covarianc structur of th population. Sampl siz should b at last to 20 tims largr than th numbr of stimatd paths to nsur rliabl rsults. Using catgorical variabls with fixd tratmnt lvls gnrally inflats th stimats of path cofficints. So, continuous variabls ar prfrrd [12]. IV. STRUCTURAL EQUATION MODEL (SEM) Path analysis is basd on a st of rstrictiv assumptions, som of which ar th 1) variabls ar masurd without rror, 2) rsiduals ar not corrlatd and 3) causal flow is unidirctional (rcursiv modl). Howvr, usually, it is vry hard t masur without rror. Classical approachs tratd rrors as bing random, but, many sourcs of rrors ar nonrandom (systmatic), affcting validity of masurmnt. Also, oftn, it is unrasonabl to assum that rsiduals from diffrnt quations ar not corrlatd. For xampl, in longitudinal rsarch whn subjcts ar masurd at svral points on th sam variabls, such assumption is untnabl. Finally, th third assumption about rcursiv modl is unralistic in many rsarchs which show rciprocal causation. Incom Education Discrimination Slf Estm Opprssion.5 Rsistanc Social Support Fig. 3 An xampl of structural quation modl Structural quation modl (SEM) with latnt variabl considrs th abov limitation of path analysis. SEM is composd of two major componnts; masurmnt quations Dprssion A B C (by confirmatory factor analysis) and structural quations (by path analysis). Confirmatory factor analysis modls (CFA), a spcial cas of SEM, ar widly usd in masurmnt applications for a varity of purpos. Dsigns for construct validation and scal rfinmnt, masurmnt invarianc can b valuatd through tsting of CFA. In ach componnt, masurmnt rror and structural rror is includd in analysis. Compard that path analysis has only structural rror, SEM includs both rrors in analysis. A. Advantags of SEM 1) Masurmnt Variabls and Latnt Variabl Masurmnt quations rfr to capturing latnt variabls. Th rprsntativ charactr of SEM is th us of latnt variabl which ar not applid at any othr analysis mthod. Latnt variabl rfr to constructs so that it is not obsrvabl. For xampl, mntal ability, motivation, slf-concpt, attitud ar latnt variabls. It is unralistic to xpct singl indicators to captur validly and rliably such complx constructs. Instad, multipl indicators ar ncssary to captur th ssnc of such variabls. To captur th constructs, masurmnt rrors should b prsntd in th modl. Th masurmnt rror rfrs to rror trm of indicators of latnt variabl and occurs whn a rsarchr input wrong data, whn rspondnts do not undrstand survy qustions, and whn rspondnts hav difficultis to provid ral information such as incom or wight. Idntifying masurmnt rror maks th causal quation modl btwn latnt variabls mor clar, compard path analysis or rgrssion. For xampl, th masurmnt rrors ar nglctd in multipl rgrssion analysis. In th procss of multipl rgrssion analysis, on or mor indpndnt variabls ar allowd, but only on dpndnt variabl is allowd. So, whn producing on dpndnt variabl, a rsarchr nds to combin svral variabls, which rquir rliability stimation (.g. tst-rtst, intrnal consistncy). Usually Cronbach s alpha is chckd, th sum or man of thm is usd in analysis aftr dlting th variabl that has alpha valu of smallr than.7 (or.6). In that procss, masurmnt rror is not considrd. (.g. th us of scal). If th rliability of a scal is qual to 1, it mans thr is no masurmnt rror. But it is impossibl that th valu of rliability is 1 in social scinc. On th othr hand, SEM considrs th latnt variabl with masurmnt rror which cannot b xplaind by latnt variabl. So, in SEM, a rsarchr can produc mor accurat causal rlationship btwn constructs. Although a rsarchr us sam st of data, th standardizd cofficint ar diffrnt in ach analysis mthod (SEM may show.67 and rgrssion analysis may show.60) Bcaus SEM considr th obsrvd variabls and masurmnt rror, it is possibl to infrnc causal rlationship btwn pur constructs (latnt variabls). A major advantag of using multipl indicators in SEM is that thy afford th study of rlations among latnt variabls uncontaminatd by rrors of masurmnt in th indicators. Hr, structural rror should b includd in modl. This is similar as th part unxplaind by proportion of varianc in multipl rgrssion analysis. This is calld as rsidual, 1639

7 disturbanc, quation rror, or prdiction rror. Bcaus ndognous latnt variabl ar not influncd only by xognous latnt variabls introducd in modl, structural rror occurs. 2) Simultanous Estimation Th various statistical mthods such as t-tst, ANOVA, MANOVA, multipl rgrssion analysis, canonical corrlation analysis hav a common limitation. Most of mthods can show th singl rlation btwn indpndnt variabl and dpndnt variabl. In rgrssion analysis, on or mor indpndnt variabls ar includd in analysis, but dpndnt variabl should b on. In canonical corrlation analysis and MANOVA, mor than on indpndnt variabls and dpndnt variabls ar considrd, but th analysis is rstrictd bcaus it can only show th rlationship btwn indpndnt variabl and dpndnt variabl. On th othr hand, SEM can show th rlationship among dpndnt variabls. In SEM, mor than on of xognous variabls and ndognous variabls ar stimatd simultanously. Also, th causal rlationship btwn ndognous variabls can b stimatd. For xampl, whn a rsarchr wants to s th rlationship, A-> B -> C-> D, total 4 analyss should b conductd in multipl rgrssion analysis. On th othr hand, through SEM, th simultanous stimation is possibl. 3) Dirct Effct, Indirct Effct, and Total Effct In SEM, a rsarchr can show th dirct ffct, indirct ffct, and total ffct bcaus of mor than on of xognous variabls and ndognous variabls ar stimatd simultanously. For xampl, s Fig. 3. Th dirct ffct of opprssion on dprssion is.7. Th indirct ffct of opprssion on dprssion via rsistanc is -.1 (=-0.2*0.5). Total ffct is.6 (= ). 4) Applying Multipl Statistical Mthod in On Modl SEM is composd of masurmnt quations (by confirmatory factor analysis) and structural quations (by path analysis). Also th corrlations btwn xognous variabl ar considrd in on modl and prsntd as curvd lin. Morovr, structural rrors in ndognous variabl ar considrd. Thrfor, confirmatory factor analysis, corrlation analysis, and rgrssion analysis can b conductd at on tim in a modl. 5) Rciprocal Causal Rlationship SEM can show rciprocal causal rlationship btwn latnt variabl. 6) Easily Accssibl Softwar program, AMOS allows rsarchrs to analyz data convnintly. For xampl, multi-sampl modling, whrin a modl is fit simultanously to sampl data from diffrnt populations, is possibl. This approach involvs th tsting of invarianc of critical paramtrs across groups (.g. comparing mal and fmal to invstigat prdictors of motional wll-bing). B. Th Disadvantags of SEM SEM has various advantags as I mntiond abov, but has bn criticizd by famous scholars such as Cox, Frdman, Rogosa, Rubin, Spd, Wrmuth and so on [14]. Th limitations of SEM ar following. 1) Inappropriat Intrprtation Som rsarchrs usd to analyz modl inappropriatly or to intrprt th rsult incorrctly. Ths problms ar causd by poor undrstanding on rgrssion analysis, factor analysis, or corrlation analysis. Rsarchrs should hav knowldg about SEM rlatd mthods. Without undrstanding basic concpt of thm, to apply SEM rsults in th poor and inappropriat intrprtation and th wrong application of SEM. 2) Various Modifid Modls In SPSS, if diffrnt rsarchrs us sam data and apply sam statistical mthod, thir rsults ar sam. Howvr, SEM provids various tools to rsarchrs. So, whn givn sam data and sam rsarch modls, various modls can b mad by diffrnt rsarchrs. For xampl, by using obsrvd variabls without latnt variabls, path analysis modl can b mad instad of SEM. Also, by putting in or gtting out latnt variabls in modl, or by adding or dlting paths, various modifid modl can b mad. In a discussion of tsts of SEM, Jorskog and Sorbom (1993) distinguishd among th following rsarch situation: SC, AM, and MG [15]. First, SC (Strictly Confirmatory) situation mans that th rsarchr has formulatd on singl modl and has obtaind mpirical data to tst it in a strictly confirmatory situation. Th modl should b accptd or rjctd. Scond, AM (Altrnativ Modls) situation mans that th rsarchr has spcifid svral altrnativ modls or compting modls and on th basis of a singl st of mpirical data, on of th modls should b slctd. Third, MG (Modl Gnrating) situation mans that th rsarchr has spcifid a tntativ initial modl. If th initial modl dos not fit th givn data, th modl should b modifid and tstd again using th sam data. Th goal is to find a modl which not only fits th data wll, but also has th proprty that vry paramtr of th modl can b givn a substantivly maningful intrprtation. Th spcification of ach modl may b thory-drivn or data-drivn. Although th modl may b tstd in ach round, th actual whol approach is modl gnrating, not modl tsting. Among thm, MG situation is most common. Th rsarchrs may kp on making adjustmnts by adding nw variabls and dropping significant ons until th most prfrrd modl is gnratd. So, SEM is criticizd as probably poor tool in xplanatory situations with many variabls and wak or non-xisting substantiv thory [15]. 3) Errors from th Us of Multipl Statistical Mthods In SEM, multipl statistical mthods such as confirmatory factor analysis, path analysis, and corrlation analysis ar applid in on modl and stimatd simultanously. This is an advantag and disadvantag of SEM at th sam tim bcaus rrors may occur in rsults. For xampl, th positiv rlationship btwn two variabls in corrlation analysis may 1640

8 b shown as ngativ rlationship in th rsult of SEM analysis. Or, path cofficint is shown as ovr 1 in th rsult of SEM analysis, which is not mak sns in rgrssion analysis bcaus standardizd cofficint cannot b ovr 1. Ths strang and difficult situations may happn in SEM analysis. By modifying modl or by dlting a variabl, rsarchrs can solv th problms, but bginnrs who ar not familiar with SEM may intrprt th rsult inappropriatly. 4) Gnralization Thr is a problm of gnralization of findings from SEM bcaus rsults from SEM ar subjct to sampling or slction ffcts with rspct to at last thr aspcts: individuals, masurs, and occasions [1]. First, thr is sampling ffct with rspct to individuals in most rsarchs, which caus th limitation in gnralizing th rsults. By th us of cross-validation indx, it is possibl to provid an indication of which modl yilds a solution with gratst gnralizability whn sampl siz is not larg. Cross-validation indx is computd from a singl sampl, as an indx of how wll a solution obtaind in on sampl is likly to fit an indpndnt sampl. This indx is usful for comparison of altrnativ modls. Scond, slction ffcts ar in th choic of masurd variabls in a givn study. Espcially, in SEM, this issu is prominnt with rgard to th choic of indicators to compos of latnt variabls. Th natur of th latnt variabls dpnds on th choic of indicators, which may influnc rsults and intrprtation. Valid rsults and intrprtation rly on having appropriat latnt variabls. Third, slction ffcts involvs occasions of masurmnt. In any study whr on invstigats ffcts that oprat ovr tim, ths ffcts may vary with th lngth of th tim intrval. 5) Confirmation Bias It is asy to accpt an xplanation that fits data wll, and that rsarchrs ar not motivatd to considr altrnativ modls. Espcially, with th xistnc of quivalnt modls, which ar altrnativ modls that fit any data to th sam dgr, rsarchrs ar almost unawar of this phnomnon, or thy choos to ignor it. Ruling out thir xistnc may strngthn th support of a favord modl. MacCallum t al (2000) statd that quivalnt modls occur routinly in practic, oftn in larg numbrs and rsarchrs nd to gnrat th substantiv maningfulnss of quivalnt modls [1]. 6) Whn Singl Indicator for Latnt Variabl Is Availabl A full latnt variabls (LV) modl spcifis rlationships of th indicators to th LVs as wll as rlationships of th LVs to ach othr. Somtims, only on singl indicator is availabl for ach LV. This is similar as path analysis. In this cas, it is a problm that th singl variabl is not nough to rprsnt LV. If th singl variabl is composd of multi itms scal (.g. CESD, dprssion scal), it can b a solution to construct parcls. A parcl is simply a sum of a subst of itms from th scal. Multipl parcls can b dfind by aggrgating distinct subst itms and parcls srv as indicators of LVs. A rsarchr can gt advantag of full LVs modls and avoid som difficultis associatd with masurd variabls path analysis modl. 7) Issu of Tim Dirctional ffcts in SEM can b considrd as causal ffcts whrin a chang in on variabl rsults in a chang in anothr variabl, and thr ar thr proprtis of such ffcts [1]: (a) ths ffcts tak som finit amount of tim to oprat (b) a variabl may b influncd by th sam variabl at an arlir point in tim (autorgrssiv ffct) (c) th magnitud of an ffct may vary as a function of th tim lag [1]. Espcially, a rsarchr should mntion about ths problms for cross-sctional modls that includ dirctional influncs. Also, thy should provid autorgrssiv ffct for longitudinal dsigns. Unfortunatly, howvr, many studis show inadquat considration of tim issu in dsign. 8) Sampl Siz Th modl than can b bst supportd may dpnd on sampl siz. Simplr modls ar favord whn sampl siz is small [1]. 9) Issu of Tim In application of SEM, rsarchr must dcid whthr to fit a modl to a covarianc matrix, S or a corrlation matrix, R. Currntly, rsarchrs sm unawar that fitting a modl to R vrsus S introduc potntial problm and about 50% of th publishd applications fit modls to corrlational matrix [1]. Actually, thr ar intrprtational advantags to using R. So, MacCallum and Austin urgd rsarchrs fitting modls to corrlation matrix to b crtain that thir SEM softwar trats such matrix corrctly. Othrwis, it would b prfrabl to fit modl to covarianc matrix. 10) Intrprtation of Rsult A finding of good fit dos not imply that th modl is corrct or not, but only plausibl. In addition, good modl fit dos not man that ffcts hypothsizd in th modl ar strong. Th actual rlationship may b vry wak, vn zro, bcaus th rlationship can b mad by rsidual varianc fro ndognous variabls. Good modl fit dos not imply at all that such rsidual variancs ar small. Thrfor, such information should b discussd and rportd for full undrstanding of th magnitud of ffcts. Application of SEM should provid at last th following information: a clar modls and variabls, including clar indicators of ach LV, a clar statmnt of th typ of data, with prsntation of th sampl corrlation or covarianc matrix; spcification of th softwar and mthod of stimation; and complt rsults including modl fit indx such as RMSEA, NNFI, and GFI. REFERENCES [1] MacCallum, R. C., & Austin, J. T. (2000). Applications of Structural Equation Modling in Psychological Rsarch. Annual Rviw of Psychology, 51(1), doi: doi: /annurv.psych [2] Pdhazur, E. J. (1997). Multipl rgrssion in bhavioral rsarch (Third d.). Fort Worth, TX: Harcourt Brac Collg Publishrs. [3] Darlington, R.B. (1968). Multipl Rgrssion In Psychological Rsarch And Practic. Psychological Bulltin, Vol 69(3),

9 [4] Ward, J. H. (1969).Synthsizing Rgrssion Modls -- An Aid to Larning Effctiv Problm Analysis,'' Th Amrican Statistician, 23, [5] Goldbrgr A.S. (1991) A cours in conomtrics. Cambridg, MA. Harvard Univrsity Prss. [6] Lwis-Bck M.S. and Skalaban A.(1991) Th R-squard: Som straight talk In J. A. Stimson (Ed.) Political analysis: Vol 2. Ann Arbor MI: Th Univrsity of Michigan. [7] Cohn J. and Cohn P. (1983) Applid multipl rgrssion/corrlation analysis for th bhavioral scincs (2nd. Ed.). Hillsdal, NJ: Lawrnc Erlbaum Associats. [8] Mallinckrodt, B. (1992) Childhood motional bonds with parnts, dvlopmnt of adult social comptncis, and availability of social support. Journal of Counsling Psychology, 39, [9] Konovsky, M.A. Folgr, R. &Cropanzano, R. (1987) Rlativ ffcts of procdural and distributiv justic on mploy attituds. Rprsntativ Rsarch in Social Psychology, 17, [10] Ruttr M. (2007) Procding from obsrvd corrlation to causal infrnc: th us of natural xprimnts, Prspctivs on Psychological Scinc, 2 (4): [11] Mitchll, R. J. (1992). Tsting Evolutionary and Ecological Hypothss Using Path Analysis and Structural Equation Modlling. Functional Ecology, 6(2), [12] Ptraitis, P. S., Dunham, A. E., &Niwiarowski, P. H. (1996). Infrring multipl causalitis: Th Limitations of Path Analysis. Functional Ecology, 10(4), [13] Myrs R. (1990). Classical and modrn rgrssion with applications 2nd d. Duxbury Prss, Boston [14] Hoyl, R.H.&Pantr, A.T. (1995) Writing about structural quation modls. In R.H. Hoyl (Ed.), Structural quation modling: Commnts, issus and applications Thousand Oaks, CA:Sag [15] Jorskog K.G. and Sorbom, D. (1993) LISREL8: Structural quation modling with th SIMPLIS command languag. Hillsdal, NJ: Lawrnc Erlbaum Associats. Jihy Jon rcivd B.A. and M.A. in Social Wlfar from Yonsi Univrsity in Soul, South Kora in 2000 and 2002 rspctivly. Sh rcivd anothr M.A. in Social Policy and Planning from London School of Economics and Political Scincs, UK in 2004 and rcivd Ph.D. in Disability Study from Univrsity of Illinois at Chicago, USA in Sh is currntly snior rsarchr in Kora Disabld Popl s Dvlopmnt Institut undr Ministry of Halth and Wlfar. 1642