44:, in CCA all variables can be observable, with their interrelationships expressed in terms of composites, i.e., linear compounds of subsets of the variables. The composites are treated as the fundamental objects and path diagrams can be used to illustrate their relationships. This makes CCA particularly useful for disciplines examining theoretical concepts that are designed to attain certain goals, so-called artifacts, and their interplay with theoretical concepts of behavioral sciences.
62:
1197:
reflective and formative measurement models, CCA aims at assessing composite models; (ii) PLS-CCA omits overall model fit assessment, which is a crucial step in CCA as well as SEM; (iii) PLS-CCA is strongly linked to PLS-PM, while for CCA PLS-PM can be employed as one estimator, but this is in no way mandatory. Hence, researchers who employ need to be aware to which technique they are referring to.
1188:) In contrast to fit measures for common factor models, fit measures for composite models are relatively unexplored and reliable thresholds still need to be determined. To assess the overall model fit by means of statistical testing, the bootstrap test for overall model fit, also known as Bollen-Stine bootstrap test, can be used to investigate whether a composite model fits to the data.
53:
developments of CCA were shared with the scientific community in written form. Moreover, CCA was presented at several conferences including the 5th Modern
Modeling Methods Conference, the 2nd International Symposium on Partial Least Squares Path Modeling, the 5th CIM Community Workshop, and the Meeting of the SEM Working Group in 2018.
970:
to a certain value. If the composites are embedded in a structural model, also the structural model needs to be identified. Finally, since the weight signs are still undetermined, it is recommended to select a dominant indicator per block of indicators that dictates the orientation of the composite.
969:
of the composite model, each composite must be correlated with at least one variable not forming the composite. Additionally to this non-isolation condition, each composite needs to be normalized, e.g., by fixing one weight per composite, the length of each weight vector, or the composite’s variance
1196:
Besides the originally proposed CCA, the evaluation steps known from partial least squares structural equation modeling (PLS-SEM) are dubbed CCA. It is emphasized that PLS-SEM's evaluation steps, in the following called PLS-CCA, differ from CCA in many regards:. (i) While PLS-CCA aims at conforming
52:
The initial idea of CCA was sketched by Theo K. Dijkstra and Jörg
Henseler in 2014. The scholarly publishing process took its time until the first full description of CCA was published by Florian Schuberth, Jörg Henseler and Theo K. Dijkstra in 2018. As common for statistical developments, interim
429:
790:
1159:, can be assessed in two non-exclusive ways. On the one hand, measures of fit can be employed; on the other hand, a test for overall model fit can be used. While the former relies on heuristic rules, the latter is based on statistical inferences.
314:
of the sub-vectors are not constrained beyond being positive definite. Similar to the latent variables of a factor model, the composites explain the covariances between the sub-vectors leading to the following inter-block covariance matrix:
280:
1683:
69:
A composite is typically a linear combination of observable random variables. However, also so-called second-order composites as linear combinations of latent variables and composites, respectively, are conceivable.
1362:
Henseler, Jörg; Dijkstra, Theo K.; Sarstedt, Marko; Ringle, Christian M.; Diamantopoulos, Adamantios; Straub, Detmar W.; Ketchen, David J.; Hair, Joseph F.; Hult, G. Tomas M.; Calantone, Roger J. (2014).
213:
321:
598:
1406:
Dijkstra, Theo K. (2010). "Latent
Variables and Indices: Herman Wold's Basic Design and Partial Least Squares". In Esposito Vinzi, Vincenzo; Chin, Wynne W.; Henseler, Jörg; Wang, Huiwen (eds.).
40:(CFA). It shares with CFA the process of model specification, model identification, model estimation, and model assessment. However, in contrast to CFA which always assumes the existence of
911:
733:
1135:
664:
696:
549:
312:
122:
1157:
997:
955:
933:
882:
860:
838:
816:
721:
620:
93:
1186:
1162:
Fit measures for composite models comprises statistics such as the standardized root mean square residual (SRMR), and the root mean squared error of outer residuals (RMS
463:
282:. Moreover, it is assumed that the observable random variables are standardized having a mean of zero and a unit variance. Generally, the variance-covariance matrices
517:
490:
153:
2043:
Hair, Joe F.; Howard, Matt C.; Nitzl, Christian (March 2020). "Assessing measurement model quality in PLS-SEM using confirmatory composite analysis".
1452:
Dijkstra, Theo K.; Henseler, Jörg (2011). "Linear indices in nonlinear structural equation models: best fitting proper indices and other composites".
36:(PLS-PM), it has become an independent approach and the two should not be confused. In many ways it is similar to, but also quite distinct from
1881:
Hu, Li-tze; Bentler, Peter M. (1998). "Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification".
226:
1511:
1433:
2117:
1095:
33:
2027:
1919:
1740:
1083:
424:{\displaystyle \mathbf {\Sigma } _{ij}=\rho _{ij}\mathbf {\Sigma } _{ii}\mathbf {w} _{i}(\mathbf {\Sigma } _{jj}\mathbf {w} _{j})'}
1651:"Estimating hierarchical constructs using consistent partial least squares: The case of second-order composites of common factors"
974:
554:
223:). In the following, it is assumed that the weights are scaled in such a way that each composite has a variance of one, i.e.,
1098:
and generalized structured component analysis can be employed to estimate weights and the correlations among the composites.
161:
1082:
To estimate the parameters of a composite model, various methods that create composites can be used such as approaches to
1091:
1087:
724:
37:
29:
1731:
Henseler, Jörg & Schuberth, Florian (2021). "Chapter 8: Confirmatory
Composite Analysis". In Henseler, Jörg (ed.).
1968:
Bollen, Kenneth A.; Stine, Robert A. (1992). "Bootstrapping
Goodness-of-Fit Measures in Structural Equation Models".
887:
785:{\displaystyle \mathbf {B} \mathbf {c} _{\text{endogenous}}=\mathbf {C} \mathbf {c} _{\text{exogenous}}+\mathbf {z} }
1757:
1494:
Dijkstra, Theo K. (2017). "A Perfect Match
Between a Model and a Mode". In Latan, Hengky; Noonan, Richard (eds.).
1109:
625:
1805:"Specifying composites in structural equation modeling: A refinement of the Henseler-Ogasawara specification"
669:
522:
285:
1106:
In CCA, the model fit, i.e., the discrepancy between the estimated model-implied variance-covariance matrix
1411:
701:
In addition, the composites can be related via a structural model which constrains the correlation matrix
977:
of the basic composite model, i.e., with no constraints imposed on the composites' correlation matrix
98:
1684:"Estimating and assessing second-order constructs using PLS-PM: the case of composites of composites"
1416:
1140:
980:
938:
916:
865:
843:
821:
799:
704:
603:
76:
2060:
1985:
1863:
1785:
1713:
1469:
1758:"The Henseler-Ogasawara specification of composites in structural equation modeling: A tutorial"
1165:
438:
1548:
2023:
1915:
1777:
1736:
1631:
1586:
Is the whole more than the sum of its parts? On the interplay of marketing and design research
1507:
1429:
1299:
2091:
2052:
1977:
1948:
1890:
1855:
1826:
1816:
1769:
1703:
1695:
1662:
1621:
1613:
1563:
1499:
1461:
1421:
1386:
1376:
1335:
1289:
1279:
1237:
1227:
1496:
Partial Least
Squares Path Modeling: Basic Concepts, Methodological Issues and Applications
495:
468:
131:
2080:"Confirmatory composite analysis using partial least squares: Setting the record straight"
1549:"Bridging Design and Behavioral Research With Variance-Based Structural Equation Modeling"
966:
519:. The composite model imposes rank one constraints on the inter-block covariance matrices
41:
1602:"Three Cs in measurement models: Causal indicators, composite indicators, and covariates"
1216:"Using confirmatory composite analysis to assess emergent variables in business research"
1051:
number of free non-redundant off-diagonal elements of each intra-block covariance matrix
1031:
number of free covariances between the composites and indicators not forming a composite
1626:
1601:
1294:
1267:
1094:. Moreover, a maximum-likelihood estimator and composite-based methods for SEM such as
1410:. Berlin, Heidelberg: Springer Handbooks of Computational Statistics. pp. 23–46.
2111:
2064:
1989:
1867:
1846:
Hwang, Heungsun; Takane, Yoshio (2004). "Generalized structured component analysis".
1789:
1733:
Composite-based
Structural Equation Modeling: Analyzing Latent and Emergent Variables
1717:
1473:
884:
contains the structural error terms having a zero mean and being uncorrelated with
2056:
1568:
1232:
1215:
1909:
1649:
van Riel, Allard C. R.; Henseler, Jörg; Kemény, Ildikó; Sasovova, Zuzana (2017).
1011:
number of non-redundant off-diagonal elements of the indicator covariance matrix
32:(SEM). Although, historically, CCA emerged from a re-orientation and re-start of
1981:
1503:
1425:
61:
2096:
2079:
2003:
Hair, Joe F.; Hult, G Tomas M.; Ringle, Christian M.; Sarstedt, Marko (2014).
1894:
1699:
1667:
1650:
1465:
1340:
1323:
862:
contain the so-called path (and feedback) coefficients. Moreover, the vector
17:
1953:
1937:"Bootstrap Tests and Confidence Regions for Functions of a Covariance Matrix"
1936:
1584:
1381:
1364:
1284:
1781:
1635:
1303:
2018:
Hair, Joseph F.; Anderson, Drexel; Babin, Barry; Black, William (2018).
2005:
A Primer on
Partial Least Squares Structural Equation Modeling (PLS-SEM)
1831:
1708:
1391:
1324:"Using PLS path modeling in new technology research: updated guidelines"
1242:
818:
is partitioned in an exogenous and an endogenous part, and the matrices
275:{\displaystyle \mathbf {w} _{i}'\mathbf {\Sigma } _{ii}\mathbf {w} _{i}}
1859:
1773:
1821:
1804:
219:
where the weights of each composite are appropriately normalized (see
1617:
124:, composites can be defined as weighted linear combinations. So the
1041:
number of covariances among the indicators not forming a composite
622:
is positive definite iff the correlation matrix of the composites
60:
1682:
Schuberth, Florian; Rademaker, Manuel E; Henseler, Jörg (2020).
1266:
Schuberth, Florian; Henseler, Jörg; Dijkstra, Theo K. (2018).
95:
of observable variables that is partitioned into sub-vectors
1498:. Cham: Springer International Publishing. pp. 55–80.
1322:
Henseler, Jörg; Hubona, Geoffrey; Ray, Pauline Ash (2016).
1911:
Latent
Variable Path Modeling with Partial Least Squares
593:{\displaystyle {\text{rank}}(\mathbf {\Sigma } _{ij})=1}
208:{\displaystyle c_{i}=\mathbf {w} _{i}'\mathbf {x} _{i}}
1168:
1143:
1112:
983:
941:
919:
913:. As the model needs not to be recursive, the matrix
890:
868:
846:
824:
802:
736:
707:
672:
628:
606:
557:
525:
498:
471:
441:
324:
288:
229:
164:
134:
101:
79:
221:
Confirmatory composite analysis#Model identification
1803:Yu, Xi; Schuberth, Florian; Henseler, Jörg (2023).
1180:
1151:
1129:
991:
949:
935:is not necessarily triangular and the elements of
927:
905:
876:
854:
832:
810:
784:
715:
690:
658:
614:
592:
543:
511:
484:
457:
423:
306:
274:
207:
147:
116:
87:
1021:number of free correlations among the composites
600:. Generally, the variance-covariance matrix of
1261:
1259:
1257:
1255:
1253:
906:{\displaystyle \mathbf {c} _{\text{exogenous}}}
1542:
1540:
1538:
1489:
1487:
1485:
1483:
1447:
1445:
1357:
1355:
1353:
1351:
1317:
1315:
1313:
8:
1935:Beran, Rudolf; Srivastava, Muni S. (1985).
1600:Bollen, Kenneth A.; Bauldry, Shawn (2011).
1214:Henseler, Jörg; Schuberth, Florian (2020).
1130:{\displaystyle {\hat {\mathbf {\Sigma } }}}
659:{\displaystyle \mathbf {R} :=(\rho _{ij})}
465:is the correlation between the composites
65:Example of a model containing 3 composites
2095:
1952:
1830:
1820:
1707:
1666:
1625:
1567:
1531:(3rd ed.). Cambridge, MA: MIT Press.
1415:
1390:
1380:
1339:
1293:
1283:
1241:
1231:
1172:
1167:
1144:
1142:
1116:
1114:
1113:
1111:
984:
982:
942:
940:
920:
918:
897:
892:
889:
869:
867:
847:
845:
825:
823:
803:
801:
777:
768:
763:
757:
748:
743:
737:
735:
708:
706:
679:
674:
671:
644:
629:
627:
607:
605:
572:
567:
558:
556:
532:
527:
524:
503:
497:
476:
470:
446:
440:
407:
402:
392:
387:
377:
372:
362:
357:
347:
331:
326:
323:
295:
290:
287:
266:
261:
251:
246:
236:
231:
228:
220:
199:
194:
184:
179:
169:
163:
139:
133:
108:
103:
100:
80:
78:
1735:. The Guilford Press. pp. 179–201.
1688:Industrial Management & Data Systems
1655:Industrial Management & Data Systems
1328:Industrial Management & Data Systems
1206:
691:{\displaystyle \mathbf {\Sigma } _{jj}}
544:{\displaystyle \mathbf {\Sigma } _{ij}}
307:{\displaystyle \mathbf {\Sigma } _{ii}}
1365:"Common Beliefs and Reality About PLS"
2022:(8 ed.). Cengage Learning EMEA.
666:and the variance-covariance matrices
7:
1809:Statistical Analysis and Data Mining
1970:Sociological Methods & Research
1096:partial least squares path modeling
34:partial least squares path modeling
14:
1589:. Enschede: University of Twente.
1408:Handbook of Partial Least Squares
1268:"Confirmatory Composite Analysis"
1084:generalized canonical correlation
1145:
1117:
985:
943:
921:
893:
870:
848:
826:
804:
778:
764:
758:
744:
738:
709:
675:
630:
608:
568:
528:
403:
388:
373:
358:
327:
291:
262:
247:
232:
195:
180:
117:{\displaystyle \mathbf {x} _{i}}
104:
81:
1369:Organizational Research Methods
698:'s are both positive definite.
22:confirmatory composite analysis
1529:The sciences of the artificial
1121:
653:
637:
581:
563:
414:
383:
1:
2057:10.1016/j.jbusres.2019.11.069
1914:. Physica-Verlag Heidelberg.
1908:Lohmöller, Jan-Bernd (1989).
1569:10.1080/00913367.2017.1281780
1233:10.1016/j.jbusres.2020.07.026
999:, are calculated as follows:
2084:Review of Managerial Science
2045:Journal of Business Research
1220:Journal of Business Research
1152:{\displaystyle \mathbf {S} }
1092:linear discriminant analysis
1088:principal component analysis
992:{\displaystyle \mathbf {R} }
950:{\displaystyle \mathbf {z} }
928:{\displaystyle \mathbf {B} }
877:{\displaystyle \mathbf {z} }
855:{\displaystyle \mathbf {C} }
833:{\displaystyle \mathbf {B} }
811:{\displaystyle \mathbf {c} }
716:{\displaystyle \mathbf {R} }
615:{\displaystyle \mathbf {x} }
88:{\displaystyle \mathbf {x} }
38:confirmatory factor analysis
30:structural equation modeling
2078:Schuberth, Florian (2021).
1982:10.1177/0049124192021002004
1756:Schuberth, Florian (2023).
1504:10.1007/978-3-319-64069-3_4
1426:10.1007/978-3-540-32827-8_2
1137:and its sample counterpart
73:For a random column vector
2134:
2118:Structural equation models
2097:10.1007/s11846-020-00405-0
2020:Multivariate data analysis
1527:Simon, Herbert A. (1969).
1181:{\displaystyle _{\theta }}
458:{\displaystyle \rho _{ij}}
1895:10.1037/1082-989X.3.4.424
1700:10.1108/IMDS-12-2019-0642
1668:10.1108/IMDS-07-2016-0286
1466:10.1007/s11135-010-9359-z
1341:10.1108/IMDS-09-2015-0382
1941:The Annals of Statistics
1382:10.1177/1094428114526928
1285:10.3389/fpsyg.2018.02541
1192:Alternative views on CCA
723:indirectly via a set of
1583:Henseler, Jörg (2015).
1547:Henseler, Jörg (2017).
1272:Frontiers in Psychology
2007:. Thousand Oaks: Sage.
1954:10.1214/aos/1176346579
1556:Journal of Advertising
1454:Quality & Quantity
1182:
1153:
1131:
993:
951:
929:
907:
878:
856:
834:
812:
786:
725:simultaneous equations
717:
692:
660:
616:
594:
545:
513:
486:
459:
425:
308:
276:
209:
149:
118:
89:
66:
1883:Psychological Methods
1762:Psychological Methods
1606:Psychological Methods
1183:
1154:
1132:
994:
952:
930:
908:
879:
857:
835:
813:
787:
718:
693:
661:
617:
595:
546:
514:
512:{\displaystyle c_{i}}
487:
485:{\displaystyle c_{j}}
460:
426:
309:
277:
210:
150:
148:{\displaystyle c_{i}}
119:
90:
64:
1166:
1141:
1110:
1102:Evaluating model fit
981:
961:Model identification
939:
917:
888:
866:
844:
822:
800:
734:
705:
670:
626:
604:
555:
523:
496:
469:
439:
322:
286:
227:
162:
132:
99:
77:
957:may be correlated.
244:
192:
28:) is a sub-type of
1860:10.1007/BF02295841
1774:10.1037/met0000432
1178:
1149:
1127:
1061:number of weights
989:
975:degrees of freedom
947:
925:
903:
874:
852:
830:
808:
782:
713:
688:
656:
612:
590:
541:
509:
482:
455:
421:
304:
272:
230:
205:
178:
145:
114:
85:
67:
1822:10.1002/sam.11608
1694:(12): 2211–2241.
1513:978-3-319-64068-6
1435:978-3-540-32825-4
1124:
1075:
1074:
1071:number of blocks
900:
796:where the vector
771:
751:
561:
57:Statistical model
2125:
2102:
2101:
2099:
2090:(5): 1311–1345.
2075:
2069:
2068:
2040:
2034:
2033:
2015:
2009:
2008:
2000:
1994:
1993:
1965:
1959:
1958:
1956:
1932:
1926:
1925:
1905:
1899:
1898:
1878:
1872:
1871:
1843:
1837:
1836:
1834:
1824:
1800:
1794:
1793:
1753:
1747:
1746:
1728:
1722:
1721:
1711:
1679:
1673:
1672:
1670:
1646:
1640:
1639:
1629:
1618:10.1037/a0024448
1597:
1591:
1590:
1580:
1574:
1573:
1571:
1553:
1544:
1533:
1532:
1524:
1518:
1517:
1491:
1478:
1477:
1460:(6): 1505–1518.
1449:
1440:
1439:
1419:
1403:
1397:
1396:
1394:
1384:
1359:
1346:
1345:
1343:
1319:
1308:
1307:
1297:
1287:
1263:
1248:
1247:
1245:
1235:
1211:
1187:
1185:
1184:
1179:
1177:
1176:
1158:
1156:
1155:
1150:
1148:
1136:
1134:
1133:
1128:
1126:
1125:
1120:
1115:
1078:Model estimation
1002:
1001:
998:
996:
995:
990:
988:
956:
954:
953:
948:
946:
934:
932:
931:
926:
924:
912:
910:
909:
904:
902:
901:
898:
896:
883:
881:
880:
875:
873:
861:
859:
858:
853:
851:
839:
837:
836:
831:
829:
817:
815:
814:
809:
807:
791:
789:
788:
783:
781:
773:
772:
769:
767:
761:
753:
752:
749:
747:
741:
722:
720:
719:
714:
712:
697:
695:
694:
689:
687:
686:
678:
665:
663:
662:
657:
652:
651:
633:
621:
619:
618:
613:
611:
599:
597:
596:
591:
580:
579:
571:
562:
559:
550:
548:
547:
542:
540:
539:
531:
518:
516:
515:
510:
508:
507:
491:
489:
488:
483:
481:
480:
464:
462:
461:
456:
454:
453:
430:
428:
427:
422:
420:
412:
411:
406:
400:
399:
391:
382:
381:
376:
370:
369:
361:
355:
354:
339:
338:
330:
313:
311:
310:
305:
303:
302:
294:
281:
279:
278:
273:
271:
270:
265:
259:
258:
250:
240:
235:
214:
212:
211:
206:
204:
203:
198:
188:
183:
174:
173:
154:
152:
151:
146:
144:
143:
123:
121:
120:
115:
113:
112:
107:
94:
92:
91:
86:
84:
42:latent variables
2133:
2132:
2128:
2127:
2126:
2124:
2123:
2122:
2108:
2107:
2106:
2105:
2077:
2076:
2072:
2042:
2041:
2037:
2030:
2017:
2016:
2012:
2002:
2001:
1997:
1967:
1966:
1962:
1934:
1933:
1929:
1922:
1907:
1906:
1902:
1880:
1879:
1875:
1845:
1844:
1840:
1802:
1801:
1797:
1755:
1754:
1750:
1743:
1730:
1729:
1725:
1681:
1680:
1676:
1648:
1647:
1643:
1599:
1598:
1594:
1582:
1581:
1577:
1551:
1546:
1545:
1536:
1526:
1525:
1521:
1514:
1493:
1492:
1481:
1451:
1450:
1443:
1436:
1417:10.1.1.579.8461
1405:
1404:
1400:
1361:
1360:
1349:
1321:
1320:
1311:
1265:
1264:
1251:
1213:
1212:
1208:
1203:
1194:
1169:
1164:
1163:
1139:
1138:
1108:
1107:
1104:
1080:
979:
978:
963:
937:
936:
915:
914:
891:
886:
885:
864:
863:
842:
841:
820:
819:
798:
797:
762:
742:
732:
731:
703:
702:
673:
668:
667:
640:
624:
623:
602:
601:
566:
553:
552:
526:
521:
520:
499:
494:
493:
472:
467:
466:
442:
437:
436:
413:
401:
386:
371:
356:
343:
325:
320:
319:
289:
284:
283:
260:
245:
225:
224:
193:
165:
160:
159:
135:
130:
129:
102:
97:
96:
75:
74:
59:
50:
12:
11:
5:
2131:
2129:
2121:
2120:
2110:
2109:
2104:
2103:
2070:
2035:
2029:978-1473756540
2028:
2010:
1995:
1976:(2): 205–229.
1960:
1927:
1920:
1900:
1889:(4): 424–453.
1873:
1838:
1815:(4): 348–357.
1795:
1768:(4): 843–859.
1748:
1741:
1723:
1674:
1661:(3): 459–477.
1641:
1612:(3): 265–284.
1592:
1575:
1562:(1): 178–192.
1534:
1519:
1512:
1479:
1441:
1434:
1398:
1375:(2): 182–209.
1347:
1309:
1249:
1205:
1204:
1202:
1199:
1193:
1190:
1175:
1171:
1147:
1123:
1119:
1103:
1100:
1079:
1076:
1073:
1072:
1069:
1066:
1063:
1062:
1059:
1056:
1053:
1052:
1049:
1046:
1043:
1042:
1039:
1036:
1033:
1032:
1029:
1026:
1023:
1022:
1019:
1016:
1013:
1012:
1009:
1006:
987:
967:identification
962:
959:
945:
923:
895:
872:
850:
828:
806:
794:
793:
780:
776:
766:
760:
756:
746:
740:
711:
685:
682:
677:
655:
650:
647:
643:
639:
636:
632:
610:
589:
586:
583:
578:
575:
570:
565:
538:
535:
530:
506:
502:
479:
475:
452:
449:
445:
433:
432:
419:
416:
410:
405:
398:
395:
390:
385:
380:
375:
368:
365:
360:
353:
350:
346:
342:
337:
334:
329:
301:
298:
293:
269:
264:
257:
254:
249:
243:
239:
234:
217:
216:
202:
197:
191:
187:
182:
177:
172:
168:
142:
138:
128:-th composite
111:
106:
83:
58:
55:
49:
46:
13:
10:
9:
6:
4:
3:
2:
2130:
2119:
2116:
2115:
2113:
2098:
2093:
2089:
2085:
2081:
2074:
2071:
2066:
2062:
2058:
2054:
2050:
2046:
2039:
2036:
2031:
2025:
2021:
2014:
2011:
2006:
1999:
1996:
1991:
1987:
1983:
1979:
1975:
1971:
1964:
1961:
1955:
1950:
1947:(1): 95–115.
1946:
1942:
1938:
1931:
1928:
1923:
1921:9783642525148
1917:
1913:
1912:
1904:
1901:
1896:
1892:
1888:
1884:
1877:
1874:
1869:
1865:
1861:
1857:
1853:
1849:
1848:Psychometrika
1842:
1839:
1833:
1828:
1823:
1818:
1814:
1810:
1806:
1799:
1796:
1791:
1787:
1783:
1779:
1775:
1771:
1767:
1763:
1759:
1752:
1749:
1744:
1742:9781462545605
1738:
1734:
1727:
1724:
1719:
1715:
1710:
1705:
1701:
1697:
1693:
1689:
1685:
1678:
1675:
1669:
1664:
1660:
1656:
1652:
1645:
1642:
1637:
1633:
1628:
1623:
1619:
1615:
1611:
1607:
1603:
1596:
1593:
1588:
1587:
1579:
1576:
1570:
1565:
1561:
1557:
1550:
1543:
1541:
1539:
1535:
1530:
1523:
1520:
1515:
1509:
1505:
1501:
1497:
1490:
1488:
1486:
1484:
1480:
1475:
1471:
1467:
1463:
1459:
1455:
1448:
1446:
1442:
1437:
1431:
1427:
1423:
1418:
1413:
1409:
1402:
1399:
1393:
1388:
1383:
1378:
1374:
1370:
1366:
1358:
1356:
1354:
1352:
1348:
1342:
1337:
1333:
1329:
1325:
1318:
1316:
1314:
1310:
1305:
1301:
1296:
1291:
1286:
1281:
1277:
1273:
1269:
1262:
1260:
1258:
1256:
1254:
1250:
1244:
1239:
1234:
1229:
1225:
1221:
1217:
1210:
1207:
1200:
1198:
1191:
1189:
1173:
1170:
1160:
1101:
1099:
1097:
1093:
1089:
1085:
1077:
1070:
1067:
1065:
1064:
1060:
1057:
1055:
1054:
1050:
1047:
1045:
1044:
1040:
1037:
1035:
1034:
1030:
1027:
1025:
1024:
1020:
1017:
1015:
1014:
1010:
1007:
1004:
1003:
1000:
976:
971:
968:
960:
958:
774:
754:
730:
729:
728:
726:
699:
683:
680:
648:
645:
641:
634:
587:
584:
576:
573:
536:
533:
504:
500:
477:
473:
450:
447:
443:
417:
408:
396:
393:
378:
366:
363:
351:
348:
344:
340:
335:
332:
318:
317:
316:
299:
296:
267:
255:
252:
241:
237:
222:
200:
189:
185:
175:
170:
166:
158:
157:
156:
140:
136:
127:
109:
71:
63:
56:
54:
47:
45:
43:
39:
35:
31:
27:
23:
19:
2087:
2086:. In print.
2083:
2073:
2048:
2044:
2038:
2019:
2013:
2004:
1998:
1973:
1969:
1963:
1944:
1940:
1930:
1910:
1903:
1886:
1882:
1876:
1854:(1): 81–99.
1851:
1847:
1841:
1832:10362/148024
1812:
1808:
1798:
1765:
1761:
1751:
1732:
1726:
1709:10362/104253
1691:
1687:
1677:
1658:
1654:
1644:
1609:
1605:
1595:
1585:
1578:
1559:
1555:
1528:
1522:
1495:
1457:
1453:
1407:
1401:
1392:10362/117915
1372:
1368:
1331:
1327:
1275:
1271:
1243:10362/103667
1223:
1219:
1209:
1195:
1161:
1105:
1081:
972:
964:
795:
700:
434:
218:
125:
72:
68:
51:
25:
21:
15:
2051:: 101–110.
1334:(1): 2–20.
1226:: 147–156.
48:Development
1201:References
965:To ensure
750:endogenous
18:statistics
2065:214571652
1990:121228129
1868:120403741
1790:237984577
1718:225288321
1474:120868602
1412:CiteSeerX
1174:θ
1122:^
1118:Σ
899:exogenous
770:exogenous
676:Σ
642:ρ
569:Σ
529:Σ
444:ρ
389:Σ
359:Σ
345:ρ
328:Σ
292:Σ
248:Σ
155:equals:
2112:Category
1782:34914475
1636:21767021
1304:30618962
1278:: 2541.
551:, i.e.,
418:′
242:′
190:′
1627:3889475
1295:6300521
2063:
2026:
1988:
1918:
1866:
1788:
1780:
1739:
1716:
1634:
1624:
1510:
1472:
1432:
1414:
1302:
1292:
1090:, and
435:where
2061:S2CID
1986:S2CID
1864:S2CID
1786:S2CID
1714:S2CID
1552:(PDF)
1470:S2CID
2024:ISBN
1916:ISBN
1778:PMID
1737:ISBN
1632:PMID
1508:ISBN
1430:ISBN
1300:PMID
973:The
840:and
560:rank
492:and
2092:doi
2053:doi
2049:109
1978:doi
1949:doi
1891:doi
1856:doi
1827:hdl
1817:doi
1770:doi
1704:hdl
1696:doi
1692:120
1663:doi
1659:117
1622:PMC
1614:doi
1564:doi
1500:doi
1462:doi
1422:doi
1387:hdl
1377:doi
1336:doi
1332:116
1290:PMC
1280:doi
1238:hdl
1228:doi
1224:120
26:CCA
16:In
2114::
2088:15
2082:.
2059:.
2047:.
1984:.
1974:21
1972:.
1945:13
1943:.
1939:.
1885:.
1862:.
1852:69
1850:.
1825:.
1813:16
1811:.
1807:.
1784:.
1776:.
1766:28
1764:.
1760:.
1712:.
1702:.
1690:.
1686:.
1657:.
1653:.
1630:.
1620:.
1610:16
1608:.
1604:.
1560:46
1558:.
1554:.
1537:^
1506:.
1482:^
1468:.
1458:45
1456:.
1444:^
1428:.
1420:.
1385:.
1373:17
1371:.
1367:.
1350:^
1330:.
1326:.
1312:^
1298:.
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1274:.
1270:.
1252:^
1236:.
1222:.
1218:.
1086:,
1005:df
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635::=
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2100:.
2094::
2067:.
2055::
2032:.
1992:.
1980::
1957:.
1951::
1924:.
1897:.
1893::
1887:3
1870:.
1858::
1835:.
1829::
1819::
1792:.
1772::
1745:.
1720:.
1706::
1698::
1671:.
1665::
1638:.
1616::
1572:.
1566::
1516:.
1502::
1476:.
1464::
1438:.
1424::
1395:.
1389::
1379::
1344:.
1338::
1306:.
1282::
1276:9
1246:.
1240::
1230::
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1038:-
1028:-
1018:-
1008:=
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871:z
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765:c
759:C
755:=
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739:B
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