Psychological Methods 2002 Vol 7 No 1 64 82 Copyright 2002 by the American Psychological Association Inc 1082 989X 02 5 00 DOI 10 1037 1082 989X 7 1 64 Principles and Practice in Reporting Structural Equation Analyses Roderick P McDonald and Moon Ho Ringo Ho University of Illinois at Urbana Champaign Principles for reporting analyses using structural equation modeling are reviewed with the goal of supplying readers with complete and accurate information It is recommended that every report give a detailed justification of the model used along with plausible alternatives and an account of identifiability Nonnormality and missing data problems should also be addressed A complete set of parameters and their standard errors is desirable and it will often be convenient to supply the correlation matrix and discrepancies as well as goodness of fit indices so that readers can exercise independent critical judgment A survey of fairly representative studies compares recent practice with the principles of reporting recommended here those listed supply essentially the same basic information with minor variations in the details supplied Thus the eight parameter LISREL model which arose out of the work of Keesling and Wiley see Wiley 1973 and was subsequently developed to its current state by Jo reskog see Jo reskog and So rbom 1996 the four matrix model of Lohmoller 1981 the three matrix EQS model of Bentler and Weeks 1980 and the two matrix RAM model see McArdle McDonald 1984 rearrange the same set of parameters Not surprisingly and perhaps not regrettably user guides and texts on this topic are not in agreement in their recommendations about the style of presentation of results e g see Bollen 1989 Loehlin 1992 Long 1983a 1983b There is even less agreement in the form of the results actually reported in articles on applications It would be immodest for any journal article to offer a code of practice for the presentation of SEM results It could also be counterproductive We note that for a long time there was a uniformly accepted convention for the publication of analysis of variance or ANOVA results the standard ANOVA table and the table of cell means The near disappearance of this from journals is regrettable Sound guidelines for the reporting of SEM results have been offered previously by Steiger 1988 Breckler 1990 Raykov Tomer and Nesselroade 1991 Hoyle and Panter 1995 and Boomsma 2000 MacCallum and Austin 2000 provided an excellent general survey of problems in applications of SEM Structural equation modeling SEM also known as path analysis with latent variables is now a regularly used method for representing dependency arguably causal relations in multivariate data in the behavioral and social sciences Following the seminal work of Jo reskog 1973 a number of models for linear structural relations have been developed Bentler Weeks 1980 Lohmoller 1981 McDonald 1978 and work continues on these Commercial statistical packages include LISREL Jo reskog So rbom 1989 1996 EQS Bentler 1985 1995 CALIS Hartmann 1992 MPLUS Muthe n Muthe n 1998 RAMONA Browne Mels Cowan 1994 SEPATH Steiger 1995 and AMOS Arbuckle 1997 Available freeware includes COSAN Fraser McDonald 1988 and Mx Neale 1997 McArdle and McDonald 1984 proved that different matrix formulations of a path model with latent variables are essentially equivalent Programs such as Roderick P McDonald and Moon Ho Ringo Ho Department of Psychology University of Illinois at Urbana Champaign We thank Jack McArdle Malgorzata Szewczyk and Bob Henson for their comments on this article Any errors are our responsibility Correspondence concerning this article should be addressed to Roderick P McDonald Department of Psychology University of Illinois at Urbana Champaign 603 East Daniel Street Champaign Illinois 61820 E mail rmcdonal s psych uiuc edu 64 REPORTING STRUCTURAL EQUATION ANALYSES Our objective is to review some principles for reporting SEM results We also summarize some observations on the variety of treatments of results given in a selected set of reports on applications The comparison of principles with practice is intended to underscore the importance of the recommendations made here These are aimed at increasing the information supplied to the reader Increased information should allow a more critical assessment of the study reported and serve to advance scientific knowledge Naturally some of our recommendations are essentially endorsements of those already given Furthermore this topic may need occasional revisiting until practice conforms with principles We concentrate appropriately on matters in which there should be little disagreement However we do address a number of fresh elements here We try to give fairly specific guidance on implementing previously published recommendations as well as our own We also offer a few mild departures from previous suggestions It is assumed that the reader is familiar with basic SEM method and with common terminology However we do offer occasional reminders about method as well as remarks about recent developments that the reader may have missed From well known SEM principles we can formulate a list of results that we might hope to find in a comprehensive report and we can check current practice against this list Of course there can be a conflict between an ideal of completeness and the understandable desire for conciseness in journal publications This conflict is severe in the case of very large models We surveyed articles using SEM from 1995 to 1997 in the following journals British Journal of Psychology Child Development Developmental Psychology Journal of Abnormal Psychology Journal of Applied Psychology Journal of Applied Social Psychology Journal of Consulting and Clinical Psychology Journal of Counseling Psychology Journal of Educational Psychology Journal of Family Psychology Journal of Personality and Social Psychology Journal of Research in Personality and Psychological Assessment The method of search was simply to look for all path diagrams in the journals and period named The intention was to find a reasonably representative sample limited to path models with latent variables and to single population studies 1 This survey yielded 100 possible articles for review of which 41 met the criteria a path diagrams must be provided b models being fitted must include both measurement and 65 structural parts pure factor analytic models or path analytic models without latent variables were excluded and c