v.2, N.K. Bowen, 2014
List of Resource Readings on SEM
(with brief annotations)
Allison, P. D. (2003). Missing data techniques for structural equation modeling. Journal of
Abnormal Psychology, 112, 545-557.
Allison reviews approaches to modeling with missing values, and provides support for using full
information maximum likelihood (FIML) and multiple imputation.
Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice: A review
and recommended two-step approach. Psychological Bulletin, 103(3), 411-423.
Seminal citation for the establishment of an adequate measurement model before proceeding
to a test of the structural model in a general SEM.
Beauducel, A., & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus
means and variance adjusted weighted least squares estimation in CFA. Structural
Equation Modeling, 13(2), 186-203.
In addition to the Flora and Curran reference below, this article serves as a reference for the
use of WLSMV with categorical data. Their simulations took into account the number of
categories, the number of factors, and sample size.
Bentler, P. M., & Mooijaart, A. (1989). Choice of structural model via parsimony: A rationale
based on precision. Psychological Bulletin, 106(2), 315-317.
A general rule in SEM is that when choosing between two competing models, the more
parsimonious model is desirable. This article justifies the choice of the parsimonious model by
demonstrating that parameter estimates are more precise in parsimonious models.
Bollen, K. A. (2000). Modeling strategies: In search of the Holy Grail. Structural Equation
Modeling, 7(1), 74-81.
This article presents discusses different approaches to finding the correct number of factors in a
measurement model. It provides support for the use of a “piecewise jigsaw technique,” which
can be useful when complicated, multi-factor models are being tested.
Bollen, K. A. (1989). Structural equations with latent variables. New York: John Wiley & Sons.
Bollen’s book is a seminal and comprehensive source on virtually all aspects of SEM. If you plan
to become a regular user of SEM, this book needs to be on your shelf.
Boomsa, A. (2000). Reporting analyses of covariance structures, Structural Equation Modeling
7, 461-483.
This article provides guidelines for writing SEM articles for peer review.
Bovaird, J. A., & Koziol, N., A. (2012). Measurement models for ordered-categorical indicators.
In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 495-511). New
York: Guilford Press.
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Bowen, N. K., & Guo, S. (2012). Structural equation modeling. New York, NY: Oxford
University Press.
This is the book I wished for when I was doing my dissertation. Extensive guides to Mplus and
Amos syntax for CFA and SEM analyses are freely available at OUP’s website. Go to:
http://www.oup.com/us/catalog/general/subject/SocialWork/?view=usa&ci=9780195367621
Companion_Site_Resources (Or search book title, click on title, then click on
“companion resources”)
Bower, H. A., Bowen, N. K., & Powers, J. D. (2011). Family-faculty trust as measured with the
ESSP. Children & Schools, 33, 158-167.
The analysis in this article is an example of a second order confirmatory factor model.
Byrne, B. M. (2010). Structural equation modeling with Amos: Basic concepts, applications, and
programming (2nd ed.). New York, NY: Taylor and Francis Group.
Byrne’s book provides instructions on using Amos as well as on SEM analyses in general. She
includes many examples on multiple group analyses.
Byrne, B. M. (2010). Structural equation modeling with Mplus: Basic concepts, applications,
and programming. New York, NY: Taylor and Francis Group.
Byrne has a series of book about SEM with different programs. The Mplus book’s utility is
reduced by her lack of attention to WLSMV estimation with ordinal variables, but otherwise it is
a good resource for using the program.
Byrne, B. M., Shavelson, R. J., & Muthén, B. (1989). Testing for the equivalence of factor
covariance and mean structures: The issue of partial measurement invariance.
Psychological Bulletin, 105(3), 456-466.
This article describes conceptual and statistical issues in studying the invariance of
measurement models across groups. Byrne is an authoritative source on invariance and this is a
seminal article.
Chen, C., Bollen, K. A., Paxton, P., Curran, P. J., & Kirby, J. B. (2001). Improper solutions in
structural equation models. Sociological Methods and Research, 29(4), 468-508.
Chen and Bollen present results from a simulation study to support recommendations to
researchers about how to problem-solve estimation failures.
Cheung, G. W. & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing
measurement invariance. Structural Equation Modeling, 9, 233-255.
Curran, P. J., & Willoughby, M. T. (2003). Implications of latent trajectory models for the study
of developmental psychopathology. Development and Psychopathology, 15. 581-612.
An impressive article demonstrating how SEM can be used to answer many different types of
longitudinal questions.
Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysis for the
behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.
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Cohen and Cohen is an essential source on basic and advanced topics of regression and
correlation and their relationship to each other. These procedures are foundational to SEM.
Cole, D. A., & Maxwell, S. E. (2003). Testing mediational models with longitudinal data:
Questions and tips in the use of structural equation modeling. Journal of Abnormal
Psychology.
This article is a useful source on various modeling techniques for repeated measures data with
cross-lagged models.
DeVellis, R. F. (2003). Scale development: Theory and applications (2nd ed.). Thousand Oaks,
CA: Sage.
DeVellis provides a useful conceptual discussion of latent variables.
Dimitrov, D. M. (2010). Testing for factorial invariance in the context of construct validation.
Measurement and Evaluation in Counseling and Development, 43, 121-149.
Dimitrov provides user-friendly instructions for conducting invariance tests of first and second
order measurement models. The article includes definitions of different levels of invariance,
and Mplus code. An excellent resource if you are planning to conduct a CFA.
Eid, M., Nussbeck, F. W., Geiser, C., Cole, D. A., Gollwitzer, M., & Lischetzke, T. (2008).
Structural equation modeling of multitrait-multimethod data: Different models for
different types of methods. Psychological Methods,13(3), 230-253.
doi:10.1037/a0013219
This is a good source article on the different ways of modeling CFA models with method effects.
Enders, C. K., & Bandalos, D. L. (2001). The relative performance of full information maximum
likelihood estimation for missing data in structural equation models. Structural Equation
Modeling, 8, 430-457.
This article provides empirical support for using Full Information Maximum Likelihood
estimation in SEM.
Fabrigar, L. R., Porter, R. D., & Norris, M. E. (2010). Some things you should know about
structural equation modeling but never thought to ask. Journal of Consumer
Psychology, 20, 221-225. doi:10.1016/j.jcps.2010.03.003
In conjunction with the Iacobucci articles cited below, this is a easy-reading discussion of some
important issues in SEM, such as inferring causality, sample size, and fit indices.
Ferron, J. M., & Hess, M. R. (2007). Estimation in SEM: A concrete example. Journal of
Educational and Behavioral Statistics, 32(1), 110-120.
This article provides a concrete example of the matrix calculations and calculus used in ML
estimation of a simple model.
Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative methods of
estimation for confirmatory factor analysis with ordinal data. Psychological Methods,
9(4), 466-491.
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This article provides an understandable explanation of how ordinal variables are handled in
common SEM software (converted into polychoric correlations). After presenting methods and
results from a simulation study, the authors recommend the use of robust weighted least
squares estimation with ordinal data.
Fox, J. (1980). Effect analysis in structural equation models: Extensions and simplified methods
of computation. Sociological Methods and Research, 9(1), 3-28.
doi:10.1177/0049124185014001005
This article provides an in-depth discussion of the matrices and equations behind the
calculation of indirect effects in path analysis.
Gerbing, D. W., & Anderson, J. C. (1984). On the meaning of within-factor correlated
measurement errors. Journal of Consumer Research, 11, 572-580.
Read this article carefully to get a good understanding of how error variance is modeled in
measurement models. Different ways of modeling factors and indicators can mean very
different things about the sources and nature of error.
Graham, J. W. (2009). Missing data analysis: Making it work in the real world. Annual Review of
Psychology, 60, 549-576.
A general source on the nature of missing data and how to address them in analyses.
Hayduk, L. A., & Glaser, D. N. (2000). Jiving the four-step, waltzing around factor analysis, and
other serious fun. Structural Equation Modeling, 7(1), 1-35.
doi:10.1207/S15328007SEM0701_01
A substantial reading that demonstrates how SEM scholars can argue about SEM procedures at
great length. This reading can be considered along with Anderson and Gerbing (1988) and
Bollen (2000), as well as others cited in Hayduk, when thinking about how best to find a correct
model.
Hoyle, Rick. H. (Ed.) (2012). Handbook of structural equation modeling. New York, NY:
Guilford Press.
A new and updated source on major aspects of SEM with chapters by the big names in the field.
The chapters in this book will be references you will use often.
Iacobucci, D. (2009). Everything you always wanted to know about SEM (structural equation
modeling) but were afraid to ask. Journal of Consumer Psychology, 19, 673-680.
This author provides a user-friendly summary of SEM notation and its relationship to the
matrices. The article is good for reinforcing emerging knowledge of SEM. Fabrigar above refers
to this article.
Iacobucci, D. (2010). Structural equation modeling: Fit indices, sample size, and advanced
topics. Journal of Consumer Psychology, 20, 90-98. doi:10.1016/j.jcps.20090.09.003
More user-friendly discussion of SEM basics.
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Jöreskog, K. G. (1993). Testing structural equation models. In K. Bollen, & J. S. Long
(Eds.), Testing structural equation models (pp. 294-316). Newbury Park: Sage
Publications.
A seminal piece on SEM by the developer of LISREL.
Jöreskog, K. G. (2005). Structural equation modeling with ordinal variables using
LISREL. Scientific Software International.
A seminal piece on analyzing polychoric correlation matrices when data are ordinal, by the
developer of LISREL.
Jöreskog, K. G. (1971). Simultaneous factor analysis in several populations. Psychometrika,
36(4), 409-426.
A seminal piece on multiple group SEM by the developer of LISREL.
Kano, Y., & Azuma, Y. (n.d.). Use of SEM programs to precisely measure scale reliability.
retrieved April 20, 2014 from, http://www.sigmath.es.osakau.ac.jp/~kano/research/paper/dvi/kano_azuma.pdf
This web posting discusses issues of reliability of scales modeled in CFAs, and a method for
calculating it using SEM output.
Kaplan, D. (2009). Structural equation modeling: Foundations and extensions (2nd ed.).
Thousand Oaks, CA: Sage Publications, Inc.
Kaplan’s book is a recent comprehensive source on SEM.
Kline, R. B. (2011). Principles and practice of structural equation modeling (3rd ed.). New York:
Guilford.
Kline’s presentation of SEM topics is user-friendly and practical. The third edition was released
in 2011. Kline’s discussion of direct, indirect, and reciprocal effects in path analysis is especially
useful and thorough.
Lee, T, Cai, L., MacCallum, R. C. (2012). Power analysis for tests of structural equation models.
In R. H. Hoyle (Ed.). Handbook of structural equation modeling. (pp. 181-194). New
York: Guilford Press.
A recent chapter that provides an overview and update of MacCallum’s previous work on using
RMSEA estimates for power analysis.
Little, R. A., & Rubin, D. B. (2002). Statistical analysis with missing data (2nd ed.). New York,
NY: Wiley & Sons.
This book is a source of information on missing data and multiple imputation.
Long, J. S. (1983). Confirmatory factor analysis. New York: Sage.
Long provides a technical, yet accessible, presentation that helps the reader gain a deep
understanding of CFA.
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MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and
determination of sample size for covariance structure modeling. Psychological Methods,
1, 130-149.
This article is a must-read for those interested in gaining a deeper understanding of power
analysis using RMSEA. The tables can be used on their own to estimate power. (See also
handout by Bowen on power.)
MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor
analysis. Psychological Methods, 4(1), 84-99.
The article demonstrates how sample size requirements for confirmatory factor analyses may
vary based on the magnitude of factor loadings and the number of indicators loading on a
factor. The point is that rules of thumb about how many cases are needed for analyses may not
be valid.
MacCallum, R. C., Browne, M. W., & Cai, L. (2006). Testing differences between covariance
structure models: Power analysis and null hypothesis. Psychological Methods, 11(1), 1935. doi:10.1037/1082-989X.11.1.19; 10.1037/1082-989X.11.1.19.supp
The authors propose the use of RMSEA values from nested models to determine the power
available for testing model differences.
McDonald, R. P., & Ho, M. R. (2002). Principles and practice in reporting structural equation
analyses. Psychological Methods, 7(1), 64-82. doi:10.1037//1082-989X.7.1.64
This article is good for reinforcing emerging knowledge of SEM. It talks about important aspects
of SEM while providing advice on how to report SEM analyses in manuscripts for publication.\
Millsap, R. E., & Yun-Tein, J. (2004). Assessing factorial invariance in ordered-categorical
measures. Journal of Multivariate Behavioral Research, 39, 479–515.
One of the rather daunting sources on invariance testing of CFA models with ordinal data.
Muthén, B. O. (1989). Latent variable modeling in heterogeneous
populations. Psychometrika, 54(4), 557-585.
This article started as a presidential address to the Psychometric Society. It describes how
MIMIC modeling can be useful when multiple group modeling may not be feasible.
Muthén, B., & Asparouhov, T. (2002). Latent variable analysis with categorical outcomes:
Multiple-group and growth modeling in Mplus. Mplus Web Note #4. Retrieved April 20,
2014 from, https://www.statmodel.com/examples/webnote.shtml#web4
Muthén’s webnotes are not for the faint at heart, but they are primary sources from a leader in
the field! One of the rather daunting sources on invariance testing of CFA models with ordinal
data.
Muthén, B. O. (2014). Version7.1 mplus language
addendum.pdf. http://www.statmodel.com/download/Version7.1xLanguage.pdf:
Part of this short addendum explains how to request tests of configural, metric, and scalar
invariance in one line of code. The code can also be modified to allow tests of partial invariance
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if full invariance is not found. The code saves invariance tester a lot of coding because Mplus’
default is a constrained model, while it is easiest to start a series of invariance tests with an
unconstrained model.
Muthén, L. K., & Muthén, B. O. (2010). Http://statmodel.com/
The Mplus website includes the User’s Guide, technical notes, webnotes, publications using and
about Mplus and informative, searchable discussion threads on all Mplus analysis topics.
Pohl, S., & Steyer, R. (2012). Modeling traits and method effects as latent variables. In S.
Salzborn, E. Davidov & J. Reinecke (Eds.), Methods, theories, and empirical
applications in the social sciences (pp. 57-65; 2) VS Verlag für Sozialwissenschaften.
doi:10.1007/978-3-531-18898-0_8
Along with the Eid article above, this one is a good source on modeling method effects. This
one is shorter!
Raykov, T., Marcoulides, G. A., & Li, C. (2012). Measurement invariance for latent constructs in
multiple populations: A critical view and refocus. Educational and Psychological
Measurement, 72, 954-972.
One of the rather daunting sources on invariance testing of CFA models with ordinal data.
Sass, D. A. (2011). Testing measurement invariance and comparing latent factor means within a
confirmatory factor analysis framework. Journal of Psychoeducational
Assessment, 29(4), 347-363. doi:10.1177/0734282911406661
This source on invariance testing with ordinal data is more accessible than most, but doesn’t
resolve the differences in approaches that are found in the literature.
Schreiber, J. B., Amaury, N., Stage, F. K., Barlow, E. A., & King, J. (2006). Reporting structural
equation modeling and confirmatory factor analysis results: A review. The Journal of
Educational Research, 99(6), 323-337.
Another source on how to write up an SEM analysis that includes good basic information about
structural equation modeling in general.
Sivo, S. A., Fan, X., Witta, E. L., & Willse, J. T. (2006). The search for "optimal" cutoff
properties: Fit index criteria in structural equation modeling. The Journal of Experimental
Education, 74(3), 267-288.
The authors present results of a study of how well difference cutoff values for fit indices
identify correct models and reject poor models. Based on the study they make
recommendations about which fit indices to use and under which conditions they work best.
Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Boston: Allyn
& Bacon.
This book is a comprehensive source on statistical procedures. It includes useful information on
diagnosing distributional problems and transforming variables, among many other topics. It
also has chi square and normal distribution tables.
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Tomarken, A. J., & Waller, N. G. (2003). Potential problems with "well fitting" models. Journal
of Abnormal Psychology, 112(4), 578-598. doi:10.1037/0021-843X.112.4.578
The two Tomarken and Waller articles listed here are good for reinforcing the growing
knowledge of SEM in emerging learners because they cover many central issues. They also
remind us to be humble in the use of statistics.
Tomarken, A. J., & Waller, N. G. (2005). Structural equation modeling: Strengths, limitations,
and misconceptions. Annual Review of Clinical Psychology, 1, 31-65.
doi:10.1146/annurev.clinpsy.1.102803.144239
Wegmann, K. M., Thompson, A. M., & Bowen, N. K. (2010). A confirmatory factor analysis of
home environment and home social behavior data from the ESSP for Families. Social
Work Research, 35, 65-128.
This article provides a social work example of a CFA with Mplus using ordinal, clustered data.
Werts, C. E., Rock, D. A., Linn, R. L., & Jöreskog, K. G. (1976). Comparison of correlations,
variances, covariances, and regression weights with or without measurement
error. Psychological Bulletin, 83(6), 1007-1013.
West, S. G., Taylor A. B., & Wu, W. (2012). Model fit and model selection in structural equation
modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 209231). New York, NY: Guilford Press.
This chapter is an authoritative recent source for recommended fit indices and cutoffs.
Yang, Y., & Green, S. B. (2010). A note on structural equation modeling estimates of
reliability. Structural Equation Modeling, 17(1), 66-81.
doi:10.1080/10705510903438963
The authors relate results of a Monte Carlo study comparing reliability estimates from SEM
analyses versus coefficient alpha.
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