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R3(39) on "What are the most important statistical ideas of the past 50 years? " Andrew Gelman, Aki Vehtari

Last updated at Posted at 2021-11-03

R3(References on References on References) on "What are the most important statistical ideas of the past 50 years? " Andrew Gelman, Aki Vehtari(39)

R3(0) on "W.a.t.m.i. statistical ideas of the past 50 years? " Andrew Gelman, Aki Vehtari
https://qiita.com/kaizen_nagoya/items/a8eac9afbf16d2188901

What are the most important statistical ideas of the past 50 years?
Andrew Gelman, Aki Vehtari
https://arxiv.org/abs/2012.00174

References

39

Duncan, O. D. (1975). Introduction to Structural Equation Models. New York: Academic Press.

Reference on 39

##Books

39.1

Jöreskog, K. G., Olsson, U. H., & Wallentin, F. Y. (2016). Multivariate analysis with LISREL. Basel, Switzerland: Springer.

39.2

Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford publications.

Reference on 39.2

39.2.1

Achen, C. H. (2005). Let’s put garbage-can regressions and garbage-can probits where they belong. Conflict Management and Peace Science, 22, 327–339.

39.2.2

Acock, A. C. (2013). Discovering structural equation modeling using Stata 13. College Station, TX: Stata Press.

39.2.3

Agresti, A. (2007). An introduction to categorical data analysis. Hoboken, NJ: Wiley.

39.2.4

Aguinis, H. (1995). Statistical power with moderated multiple regression in management research. Journal of Management, 21, 1141–1158.

39.2.5

Aguinis, H., Werner, S., Abbott, J. L., Angert, C., Park, J. H., & Kohlhausen, D. (2010). Customer-centric science: Reporting significant research results with rigor, relevance, and practical impact in mind. Organizational Research Methods, 13, 515–539.

39.2.6

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.

39.2.7

Allison, P. D. (2003). Missing data techniques for structural equation modeling. Journal of Abnormal Psychology, 112, 545–557.

39.2.8

American Psychological Association Publication and Communications Board Working Group on Journal Article Reporting Standards. (2008). Reporting standards for research in psychology:
Why do we need them? What might they be? American Psychologist, 63, 839–851.

39.2.9

Amos Development Corporation. (1983–2013). IBM SPSS Amos (Version 22.0) [computer software]. Meadville, PA: Author.

39.2.10

Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin, 103, 411–423.

39.2.11

Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (2010). On making causal claims: A review and recommendations. The Leadership Quarterly, 21, 1086–1120.

39.2.12

Armstrong, J. S. (2007). Significance tests harm progress in forecasting. International Journal of Fore-casting, 23, 321–327.

39.2.13

Asparouhov, T., & Muthén, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling, 21, 495–508.

39.2.14

Bandalos, D. L., & Gagné, P. (2012). Simulation methods in structural equation modeling. In R. H.Hoyle (Ed.), Handbook of structural equation modeling (pp. 92–108). New York: Guilford Press.

39.2.15

Bandalos, D. L., & Leite, W. (2013). Use of Monte Carlo studies in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed.,pp. 625–666). Charlotte, NC: IAP.

39.2.16

Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psycho- logical research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173–1182.

39.2.17

Barrett, P. (2007). Structural equation modeling: Adjudging model fit. Personality and Individual Dif- ferences, 42, 815–824.

39.2.18

Bartholomew, D. J. (2002). Old and new approaches to latent variable modeling. In G. A. Marcoulides & I. Moustaki (Eds.), Latent variable and latent structure models (pp. 1–13). Mahwah, NJ: Erl- baum.

39.2.19

Bauer, D. J. (2003). Estimating multilevel linear models as structural equation models. Journal of Edu- cational and Behavioral Statistics, 28, 135–167.

39.2.20

Baylor, C., Hula, W., Donovan, N. J., Doyle, P. J., Kendall, D., & Yorkston, K. (2011). An introduction to item response theory and Rasch models for speech–language pathologists. American Journal of Speech–Language Pathology, 20, 243–259.
Beauducel, A., & Wittman, W. (2005). Simulation study on fit indices in confirmatory factor analy- sis based on data with slightly distorted simple structure. Structural Equation Modeling, 12, 41–75.
Beaujean, A. A. (2014). Latent variable modeling using R: A step-by-step guide. New York: Routledge. Bentler, P. M. (1980). Multivariate analysis with latent variables: Causal modeling. Annual Review of
Psychology, 31, 419–456.
Bentler, P. M. (1987). Drug use and personality in adolescence and young adulthood: Structured mod-
els with nonnormal variables. Child Development, 58, 65–79.
Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107, 238–
246.
Bentler, P. M. (2000). Rites, wrongs, and gold in model testing. Structural Equation Modeling, 7, 82–91. Bentler, P. M. (2006). EQS 6 structural equations program manual. Encino, CA: Multivariate Software. Bentler, P. M. (2009). Alpha, dimension-free, and model-based internal consistency reliability. Psy-
chometrika, 74, 137–143.
Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness-of-fit in the analysis of covari-
ance structures. Psychological Bulletin, 88, 588–600.
Bentler, P. M., & Raykov, T. (2000). On measures of explained variance in nonrecursive structural
equation models. Journal of Applied Psychology, 85, 125–131.
Benyamini, Y., Ein-Dor, T., Ginzburg, K., & Solomon, Z. (2009). Trajectories of self-rated health
among veterans: A latent growth curve analysis of the impact of posttraumatic symptoms. Psy-
chosomatic Medicine, 71, 345–352.
Bergsma, W., Croon, M. A., & Hagenaars, J. A. (2009). Marginal models: For dependent, clustered, and
longitudinal categorical data. New York: Springer.
Bernstein, I. H., & Teng, G. (1989). Factoring items and factoring scales are different: Spurious evi-
dence for multidimensionality due to item categorization. Psychological Bulletin, 105, 467–477. Berry, W. D. (1984). Nonrecursive causal models. Beverly Hills, CA: Sage.
Bishop, J., Geiser, C., & Cole, D. A. (2015). Modeling latent growth with multiple indicators: A com-
parison of three approaches. Psychological Methods, 20, 43–62.
Blalock, H. M. (1961). Correlation and causality: The multivariate case. Social Forces, 39, 246–251. Blest, D. C. (2003). A new measure of kurtosis adjusted for skewness. Australian and New Zealand
Journal of Statistics, 45, 175–179.
Block, J. (1995). On the relation between IQ, impulsivity, and delinquency: Remarks on the Lynam,
Moffitt, and Stouthamer-Loeber (1993) interpretation. Journal of Abnormal Psychology, 104, 395–
398.
Blunch, N. (2013). Introduction to structural equation modeling using IBM SPSS Statistics and Amos (2nd
ed.). Thousand Oaks, CA: Sage.
Boker, S., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T., et al. (2011). OpenMx: An open source
extended structural equation modeling framework. Psychometrika, 76, 306–317.
Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.
Bollen, K. A. (1996). A limited-information estimator for LISREL models with and without heterosce-

References 491
dastic errors. In G. Marcoulides & R. Schumacker (Eds.), Advanced structural equation modeling
techniques (pp. 227–241). Mahwah, NJ: Erlbaum.
Bollen, K. A. (2000). Modeling strategies: In search of the Holy Grail. Structural Equation Modeling, 7,
74 – 81.
Bollen, K. A. (2002). Latent variables in psychology and the social sciences. Annual Review of Psychol-
ogy, 53, 605–634.
Bollen, K. A. (2007). Interpretational confounding is due to misspecification, not to type of indicator:
Comment on Howell, Breivik, and Wilcox (2007). Psychological Methods, 12, 219–228.
Bollen, K. A. (2012). Instrumental variables in sociology and the social sciences. Annual Review of
Sociology, 38, 37–72.
Bollen, K. A., & Bauldry, S. (2010). Model identification and computer algebra. Sociological Methods
and Research, 39, 127–156.
Bollen, K. A., & Bauldry, S. (2011). Three Cs in measurement models: Causal indicators, composite
indicators, and covariates. Psychological Methods, 16, 265–284.
Bollen, K. A., & Curran, P. J. (2004). Autoregressive latent trajectory (ALT) models: A synthesis of two
traditions. Sociological Methods Research, 32, 336–383.
Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. Hoboken,
NJ: Wiley.
Bollen, K. A., & Hoyle, R. H. (2012). Latent variable models in structural equation modeling. In R. H.
Hoyle (Ed.), Handbook of structural equation modeling (pp. 56–67). New York: Guilford Press. Bollen, K. A., Kirby, J. B., Curran, P. J., Paxton, P. M., & Chen, F. (2007). Latent variable models under misspecification: Two-stage least squares (TSLS) and maximum likelihood (ML) estimators.
Sociological Methods and Research, 36, 48–86.
Bollen, K. A., & Pearl, J. (2013). Eight myths about causality and structural equation models. In S. L.
Morgan (Ed.), Handbook of causal analysis for social research (pp. 301–328). New York: Springer. Bollen, K. A., & Stine, R. A. (1993). Bootstrapping goodness-of-fit measures in structural equation models. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 111–135).
Newbury Park, CA: Sage.
Bollen, K. A., & Ting, K. (1993). Confirmatory tetrad analysis. In P. M. Marsden (Ed.), Sociological
Methodology 1993 (pp. 147–175). Washington, DC: American Sociological Association. Boomsma, A., Hoyle, R. H., & Panter, A. T. (2012). The structural equation modeling research report. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 341–358). New York: Guilford
Press.
Box, G. E. P. (1976). Science and statistics. Journal of the American Statistical Association, 71, 791–799. Box, G. E. P., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Soci-
ety, Series B (Methodological), 26, 211–252.
Breitling, L. P. (2010). dagR: A suite of R functions for directed acyclic graphs. Epidemiology, 21,
5 8 6 – 5 8 7.
Breivik, E., & Olsson, U. H. (2001). Adding variables to improve fit: The effect of model size on fit
assessment in LISREL. In R. Cudeck, S. Du Toit, & D. Sörbom (Eds.), Structural equation mod- eling: Present and future. A Festschrift in honor of Karl Jöreskog (pp. 169–194). Lincolnwood, IL: Scientific Software International.
Brito, C., & Pearl, J. (2002). A new identification condition for recursive models with correlated errors. Structural Equation Modeling, 9, 459–474.
Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: Guilford Press. Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). New York: Guilford
Press.
Browne, M. W. (1982). Covariance structures. In D. M. Hawkins (Ed.), Topics in applied multivariate
analysis (pp. 72–141). Cambridge, UK: Cambridge University Press.
Browne, M. W. (1984). Asymptotically distribution-free methods in the analysis of covariance struc-
tures. British Journal of Mathematical and Statistical Psychology, 37, 62–83.
Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen and J. S.
Long (Eds.), Testing structural equation models (pp. 136–162). Newbury Park, CA: Sage.

492 References
Browne, M. W., & Du Toit, S. H. C. (1991). Models for learning data. In L. M. Collins & J. L. Horn (Eds.), Best methods for the analysis of change (pp. 47–68). Washington, DC: American Psycho- logical Association.
Bryant, F. B., & Satorra, A. (2012). Principles and practice of scaled difference chi-square testing. Structural Equation Modeling, 19, 372–398.
Bryant, F. B., & Satorra, A. (2013). EXCEL macro file for conducting scaled difference chi-square tests via LISREL 8, LISREL 9, EQS, and Mplus. Retrieved from www.econ.upf.edu/~satorra
Budtz-Jørgensen, E., Keiding, N., Grandjean, P., & Weihe, P. (2002). Estimation of health effects of prenatal methylmercury exposure using structural equation models. Environmental Health: A Global Access Science Source, 1(2). Retrieved from www.ehjournal.net
Bullock, J. G., Green, D. P., & Ha, S. E. (2010). Yes, but what’s the mechanism? (Don’t expect an easy answer). Journal of Personality and Social Psychology, 98, 550–558.
Burt, R. S. (1976). Interpretational confounding of unobserved variables in structural equation mod- els. Sociological Methods and Research, 5, 3–52.
Byrne, B. M. (2006). Structural equation modeling with EQS: Basic concepts, applications, and program- ming (2nd ed.). New York: Routledge.
Byrne, B. M. (2010). Structural equation modeling with Amos: Basic concepts, applications, and program- ming (2nd ed.). New York: Routledge.
Byrne, B. M. (2012a). Choosing structural equation modeling computer software: Snapshots of LIS- REL, EQS, Amos, and Mplus. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 307–324). New York: Guilford Press.
Byrne, B. M. (2012b). Structural equation modeling with Mplus: Basic concepts, applications, and pro- gramming. New York: Routledge.
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, 456–466.
Byrne, D. (2009). Bicycle diaries. New York: Viking.
Cameron, L. C., Ittenbach R. F., McGrew, K. S., Harrison, P., Taylor, L. R., & Hwang, Y. R. (1997).
Confirmatory factor analysis of the K-ABC with gifted referrals. Educational and Psychological
Measurement, 57, 823–840.
Campbell, D. T., & Fiske, D. W. (1959). Convergent and discriminant validation by the multitrait–
multimethod matrix. Psychological Bulletin, 56, 81–105.
Carlson, J. F., Geisinger, K. F., & Jonson, J. L. (Eds.). (2014). The Nineteenth Mental Measurements Year-
book. Lincoln: Buros Institute of Mental Measurements, University of Nebraska.
Chan, F., Lee, G. K., Lee, E.-J., Kubota, C., & Allen, C. A. (2007). Structural equation modeling in
rehabilitation counseling research. Rehabilitation Counseling Bulletin, 51(1), 53–66.
Chang, H.-T., Chi, N. W., & Miao, M. C. (2007). Testing the relationship between three-component organizational/occupational commitment and organizational/occupational turnover intention
using a non-recursive model. Journal of Vocational Behavior, 70, 352–368.
Chen, B., & Pearl, J. (2015). Graphical tools of linear structural equation modeling. Retrieved from
http://ftp.cs.ucla.edu/pub/stat_ser/r432.pdf
Chen, F., Bollen, K. A., Paxton, P., Curran, P. J., & Kirby, J. B. (2001). Improper solutions in structural equation models: Causes, consequences, and strategies. Sociological Methods and Research, 29, 468–508.
Chen, F., Curran, P. J., Bollen, K. A., & Paxton, P. (2008). An empirical evaluation of the use of fixed cutoff points in RMSEA test statistic in structural equation models. Sociological Methods and Research, 36, 462–494.
Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling, 14, 464–504.
Chen, F. F., West, S. G., & Sousa, K. H. (2006). A comparison of bifactor and second-order models of quality of life. Multivariate Behavioral Research, 41, 189–225.
Cheung, G. W., & Rensvold, R. B. (2000). Assessing extreme and acquiescence response sets in cross-

References 493
cultural research using structural equations modeling. Journal of Cross-Cultural Psychology, 31,
187–212.
Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement
invariance. Structural Equation Modeling, 9, 233–255.
Chin, W. W. (2001). PLS-Graph user’s guide. Houston, TX: Soft Modeling.
Chin, W. W., Peterson, R. A., & Brown, S. P. (2008). Structural equation modeling in marketing: Some
practical reminders. Journal of Marketing Theory and Practice, 16, 287–298.
Choi, J., Fan, W., & Hancock, G. R. (2009). A note on confidence intervals for two-group latent mean
effect size measures. Multivariate Behavioral Research, 44, 396–406.
Choi, Y. Y., Song, J.-I., Chun, J. S., Lee, K. O., & Song, W. K. (2013). A structural equation modeling
approach for the estimation of genetic and environmental effects from twin fMRI data. Interna-
tional Journal of Bioscience, Biochemistry and Bioinformatics, 3, 167–169.
Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis
for the behavioral sciences (3rd ed.). New York: Routledge.
Cole, D. A., Ciesla, J. A., & Steiger, J. H. (2007). The insidious effects of failing to include design-
driven correlated residuals in latent-variable covariance structure analysis. Psychological Meth-
ods, 12, 381–398.
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, 112, 558–577. Cole, D. A., & Preacher, K. J. (2014). Manifest variable path analysis: Potentially serious and mislead-
ing consequences due to uncorrected measurement error. Psychological Methods, 19, 300–315. Cornoni-Huntley, J., Barbano, H. E., Brody, J. A., Cohen, B., Feldman, J. J., Kleinman, J. C., et al. (1983). National Health and Nutrition Examination I—Epidemiologic followup survey. Public
Health Reports, 98, 245–251.
Crawford, J. R. (2007). SBDIFF.EXE [computer software]. Retrieved from http://homepages.abdn.
ac.uk/j.crawford/pages/dept/sbdiff.htm
Crowne, D. P., & Marlowe, D. (1960). A new scale of social desirability independent of psychopathol- ogy. Journal of Consulting Psychology, 24, 349–354.
Cudeck, R. (1989). Analysis of correlation matrices using covariance structure models. Psychological Bulletin, 105, 317–327.
Cumming, G. (2012). Understanding the new statistics: Effect sizes, confidence intervals, and meta- analysis. New York: Routledge.
Curran, P. J. (2003). Have multilevel models been structural equation models all along? Multivariate Behavioral Research, 38, 529–569.
Curran, P. J., & Bauer, D. J. (2007). Building path diagrams for multilevel models. Psychological Meth- ods, 12, 283–297.
Curran, T., Hill, A. P., & Niemiec, C. P. (2013). A conditional process model of children’s behavioral engagement and behavioral disaffection in sport based on self-determination theory. Journal of Sport and Exercise Psychology, 35, 30–43.
Dawson, J. F., & Richter, A. W. (2006). Probing three-way interactions in moderated multiple regres- sion: Development and application of a slope difference test. Journal of Applied Psychology, 91, 917–926.
Deshon, R. P. (2004). Measures are not invariant across groups without error variance homogeneity. Psychology Science, 46, 137–149.
Diamantopoulos, A. (Ed.). (2008). Formative indicators [Special issue]. Journal of Business Research, 61(12).
Diamantopoulos, A., Riefler, P., & Roth, K. P. (2008). Advancing formative measurement models. Journal of Business Research, 61, 1203–1218.
Diamantopoulos, A., & Siguaw, J. A. (2000). Introducing LISREL: A guide for the uninitiated. Thousand Oaks, CA: Sage.
Diamantopoulos, A., & Winklhofer, H. M. (2001). Index construction with formative indicators: An alternative to scale development. Journal of Marketing Research, 38, 269–277.

494 References
Dillman Carpentier, F. R., Mauricio, A. M., Gonzales, N. A., Millsap, R. E., Meza, C. M., Dumka, L. E., et al. (2008). Engaging Mexican origin families in a school-based preventive intervention. Jour- nal of Primary Prevention, 28, 521–546.
DiStefano, C. (2002). The impact of categorization with confirmatory factor analysis. Structural Equa- tion Modeling, 9, 327–346.
DiStefano, C., & Hess, B. (2005). Using confirmatory factor analysis for construct validation: An empirical review. Journal of Psychoeducational Assessment, 23, 225–241.
DiStefano, C., Zhu, M., & Mîndrilă, D. (2009). Understanding and using factor scores: Considerations for the applied researcher. Practical Assessment, Research and Evaluation, 14(20). Retrieved from http://pareonline.net/pdf/v14n20.pdf
Duncan, O. D. (1966). Path analysis: Sociological examples. American Journal of Sociology, 74, 119–137. Duncan, O. D. (1975). Introduction to structural equation models. New York: Academic Press.
Duncan, T. E., Duncan, S. C., Hops, H., & Alpert, A. (1997). Multi-level covariance structure analysis
of intra-familial substance use. Drug and Alcohol Dependence, 46, 167–180.
Duncan, T. E., Duncan, S. C., Strycker, L. A., Li, F., & Alpert, A. (1999). An introduction to latent vari-
able growth curve modeling: Concepts, issues, and applications. Mahwah, NJ: Erlbaum.
Edwards, J. R. (1995). Alternatives to difference scores as dependent variables in the study of con- gruence in organizational research. Organizational Behavior and Human Decision Processes, 64,
307–324.
Edwards, J. R. (2009). Seven deadly myths of testing moderation in organizational research. In C. E.
Lance & R. J. Vandenberg (Eds.), Statistical and methodological myths and urban legends: Doc- trine, verity and fable in the organizational and social sciences (pp. 143–164). New York: Taylor & Francis.
Edwards, J. R. (2010). The fallacy of formative measurement. Organizational Research Methods, 14, 370 –3 8 8 .
Edwards, J. R., & Lambert, L. S. (2007). Methods for integrating moderation and mediation: A general analytical framework using moderated path analysis. Psychological Methods, 12, 1–22.
Edwards, M. C., Wirth, R. J., Houts, C. R., & Xi, N. (2012). Categorical data in the structural equation modeling framework. In R. Hoyle (Ed.), Handbook of structural equation modeling (pp. 195–208). New York: Guilford Press.
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1–26.
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 meth-
ods. Psychological Methods, 13, 230–253.
Ellis, P. D. (2010). The essential guide to effect sizes: Statistical power, meta-analysis, and the interpreta-
tion of research results. New York: Cambridge University Press.
Elwert, F. (2013). Graphical causal models. In S. L. Morgan (Ed.), Handbook of causal analysis for social
research (pp. 245–273). New York: Springer.
Enders, C. K. (2010). Applied missing data analysis. New York: Guilford Press.
Epskamp, S. (2014). Package semPlot. Retrieved from http://cran.r-project.org/web/packages/semPlot/
semPlot.pdf
Erceg-Hurn, D. M., & Mirosevich, V. M. (2008). Modern robust statistical methods: An easy way to maximize the accuracy and power of your research. American Psychologist, 63, 591–601.
Fabrigar, L. R., & Wegener, D. T. (2012). Exploratory factor analysis. New York: Oxford University Press.
Fan, X. (1997). Canonical correlation analysis and structural equation modeling: What do they have in common? Structural Equation Modeling, 4, 65–79.
Fan, X., & Sivo, S. A. (2005). Sensitivity of fit indexes to misspecified structural or measurement model components: Rationale of the two-index strategy revisited. Structural Equation Modeling, 12, 343–367.
Finkel, S. E. (1995). Causal analysis with panel data. Thousand Oaks, CA: Sage.
Finney, S. J., & DiStefano, C. (2006). Nonnormal and categorical data in structural equation model-

References 495
ing. In G. R. Hancock & R. O. Mueller (Eds.), A second course in structural equation modeling
(pp. 269–314). Greenwich, CT: IAP.
Finney, S. J., & DiStefano, C. (2013). Nonnormal and categorical data in structural equation modeling.
In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed.)
(pp. 439–492). Charlotte, NC: IAP.
Flora, D. B. (2008). Specifying piecewise latent trajectory models for longitudinal data. Structural
Equation Modeling, 15, 513–533.
Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009). Factor analysis with ordinal indica-
tors: A Monte Carlo study comparing DWLS and ULS estimation. Structural Equation Modeling,
16, 625–641.
Fox, J. (2006). Structural equation modeling with the sem package in R. Structural Equation Modeling,
13, 465–486.
Fox, J. (2012). Structural equation modeling in R with the sem package. Retrieved from http://socserv.
mcmaster.ca/jfox/Books/Companion/appendix/Appendix-SEMs.pdf
Frees, E. W. (2004). Longitudinal and panel data: Analysis and applications in the social sciences. New
York: Cambridge University Press.
Friendly, M. (2006). SAS macro programs: boxcox. Retrieved from www.math.yorku.ca/SCS/sasmac/
boxcox.html
Friendly, M. (2009). SAS macro programs: csmpower. Retrieved from www.datavis.ca/sasmac/
csmpower.html
Gardner, H. (1993). Multiple intelligences: The theory in practice. New York: Basic.
Garson, G. D. (Ed.). (2013) Hierarchical linear modeling: Guide and applications. Thousand Oaks, CA:
Sage.
Geary, R. C. (1947). Testing for normality. Biometrika, 34, 209–242.
Geiser, C. (2013). Data analysis with Mplus. New York: Guilford Press.
George, R. (2006). A cross-domain analysis of change in students’ attitudes toward science and atti-
tudes about the utility of science. International Journal of Science Education, 28, 571–589. Gerbing, D. W., & Anderson, J. C. (1993). Monte Carlo evaluations of fit in structural equation mod- els. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 40–65). Newbury
Park, CA: Sage.
Gignac, G. E. (2008). Higher-order models versus direct hierarchical models: g as superordinate or
breadth factor? Psychology Science Quarterly, 50, 21–43.
Glymour, C., Scheines, R., Spirtes, P., & Ramsey, J. (2014). TETRAD V [computer software]. Available
from www.phil.cmu.edu/tetrad/current.html
Glymour, M. M. (2006). Using causal diagrams to understand common problems in social epidemiol-
ogy. In M. Oakes & J. Kaufman (Eds.), Methods in social epidemiology (pp. 387–422). San Fran-
cisco: Jossey-Bass.
Gnambs, T. (2013). Required sample size and power for SEM. Retrieved from http://timo.gnambs.at/en/
scripts/powerforsem
Goldman, B. A., & Mitchell, D. F. (2007). Directory of unpublished experimental mental measures (vol.
9). Washington, DC: American Psychological Association.
Goldstein, H., Bonnet, G., & Rocher, T. (2007). Multilevel structural equation models for the analysis
of comparative data on educational performance. Journal of Educational and Behavioral Statistics,
32, 252–286.
Gonzalez, R., & Griffin, D. (2001). Testing parameters in structural equation modeling: Every “one”
matters. Psychological Methods, 6, 258–269.
Goodwin, L. D., & Leech, N. L. (2006). Understanding correlation: Factors that affect the size of r.
Journal of Experimental Education, 74, 251–266.
Grace, J. B. (2006). Structural equation modeling and natural systems. New York: Cambridge University
Press.
Grace, J. B., & Bollen, K. A. (2008). Representing general theoretical concepts in structural equation
models: The role of composite variables. Environmental and Ecological Statistics, 15, 191–213.

496 References
Graham, J. M., Guthrie, A. C., & Thompson, B. (2003). Consequences of not interpreting structure coefficients in published CFA research: A reminder. Structural Equation Modeling, 10, 142–153.
Graham, J. W., & Coffman, D. L. (2012). Structural equation modeling with missing data. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 277–295). New York: Guilford Press.
Gregorich, S. E. (2006). Do self-report instruments allow meaningful comparisons across diverse population groups? Testing measurement invariance using the confirmatory factor analysis framework. Medical Care, 44(Suppl. 3), S78–S94.
Hagenaars, J. A., & McCutcheon, A. L. (Eds.). (2002). Applied latent class analysis. New York: Cam- bridge University Press.
Haller, H., & Krauss, S. (2002). Misinterpretations of significance: A problem students share with their teachers? Methods of Psychological Research Online, 7(1), 1–17. Retrieved from www.dgps.de/ fachgruppen/methoden/mpr-online
Hallquist, M., & Wiley, J. (2015). MplusAutomation: Automating Mplus model estimation and interpretation. R package version 0.6-3 [computer software]. Retrieved from http://cran.r-project. org/web/packages/MplusAutomation
Hancock, G. R., & Freeman, M. J. (2001). Power and sample size for the Root Mean Square Error of Approximation of not close fit in structural equation modeling. Educational and Psychological Measurement, 61, 741–758.
Hancock, G. R., & French, B. F. (2013). Power analysis in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed.) (pp. 117– 159). Charlotte, NC: IAP.
Hancock, G. R., & Liu, M. (2012). Bootstrapping standard errors and data–model fit statistics in structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 296–306). New York: Guilford Press.
Hancock, G. R., & Mueller, R. O. (2001). Rethinking construct reliability within latent variable sys- tems. In R. Cudeck, S. du Toit, & D. Sörbom (Eds.), Structural Equation Modeling: Present and future. A Festschrift in honor of Karl Jöreskog (pp. 195–216). Lincolnwood, IL: Scientific Software International.
Hardt, J., Herke, M., & Leonhart, R. (2012). Auxiliary variables in multiple imputation in regression with missing X: A warning against including too many in small sample research. BMC Medical Research Methodology, 12(184). Retrieved from www.biomedcentral.com/1471-2288/12/184
Harrington, D. (2009). Confirmatory factor analysis. New York: Oxford University Press.
Hayduk, L. A. (1996). LISREL issues, debates and strategies. Baltimore, MD: Johns Hopkins University
Press.
Hayduk, L. A. (2006). Blocked-error-R2: A conceptually improved definition of the proportion of
explained variance in models containing loops or correlated residuals. Quality and Quantity, 40,
629–649.
Hayduk, L. A. (2014a). Seeing perfectly-fitting factor models that are causally misspecified: Under-
standing that close-fitting models can be worse. Educational and Psychological Measurement, 74,
905–926.
Hayduk, L. A. (2014b). Shame for disrespecting evidence: The personal consequences of insufficient
respect for structural equation model testing. BMC: Medical Research Methodology, 14(124).
Retrieved from www.biomedcentral.com/1471-2288/14/124
Hayduk, L., Cummings, G., Boadu, K., Pazderka-Robinson, H., & Boulianne, S. (2007). Testing! test-
ing! one, two, three—Testing the theory in structural equation models! Personality and Indi-
vidual Differences, 42, 841–850.
Hayduk, L., Cummings, G., Stratkotter, R., Nimmo, M., Grygoryev, K., Dosman, D., et al. (2003). Pearl’s
d-separation: One more step into causal thinking. Structural Equation Modeling, 10, 289–311. Hayduk, L. A., & Glaser, D. N. (2000). Jiving the four-step, waltzing around factor analysis, and other
serious fun. Structural Equation Modeling, 7, 1–35.
Hayduk, L. A., & Littvay, L. (2012). Should researchers use single indicators, best indicators, or mul-
tiple indicators in structural equation models? BMC Medical Research Methodology, 12(159). Retrieved from www.biomedcentral.com/1471-2288/12/159

References 497
Hayduk, L. A., Pazderka-Robinson, H., Cummings, G. C., Levers, M.-J. D., & Beres, M. A. (2005). Structural equation model testing and the quality of natural killer cell activity measurements. BMC Medical Research Methodology, 5(1). Retrieved from www.ncbi.nlm.nih.gov/pmc/articles/ PMC546216
Hayes, A. F. (2013a). Conditional process modeling: Using structural equation modeling to examine contingent causal processes. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation model- ing: A second course (2nd ed.) (pp. 219–266). Greenwich, CT: IAP.
Hayes, A. F. (2013b). Introduction to mediation, moderation, and conditional process analysis: A regression- based approach. New York: Guilford Press.
Hayes, A. F., & Matthes, J. (2009). Computational procedures for probing interactions in OLS and logistic regression: SPSS and SAS implementations. Behavior Research Methods, 41, 924–936.
Henningsen, A., & Hamann, J. D. (2007). systemfit: A package for estimating systems of simulta- neous equations in R. Journal of Statistical Software, 23(4). Retrieved from www.jstatsoft.org/v23/ i04/paper
Hershberger, S. L. (1994). The specification of equivalent models before the collection of data. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis (pp. 68–105). Thousand Oaks, CA: Sage. Hershberger, S. L. (2006). The problem of equivalent structural models. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed.) (pp. 13–41). Greenwich,
CT: IAP.
Hershberger, S. L., & Marcoulides, G. A. (2013). The problem of equivalent structural models. In G. R.
Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed., pp. 3–39).
Charlotte, NC: IAP.
Hicks, R., & Tingley, D. (2011). Causal mediation analysis. Stata Journal, 11, 605–619.
Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R—A tuto-
rial in measurement invariance with continuous and ordinal indicators. Practical Assessment,
Research and Evaluation, 19(7). Retrieved from http://pareonline.net/getvn.asp?v=19&n=7 Hoekstra, R., Kiers, H. A. L., & Johnson, A. (2013). Are assumptions of well-known statistical tech- niques checked, and why (not)? Frontiers in Psychology, 3. Retrieved from www.frontiersin.org/
article/10.3389/fpsyg.2012.00137/full
Holland, P. W. (1986). Statistics and causal inference. Journal of the American Statistical Association,
81, 945–960.
Holsta, K. K., & Budtz-Jørgensena, E. (2012). Linear latent variable models: The lava package. Com-
putational Statistics, 28, 1385–1452.
Horn, J. L., & McArdle, J. J. (1992). A practical and theoretical guide to measurement invariance in
aging research. Experimental Aging Research, 18, 117–144.
Houghton, J. D., & Jinkerson, D. L. (2007). Constructive thought strategies and job satisfaction: A
preliminary examination. Journal of Business Psychology, 22, 45–53.
Howell, R. D., Breivik, E., & Wilcox, J. B. (2007). Reconsidering formative measurement. Psychological
Methods, 12, 205–218.
Hoyle, R. H. (2012). Model specification in structural equation modeling. In R. H. Hoyle (Ed.), Hand-
book of structural equation modeling (pp. 126–144). New York: Guilford Press.
Hoyle, R. C., & Isherwood, J. C. (2011). Reporting results from structural equation modeling analyses
in Archives of Scientific Psychology. Archives of Scientific Psychology, 1, 14–22.
Hu, L., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underpa-
rameterized model misspecification. Psychological Methods, 3, 424–453.
Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conven-
tional criteria versus new alternatives. Structural Equation Modeling, 6, 1–55.
Huck, S. W. (1992). Group heterogeneity and Pearson’s r. Educational and Psychological Measurement,
52, 253–260.
Hunter, J. E., & Gerbing, D. W. (1982). Unidimensional measurement, second order factor analysis,
and causal models. Research in Organizational Behavior, 4, 267–320.
Hurlbert, S. H., & Lombardi, C. M. (2009). Final collapse of the Neyman-Pearson decision theory
framework and rise of the neoFisherian. Annales Zoologici Fennici, 46, 311–349.

498 References
Imai, K., Keele, L., & Yamamoto, T. (2010). Identification, inference, and sensitivity analysis for causal mediation effects. Statistical Science, 25, 51–71.
Ioannidis, J. P. A. (2005). Why most published research findings are false. PLoS Medicine, 2(8): e124. Retrieved from www.plosmedicine.org
Jackson, D. L. (2003). Revisiting sample size and number of parameter estimates: Some support for the N:q hypothesis. Structural Equation Modeling, 10, 128–141.
Jackson, D. L., Gillaspy, J. A., Jr., & Purc-Stephenson, R. (2009). Reporting practices in confirmatory factor analysis: An overview and some recommendations. Psychological Methods, 14, 6–23. James, G. S. (1951). The comparison of several groups of observations when the ratios of the popula-
tion variances are unknown. Biometrika, 38, 324–329.
James, L. R., & Brett, J. M. (1984). Mediators, moderators, and tests for mediation. Journal of Applied
Psychology, 69, 307–321.
Jarvis, C. B., MacKenzie, S. B., & Podsakoff, P. M. (2003). A critical review of construct indicators and
measurement model misspecification in marketing and consumer research. Journal of Consumer
Research, 30, 199–218.
Jöreskog, K. G. (1993). Testing structural equation models. In K. A. Bollen & J. S. Lang (Eds.), Testing
structural equation models (pp. 294–316). Newbury Park, CA: Sage.
Jöreskog, K. G. (2004). On chi-squares for the independence model and fit measures in LISREL. Retrieved
from www.ssicentral.com/lisrel/techdocs/ftb.pdf
Jöreskog, K. G., & Yang, F. (1996). Nonlinear structural equation models: The Kenny–Judd model
with interaction effects. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural
equation modeling (pp. 57–88). Mahwah, NJ: Erlbaum.
Judd, C. M., Kenny, D. A., & McClelland, G. H. (2001). Estimating and testing mediation and modera-
tion in within-participant designs. Psychological Methods, 6, 115–134.
Jung, S. (2013). Structural equation modeling with small sample sizes using two-stage ridge least-
squares estimation. Behavior Research Methods, 45, 75–81.
Kane, M. T. (2013). Validating the interpretations and uses of test scores. Journal of Educational Mea-
surement, 50, 1–73.
Kanfer, R., & Ackerman, P. L. (1989). Motivation and cognitive abilities: An integrative/aptitude-
treatment interaction approach to skill acquisition. Journal of Applied Psychology, 74, 657–690. Kaplan, D. (2000). Structural equation modeling: Foundations and extensions. Thousand Oaks, CA: Sage. Kaplan, D. (2009). Structural equation modeling: Foundations and extensions (2nd ed.). Thousand Oaks,
CA: Sage.
Kaplan, D., & Depaoli, S. (2012). Bayesian structural equation modeling. In R. H. Hoyle (Ed.), Hand-
book of structural equation modeling (pp. 650–673). New York: Guilford Press.
Kaplan, D., Harik, P., & Hotchkiss, L. (2001). Cross-sectional estimation of dynamic structural equa- tion models in disequilibrium. In R. Cudeck, S. Du Toit, and D. Sörbom (Eds.), Structural equa- tion modeling: Present and future. A Festschrift in honor of Karl Jöreskog (pp. 315–339). Lincoln-
wood, IL: Scientific Software International.
Karami, H. (2012). An introduction to differential item functioning. International Journal of Educa-
tional and Psychological Assessment, 11, 56–76.
Kaufman, A. S., & Kaufman, N. L. (1983). K-ABC administration and scoring manual. Circle Pines, MN:
American Guidance Service.
Keith, T. Z. (1985). Questioning the K-ABC: What does it measure? School Psychology Review, 14, 9–20. Kenny, D. A. (1979). Correlation and causality. New York: Wiley.
Kenny, D. A. (2011a). Estimation with instrumental variables. Retrieved from http://davidakenny.net/
cm/iv.htm
Kenny, D. A. (2011b). Terminology and basics of SEM. Retrieved from http://davidakenny.net/cm/basics.
htm
Kenny, D. (2013). Moderator variables: Introduction. Retrieved from http://davidakenny.net/cm/mod-
eration.htm
Kenny, D. A. (2014a). Measuring model fit. Retrieved from http://davidakenny.net/cm/fit.htm

Kenny, D. A. (2014b). Mediation. Retrieved from http://davidakenny.net/cm/mediate.htm#CI
Kenny, D. A., & Judd, C. M. (1984). Estimating the nonlinear and interactive effects of latent variables.
Psychological Bulletin, 96, 201–210.
Kenny, D. A., & Kashy, D. A. (1992). Analysis of the multitrait-multimethod matrix by confirmatory
factor analysis. Psychological Bulletin, 112, 165–172.
Kenny, D. A., Kashy, D. A., & Bolger, N. (1998). Data analysis in social psychology. In D. Gilbert, S.
Fiske, & G. Lindzey (Eds.), The handbook of social psychology (Vol. 1, 4th ed., pp. 233–265).
Boston: McGraw–Hill.
Kenny, D. A., & Milan, S. (2012). Identification: A nontechnical discussion of a technical issue. In R. H.
Hoyle (Ed.), Handbook of structural equation modeling (pp. 145–163). New York: Guilford Press. Keselman, H. J., Huberty, C. J., Lix, L. M., Olejnik, S., Cribbie, R. A., Donahue, B., et al. (1998). Sta- tistical practices of education researchers: An analysis of the ANOVA, MANOVA, and ANCOVA
analyses. Review of Educational Research, 68, 350–368.
Khine, M. S. (Ed.). (2013). Application of structural equation modeling in educational research and prac-
tice. Rotterdam, The Netherlands: Sense.
Kim, K. H. (2005). The relation among fit indexes, power, and sample size in structural equation mod-
eling. Structural Equation Modeling, 12, 368–390.
Klein, A., & Moosbrugger, A. (2000). Maximum likelihood estimation of latent interaction effects
with the LMS method. Psychometrika, 65, 457–474.
Klein, A. G., & Muthén, B. O. (2007). Quasi-maximum likelihood estimation of structural equa-
tion models with multiple interaction and quadratic effects. Multivariate Behavioral Research, 42,6 47– 673.
Kline, R. B. (2012). Assumptions in structural equation modeling. In R. H. Hoyle (Ed.), Handbook of
structural equation modeling (pp. 111–125). New York: Guilford Press.
Kline, R. B. (2013a). Beyond significance testing: Statistics reform in the behavioral sciences (2nd ed.).
Washington, DC: American Psychological Association.
Kline, R. B. (2013b). Exploratory and confirmatory factor analysis. In Y. Petscher & C. Schatsschnei-
der (Eds.), Applied quantitative analysis in the social sciences (pp. 171–207). New York: Routledge. Kline, R. B., Snyder, J., & Castellanos, M. (1996). Lessons from the Kaufman Assessment Battery for
Children (K-ABC): Toward a new assessment model. Psychological Assessment, 8, 7–17.
Knight, C. R., & Winship, C. (2013). The causal implications of mechanistic thinking: Identification using directed acyclic graphs (DAGs). In S. L. Morgan (Ed.), Handbook of causal analysis for social
research (pp. 275–299). New York: Springer.
Knüppel, S., & Stang, A. (2010). DAG program: Identifying minimal sufficient adjustment sets. Epi-
demiology, 21, 159.
Kühnel, S. (2001). The didactical power of structural equation modeling. In R. Cudeck, S. du Toit, &
D. Sörbom (Eds.), Structural equation modeling: Present and future. A Festschrift in honor of Karl
Jöreskog (pp. 79–96). Lincolnwood, IL: Scientific Software International.
Lambdin, C. (2012). Significance tests as sorcery: Science is empirical—significance tests are not.
Theory and Psychology, 22, 67–90.
Lance, C. E. (1988). Residual centering, exploratory and confirmatory moderator analysis, and decom-
position of effects in path models containing interaction effects. Applied Psychological Measure-
ment, 12, 163–175.
Lee, S., & Hershberger, S. L. (1990). A simple rule for generating equivalent models in covariance
structure modeling. Multivariate Behavioral Research, 25, 313–334.
Lee, S. Y., Poon, W. Y., & Bentler, P. M. (1995). A two-stage estimation of structural equation models
with continuous and polytomous variables. British Journal of Mathematical and Statistical Psy-
chology, 48, 339–358.
Lei, P.-W., & Wu, Q. (2012). Estimation in structural equation modeling. In R. H. Hoyle (Ed.), Hand-
book of structural equation modeling (pp. 164–179). New York: Guilford Press.
Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data (2nd ed.). New York: Wiley. Little, T. D. (2013). Longitudinal structural equation modeling. New York: Guilford Press.

Little, T. D., Bovaird, J. A., & Widaman, K. F. (2006). On the merits of orthogonalizing powered and product terms: Implications for modeling interactions among latent variables. Structural Equa- tion Modeling, 13, 497–519.
Little, T. D., Lindenberger, U., & Nesselroade, J. R. (1999). On selecting indicators for multivariate measurement and modeling with latent variables: When “good” indicators are bad and “bad” indicators are good. Psychological Methods, 4, 192–211.
Little, T. D., Slegers, D. W., & Card, N. A. (2006). A non-arbitrary method of identifying and scaling latent variables in SEM and MACS models. Structural Equation Modeling, 13, 59–72.
Loehlin, J. C. (2004). Latent variable models: An introduction to factor, path, and structural equation analysis (4th ed.). Mahwah, NJ: Erlbaum.
Lynam, D. R., Moffitt, T., & Stouthamer-Loeber, M. (1993). Explaining the relation between IQ and delinquency: Class, race, test motivation, or self-control? Journal of Abnormal Psychology, 102, 187–196.
Maasen, G. H., & Bakker, A. B. (2001). Suppressor variables in path models: Definitions and interpre- tations. Sociological Methods and Research, 30, 241–270.
MacCallum, R. C. (1986). Specification searches in covariance structure modeling. Psychological Bul- letin, 100, 107–120.
MacCallum, R. C., & Austin, J. T. (2000). Applications of structural equation modeling in psychologi- cal research. Annual Review of Psychology, 51, 201–236.
MacCallum, R. C., & Browne, M. W. (1993). The use of causal indicators in covariance structure mod- els: Some practical issues. Psychological Bulletin, 114, 533–541.
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.
MacCallum, R. C., Wegener, D. T., Uchino, B. N., & Fabrigar, L. R. (1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin, 114, 185–199.
MacKinnon, D. P. (2008). Introduction to statistical mediation analysis. New York: Erlbaum. MacKinnon, D. P., Krull, J. L., & Lockwood, C. M. (2000). Equivalence of the mediation, confound-
ing, and suppression effect. Prevention Science, 1, 173–181.
MacKinnon, D. P., & Pirlott, A. G. (2015). Statistical approaches for enhancing causal interpreta-
tion of the M to Y relation in mediation analysis. Personality and Social Psychology Review, 19,
30–43.
Madans, J. H., Kleinman, J. C., Cox, C. S., Barbano, H. E., Feldman, J. J., Cohen, B., et al. (1986).
10 years after NHANES I—Report of initial followup, 1982–84. Public Health Reports, 101,
465–473.
Maddox, T. (2008). Tests: A comprehensive reference for assessments in psychology, education and busi-
ness (6th ed.). Austin, TX: PRO-ED.
Mair, P., Wu, E., & Bentler, P. M. (2010). EQS goes R: Simulations for SEM using the package REQS.
Structural Equation Modeling, 17, 333–349.
Malone, P. S., & Lubansky, J. B. (2012). Preparing data for structural equation modeling: Doing your
homework. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 263–276). New
York: Guilford Press.
Marcoulides, G. A., & Ing, M. (2012). Automated structural equation modeling strategies. In R. H.
Hoyle (Ed.), Handbook of structural equation modeling (pp. 690–704). New York: Guilford Press. Mardia, K. V. (1985). Mardia’s test of multinormality. In S. Kotz & N. L. Johnson (Eds.), Encyclopedia
of statistical sciences (Vol. 5, pp. 217–221). New York: Wiley.
Markland, D. (2007). The golden rule is that there are no golden rules: A commentary on Paul Bar-
rett’s recommendations for reporting model fit in structural equation modeling. Personality and
Individual Differences, 42, 851–858.
Marsh, H. W., & Bailey, M. (1991). Confirmatory factor analysis of multitrait-multimethod data: A
comparison of alternative models. Applied Psychological Measurement, 15, 47–70.
Marsh, H. W., Balla, J. R., & Hau, K.-T. (1996). An evaluation of incremental fit indices: A clarifica- tion of mathematical and empirical properties. In G. A. Marcoulides & R. E. Schumaker (Eds.),
Advanced structural equation modeling (pp. 315–353). Mahwah, NJ: Erlbaum.

Marsh, H. W., & Grayson, D. (1995). Latent variable models of multitrait-multimethod data. In R. H. Hoyle (Ed.), Structural equation modeling (pp. 177–198). Thousand Oaks, CA: Sage.
Marsh, H. W., & Hau, K.-T. (1999). Confirmatory factor analysis: Strategies for small sample sizes. In R. H. Hoyle (Ed.), Statistical strategies for small sample research (pp. 252–284). Thousand Oaks, CA: Sage.
Marsh, H. W., Hau, K.-T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis test- ing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler’s (1999) findings. Structural Equation Modeling, 11, 320–341.
Marsh, H. W., Morin, A. J. S., Parker, P. D., & Kaur, G. (2014). Exploratory structural equation mod- eling: Integration of the best features of exploratory and confirmatory factor analysis. Annual Review of Clinical Psychology, 10, 85–110.
Marsh, H. W., Wen, Z., & Hau, K. T. (2004). Structural equation models of latent interactions: Evalu- ation of alternative estimation strategies and indicator construction. Psychological Methods, 9, 275 –300.
Marsh, H. W., Wen, Z., & Hau, K. T. (2006). Structural equation modeling of latent interaction and quadratic effects. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed., pp. 225–265). Greenwich, CT: IAP.
Marsh, H. W., Wen, Z., Nagengast, B., & Hau, K. T. (2012). Structural equation models of latent inter- action. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 436–458). New York: Guilford Press.
Masyn, K. E., Petras, H., & Liu, W. (2014). Growth curve models with categorical outcomes. In G. Bru- insma & D. Weisburd (Eds.), Encyclopedia of Criminology and Criminal Justice (pp. 2013–2025). New York: Springer Verlag.
MathWorks. (2013). MATLAB (Version 8.2) [computer software]. Natick, MA: Author.
Matsueda, R. L. (2012). Key advances in structural equation modeling. In R. H. Hoyle (Ed.), Handbook
of structural equation modeling (pp. 3–16). New York: Guilford Press.
Mauro, R. (1990). Understanding L.O.V.E. (left out variables error): A method for estimating the
effects of omitted variables. Psychological Bulletin, 108, 314–329.
Maxwell, S. E., & Cole, D. A. (2007). Bias in cross-sectional analyses of longitudinal mediation. Psy-
chological Methods, 12, 23–44.
McArdle, J. J., & McDonald, R. P. (1984). Some algebraic properties of the Reticular Action Model for
moment structures. British Journal of Mathematical and Statistical Psychology, 37, 234–251. McCoach, D. B., Black, A. C., & O’Connell, A. A. (2007). Errors of inference in structural equation
modeling. Psychology in the Schools, 44, 461–470.
McDonald, R. A., Behson, S. J., & Seifert, C. F. (2005). Strategies for dealing with measurement error
in multiple regression. Journal of Academy of Business and Economics, 5, 80–97.
McDonald, R. P. (1989). An index of goodness of fit based on noncentrality. Journal of Classification,
6, 97–103.
McDonald, R. P., & Ho, M.-H. R. (2002). Principles and practice in reporting structural equation
analyses. Psychological Methods, 7, 64–82.
McDonald, R. P., & Marsh, H. W. (1990). Choosing a multivariate model: Noncentrality and goodness
of fit. Psychological Bulletin, 107, 247–255.
McIntosh, C. N., Edwards, J. R., & Antonakis, J. (2014). Reflections on partial least squares path mod-
eling. Organizational Research Methods, 17, 210–251.
McKnight, P. E., McKnight, K. M., Sidani, S., & Figueredo, A. J. (2007). Missing data: A gentle introduc-
tion. New York: Guilford Press.
Meade, A. W., & Bauer, D. J. (2007). Power and precision in confirmatory factor analytic tests of mea-
surement invariance. Structural Equation Modeling, 14, 611–635.
Meade, A. W., Johnson, E. C., & Braddy, P. W. (2008). Power and sensitivity of alternative fit indices
in tests of measurement invariance. Journal of Applied Psychology, 93, 568–592.
Meade, A. W., & Lautenschlager, G. J. (2004). A comparison of item response theory and confirmatory factor analytic methodologies for establishing measurement equivalence/invariance. Organiza-
tional Research Methods, 7, 361–388.

Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122.
Messick, S. (1995). Validation of inferences from persons’ responses and performances as scientific
inquiry into score meaning. American Psychologist, 50, 741–749.
Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bul-
letin, 105, 156–166.
Miles, J., & Shevlin, M. (2007). A time and a place for incremental fit indices. Personality and Individual
Differences, 42, 869–874.
Millsap, R. E. (2001). When trivial constraints are not trivial: The choice of uniqueness constraints in
confirmatory factor analysis. Structural Equation Modeling, 8, 1–17.
Millsap, R. E. (2007). Structural equation modeling made difficult. Personality and Individual Differ-
ences, 42, 875–881.
Millsap, R. E. (2011). Statistical approaches to measurement invariance. New York: Routledge.
Millsap, R. E., & Olivera-Aguilar, M. (2012). Investigating measurement invariance using confirma-
tory factor analysis. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 380–392).
New York: Guilford Press.
Millsap, R. E., & Yun-Tein, J. (2004). Assessing factorial invariance in ordered-categorical measures.
Multivariate Behavioral Research, 39, 479–515.
Molina, K. M., Alegría, M., & Mahalingam, R. (2013). A multiple-group path analysis of the role of
everyday discrimination on self-rated physical health among Latina/os in the U.S. Annals of
Behavioral Medicine, 45(1), 33–44.
Monecke, A. (2014). Package semPLS [computer software]. Retrieved from http://cran.r-project.org/
web/packages/semPLS/semPLS.pdf
Mooijaart, A., & Satorra, A. (2009). On insensitivity of the chi-square model test to non-linear mis- specification in structural equation models. Psychometrika, 74, 443–455.
Mueller, R. O., & Hancock, G. R. (2008). Best practices in structural equation modeling. In J. W. Osborne (Ed.), Best practices in quantitative methods (pp. 488–508). Thousand Oaks, CA: Sage.
Mulaik, S. A. (1987). A brief history of the philosophical foundations of exploratory factor analysis. Multivariate Behavioral Research, 22, 267–305.
Mulaik, S. A. (2009a). Foundations of factor analysis (2nd ed.). Boca Raton, FL: Chapman & Hall/CRC. Mulaik, S. A. (2009b). Linear causal modeling with structural equations. New York: CRC Press. Mulaik, S. A., & Millsap, R. E. (2000). Doing the four-step right. Structural Equation Modeling, 7,
36–73.
Muthén, B. O. (1984). A general structural equation model with dichotomous, ordered categorical,
and continuous latent variable indicators. Psychometrika, 49, 115–132.
Muthén, B. O. (1994). Multilevel covariance structure analysis. Sociological Methods and Research, 22,
376 –398.
Muthén, B. O. (2001). Latent variable mixture modeling. In G. A. Marcoulides and R. E. Schumaker
(Eds.), New developments and techniques in structural equation modeling (pp. 1–33). Mahwah, NJ:
Erlbaum.
Muthén, B. O. (2011). Applications of causally defined direct and indirect effects in mediation analysis
using SEM in Mplus. Retrieved from www.statmodel.com/download/causalmediation.pdf
Muthén, B., & Asparouhov, T. (2015). Causal effects in mediation modeling: An introduction with
applications to latent variables. Structural Equation Modeling, 22, 12–23.
Muthén, B. O., du Toit, S. H. C., & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous
outcomes. Retrieved from www.statmodel.com/bmuthen/articles/Article_075.pdf
Muthén, L. K., & Muthén, B. O. (1998–2014). Mplus (Version 7.3) [computer software]. Los Angeles:
Author.
Myers, T. A. (2011). Goodbye, listwise deletion: Presenting hot deck imputation as an easy and effec-
tive tool for handling missing data. Communication Methods and Measures, 5, 297–310. Narayanan, A. (2012). A review of eight software packages for structural equation modeling. American
Statistician, 66, 129–138.

Neale, M. C., Boker, S. M., Xie, G., & Maes, H. H. (2004). Mx: Statistical modeling (6th ed.). Richmond: Virginia Commonwealth University, Virginia Institute for Psychiatric and Behavioral Genetics.
Nevitt, J., & Hancock, G. R. (2000). Improving the root mean square error of approximation for nonnormal conditions in structural equation modeling. Journal of Experimental Education, 68, 251–268.
Nevitt, J., & Hancock, G. R. (2001). Performance of bootstrapping approaches to model test statistics and parameter standard error estimation in structural equation modeling. Structural Equation Modeling, 8, 353–377.
Newsom, J. (2015). Longitudinal structural equation modeling: A comprehensive introduction. New York: Routledge.
Nimon, K., & Reio, T., Jr. (2011). Measurement invariance: A foundational principle for quantitative theory building. Human Resource Development Review, 10, 198–214.
Nunkoo, R., Ramkissoon, H., & Gursoy, D. (2013). Use of structural equation modeling in tourism research: Past, present, and future. Journal of Travel Research, 52, 759–771.
Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). New York: McGraw-Hill. O’Brien, R. M. (1994). Identification of simple measurement models with multiple latent variables and
correlated errors. Sociological Methodology, 24, 137–170.
Okech, D., Kim, J., & Little, T. D. (2013). Recent developments in structural equation modeling
research in social work publications. British Journal of Social Work. Advance access publication.
Retrieved from http://bjsw.oxfordjournals.org
Oliveri, M. E., Olson, B. D., Ercikan, K., & Zumbo, B. D. (2012). Methodologies for investigating item-
and test-level measurement equivalence in international large-scale assessments. International
Journal of Testing, 12, 203–223.
Olsson, U. H., Foss, T., & Breivik, E. (2004). Two equivalent discrepancy functions for maximum
likelihood estimation: Do their test statistics follow a non-central chi-square distribution under
model misspecification. Sociological Methods and Research, 32, 453–500.
Olsson, U. H., Foss, T., Troye, S. V., & Howell, R. D. (2000). The performance of ML, GLS, and WLS estimation in structural equation modeling under conditions of misspecification and non-
normality. Structural Equation Modeling, 7, 557–595.
O’Rourke, R., & Hatcher, L. (2013). A step-by-step approach to using SAS for factor analysis and struc-
tural equation modeling (2nd ed.). Cary, NC: SAS Institute.
Osborne, J. W. (2002). Notes on the use of data transformations. Practical Assessment, Research and
Evaluation, 8(6). Retrieved from http://pareonline.net/getvn.asp?v=8&n=6
Osborne, J. W. (2010). Improving your data transformations: Applying the Box–Cox transformation. Practical Assessment, Research and Evaluation, 15(12). Retrieved from http://pareonline.net/getvn.
asp?v=15&n=12
Osborne, J. W., & Fitzpatrick, D. C. (2012). Replication analysis in exploratory factor analysis: What it is and why it makes your analysis better. Practical Assessment, Research and Evaluation, 17. Retrieved from http://pareonline.net/pdf/v17n15.pdf
Park, I. & Schutz, R. W. (2005). An introduction to latent growth models: Analysis of repeated mea- sures physical performance data. Research Quarterly for Exercise and Sport, 76, 176–192.
Paxton, P., Hipp, J. R., & Marquart-Pyatt, S. T. (2011). Nonrecursive models: Endogeneity, reciprocal relationships, and feedback loops. Thousand Oaks, CA: Sage.
Pearl, J. (2000). Causality: Models, reasoning, and inference. New York: Cambridge University Press. Pearl, J. (2009a). Causal inference in statistics: An overview. Statistics Surveys, 3, 96–146.
Pearl, J. (2009b). Causality: Models, reasoning, and inference (2nd ed.). New York: Cambridge Univer-
sity Press.
Pearl, J. (2012). The causal foundations of structural equation modeling. In R. H. Hoyle (Ed.), Hand-
book of structural equation modeling (pp. 68–91). New York: Guilford Press.
Pearl, J. (2014). Interpretation and identification of causal mediation. Psychological Methods, 19, 459–
481.
Pearl, J., & Meshkat, P. (1999). Testing regression models with fewer regressors. In D. Heckerman &

J. Whittaker (Eds.), Proceedings of the Seventh International Workshop on Artificial Intelligence and
Statistics (pp. 255–259). San Francisco: Morgan Kaufmann.
Pedhazur, E. J., & Schmelkin, L. P. (1991). Measurement, design, and analysis: An integrated approach.
Hillsdale, NJ: Erlbaum.
Peters, C. L. O., & Enders, C. (2002). A primer for the estimation of structural equation models in the
presence of missing data. Journal of Targeting, Measurement and Analysis for Marketing, 11, 81–95. Petersen, M. L., Sinisi, S. E., & van der Laan, M. J. (2006). Estimation of direct causal effects. Epide-
miology, 17, 276–284.
Ping, R. A. (1996). Interaction and quadratic effect estimation: A two-step technique using structural
equation analysis. Psychological Bulletin, 119, 166–175.
Pinter, J. (1996). Continuous global optimization software: A brief review. Optima, 52, 1–8. Pornprasertmanit, S., Miller, P., Schoemann, A., Quick, C., & Jorgensen, T. (2014). Package simsem.
Retrieved from http://cran.r-project.org/web/packages/simsem/simsem.pdf
Pornprasertmanit, S., Miller, P., Schoemann, A., Rosseel, Y., Quick, C., Garnier–Villarreal, M., et al. (2014). Package semTools. Retrieved from http://cran.r-project.org/web/packages/semTools/sem-
Tools.pdf
Porter, K., Poole, D., Kisynski, J., Sueda, S., Knoll, B., Mackworth, A., et al. (1999–2009). Belief and Decision Network Tool (Version 5.1.10) (computer software). Retrieved from http://aispace.org/ bayes
Preacher, K. J., & Coffman, D. L. (2006). Computing power and minimum sample size for RMSEA. Retrieved from www.quantpsy.org/rmsea/rmsea.htm
Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and compar- ing indirect effects in multiple mediator models. Behavior Research Methods, 40, 879–891.
Preacher, K. J., & Kelley, K. (2011). Effect size measures for mediation models: Quantitative strategies for communicating indirect effects. Psychological Methods, 16, 93–115.
Preacher, K. J., & Merkle, E. C. (2012). The problem of model selection uncertainty in structural equa- tion modeling. Psychological Methods, 17, 1–14.
Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Addressing moderated mediation hypotheses: Theory, methods, and prescriptions. Multivariate Behavioral Research, 42, 185–227.
Preacher, K. J., Wichman, A. L., MacCallum, R. C., & Briggs, N. E. (2008). Latent growth curve model- ing. Thousand Oaks, CA: Sage.
Preacher, K. J., Zhang, Z., & Zyphur, M. J. (2011). Alternative methods for assessing mediation in multilevel data: The advantages of multilevel SEM. Structural Equation Modeling, 18, 161–182.
Provalis Research. (1995–2011). SimStat (Version 2.6.1) [Computer software]. Montreal, Quebec, Canada: Author.
Radloff, L. S. (1977). The CES-D scale: A self-report depression scale for research in the general popu- lations. Applied Psychological Measurement, 1, 385–401.
Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, 111– 163.
Raykov, T. (2004). Behavioral scale reliability and measurement invariance evaluation using latent variable modeling. Behavior Therapy, 35, 299–331.
Raykov, T. (2011). Introduction to psychometric theory. New York: Routledge.
Raykov, T., & Marcoulides, G. A. (2000). A first course in structural equation modeling. Mahwah, NJ:
Erlbaum.
Raykov, T., & Marcoulides, G. A. (2001). Can there be infinitely many models equivalent to a given
covariance structure? Structural Equation Modeling 8, 142–149.
Rensvold, R. B., & Cheung, G. W. (1999). Identification of influential cases in structural equation
models using the jackknife method. Organizational Research Methods, 2, 293–308.
Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under
suboptimal conditions. Psychological Methods, 17, 354–373.
Richardson, H. A., Simmering, M. J., & Sturman, M. C. (2009). A tale of three perspectives examining

post hoc statistical techniques for detection and correction of common method variance. Orga-
nizational Research Methods, 12, 762–800.
Rigdon, E. E. (1995). A necessary and sufficient identification rule for structural models estimated in
practice. Multivariate Behavioral Research, 30, 359–383.
Rigdon, E. E. (1997). Not positive definite matrices—Causes and cures. Retrieved from www2.gsu.
edu/~mkteer/npdmatri.html
Rigdon, E. E. (2013). Partial least squares path modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed., pp. 81–116). Charlotte, NC: IAP.
Rigdon, E. E. (2014, May). Factor indeterminacy and factor-based structural equation modeling. Paper presented at the second Modern Modeling Methods Conference. Retrieved from www.modeling. uconn.edu/archive/2014/slides-from-paper-symposia
Rindskopf, D. (1984). Structural equation models: Empirical identification, Heywood cases, and related problems. Sociological Methods and Research, 13, 109–119.
Ringle, C. M., Wende, S., & Becker, J.-M. (2014). SmartPLS 3 [computer software]. Retrieved www. smartpls.com
Rodgers, J. L. (2010). The epistemology of mathematical and statistical modeling: A quiet method- ological revolution. American Psychologist, 65, 1–12.
Rodgers, J. L., & Nicewander, W. A. (1988). Thirteen ways to look at the correlation coefficient. Ameri- can Statistician, 42, 59–66.
Rogosa, D. R. (1988). Ballad of the casual modeler. Retrieved from www.stanford.edu/class/ed260/ballad Romney, D. M., Jenkins, C. D., & Bynner, J. M. (1992). A structural analysis of health-related quality
of life dimensions. Human Relations, 45, 165–176.
Rosenberg, J. F. (1998). Kant and the problem of simultaneous causation. International Journal of
Philosophical Studies, 6, 167–188.
Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Soft-
ware, 48(2). Retrieved from www.jstatsoft.org/v48/i02/paper
Roth, D. L., Wiebe, D. J., Fillingham, R. B., & Shay, K. A. (1989). Life events, fitness, hardiness, and
health: A simultaneous analysis of proposed stress-resistance effects. Journal of Personality and
Social Psychology, 57, 136–142.
Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern epidemiology (3rd ed.). Philadelphia: Lip-
pincott Williams & Wilkins.
Royston, P., Altman, D. G., & Sauerbrei, W. (2006). Dichotomizing continuous predictors in multiple
regression: A bad idea. Statistics in Medicine, 25, 127–141.
Rubin, D. B. (2005). Causal inference using potential outcomes: Design, modeling, decisions. Journal
of the American Statistical Association, 100, 322–331.
Rubin, D. B. (2009). Should observational studies be designed to allow lack of balance in covariate
distributions across treatment groups? Statistics in Medicine, 28, 1420–1423.
Ryder, A. G., Yang, J., Zhu, X., Yao, S., Yi, J., Heine, S. J., et al. (2008). The cultural shaping of depres- sion: Somatic symptoms in China, psychological symptoms in North America? Journal of Abnor-
mal Psychology, 117, 300–313.
Saris, W. E., & Alberts, C. (2003). Different explanations for correlated disturbance terms in MTMM
studies. Structural Equation Modeling, 10, 193–213.
Saris, W. E., & Satorra, A. (1993). Power evaluations in structural equation models. In K. A. Bollen
& J. S. Long (Eds.), Testing structural equation models (pp. 181–204). Newbury Park, CA: Sage. SAS Institute. (2014). SAS/STAT (Version 9.4) [computer software]. Cary, NC: Author.
Sass, D. A., Schmitt, T. A., & Marsh, H. W. (2014). Evaluating model fit with ordered categorical data
within a measurement invariance framework: A comparison of estimators. Structural Equation
Modeling, 21, 167–180.
Satorra, A., & Bentler, P. M. (1988). Scaling corrections for chi-square statistics in covariance struc-
ture analysis. In American Statistical Association 1988 Proceedings of the Business and Economic
Statistics Section (pp. 308–313). Alexandria, VA: American Statistical Association.
Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors on covariance

structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis (pp. 399–419).
Thousand Oaks, CA: Sage.
Satorra, A., & Bentler, P. M. (2001). A scaled difference chi-square test statistic for moment structure
analysis. Psychometrika, 66, 507–514.
Satorra, A., & Bentler, P. M. (2010). Ensuring positiveness of the scaled chi-square test statistic. Psy-
chometrika, 75, 243–248.
Savalei, V. (2014). Understanding robust corrections in structural equation modeling. Structural Equa-
tion Modeling, 21, 149–160.
Schreiber, J. B. (2008). Core reporting practices in structural equation modeling. Research in Social and
Administrative Pharmacy, 4, 83–97.
Schumaker, R. E., & Lomax, R. G. (2010). A beginner’s guide to structural equation modeling (3rd ed.).
Mahwah, NJ: Erlbaum.
Schumaker, R. E., & Marcoulides, G. A. (Eds.). (1998). Interaction and nonlinear effects in structural
equation modeling. Mahwah, NJ: Erlbaum.
Scientific Software International. (2006). LISREL (Version 8.8) [computer software]. Skokie, IL:
Author.
Scientific Software International. (2013). LISREL (Version 9.1) [computer software]. Skokie, IL:
Author.
Selig, J. P., & Preacher, K. J. (2009). Mediation models for longitudinal data in developmental research.
Research in Human Development, 6, 144–164.
Shadish, W. R., Cook, T. D., & Campbell, D. T. (2001). Experimental and quasi-experimental designs for
generalized causal inference. New York: Houghton Mifflin.
Shah, R., & Goldstein, S. M. (2006). Use of structural equation modeling in operations management
research: Looking back and forward. Journal of Operations Management, 24, 148–169.
Shapiro, A., & Browne, M. W. (1987). Analysis of covariance structures under elliptical distributions.
Journal of the American Statistical Association, 82, 1092–1097.
Shieh, G. (2006). Suppression situations in multiple linear regression. Educational and Psychological
Measurement, 66, 435–447.
Shipley, B. (2000). A new inferential test for path models based on directed acyclic graphs. Structural
Equation Modeling, 7, 206–218.
Silvia, E. S. M., & MacCallum, R. C. (1988). Some factors affecting the success of specification searches
in covariance structure modeling. Multivariate Behavioral Research, 23, 297–326.
Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal,
and structural equation models. Boca Raton, FL: Chapman & Hall/CRC.
Sobel, M. E. (1982). Asymptotic intervals for indirect effects in structural equations models. In S.
Leinhart (Ed.), Sociological methodology (pp. 290–312). San Francisco: Jossey-Bass.
Spearman, C. (1904). General intelligence, objectively determined and measured. American Journal of
Psychology, 15, 201–293.
Spirtes, P. (1995). Directed cyclic graphical representations of feedback models. In P. Besnard &
S. Hanks (Eds.), Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence
(pp. 491–498). San Francisco: Morgan Kaufmann.
Spirtes, P., Glymour, C., & Scheines, R. (2001). Causation, prediction, and search (2nd ed.). Cambridge,
MA: MIT Press.
Stapleton, L. M. (2013). Using multilevel structural equation modeling techniques with complex sam-
ple data. In G. R. Hancock & R. O. Mueller (Eds.), A second course in structural equation modeling
(2nd ed., pp. 521–562). Greenwich, CT: IAP.
Stark, S., Chernyshenko, O. S., & Drasgow, F. (2006). Detecting differential item functioning with
confirmatory factor analysis and item response theory: Toward a unified strategy. Journal of
Applied Psychology, 91, 1292–1306.
StataCorp. (1985–2015). Stata statistical software: Release 14 [computer software]. College Station, TX:
Author.
StatPoint Technologies, Inc. (1982–2013). Statgraphics Centurion (Version 16.2.04). [Computer soft-
ware]. Warrenton, VA: Author.

StatSoft. (2013). STATISTICA Advanced (Version 12) [computer software]. Tulsa, OK: Author. Steenkamp, J.-B. E. M., & Baumgartner, H. (1998). Assessing measurement invariance in cross-
national consumer research. Journal of Consumer Research, 25, 78–107.
Steiger, J. H. (1990). Structural model evaluation and modification: An interval estimation approach.
Multivariate Behavioral Research, 25, 173–180.
Steiger, J. H. (2001). Driving fast in reverse: The relationship between software development, theory,
and education in structural equation modeling. Journal of the American Statistical Association,
96, 331–338.
Steiger, J. H. (2002). When constraints interact: A caution about reference variables, identification
constraints, and scale dependencies in structural equation modeling. Psychological Methods, 7,
210 –227.
Steiger, J. H. (2007). Understanding the limitations of global fit assessment in structural equation
modeling. Personality and Individual Differences, 42, 893–898.
Steiger, J. H., & Fouladi, R. T. (1997). Noncentrality interval estimation and the evaluation of statisti-
cal models. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.), What if there were no significance
tests? (pp. 221–257). Mahwah, NJ: Erlbaum.
Steiger, J. H., & Schönemann, P. H. (1978). A history of factor indeterminacy. In S. Shye (Ed.), Theory
construction and data analysis (pp. 136–178). Chicago: University of Chicago Press.
Streiner, D. L. (2003). Starting at the beginning: An introduction to coefficient alpha and internal
consistency. Journal of Personality Assessment, 80, 99–103.
Steinmetz, H. (2011). Analyzing observed composite differences across groups: Is partial measure-
ment invariance enough? Methodology, 9, 1–12.
Stone-Romero, E. F., & Rosopa, P. J. (2011). Experimental tests of mediation models: Prospects, prob-
lems, and some solutions. Organizational Research Methods, 14, 631–646.
Systat Software. (2009). Systat (Version 13.1) [computer software]. Chicago: Author.
Textor, J., Hardt, J., & Knüppel, S. (2011). DAGitty: A graphical tool for analyzing causal diagrams.
Epidemiology, 5, 745.
Thompson, B. (1995). Stepwise regression and stepwise discriminant analysis need not apply here: A
guidelines editorial. Educational and Psychological Measurement, 55, 525–534.
Thompson, B. (2000). Ten commandments of structural equation modeling. In L. G. Grimm & P. R. Yarnold (Eds.), Reading and understanding more multivariate statistics (pp. 261–283). Washington,
DC: American Psychological Association.
Thompson, B. (2006). Foundations of behavioral statistics: An insight-based approach. New York: Guil-
ford Press.
Thompson, B., & Vacha-Haase, T. (2000). Psychometrics is datametrics: The test is not reliable. Edu-
cational and Psychological Measurement, 60, 174–195.
Thorndike, R. M., & Thorndike-Christ, T. M. (2010). Measurement and evaluation in psychology and
education (8th ed.). Upper Saddle River, NJ: Pearson.
Tomarken, A. J., & Waller, N. G. (2003). Potential problems with “well-fitting”models. Journal of
Abnormal Psychology, 112, 578–598.
Tomarken, A. J., & Waller, N. G. (2005). Structural equation modeling: Strengths, limitations, and
misconceptions. Annual Review of Clinical Psychology, 1, 31–65.
Trafimow, D., & Marks, M. (2015). Editorial. Basic and Applied Social Psychology, 37, 1–2.
Tu, Y.-K. (2009). Commentary: Is structural equation modelling a step forward for epidemiologists?
International Journal of Epidemiology, 38, 549–551.
Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis.
Psychometrika, 38, 1–10.
Vacha-Haase, T., & Thompson, B. (2011). Score reliability: A retrospective look back at 12 years of reli-
ability generalization. Measurement and Evaluation in Counseling and Development, 44, 159–168. Valeri, L., & VanderWeele, T. J. (2013). Mediation analysis allowing for exposure–mediator interac- tions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS
macros. Psychological Methods, 2, 137–150.
Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance

literature: Suggestions, practices, and recommendations for organizational research. Organiza-
tional Research Methods, 3, 4–70.
VanderWeele, T. J. (2014). A unification of mediation and interaction: A 4-way decomposition. Epide-
miology, 25, 749–761.
VanderWeele, T. J. (2015). Explanation in causal inference: Methods for mediation and interaction. New
York: Oxford University Press.
van Prooijen, J.-W., & van der Kloot, W. A. (2001). Confirmatory analysis of exploratively obtained
factor structures. Educational and Psychological Measurement, 61, 777–792.
Vernon, P. A., & Eysenck, S. B. G. (Eds.). (2007). Structural equation modeling [Special issue]. Person-
ality and Individual Differences, 42(5).
Vieira, A. L. (2011). Interactive LISREL in practice: Getting started with a SIMPLIS approach. New York:
Springer.
Voelkle, M. C. (2008). Reconsidering the use of autoregressive latent trajectory (ALT) model. Multi-
variate Behavioral Research, 43, 564–591.
von Oertzen, T., Brandmaier, A. M., & Tsang, S. (2015). Structural equation modeling with Wnyx.
Structural Equation Modeling, 22, 148–161.
Vriens, M., & Melton, E. (2002). Managing missing data. Marketing Research, 14, 12–17.
Wall, M. M., & Amemiya, Y. (2001). Generalized appended product indicator procedure for nonlinear
structural equation analysis. Journal of Educational and Behavioral Statistics, 26, 1–29.
Wang, J., & Wang, X. (2012). Structural equation modeling: Applications using Mplus. West Sussex, UK:
Wiley.
West, S. G., Taylor, A. B., & Wu, W. (2012). Model fit and model selection in structural equation mod-
eling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 209–246). New York:
Guilford Press.
Westland, C. J. (2010). Lower bounds on sample size in structural equation modeling. Electronic Com-
merce Research and Applications, 9, 476–487.
Wherry, R. J. (1931). A new formula for predicting the shrinkage of the coefficient of multiple correla-
tion. Annals of Mathematical Statistics, 2, 440–451.
Whitaker, B. G., & McKinney, J. L. (2007). Assessing the measurement invariance of latent job satis-
faction ratings across survey administration modes for respondent subgroups: A MIMIC model-
ing approach. Behavior Research Methods, 39, 502–509.
Whittingham, M. J., Stephens, P. A., Bradbury, R. B., & Freckleton, R. P. (2006). Why do we still use
stepwise modelling in ecology and behaviour? Journal of Animal Ecology, 75, 1182–1189. Widaman, K. F., & Thompson, J. S. (2003). On specifying the null model for incremental fit indexes
in structural equation modeling. Psychological Methods, 8, 16–37.
Wilcox, R. R. (2012). Introduction to robust estimation and hypothesis testing (3rd ed.). San Diego, CA:
Academic Press.
Willett, J. B., & Sayer, A. G. (1994). Using covariance structure analysis to detect correlates and pre-
dictors of individual change over time. Psychological Bulletin, 116, 363–381.
Williams, L. J. (2012). Equivalent models: Concepts, problems, alternatives. In R. H. Hoyle (Ed.),
Handbook of structural equation modeling (pp. 247–260). New York: Guilford Press.
Williams, T. H., McIntosh, D. E., Dixon, F., Newton, J. H., & Youman, E. (2010). A confirmatory factor analysis of the Stanford-Binet Intelligence Scales, fifth edition, with a high-achieving sample.
Psychology in the Schools, 47, 1071–1083.
Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: Current approaches and future directions.
Psychological Methods, 12, 58–79.
Wold, H. (1982). Soft modeling: The basic design and some extensions. In K. G. Jöreskog & H. Wold
(Eds.), Systems under indirect observation: Causality, structure, prediction (Vol. 2, pp. 1–54).
Amsterdam: North-Holland.
Wolf, E. J., Harrington, K. M., Clark, S. L., & Miller, M. W. (2013). Sample size requirements for
structural equation models: An evaluation of power, bias, and solution propriety. Educational and Psychological Measurement, 73, 913–934.

Wolfle, L. M. (2003). The introduction of path analysis to the social sciences, and some emergent themes: An annotated bibliography. Structural Equation Modeling, 10, 1–34.
Wong, C.-S., & Law, K. S. (1999). Testing reciprocal relations by nonrecursive structural equation models using cross-sectional data. Organizational Research Methods, 2, 69–87.
Worland, J., Weeks, G. G., Janes, C. L., & Strock, B. D. (1984). Intelligence, classroom behavior, and academic achievement in children at high and low risk for psychopathology: A structural equa- tion analysis. Journal of Abnormal Child Psychology, 12, 437–454.
Wothke, W. (1993). Nonpositive definite matrices in structural equation modeling. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 256–293). Newbury Park, CA: Sage.
Wright, S. (1921). Correlation and causation. Journal of Agricultural Research, 20, 557–585.
Wright, S. (1923). The theory of path coefficients: A reply to Niles’ criticism. Genetics, 20, 239–255. Wright, S. (1934). The method of path coefficients. Annals of Mathematical Statistics, 5, 161–215.
Wu, A. D., Li, Z., & Zumbo, B. D. (2007). Decoding the meaning of factorial invariance and updating
the practice of multi-group confirmatory factor analysis: A demonstration with TIMSS data. Prac-
tical Assessment Research and Evaluation, 12(3). Retrieved from http://pareonline.net/pdf/v12n3.pdf Wu, C. H. (2008). The role of perceived discrepancy in satisfaction evaluation. Social Indicators
Research, 88, 423–436.
Yang, C., Nay, S., & Hoyle, R. H. (2010). Three approaches to using lengthy ordinal scales in structural
equation models: Parceling, latent scoring, and shortening scales. Applied Psychological Measure-
ment, 34, 122–142.
Yang-Wallentin, F. (2001). Comparisons of the ML and TSLS estimators for the Kenny–Judd model.
In R. Cudeck, S. du Toit, & D. Sörbom (Eds.), Structural equation modeling: Present and future. A Festschrift in honor of Karl Jöreskog (pp. 425–442). Lincolnwood, IL: Scientific Software Interna- tional.
Yang-Wallentin, F., & Jöreskog, K. G. (2001). Robust standard errors and chi-squares for interaction models. In G. A. Marcoulides & R. Schumacker (Eds.), New developments and techniques in struc- tural equation modeling (pp. 159–171). Mahwah, NJ: Erlbaum.
Yuan, K.-H. (2005). Fit indices versus test statistics. Multivariate Behavioral Research, 40, 115–148. Yuan, K.-H., Hayashi, K., & Bentler, P. (2007). Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses. Journal of Multivariate Analysis, 9,
1262–1282.
Ziliak, S., & McCloskey, D. N. (2008). The cult of statistical significance: How the standard error costs us
jobs, justice, and lives. Ann Arbor: University of Michigan Press.
Zumbo, B. D. (2007). Three generations of DIF analyses: Considering where it has been, where it is
now, and where it is going. Language Assessment Quarterly, 4, 223–233.

##For more information on:

39.3

lavaan’s own tutorial http://lavaan.ugent.be/tutorial

39.4

extracting objects from lavaan Inspect or extract information from a fitted lavaan object
https://rdrr.io/cran/lavaan/man/lavInspect.html

##Saturated versus baseline models

39.5

What are the saturated and baseline models in sem? https://stats.idre.ucla.edu/stata/faq/what-are-the-saturated-and-baseline-models-in-sem/

39.6

Google Forums

39.7

Disentangling degrees of freedom

##Fit indexes

39.8

Research Gate Discussion about Chi-Square https://www.researchgate.net/post/Is_it_necessary_that_in_model_fit_my_Chi-square_valuep-Value_must_be_non-significant_in_structure_equation_modeling_AMOS

39.9

Assess whole SEM model–chi square and fit index

参考資料(References)

Data Scientist の基礎(2)
https://qiita.com/kaizen_nagoya/items/8b2f27353a9980bf445c

岩波数学辞典 二つの版がCDに入ってお得
https://qiita.com/kaizen_nagoya/items/1210940fe2121423d777

岩波数学辞典
https://qiita.com/kaizen_nagoya/items/b37bfd303658cb5ee11e

アンの部屋(人名から学ぶ数学:岩波数学辞典)英語(24)
https://qiita.com/kaizen_nagoya/items/e02cbe23b96d5fb96aa1

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