Because of its many advantages, structural equation modeling (SEM) has been used with increasing frequency in behavioral science, and it is a set of techniques that can be useful in analyzing forensic research data. Issues in SEM, including theory, estimation method, sample size and data requirements, identification, and fit indices are discussed. Using a sample of data from men arrested for domestic violence perpetration and court referred to treatment, examples of path analysis, confirmatory factor analysis, and full structural models with latent variables are presented.
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csaki (Eds.), Proceedings of the 2nd International Symposium on Information Theory (pp. 267-281). Budapest, Hungary: Akademiai Kiado.
2.
Akaike, H. (1987). Factor analysis and AIC. Psychometrika , 52, 317-332.
3.
Allison, P.D. (2003). Missing data techniques for structural equation models. Journal of Abnormal Psychology, 112, 545-557.
Bentler, P.M. (1990). Comparative fit indexes in structural models. Psychological Bulletin,107, 238-246.
7.
Bentler, P.M. (2003). EQS 6.1 for Windows [Computer software]. Encino, CA: Multivariate Software.
8.
Bentler, P.M., & Bonett, D.G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin,88, 588-606.
9.
Bentler, P.M., & Chou, C. (1987). Practical issues in structural modeling. Sociological Methods and Research, 16, 78-117.
10.
Berry, W.D. (1984). Nonrecursive causal models. Beverly Hills, CA: Sage.
11.
Bollen, K.A. (1989). Structural equations with latent variables. New York: John Wiley.
12.
Boomsma, A. (1982). The robustness of LISREL against small sample size in factor analysis models. In K. G. Jöreskog & H. Wold (Eds.), Systems under indirect observation, Part 1 (pp. 149-173). Amsterdam, the Netherlands: North Holland.
13.
Boomsma, A., & Hoogland, J.J. (2001). The robustness of LISREL modeling revisited. In R. Cudeck, S. du Toit, & D. Sörbom (Eds.), Structural equation models: Present and future. A Festschrift in honor of Karl Jöreskog (pp. 139-168). Chicago: Scientific Software International.
14.
Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52, 345-370.
15.
Browne, M.W. (1982). Covariance structures. In D. M. Hawkins (Ed.), Topics in
16.
applied multivariate analysis (pp. 72-141). Cambridge, UK: Cambridge University Press.
17.
Browne, M.W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.
18.
Browne, M.W., & Cudeck, R. (1989). Single sample cross-validation indices for covariance structures. Multivariate Behavioral Research, 24, 445-455.
19.
Browne, M.W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 136-162). Newbury Park, CA: Sage.
20.
Byrne, B.M. (1998). Structural equation modeling with LISREL, Prelis, and Simplis. New York: Lawrence Erlbaum.
21.
Byrne, B.M. (2001). Structural equation modeling in Amos: Basic concepts, applications, and programming. Mahwah, NJ: Lawrence Erlbaum.
22.
Byrne, B.M. (2006). Structural equation modeling with EQS: Basic concepts, application, and programming (2nd ed.). Mahwah, NJ: Lawrence Erlbaum.
23.
Cohen, J. (1994). The earth is round (p < .05). American Psychologist, 49, 997-1003.
24.
Comrey, A.L., & Lee, H.B. (1992). A first course in factor analysis (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.
25.
Cudeck, R., & Browne, M.W. (1983). Cross-validation of covariance structures. Multivariate Behavioral Research, 18, 147-167.
26.
Curran, P.J., Bollen, K.A., Paxton, P., Kirby, J., & Chen, F. (2002). The noncentral chi-square distribution in misspecified structural equation models: Finite sample results from a Monte Carlo simulation . Multivariate Behavioral Research, 37, 1-36.
27.
Curran, P.J., West, S.G., & Finch, J.F. (1997). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1, 16-29.
28.
DiStefano, C. (2002). The impact of categorization with confirmatory factor analysis. Structural Equation Modeling, 9, 327-346.
29.
First, M.B., Spitzer, R.L., Gibbon, M., & Williams, J.B.W. (2002). Structured Clinical Interview for DSM-IV-TR Axis I Disorders, Research Version, Nonpatient Edition (SCID-I/NP) . New York: Biometrics Research, New York State Psychiatric Institute.
30.
Gerbing, D.W., & Anderson, J.C. (1984). On the meaning of within-factor correlated measurement errors. Journal of Consumer Research , 11, 572-580.
31.
Hoogland, J.J., & Boomsma, A. (1998). Robustness studies in covariance structure modeling: An overview and a meta-analysis. Sociological Methods and Research, 26, 329-367.
32.
Hoyle, R. H. (Ed.). (1995). Structural equation modeling: Concepts, issues, and applications. Thousand Oaks, CA: Sage.
33.
Holtzworth-Munroe, A., Meehan, J.C., Herron, K., Rehman, U., & Stuart, G.L. (2000). Testing the Holtzworth-Munroe and Stuart batterer typology. Journal of Consulting and Clinical Psychology, 68, 1000-1019.
34.
Holtzworth-Munroe, A., & Stuart, G.L. (1994). Typologies of male batterers: Three subtypes and the differences among them. Psychological Bulletin,116, 476-497.
35.
Hu, L.-T., & Bentler, P.M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424-453.
36.
Hu, L.-T., & Bentler, P.M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.
37.
Hyler, S.E., Rieder, R.O., Willaims, J.B.W., Spitzer, R.L., Hendler, J., & Lyons, M. (1988). The Personality Diagnostic Questionnaire: Development and preliminary results. Journal of Personality Disorders , 2, 229-237.
38.
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.
39.
Jöreskog, K.G. (1973). A general method for estimating a linear structural equation system. In A. S. Goldberger & O. D. Duncan (Eds.), Structural equation models in the social sciences (pp. 85-112). New York: Academic Press.
40.
Jöreskog, K.G., & Sörbom, D. (1981). LISREL V: Analysis of linear structural relationships by the method of maximum likelihood. Chicago: National Education Resources.
41.
Jöreskog, K.G., & Sörbom, D. (2005). LISREL 8.7 for Windows [Computer software]. Lincolnwood, IL: Scientific Software International .
42.
Kaplan, D. (2000). Structural equation modeling: Foundations and extensions. Newbury Park, CA: Sage .
43.
Kenny, D.A., & Judd, C.M. (1986). Consequences of violating the independence assumption in analysis of variance. Psychological Bulletin,99, 422-431.
44.
Kline, R.B. (2005). Principles and practice of structural equation modeling (2nd ed.). New York : Guilford.
45.
Lee, S., & Hershberger, S. (1990). A simple rule for generating equivalent models in structural equation modeling. Multivariate Behavioral Research, 25, 313-334.
46.
Leonard, K.E. (1993). Drinking patterns and intoxication in marital violence: Review, critique, and future directions for research. In S. E. Martin (Ed.), Alcohol and interpersonal violence: Fostering multidisciplinary perspectives (NIAAA Research Monograph No. 24, NIH Publication No. 93-3496, pp. 253-280). Rockville, MD: Department of Health and Human Services.
47.
Leonard, K.E., & Senchak, M. (1996). Prospective prediction of husband marital aggression within newlywed couples. Journal of Abnormal Psychology, 105, 369-380.
48.
Little, R.J.A., & Rubin, D.B. (1987). Statistical analysis with missing data. New York: John Wiley.
49.
Locke, H.J., & Wallace, K.M. (1959). Short marital adjustment and prediction tests: Their reliability and validity. Marriage and Family Living , 21, 251-255.
50.
Loehlin, J.C. (1998). Latent variable models: An introduction to factor, path, and structural analysis (3rd ed.). Mahwah, NJ: Lawrence Erlbaum.
51.
Loftus, G.R. (1996). Psychology will be a much better science when we change the way we analyze data. Current Directions in Psychological Science, 5, 161-171.
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.
54.
MacCallum, R.C., Roznowski, M., & Necowitz, L.B. (1992). Model modifications in covariance structure analysis: The problem of capitalization on chance. Psychological Bulletin,111, 490-504.
55.
MacCallum, R.C., Wegener, D., Uchino, B., & Fabrigar, L. (1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin,114, 185-199.
56.
Malhotra, N.K. (1987). Analyzing market research data with incomplete information on the dependent variable. Journal of Marketing Research, 24, 74-84.
57.
Marsh, H.W., Balla, J.R., & McDonald, R.P. (1988). Goodness of fit indexes in confirmatory factor analysis: The effect of sample size. Psychological Bulletin,103, 391-410.
58.
Maruyama, G.M. (1998). Basics of structural equation modeling. London: Sage.
59.
McArdle, J.J. (1996). Current directions in structural factor analysis . Current Directions in Psychological Science, 5, 11-17.
60.
McDonald, R.P., & Marsh, H.W. (1990). Choosing a multivariate model: Noncentrality and the goodness of fit. Psychological Bulletin,107, 247-255.
61.
Mulaik, S.A., James, L.R., Van Alstine, J., Bennett, N., Lind, S., & Stilwell, C.D. (1989). Evaluation of goodness-of-fit indices for structural equation models. Psychological Bulletin,105, 430-445.
62.
Murphy, C.M., & O'Farrell, T.J. (1996). Marital violence among alcoholics. Current Directions in Psychological Science, 5, 183-186.
63.
Muthén, B. (1983). Latent variable structural equation modeling with categorical data. Journal ofEconometrics, 22, 48-65.
64.
Muthén, L., & Muthén, B. (1998-2006). Version 4.1 MPlus [Computer software]. Los Angeles: Author.
65.
Muthén, L.K., & Muthén, B.O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620.
66.
Neale, M.C., Boker, S.M., Xie, G., & Maes, H.H. (2004). MxGui (Version 1.5.01) [Computer software]. Richmond: Virginia Commonwealth University , Department of Psychiatry.
67.
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.
68.
O'Leary, K.D., Malone, J., & Tyree, A. (1989). Physical aggression in early marriage: Prerelationship and relationship effects. Journal of Consulting and Clinical Psychology, 62, 594-602.
69.
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 nonnormality . Structural Equation Modeling, 7, 557-595.
70.
Olsson, U.H., Troye, S.V., & Howell, R.D. (1999). Theoretical fit and empirical fit: The performance of maximum likelihood versus generalized least squares estimation in structural equation models. Multivariate Behavioral Research, 34(1), 31-58.
71.
Pedhazur, E., & Schmelkin, L.P. (1991). Measurement design and analysis: An integrated approach. Hillsdale, NJ: Lawrence Erlbaum.
72.
Radloff, L.S. (1977). The CES-D scale: A self-report depression scale for research in the general population. Applied Psychological Measurement, 1, 385-401.
73.
Raferty, A.E. (1993). Bayesian model selection in structural equation models. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 163-180). Newbury Park, CA: Sage.
74.
Raymond, M.R., & Roberts, D.M. (1987). A comparison of methods for treating incomplete data in selection research. Education and Psychological Measurement , 47, 13-26.
75.
Roth, P.L. (1994). Missing data: A conceptual view for applied psychologists . Personnel Psychology, 47, 537-560.
76.
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.
77.
SAS Institute Inc. (2006). SAS/STAT (Version 9.1) [Computer software]. Cary, NC: Author.
78.
Satorra, A., & Bentler, P.M. (1988). Scaling corrections for chi-square statistics in covariance structure analysis. ASA 1988 Proceedings of the Business and Economic Statistics Section of the American Statistical Association (Sections 308-313). Alexandria, VA: ASA.
79.
Satorra, A., & Bentler, P.M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 339-419). Thousand Oaks, CA: Sage.
80.
Satorra, A., & Saris, W.E. (1985). The power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50, 83-90.
81.
Saunders, J.B., Aasland, O.G., Babor, T.F., de la Fuente, J.R., & Grant, M. (1993). Development of the Alcohol Use Disorders Identification Test (AUDIT): WHO collaborative project on early detection of persons with harmful alcohol consumption-II. Addiction, 88, 791-804.
Steiger, J.H. (1990). Structural model evaluation and modification: An interval estimation approach. Multivariate Behavioral Research , 25, 173-180.
89.
Steiger, J.H., & Lind, J.C. (1980, May). Statistically based tests or the number of common factors. Paper presented at the annual meeting of the Psychometric Society, Iowa City, IA.
90.
Stevens, J. (1996). Applied multivariate statistics for the social sciences. Mahwah, NJ: Lawrence Erlbaum .
91.
Straus, M.A. (1979). Measuring intrafamily conflict and violence: The Conflict Tactics (CT) Scales. Journal of Marriage and the Family, 41, 75-88.
92.
Straus, M.A., Hamby, S.L., Boney-McCoy, S., & Sugarman, D.B. (1996). The revised Conflict Tactics Scales (CTS2): Development and preliminary psychometric data. Journal of Family Issues, 17, 283-316.
93.
Stuart, G.L., Meehan, J.C., Temple, J.R., Follansbee, K.W., Bucossi, M.M., Hellmuth, J.C., et al. (2006). Examining a conceptual framework of intimate partner violence in men and women arrested for domestic violence. Journal of Studies on Alcohol, 67, 102-112.
94.
Stuart, G.L., Moore, T.M., Kahler, C.W., & Ramsey, S.E. (2003). Substance abuse and relationship violence among men court referred to batterers intervention programs. Addictive Behaviors, 24, 107-122.
