This article describes the confa command, which fits confirmatory factor analysis models by maximum likelihood and provides diagnostics for the fitted models. Descriptions of the command and its options are given, and some illustrative examples are provided.
AndersonT. W., and AmemiyaY.1988. The asymptotic normal distribution of estimators in factor analysis under general conditions. Annals of Statistics16: 759–771.
2.
BartholomewD. J., and KnottM.1999. Kendall's Library of Statistics 7: Latent Variable Models and Factor Analysis. 2nd ed. London: Arnold.
3.
BentlerP. M.1990a. Comparative fit indexes in structural models. Psychological Bulletin107: 238–246.
4.
BentlerP. M.1990b. Fit indexes, Lagrange multipliers, constraint changes and incomplete data in structural models. Multivariate Behavioral Research25: 163–172.
5.
BeranR., and SrivastavaM. S.1985. Bootstrap tests and confidence regions for functions of a covariance matrix. Annals of Statistics13: 95–115.
6.
BollenK.1993. Liberal democracy: Validity and method factors in cross-national measures. American Journal of Political Science37: 1207–1230.
7.
BollenK., and StineR.1992. Bootstrapping goodness-of-fit measures in structural equation models. Sociological Methods and Research21: 205–229.
8.
BollenK. A.1989. Structural Equations with Latent Variables.New York: Wiley.
9.
BollenK. A.1996. An alternative two stage least squares (2SLS) estimator for latent variable equations. Psychometrika61: 109–121.
BrowneM. W.1984. Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology37: 62–83.
12.
BrowneM. W.1987. Robustness of statistical inference in factor analysis and related models. Biometrika74: 375–384.
13.
BrowneM. W., and CudeckR.1993. Alternative ways of assessing model fit. In Testing Structural Equation Models, ed. BollenK. A., and LongJ. S., 136–162. Newbury Park, CA: Sage.
14.
ByrneB. M., and GoffinR. D.1993. Modeling MTMM data from additive and multiplicative covariance structures: An audit of construct validity concordance. Multivariate Behavioral Research28: 67–96.
15.
CoxN. J.2008. Speaking Stata: Correlation with confidence, or Fisher's z revisited. Stata Journal8: 413–439.
16.
GouldW.2001. Statistical software certification. Stata Journal1: 29–50.
17.
GouldW., PitbladoJ., and SribneyW.2006. Maximum Likelihood Estimation with Stata. 3rd ed. College Station, TX: Stata Press.
18.
GraysonD., and MarshH.1994. Identification with deficient rank loading matrices in confirmatory factor analysis: Multitrait–multimethod models. Psychometrika59: 121–134.
19.
HolzingerK. J., and SwinefordF.1939. A study in factor analysis: The stability of a bifactor solution. Technical Report 48, Supplementary Educational Monographs, University of Chicago.
20.
HuberP. J.1967. The behavior of maximum likelihood estimates under nonstandard conditions. In Vol. 1 of Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, 221–233. Berkeley: University of California Press.
21.
JöreskogK. G.1969. A general approach to confirmatory maximum likelihood factor analysis. Psychometrika34: 183–202.
22.
JöreskogK. G., and GoldbergerA. S.1972. Factor analysis by generalized least squares. Psychometrika37: 243–260.
23.
JöreskogK. G., and SörbomD.1986. Lisrel VI: Analysis of linear structural relationships by the method of maximum likelihood.Mooresville, IN: Scientific Software.
24.
LawleyD. N., and MaxwellA. E.1971. Factor Analysis as a Statistical Method. 2nd ed. London: Butterworths.
25.
LittleR. J. A., and RubinD. B.2002. Statistical Analysis with Missing Data. 2nd ed. Hoboken, NJ: Wiley.
26.
MagnusJ. R., and NeudeckerH.1999. Matrix Differential Calculus with Applications in Statistics and Econometrics.Rev. ed. New York: Wiley.
27.
MarshH. W., BallaJ. R., and HauK.-T.1996. An evaluation of incremental fit indices: A clarification of mathematical and empirical properties. In Advanced Structural Equation Modeling: Issues and Techniques, ed. MarcoulidesG. A., and SchumackerR. E., 315–353. Mahwah, NJ: Erlbaum.
28.
MarshH. W., ByrneB. M., and CravenR.1992. Overcoming problems in confirmatory factor analyses of MTMM data: The correlated uniqueness model and factorial invariance. Multivariate Behavioral Research27: 489–507.
29.
MuthénL. K., and MuthénB. O.2004. Mplus: Statistical Analysis with Latent Variables. User's Guide. Los Angeles, CA, 3rd ed.
30.
Rabe-HeskethS., SkrondalA., and PicklesA.2002. Reliable estimation of generalized linear mixed models using adaptive quadrature. Stata Journal2: 1–21.
SatorraA.1990. Robustness issues in structural equation modeling: A review of recent developments. Quality and Quantity24: 367–386.
33.
SatorraA., and BentlerP. M.1994. Corrections to test statistics and standard errors in covariance structure analysis. In Latent Variables Analysis, ed. von EyeA., and CloggC. C., 399–419. Thousand Oaks, CA: Sage.
34.
SatorraA., and BentlerP. M.2001. A scaled difference chi-square test statistic for moment structure analysis. Psychometrika66: 507–514.
35.
SteigerJ. H.1990. Structural model evaluation and modification: An interval estimation approach. Multivariate Behavioral Research25: 173–180.
36.
TuckerL. R., and LewisC.1973. A reliability coefficient for maximum likelihood factor analysis. Psychometrika38: 1–10.
37.
YuanK.-H., and BentlerP. M.1997. Mean and covariance structure analysis: Theoretical and practical improvements. Journal of the American Statistical Association92: 767–774.
38.
YuanK.-H., and BentlerP. M.2007. Structural equation modeling. In Handbook of Statistics 26: Psychometrics, ed. RaoC. R., and SinharayS., 297–358. Oxford: Elsevier.