361
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Constructing Common Factors from Continuous and Categorical Data

REFERENCES

  • Almund , M. , Duckworth , A. , Heckman , J. , Kautz , T. ( 2011 ). Personality psychology and economics, NBER working paper 16822 .
  • Anderson , T. W. , Rubin , H. ( 1956 ). Statistical inference in factor analysis . In: Neyman , J. , ed. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability . Vol. V . Berkeley : University of California Press , pp. 114 – 150 .
  • Babakus , E. , Ferguson , C. , Joreskog , K. ( 1987 ). The sensitivity of confirmatory maximum likelihood factor analysis to violations of measurement scale and distributonal assumptions . Journal of Marketing Research 24 ( 2 ): 222 – 228 .
  • Bai , J. ( 2003 ). Inferential theory for factor models of large dimensions . Econometrica 71 ( 1 ): 135 – 172 .
  • Bai , J. , Ng , S. ( 2002 ). Determining the number of factors in approximate factor models . Econometrica 70 ( 1 ): 191 – 221 .
  • Bai , J. , Ng , S. ( 2008 ). Large dimensional factor analysis . Foundations and Trends in Econometrics 3 ( 2 ): 89 – 163 .
  • Boivin , J. , Ng , S. ( 2006 ). Are more data always better for factor analysis . Journal of Econometrics 132 : 169 – 194 .
  • Bollen , K. ( 1989 ). Structural Equations with Latent Variables . New York : Wiley .
  • Browne , M. W. ( 1984 ). Asymptotically distribution free methods in the analysis of covariance structures . British Journal of Mathematical and Statistical Psychology 37 : 62 – 83 .
  • Buja , A. ( 1990 ). Remarks on functional canonical variates: Alternating least squares methods and ACE . Annals of Statistics 18 ( 3 ): 1032 – 1069 .
  • Chamberlain , G. , Rothschild , M. ( 1983 ). Arbitrage, factor structure and mean-variance analysis in large asset markets . Econometrica 51 : 1281 – 2304 .
  • Cliff , N. ( 1966 ). Orthogonal rotation to congruence . Psychometrika 31 : 33 – 42 .
  • Connor , G. , Korajzcyk , R. ( 1986 ). Performance measurement with the arbitrage pricing theory: A new framework for analysis . Journal of Financial Economics 15 : 373 – 394 .
  • Conti , G. , Heckman , J. , Lopes , H. , Piatek , R. ( 2012 ). Constructing economically justified aggregates: An application to early orgins of health . Journal of Econometrics .
  • Cunha , F. , Heckman , J. ( 2008 ). Formulating, identifying and estimating the techology of cognitive and noncognitive skill formuation . Journal of Human Resources 43 ( 4 ): 738 – 782 .
  • de Leeuw , J. ( 2004 ). Least squares optimal scaling of partially observed linear systems . In: Recent Developments on Structural Equation Models . Kluwer Academic Publishers , pp. 121 – 134 .
  • de Leeuw , J. ( 2005 ). Monotonic regression . In: Everitt , B. , Howell , D. , ed. Encyclopedia of Statistics in Behavioral Science . Vol. 3 . New York : John Wiley and Sons , pp. 1260 – 1261 .
  • Dolan , C. ( 1994 ). Factor analysis of variables with 2,3,5, and 7 response categories: A comparison of categorical variable estimators using simulated data . British Journal of Mathematical and Statistical Psychology 46 : 309 – 326 .
  • Doz , C. , Giannone , D. , Reichlin , L. (2007). A Quasi-Maximum Likelihood Approach for Large Approximate Dynamic Factor Models, ECARES working paper.
  • Filmer , D. , Pritchett , L. ( 1998 ). Estimating Wealth Effect Without Expenditure Data – Or Tears: An Application to Educational Enrollments in States of India, Discussion Paper 1994, World Bank .
  • Gower , J. , Dijksterhuis , G. ( 2004 ). Procrustes Problems . Oxford : Oxford University Press .
  • Harman , H. , Jones , W. ( 1966 ). Factor analysis by minimizing residuals (Minres) . Psychometrika 31 ( 3 ): 315 – 368 .
  • Israels , A. ( 1984 ). Redundancy analysis for qualitative variables . Psychometrika 49 ( 3 ): 331 – 346 .
  • Joreskog , K. ( 1994 ). On the esetimation of polychoric correlations and their asymptotic covariance matrix . Psychometrika 59 : 381 – 389 .
  • Joreskog , K. , Moustki , I. ( 2001 ). Factor analysis of ordinal variables: A comparison of three approaches . Multivariate Behavioral Research 36 : 347 – 387 .
  • Joreskog , K. , Sorbom , S. D. ( 2006 ). LISREL User's Reference Guide , Chicago .
  • Joreskog , K. G. ( 1970 ). A genearl method for analysis of covariance structurs . Biometrika 57 : 239 – 51 .
  • Joreskog , K. G. ( 2003 ). Factor Analysis by MINRES, www.ssicentral.com/lisrel/techdocs/minres.pdf. Last accessed 31 October 2014 .
  • Keller , W. , Wansbeek , T. ( 1983 ). Multivariate methods for quantitative and qualitative data . Journal of Econometrics 22 : 91 – 111 .
  • Kiers , H. ( 1990 ). Majorization as a tool for optimizing a class of matrix functions . Psyhometrika 55 ( 3 ): 417 – 428 .
  • Kiers , H. ( 2002 ). Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems . Computational Statistics and Data Analysis 41 : 157 – 170 .
  • Kiers , H. , Takane , Y. , Mooijaart , A. ( 1993 ). A mononotically convergent algorithm for FACTALS . Psychometrika 58 ( 4 ): 567 – 574 .
  • Kolenikov , S. , Angeles , G. ( 2009 ). Socioeconomic status measurement with discrete proxy variables: Is principal component analysis a reliable answer . Review of Income and Wealth 55 : 128 – 165 .
  • Kruskal , J. ( 1964 ). Nonmetric multidimensional scaling: A numerical method . Psychometrika 29 : 115 – 129 .
  • Kruskal , J. , Shepard , R. ( 1974 ). A nonmetric variety of linear factor analysis . Psychometrika 39 : 123 – 157 .
  • Lancaster , H. ( 1957 ). Some properties of the bivariate normal distribution considered in the form of a contingency table . Biometrika 44 ( 1/2 ): 289 – 292 .
  • Lawley , D. N. , Maxwell , A. E. ( 1971 ). Factor Analysis in a Statistical Method . London : Butterworth .
  • McDonald , R. P. ( 1985 ). Factor Analysis and Related Methods . Hilsdale , NJ : Erlbaum .
  • Meulman , J. , Heiser , W. ( 2001 ). SPSS Categories. 11.0 edn. SPSS Inc .
  • Michailidis , G. , de Leeuw , J. ( 1998 ). The gifi system of descriptive multivariate analysis . Statistical Science 13 ( 4 ): 307 – 336 .
  • Muthén , B. ( 1984 ). A general structural equation model with dichotomous, ordered, categorical, and continuous latent variable indicators . Psychometrika 49 : 115 – 132 .
  • Muthen , B. , Kaplan , D. ( 1985 ). A comparison of some methodologies for the factor analysis of non-normal Likert variables . British Journal of Mathematical and Psychology 38 : 71 – 189 .
  • Nevels , K. ( 1989 ). An improved solution for factals: A nonmetric common factor analysis . Psychometrika 54 ( 3390343 ).
  • Olsson , U. , Drasgow , F. , Dorans , N. ( 1982 ). The polyserial correlation coefficient . Psychometrika 47 ( 3 ): 337 – 347 .
  • Onatski , A. ( 2010 ). Determining the number of factors from empirical distribution of eigenvalues . Review of Economics and Statistics 92 ( 4 ): 1004 – 1016 .
  • Pearson , K. ( 1900 ). On the correlation of charcters not quantitatively measurable . In: Mathematical Contributions to the Theory of Evolution: Philosophical Transactions of the Royal Society of London, Series A. Vol. 195 , pp. 1 – 46 .
  • Racine , J. , Li , Q. ( 2004 ). Nonparametric estimation of regression functions with both discrete and continuous data . Journal of Econometrics 119 : 99 – 130 .
  • Schonmenn , P. ( 1966 ). A generalized solution of the orthogonal procustes problem . Psychometrika 31 ( 1 ): 1 – 10 .
  • Socan , G. ( 2003 ). The Incremental Value of Minimum Rank Factor Analysis. Ph.D. dissertation, University of Groningen .
  • Spearman , C. (1904). General intelligence, objectively determined and measured. American Journal of Psychology 15:201–293.
  • Su , L. , Ullah , A. ( 2009 ). Functional coefficient estimation with both categorical and continuous data . In: Li , Q. , Racine , J. , ed. Advances in Econometrics . Vol. 25 . Emerald Group Publishing Limited , pp. 131 – 167 .
  • Takane , Y. , Young , F. , de Leeuw , J. ( 1979 ). Nonmetric common factor analysis an alternating least squares method with optimal scaling features . Behaviormetrika 6 : 45 – 56 .
  • ten Berge , J. ( 1993 ). Least Squares Optimization in Multivariate Analysis . Leiden : DSWO Press .
  • ten Berge , J. , Nevels , K. ( 1997 ). A general solution to mosier's oblque procrustes problem . Psychometrika 42 : 593 – 600 .
  • Tenenhaus , M. , Young , F. ( 1985 ). An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data . Psychometrika 50 ( 1 ): 91 – 119 .
  • Trendafilov , N. , Unkel , S. ( 2011 ). Exploratory factor analysis of data matrices with more variables than observations . Journal of Computational Graphical Statistics 20 . Forthcoming .
  • Unkel , S. , Trendafilov , N. ( 2010 ). Simultaneous parameter estimation in exploratory factor analysis: An expository review . International Statistical Review 78 ( 3 ): 363 – 382 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.