IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v37y2010i3p473-487.html
   My bibliography  Save this article

A skew-normal factor model for the analysis of student satisfaction towards university courses

Author

Listed:
  • Angela Montanari
  • Cinzia Viroli

Abstract

Classical factor analysis relies on the assumption of normally distributed factors that guarantees the model to be estimated via the maximum likelihood method. Even when the assumption of Gaussian factors is not explicitly formulated and estimation is performed via the iterated principal factors' method, the interest is actually mainly focussed on the linear structure of the data, since only moments up to the second ones are involved. In many real situations, the factors could not be adequately described by the first two moments only. For example, skewness characterizing most latent variables in social analysis can be properly measured by the third moment: the factors are not normally distributed and covariance is no longer a sufficient statistic. In this work we propose a factor model characterized by skew-normally distributed factors. Skew-normal refers to a parametric class of probability distributions, that extends the normal distribution by an additional shape parameter regulating the skewness. The model estimation can be solved by the generalized EM algorithm, in which the iterative Newthon-Raphson procedure is needed in the M-step to estimate the factor shape parameter. The proposed skew-normal factor analysis is applied to the study of student satisfaction towards university courses, in order to identify the factors representing different aspects of the latent overall satisfaction.

Suggested Citation

  • Angela Montanari & Cinzia Viroli, 2010. "A skew-normal factor model for the analysis of student satisfaction towards university courses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 473-487.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:3:p:473-487
    DOI: 10.1080/02664760902736737
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760902736737
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760902736737?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    2. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    3. McLachlan, G. J. & Peel, D. & Bean, R. W., 2003. "Modelling high-dimensional data by mixtures of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 379-388, January.
    4. Ab Mooijaart, 1985. "Factor analysis for non-normal variables," Psychometrika, Springer;The Psychometric Society, vol. 50(3), pages 323-342, September.
    5. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
    6. Yiu-Fai Yung, 1997. "Finite mixtures in confirmatory factor-analysis models," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 297-330, September.
    7. Reinaldo B. Arellano‐Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew‐normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574, September.
    8. Arthur Pewsey, 2000. "Problems of inference for Azzalini's skewnormal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(7), pages 859-870.
    9. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.
    10. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    11. Monica Chiogna, 2005. "A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 331-341, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sharon X. Lee & Tsung-I Lin & Geoffrey J. McLachlan, 2021. "Mixtures of factor analyzers with scale mixtures of fundamental skew normal distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(2), pages 481-512, June.
    2. Hashemi, Farzane & Naderi, Mehrdad & Jamalizadeh, Ahad & Bekker, Andriette, 2021. "A flexible factor analysis based on the class of mean-mixture of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    3. Tsung-I Lin & I-An Chen & Wan-Lun Wang, 2023. "A robust factor analysis model based on the canonical fundamental skew-t distribution," Statistical Papers, Springer, vol. 64(2), pages 367-393, April.
    4. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2014. "Mixtures of skew-t factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 326-335.
    5. Winfried Zinn & Sebastian Sauer & Richard Göllner, 2016. "The German Inpatient Satisfaction Scale," SAGE Open, , vol. 6(2), pages 21582440166, April.
    6. Kim, Hea-Jung, 2018. "Bayesian hierarchical robust factor analysis models for partially observed sample-selection data," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 65-82.
    7. Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.
    8. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 141-156.
    9. Mariano Ruiz Espejo & Miguel Delgado Pineda & Saralees Nadarajah, 2013. "Optimal unbiased estimation of some population central moments," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 39-62, June.
    10. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "A mixture of SDB skew-t factor analyzers," Econometrics and Statistics, Elsevier, vol. 3(C), pages 160-168.
    11. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    12. Kim, Hyoung-Moon & Maadooliat, Mehdi & Arellano-Valle, Reinaldo B. & Genton, Marc G., 2016. "Skewed factor models using selection mechanisms," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 162-177.
    13. Lin, Tsung-I & McLachlan, Geoffrey J. & Lee, Sharon X., 2016. "Extending mixtures of factor models using the restricted multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 398-413.
    14. Wan-Lun Wang & Min Liu & Tsung-I Lin, 2017. "Robust skew-t factor analysis models for handling missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 649-672, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kim, Hyoung-Moon & Maadooliat, Mehdi & Arellano-Valle, Reinaldo B. & Genton, Marc G., 2016. "Skewed factor models using selection mechanisms," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 162-177.
    2. Kahrari, F. & Rezaei, M. & Yousefzadeh, F. & Arellano-Valle, R.B., 2016. "On the multivariate skew-normal-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 80-88.
    3. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Zeller, Camila Borelli, 2014. "Multivariate measurement error models using finite mixtures of skew-Student t distributions," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 179-198.
    5. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2013. "The centred parameterization and related quantities of the skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 73-90.
    6. Ley, Christophe & Paindaveine, Davy, 2010. "On the singularity of multivariate skew-symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1434-1444, July.
    7. Lin, Tsung-I & McLachlan, Geoffrey J. & Lee, Sharon X., 2016. "Extending mixtures of factor models using the restricted multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 398-413.
    8. Thomas J. DiCiccio & Anna Clara Monti, 2018. "Testing for sub-models of the skew t-distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 25-44, March.
    9. Ahmed Hossain & Joseph Beyene, 2015. "Application of skew-normal distribution for detecting differential expression to microRNA data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 477-491, March.
    10. Kim, Hyoung-Moon & Ryu, Duchwan & Mallick, Bani K. & Genton, Marc G., 2014. "Mixtures of skewed Kalman filters," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 228-251.
    11. Jose, K.K. & Naik, Shanoja R., 2008. "A class of asymmetric pathway distributions and an entropy interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(28), pages 6943-6951.
    12. Yulia V. Marchenko & Marc G. Genton, 2012. "A Heckman Selection- t Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 304-317, March.
    13. Ley, Christophe, 2023. "When the score function is the identity function - A tale of characterizations of the normal distribution," Econometrics and Statistics, Elsevier, vol. 26(C), pages 153-160.
    14. Panagiotelis, Anastasios & Smith, Michael, 2010. "Bayesian skew selection for multivariate models," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1824-1839, July.
    15. Fang, B.Q., 2006. "Sample mean, covariance and T2 statistic of the skew elliptical model," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1675-1690, August.
    16. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    17. Phil D. Young & Joshua D. Patrick & John A. Ramey & Dean M. Young, 2020. "An Alternative Matrix Skew-Normal Random Matrix and Some Properties," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 28-49, February.
    18. Zinoviy Landsman & Udi Makov & Tomer Shushi, 2017. "Extended Generalized Skew-Elliptical Distributions and their Moments," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-100, February.
    19. Sharon Lee & Geoffrey McLachlan, 2013. "On mixtures of skew normal and skew $$t$$ -distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 241-266, September.
    20. Young, Phil D. & Harvill, Jane L. & Young, Dean M., 2016. "A derivation of the multivariate singular skew-normal density function," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 40-45.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:37:y:2010:i:3:p:473-487. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.