1 / 19

GRA 6020 Multivariate Statistics Factor Analysis

GRA 6020 Multivariate Statistics Factor Analysis. Ulf H. Olsson Professor of Statistics. EFA. Eigenvalue of factor j The total contribution of factor j to the total variance of the entire set of variables Comunality of variable i

dyani
Download Presentation

GRA 6020 Multivariate Statistics Factor Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. GRA 6020Multivariate StatisticsFactor Analysis Ulf H. Olsson Professor of Statistics

  2. EFA • Eigenvalue of factor j • The total contribution of factor j to the total variance of the entire set of variables • Comunality of variable i • The common variance of a variable. The portion of a variable’s total variance that is accounted for by the common factors Ulf H. Olsson

  3. EFA-How many factors to retain • Based on theory • Eigenvalues 1 • Checking the rows in the pattern matrix Ulf H. Olsson

  4. Factor Solutions • Principal Factor Method • Extracts factors such that each factor accounts for the maximum possible amount of the variance contained in the set of variables being factored • No distributional assumptions • Maximum Likelihood • Will be treated in detail later • Multivariate normality Ulf H. Olsson

  5. Rotation of Factors • The objective is • To achieve a simpler factor structure • To achieve a meaningful structure • Orthogonal rotation • Oblique Rotation Ulf H. Olsson

  6. Rotation • Varimax • Major objective is to have a factor structure in which each variable loads highly on one and only one factor. • Quartimax • All the variables have a fairly high loading on one factor • Each variable should have a high loading on one other factor and near zero loadings on the remaining factors Ulf H. Olsson

  7. Rotation The rationale for rotation is very much akin to sharpening the focus of a microscope in order to see the details more clearly Ulf H. Olsson

  8. The CFA model • In a confirmatory factor analysis, the investigator has such a knowledge about the factorial nature of the variables that he/she is able to specify that each xi depends only on a few of the factors. If xi does not depend on faktor j, the factor loading lambdaij is zero Ulf H. Olsson

  9. CFA • If does not depend on then • In many applications, the latent factor represents a theoretical construct and the observed measures are designed to be indicators of this construct. In this case there is only (?) one non-zero loading in each equation Ulf H. Olsson

  10. CFA Ulf H. Olsson

  11. CFA Ulf H. Olsson

  12. CFA • The covariance matrices: Ulf H. Olsson

  13. CFA and ML k is the number of manifest variables. If the observed variables comes from a multivariate normal distribution, then Ulf H. Olsson

  14. Testing Fit Ulf H. Olsson

  15. Problems with the chi-square test • The chi-square tends to be large in large samples if the model does not hold • It is based on the assumption that the model holds in the population • It is assumed that the observed variables comes from a multivariate normal distribution • => The chi-square test might be to strict, since it is based on unreasonable assumptions?! Ulf H. Olsson

  16. Alternative test- Testing Close fit Ulf H. Olsson

  17. How to Use RMSEA • Use the 90% Confidence interval for EA • Use The P-value for EA • RMSEA as a descriptive Measure • RMSEA< 0.05 Good Fit • 0.05 < RMSEA < 0.08 Acceptable Fit • RMSEA > 0.10 Not Acceptable Fit Ulf H. Olsson

  18. Other Fit Indices • CN • RMR • GFI • AGFI • Evaluation of Reliability • MI: Modification Indices Ulf H. Olsson

  19. Nine Psychological Tests Ulf H. Olsson

More Related