Factor Analysis FOR PHD EXAMS RM2.ppt.pptx

RESEARCH METHODOLGY CONCEPTS

1. Factor Analysis Dr Mohsin Khan Institute of Public Enterprise

2. Selecting a Technique 1 Dependent Variable >1 Dependent Variable Interdependent Variable

3. Types of Factor Analysis

4. Types of Factor Analysis Exploratory Factor Analysis: Exploratory factor analysis (EFA) attempts to discover the nature of the constructs influencing a set of responses. Confirmatory Factor Analysis: Confirmatory factor analysis (CFA) tests whether a specified set of constructs is influencing responses in a predicted way.

5. Exploratory Factor Analysis Assumptions: Metric data (Interval) Multicollinearity must be present i.e. Correlation among variables Adequate Sample size Purpose: Obtaining Independent factors Data Reduction

6. Factor Analysis Factor Analysis transforms a set of variables into a new set of composite variables that are not correlated with each other The predictor-criterion relationship that was found in the dependence situation is replaced by a matrix of inter-correlations among several variables , none of which is dependent on another

7. Factor Analysis Factor Analysis begins with the construction of a new set of variables based on the relationships in the correlation matrix These linear combinations (lc’s) of variables, called factors , account for the variance in the data as a whole The best “lc” makes the first pc and the first factor. The second “pc” is defined as the best “lc” of variables for explaining the variance not accounted by the first factor

8. Factor Analysis

9. Factor Analysis

10. Terms used in Factor Analysis Communalities : The estimate of variance in each variable that is explained by the factors e.g. For variable A, communality of 0.65 indicates that 65% of the variance in variable A is explained in the terms of factors Eigen Values : Sum of variances of the factor values If a factor has a low eigenvalue, then it adds little to the explanation of variances in the variables and may be disregarded

11. Factor-1 Factor-2 Communality Var1 .65 .12 0.43 Var2 .54 .26 0.35 Var3 .29 .48 0.31 Var4 .09 .65 0.43 Eigen Value 0.80 0.73 Variance Explained 20.15% 18.37% 38.52% Terms used in Factor Analysis

12. Terms used in Factor Analysis Total Variance Explained: Eigen-value divided by the number of variables Factor Loading: Coefficient of Correlation between a variable & the factor Factor Score: Regression method is used to compute score of every method.

13. Steps in Factor Analysis Check for Conditions KMO Value Method of Extraction PCA Method Maximum Likelihood Generalised Least Square Alpha Factoring No. of factors to be extracted Eigen Value Method Scree Plot

14. Steps in Factor Analysis Factor Rotation Varimax Oblimin Quartimax Equamax Name of Factor Saving Factor Score Validity & Reliability Analysis Factor Analysis: Dr Neeraj Kaushik, NIT Kurukshetra

15. Validity in Factor Analysis Content Validity Construct Validity Convergence Factor Loading > 0.45 Var extracted > 0.45 Cronbach Alpha > 0.6 Discriminant Nomological Criterion Related Validity

16. Working further on Factor Analysis After saving Factor score they can be further used as Independent variable Dependent variable Used in ANOVA / MANOVA Used in Cluster Analysis

17. Limitations of Factor Analysis Highly Subjective technique Names of the factors not provided Too many extracting method / rotation method

18. Factor Analysis in SPSS Go to Analyse Menu Choose Dimension Reduction or Data Reduction (Depending on the version of SPSS) It has 5 sub-menu: Descriptive Extraction Rotation Score Option

19. Factor Analysis in SPSS Descriptive Tick on KMO Value Extraction By Default it uses Principal Component Method & extracts Factor with Eigen Value more than one However if we want to extract any particular no. of variables then we can specify the no. of factors to be extracted

20. Factor Analysis in SPSS Rotation Rotation is not compulsory but it improves the quality of results Check on Varimax Rotation Score Use it for saving the Factor score Default method for saving factor is Regression Option Use it for sorting various statements/variables in factor in ascending order

21. Factor Analysis: A Snapshot Interdependent variables KMO Value > 0.8 Total Variation explained > 60% Communality > 0.4 Rotated Factor Loading > 0.45 Cronbach Alpha > 0.6

22. Presentation by: Dr. Mohsin Khan Ass istant Professor ( Business Administration ) Institute of Public Enterprise Hyderabad Telangana (India) [email protected]