1 / 61

Exploratory Factor Analysis Overview in SPSS

Learn to conduct Factor Analysis in SPSS, extract factors, interpret results, and overcome limitations. Understand EFA versus CFA, variable selection, sample size considerations, and interpretation caution.

jackj
Download Presentation

Exploratory Factor Analysis Overview in SPSS

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. An introduction to exploratory factor analysis in IBM SPSS Statistics Dr Anne Laure Humbert York University, 10 November 2017

  2. In this session: • Distinguishing between exploratory and confirmatory uses of Factor Analysis (FA) • Illustrate how to carry out a FA in SPSS using real data • Determining the number of factors to extract • Explaining the concept of rotation of factors • Describing how to name a factor • State the major limitations of factor analytic techniques

  3. Definition and purpose Factor Analysis (FA) is a statistical technique which analyses the underlying covariance structure between variables in order to identify its underlying structure Using FA allows us to: • Examine the interrelationships among a large number of variables • Attempt to explain these variables in terms of their common underlying dimensions (factors) • Summarize and reduce data without independent and dependent variables

  4. Example: Team climate We have data about a number of aspects of team climate Are all of these elements separate, or can we identify/group them into an underlying structure?

  5. Example: Team climate v_151: I am clear about what my team's objectives are v_152: I am in agreement with the team's objectives v_153: The team's objectives are clearly understood by other members of the team v_154: The team's objectives can actually be achieved v_155: The team's objectives are worthwhile to the organisation v_156: We keep each other informed about work-related issues in the team v_157: There are real attempts to share information throughout the team v_158: We have a 'we are in it together' attitude v_159: We are prepared to question the basis of what the team is doing v_160: We critically appraise potential weaknesses in what we are doing in order to achieve the best possible outcome v_161: We build on each other's ideas in order to achieve the best possible outcome v_162: We are always searching for fresh, new ways of looking at problems v_163: We take the time needed to develop new ideas v_164: We co-operate in order to help each other and apply new ideas

  6. Example: team climate

  7. Example: team climate

  8. Example: team climate

  9. Stages in Factor Analysis Stage 1: Objectives of FA Stage 2: Designing an FA Stage 3: Assumptions Stage 4: Factors & Overall Fit Stage 5: Interpreting the factors Stage 6: Validation of FA Stage 7: Additional uses of FA results

  10. Objectives of FA Exploratory Factor Analysis (EFA): Data reduction / summarisation • To discover a the factor structure of a construct and examine its reliability • Data driven Confirmatory Factor Analysis (CFA): Structure detection • To confirm the fit of the hypothesised factor structure to the observed data • Theory driven

  11. Example EFA vs CFA in a research paper

  12. Summarise vs reduce • Summarising data: derives underlying dimensions that describe the data in a much smaller number of concepts • Reducing data: extends summarisation by deriving an empirical value (factor score) for each dimension and then substitute this value for the original values

  13. Variable selection • Consider conceptual underpinnings • Use judgment on the appropriateness of variables for factor analysis Warning: FA will always provide factors… but do they make sense?

  14. Variable selection and measurement What type of variables can be used in FA? • A correlation value can be calculated among all variables. • Numerical or pseudo-numerical (e.g. Likert scales) variables only • Reflective variables, i.e. variables that reflect a latent construct How many variables should be included? • Ideally five or more variables for each proposed factor • Little use in identifying factors with one variable

  15. Sample size At least 50, preferably 100 or more At least five times as many observations as the number of variables, better at least 10:1 Employ the most parsimonious set of variables Interpret findings cautiously at lower cases-to variable ratio

  16. Assumptions in FA More conceptual than statistical • Some underlying structure does exist • Researcher should ensure that observed patterns are conceptually valid • Sample homogeneity • Some degree of multicollinearity is desirable

  17. Assumptions in FA Check the correlation matrix and avoid: • Correlations < .30 • Anti-image correlation matrix: partial correlations > .7 Check the validity of the model: • Bartlett test of sphericity (sig < .05) • Measure of sampling adequacy (MSA) • > .8 meritorious • > .7 middling • > .6 mediocre • > .5 miserable • < .5 unacceptable Examine for each variable

  18. Determining the number of factors to extract • Iterative factor extraction • Combine conceptual foundation (how many factors should be in the structure?) with some empirical evidence (how many factors can be reasonably supported?)

  19. Determining the number of factors to extract • Latent root criterion • Latent roots (eigenvalues) > 1, a.k.a Kaiser criterion • Cut-off is most reliable when number of variables is between 20 and 50 • A priori criterion • Number of factors to extract is known • Used when testing a theory or a hypothesis or when replicating previous work

  20. Determining the number of factors to extract • Percentage of variance criterion • Achieving a specified cumulative percentage of total variance extracted by successive factors • ~ 60% or more can be regarded satisfactory • Scree test criterion • Identifies the optimum number of factors that can be extracted before the amount of unique variance begins to dominate the common variance structure

  21. Scree plot

  22. Interpreting the factors • Strong conceptual foundation for the anticipated structure required • Factor loadings: correlation of each variable and the factor, the higher the better • Initial unrotated factor matrix • Rotated factor matrix: simplifies factor structure

  23. Factor rotation Orthogonal (axes are maintained at 90 degrees): • Quartimax • Varimax • Equimax Preferred when the goal is data reduction for subsequent use in other multivariate techniques Oblique (axes are not maintained at 90 degrees): • Oblimin • Promax • Orthoblique Preferred when the goal is to obtain theoretically meaningful factors or constructs

  24. Orthogonal factor rotation

  25. Oblique factor rotation

  26. Varimax Rotation Varimax –simplifies columns –as many values in each column as close to zero as possible. Frequently used. –default option

  27. Varimax Rotation Varimax –simplifies columns –as many values in each column as close to zero as possible. Frequently used. –default option

  28. Interpreting the factor matrix • Examine the factor matrix of loadings • Identify significant loadings for each variable • Cross-loadings • Assess the communalities of the variables • <.5 suggests no sufficient explanation • Respecify the factor model if needed • No significant loading • Significant loading but low communality • Cross-loading • Label the factors

  29. Validation Check and report: • Adequacy (KMO, BTS, no communalities < 0.3, total variance > 0.6 and no less than 0.5) • Convergent validity (all factors loading > 0.6 and no less than 0.5, factors loadings average to > 0.7) • Discriminant validity (no strong cross loadings, factor correlation matrix < 0.7) • Reliability (Cronbach alpha scores within each factors > 0.7 and no less than 0.6)

  30. Example using Team Climate data in IBM SPSS Statistics

  31. Correlations • Analyze > Correlations > Bivariates CORRELATIONS /VARIABLES=v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /PRINT=TWOTAIL NOSIG /MISSING=PAIRWISE.

  32. Correlations

  33. Correlation Matrix Check for evidence of strong correlations

  34. Factor Analysis Analyze > Dimension Reduction > Factor… FACTOR /VARIABLES v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /MISSING LISTWISE /ANALYSIS v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /PRINT UNIVARIATE INITIAL KMO AIC EXTRACTION ROTATION /FORMAT SORT BLANK(.5) /PLOT EIGEN /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION PC /CRITERIA ITERATE(25) /ROTATION VARIMAX /METHOD=CORRELATION.

  35. Analyze > Dimension Reduction > Factor… FACTOR /VARIABLES v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /MISSING LISTWISE /ANALYSIS v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /PRINT UNIVARIATE INITIAL KMO AIC EXTRACTION ROTATION /FORMAT SORT BLANK(.5) /PLOT EIGEN /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION PC /CRITERIA ITERATE(25) /ROTATION VARIMAX /METHOD=CORRELATION.

  36. Univariate analysis

  37. Analyze > Dimension Reduction > Factor… FACTOR /VARIABLES v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /MISSING LISTWISE /ANALYSIS v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /PRINT UNIVARIATE INITIAL KMO AIC EXTRACTION ROTATION /FORMAT SORT BLANK(.5) /PLOT EIGEN /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION PC /CRITERIA ITERATE(25) /ROTATION VARIMAX /METHOD=CORRELATION.

  38. Anti-image Correlation Matrix Check for MSAs value along the diagonal, ideally >0.5 MSA = Measure of Sampling Adequacy

  39. Analyze > Dimension Reduction > Factor… FACTOR /VARIABLES v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /MISSING LISTWISE /ANALYSIS v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /PRINT UNIVARIATE INITIAL KMO AIC EXTRACTION ROTATION /FORMAT SORT BLANK(.5) /PLOT EIGEN /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION PC /CRITERIA ITERATE(25) /ROTATION VARIMAX /METHOD=CORRELATION.

  40. Validity KMO = 0.934, well above 0.7 BTS < 0.01, evidence of valid model

  41. Communalities > 0.5 Evidence that most variables in the FA model provide sufficient explanation

  42. Analyze > Dimension Reduction > Factor… FACTOR /VARIABLES v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /MISSING LISTWISE /ANALYSIS v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /PRINT UNIVARIATE INITIAL KMO AIC EXTRACTION ROTATION /FORMAT SORT BLANK(.5) /PLOT EIGEN /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION PC /CRITERIA ITERATE(25) /ROTATION VARIMAX /METHOD=CORRELATION.

  43. Total variance explained The FA model consists of 2 components (eigenvalues > 1) that explain 59% of the variance

  44. Analyze > Dimension Reduction > Factor… FACTOR /VARIABLES v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /MISSING LISTWISE /ANALYSIS v_151 v_152 v_153 v_154 v_155 v_156 v_157 v_158 v_159 v_160 v_161 v_162 v_163 v_164 /PRINT UNIVARIATE INITIAL KMO AIC EXTRACTION ROTATION /FORMAT SORT BLANK(.5) /PLOT EIGEN /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION PC /CRITERIA ITERATE(25) /ROTATION VARIMAX /METHOD=CORRELATION.

  45. Scree Plot

More Related