Example for Factor Analysis

A human resources manager wants to identify the underlying factors that explain the 12 variables that the human resources department measures for each applicant. Human resources employees rate each job applicant on various characteristics using a 1 (low) through 10 (high) scale. The manager collects the ratings for 50 job applicants.

Previous analysis determined that 4 factors account for most of the total variability in the data.

  1. Open the sample data set, JobApplicants.MTW.
  2. Choose Stat > Multivariate > Factor Analysis.
  3. In Variables, enter C1-C12.
  4. In Number of factors to extract, enter 4.
  5. Under Method of Extraction, select Maximum likelihood.
  6. Under Type of Rotation, select Varimax.
  7. Click OK.

Interpret the results

Minitab calculates the factor loadings for each variable in the analysis. The loadings indicate how much a factor explains each variable. Large loadings (positive or negative) indicate that the factor strongly influences the variable. Small loadings (positive or negative) indicate that the factor has a weak influence on the variable.

Unrotated factor loadings are often difficult to interpret. Factor rotation simplifies the loading structure, and makes the factor loadings easier to interpret. Using the rotated factor loadings, the manager concludes the following:
  • Company Fit (0.778), Job Fit (0.844), and Potential (0.645) have large positive loadings on factor 1, so this factor describes employee fit and potential for growth in the company.
  • Appearance (0.730), Likeability (0.615), and Self-confidence (0.743) have large positive loadings on factor 2, so this factor describes personal qualities.
  • Communication (0.802) and Organization (0.889) have large positive loadings on factor 3, so this factor describes work skills.
  • Letter (0.947) and Resume (0.789) have large positive loadings on factor 4, so this factor describes writing skills.

Together, all four factors explain 0.754 or 75.4% of the variation in the data.

Factor Analysis: Academic rec, Appearance, Communicatio, Company Fit, ...

Maximum Likelihood Factor Analysis of the Correlation Matrix

Iteration for maximum likelihood Max change Function in ln(unique Step Iteration value variance) halvings 1 1.59123 0.00000 0 2 1.46511 0.60457 0 3 1.44098 0.21665 0 4 1.42962 0.34068 0 5 1.41848 0.48747 0 6 1.41058 1.03753 0 7 1.40438 0.11625 0 E 8 1.40036 0.01625 0 E 9 1.39884 0.00802 0 E 10 1.39771 0.00752 0 E 11 1.39687 0.00650 0 E 12 1.39632 0.00643 0 E 13 1.39586 0.00462 0 E E Second derivative matrix was exact
Unrotated Factor Loadings and Communalities Variable Factor1 Factor2 Factor3 Factor4 Communality Academic record 0.380 0.455 0.340 0.259 0.534 Appearance 0.359 0.530 -0.040 0.523 0.685 Communication 0.465 0.660 -0.377 -0.023 0.795 Company Fit 0.523 0.677 0.266 -0.253 0.866 Experience 0.508 0.194 0.450 0.232 0.553 Job Fit 0.532 0.632 0.415 -0.201 0.895 Letter 0.992 -0.094 -0.012 -0.007 0.994 Likeability 0.412 0.529 0.032 0.377 0.593 Organization 0.406 0.761 -0.424 -0.055 0.926 Potential 0.446 0.548 0.431 0.172 0.714 Resume 0.850 0.040 0.096 0.283 0.814 Self-Confidence 0.293 0.575 0.083 0.506 0.679 Variance 3.6320 3.3193 1.0883 1.0095 9.0491 % Var 0.303 0.277 0.091 0.084 0.754
Rotated Factor Loadings and Communalities Varimax Rotation Variable Factor1 Factor2 Factor3 Factor4 Communality Academic record 0.481 0.510 0.086 0.188 0.534 Appearance 0.140 0.730 0.319 0.175 0.685 Communication 0.203 0.280 0.802 0.181 0.795 Company Fit 0.778 0.165 0.445 0.189 0.866 Experience 0.472 0.395 -0.112 0.401 0.553 Job Fit 0.844 0.209 0.305 0.215 0.895 Letter 0.219 0.052 0.217 0.947 0.994 Likeability 0.261 0.615 0.321 0.208 0.593 Organization 0.217 0.285 0.889 0.086 0.926 Potential 0.645 0.492 0.121 0.202 0.714 Resume 0.214 0.365 0.113 0.789 0.814 Self-Confidence 0.239 0.743 0.249 0.092 0.679 Variance 2.5153 2.4880 2.0863 1.9594 9.0491 % Var 0.210 0.207 0.174 0.163 0.754
Factor Score Coefficients Variable Factor1 Factor2 Factor3 Factor4 Academic record 0.045 0.134 -0.068 -0.003 Appearance -0.109 0.339 -0.034 0.012 Communication -0.089 0.014 0.258 -0.036 Company Fit 0.454 -0.225 0.066 -0.105 Experience 0.062 0.120 -0.104 0.006 Job Fit 0.662 -0.181 -0.079 -0.123 Letter -0.159 -0.428 0.090 1.068 Likeability -0.039 0.199 -0.022 0.002 Organization -0.239 -0.027 0.822 -0.131 Potential 0.136 0.173 -0.115 -0.017 Resume -0.065 0.300 -0.117 0.049 Self-Confidence -0.064 0.332 -0.061 0.006
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