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.

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

Maximum Likelihood Factor Analysis of the Correlation Matrix

Iteration for maximum likelihood

Iteration	Function value	Max change in ln(unique variance)
1	1.59123	0.00000
2	1.46511	0.60457
3	1.44098	0.21665
4	1.42962	0.34068
5	1.41848	0.48747
6	1.41058	1.03753
7	1.40438	0.11625	E
8	1.40036	0.01625	E
9	1.39884	0.00802	E
10	1.39771	0.00752	E
11	1.39687	0.00650	E
12	1.39632	0.00643	E
13	1.39586	0.00462	E

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