Factor Analysis Dr Michael R Hyman Grouping Variables

Factor Analysis Dr. Michael R. Hyman

Grouping Variables into Constructs 2

Purpose • Data reduction – If high redundancy in measures – If construct measures require multiple items (e. g. , store image) • Substantive interpretation 3

Marketing Applications • Market segmentation – Find underlying variables to group consumers • Product research – Find underlying attributes that influence choice • Advertising research/media usage • Pricing studies – Find characteristics of price-sensitive consumers 4

Background • No (in)dependent variables • Metric inputs and outputs • Operates on correlation matrix, so assumes variables related linearly • Assumes variables sufficiently intercorrelated – Sphericity and KMO tests 5

When Factor Analysis Will Be Beneficial 6

When Factor Analysis Will Not be Beneficial 7

Key Definitions • Factor – Linear combination of variables (derived variable) – Underlying dimension that explains correlations among set of variables • Factor score – Each subject’s score on derived variable – Used in subsequent analysis 8

Key Definitions (cont. ) • Factor loadings – Correlation between factors and original variable (if standardized) – All original variables with high loading (near + 1. 0 on same factor grouped together • Communality – Percent of variation in an original variable explained by all the factors used 9

Key Definitions (cont. ) • Explained variance – Percent of variation in all the data explained by each factor (eigenvalue) 10

Stopping Rules • • A priori determination Eigenvalue > 1. 0 Break (elbow) in scree plot Percent variance explained – Should be at least 60% • Split data, run both halves, and compare • Test statistical significance of eigenvalues – Problem: With n>200, many minor factors will seem significant 11