Factor Analysis Istijanto MM, MCom

Definition Factor analysis  Data reduction technique and summarization  Identifying the underlying factors/ dimensions  Based on interdependence relationships  Example: Store image consists of six dimensions (article: “The alternative modes of measuring store image”)

Statistics Bartlett’s test of sphericity  to test H0 that the variables are uncorrelated Correlation matrix  the correlation between all possible pairs of variables included in analysis Eigenvalue  total variance explained by each factor Factor loadings  correlation between the variables and the factors Kaiser-Meyer-Olkin  measure of sampling adequacy

Conducting Factor Analysis Fig Construction of the Correlation Matrix Method of Factor Analysis Determination of Number of Factors Determination of Model Fit Problem Formulation Calculation of Factor Scores Interpretation of Factors Rotation of Factors Selection of Surrogate Variables

Example: Malhotra, p respondents were asked with 6 questions: V1: It is important to buy a toothpaste that prevents cavities V2: I like a toothpaste that gives shiny teeth V3: A toothpaste should strengthen your gums V4: I prefer a toothpaste that freshness breadth V5: Preventions of tooth decay is not an important benefit offered by a toothpaste V6: The most considerations in buying a toothpaste is attractive teeth RQ: What are the underlying dimensions of a preferable toothpaste? Using a seven-point scale (1=STS, 7=SS)

Procedures Construct correlation matrix Prerequisites:  Correlation matrix between variables: must be correlated  Barlett test of sphericity, H0: variables are uncorrelated, should be rejected  KMO, measure sampling adequacy, should be > 0,5 Method of factor analysis Principal component analysis  the total variance in the data is considered. (recommended)

Procedures (cont’d) Determine the number of factors  a priori determination (researcher’s knowledge)  based on eigenvalues: >1.0 retained  based on Scree Plot look at distinct break  based on percentage of variance: at least 60% retained  Rotate factors Factor matrix is transformed into simpler one Use varimax procedure  to enhance the interpretability of the factors  Intepret factor

Example: Malhotra, p respondents were asked with 6 questions: V1: It is important to buy a toothpaste that prevents cavities V2: I like a toothpaste that gives shiny teeth V3: A toothpaste should strengthen your gums V4: I prefer a toothpaste that freshness breadth V5: Preventions of tooth decay is not an important benefit offered by a toothpaste V6: The most considerations in buying a toothpaste is attractive teeth RQ: What are the underlying dimensions of a preferable toothpaste? Using a seven-point scale (1=STS, 7=SS)

Conducting Factor Analysis Table 19.1

Construct correlation matrix > 0.5 Ho tolak

Method of Factor analysis 

Determine the number of factors  retained

Rotate factors Sometimes, difficult to interpret Easier and simpler to interpret

Interpret factors Factor 1: V1, V3, V5  health benefit factor/ dimension Factor 2: V2, V4, V6  social benefit factor/ dimension

SPSS Workshops Open file: table 19-1.sav

SPSS Workshops Menu: Analyze  Data Reduction  Factor

SPSS Workshops Move the variables