Ch 3 MDA 6e Exploratory Factor Analysis

Chapter 3Chapter 3

Exploratory Exploratory Factor Factor

AnalysisAnalysis

Chapter 3Chapter 3

Exploratory Exploratory Factor Factor

AnalysisAnalysis

Copyright © Copyright © 20072007Prentice-Hall, Prentice-Hall, Inc.Inc.

LEARNING OBJECTIVES:LEARNING OBJECTIVES:Upon completing this chapter, you should be able to do the following:Upon completing this chapter, you should be able to do the following:

1.1. Differentiate factor analysis techniques from other multivariate Differentiate factor analysis techniques from other multivariate techniques.techniques.

2.2. Distinguish between exploratory and confirmatory uses of factor Distinguish between exploratory and confirmatory uses of factor analytic techniques.analytic techniques.

3.3. Understand the seven stages of applying factor analysis.Understand the seven stages of applying factor analysis.

4.4. Distinguish between R and Q factor analysis.Distinguish between R and Q factor analysis.

5.5. Identify the differences between component analysis and Identify the differences between component analysis and common factor analysis models.common factor analysis models.

6.6. Tell how to determine the number of factors to extract.Tell how to determine the number of factors to extract.

7.7. Explain the concept of rotation of factors.Explain the concept of rotation of factors.

8.8. Describe how to name a factor.Describe how to name a factor.

9.9. Explain the additional uses of factor analysis.Explain the additional uses of factor analysis.

10.10.State the major limitations of factor analytic techniques.State the major limitations of factor analytic techniques.

Chapter 3: Exploratory Factor AnalysisChapter 3: Exploratory Factor AnalysisChapter 3: Exploratory Factor AnalysisChapter 3: Exploratory Factor Analysis

Factor analysis . . .Factor analysis . . . is an is an interdependence technique whose interdependence technique whose primary purpose is to define the primary purpose is to define the underlying structure among the underlying structure among the variables in the analysis.variables in the analysis.

Factor Analysis DefinedFactor Analysis Defined

Factor analysis . . .Factor analysis . . .

•Examines the interrelationships among a Examines the interrelationships among a large large number of variables and then attempts number of variables and then attempts to explain to explain them in terms of their common them in terms of their common underlying underlying dimensions.dimensions.•These common underlying dimensions are These common underlying dimensions are referred to as factors.referred to as factors.•Is a summarization and data reduction Is a summarization and data reduction technique technique that does not have independent that does not have independent and dependent and dependent variables, but an variables, but an interdependence technique in interdependence technique in which all which all variables are considered simultaneously.variables are considered simultaneously.

What is Factor Analysis?What is Factor Analysis?

Factor Analysis Decision ProcessFactor Analysis Decision Process

Stage 1: Objectives of Factor AnalysisStage 1: Objectives of Factor Analysis

Stage 2: Designing a Factor AnalysisStage 2: Designing a Factor Analysis

Stage 3: Assumptions in Factor AnalysisStage 3: Assumptions in Factor Analysis

Stage 4: Deriving Factors and Assessing Stage 4: Deriving Factors and Assessing Overall FitOverall Fit

Stage 5: Interpreting the FactorsStage 5: Interpreting the Factors

Stage 6: Validation of Factor AnalysisStage 6: Validation of Factor Analysis

Stage 7: Additional uses of Factor Analysis Stage 7: Additional uses of Factor Analysis ResultsResults

Stage 1: Objectives of Factor Stage 1: Objectives of Factor AnalysisAnalysis

1.1. Is the objective exploratory or Is the objective exploratory or confirmatory?confirmatory?

2.2. Specify the unit of analysis.Specify the unit of analysis.3.3. Data summarization and/or Data summarization and/or

reduction?reduction?4.4. Using Factor analysis with other Using Factor analysis with other

techniques.techniques.

Factor Analysis OutcomesFactor Analysis Outcomes

1.1. Data summarization = derives underlying Data summarization = derives underlying dimensions that, when interpreted and dimensions that, when interpreted and understood, describe the data in a much understood, describe the data in a much smaller number of concepts than the smaller number of concepts than the original individual variables.original individual variables.

2.2. Data reduction = extends the process of Data reduction = extends the process of data summarization by deriving an data summarization by deriving an empirical value (factor score) for each empirical value (factor score) for each dimension (factor) and then substituting dimension (factor) and then substituting this value for the original values.this value for the original values.

Stage 2: Designing a Factor Stage 2: Designing a Factor AnalysisAnalysis

Three Basic Decisions:Three Basic Decisions:1.1. Calculation of input data – R vs. Calculation of input data – R vs.

Q analysis.Q analysis.2.2. Design of study in terms of Design of study in terms of

number of variables, number of variables, measurement properties of measurement properties of variables, and the type of variables, and the type of variables.variables.

3.3. Sample size necessary.Sample size necessary.

Rules of Thumb 3–1 Rules of Thumb 3–1

Factor Analysis DesignFactor Analysis Design Factor analysis is performed most often only on metric Factor analysis is performed most often only on metric

variables, although specialized methods exist for the use variables, although specialized methods exist for the use of dummy variables. A small number of “dummy of dummy variables. A small number of “dummy variables” can be included in a set of metric variables variables” can be included in a set of metric variables that are factor analyzed.that are factor analyzed.

If a study is being designed to reveal factor structure, If a study is being designed to reveal factor structure, strive to have at least five variables for each proposed strive to have at least five variables for each proposed factor.factor.

For sample size: For sample size: o the sample must have more observations than the sample must have more observations than

variables.variables.o the minimum absolute sample size should be 50 the minimum absolute sample size should be 50

observations.observations. Maximize the number of observations per variable, with Maximize the number of observations per variable, with

a minimum of five and hopefully at least ten a minimum of five and hopefully at least ten observations per variable.observations per variable.

Stage 3: Assumptions in Factor Stage 3: Assumptions in Factor AnalysisAnalysis

Three Basic Decisions:Three Basic Decisions:1.1. Calculation of input data – R vs. Calculation of input data – R vs.

Q analysis.Q analysis.2.2. Design of study in terms of Design of study in terms of

number of variables, number of variables, measurement properties of measurement properties of variables, and the type of variables, and the type of variables.variables.

3.3. Sample size necessary.Sample size necessary.

Assumptions:Assumptions:

• Multicollinearity.Multicollinearity. Assessed using MSA (measure of sampling Assessed using MSA (measure of sampling

adequacy).adequacy).

• Homogeneity of sample factor solutions.Homogeneity of sample factor solutions.

The MSA is measured by the Kaiser-Meyer-Olkin (KMO) MSA is measured by the Kaiser-Meyer-Olkin (KMO) statistics. As a measure of sampling adequacy, the KMO statistics. As a measure of sampling adequacy, the KMO predicts if data are likely to factor well based on correlation and predicts if data are likely to factor well based on correlation and partial correlation. KMO can be used to identify which partial correlation. KMO can be used to identify which variables to drop from the factor analysis because they lack variables to drop from the factor analysis because they lack multicollinearity. multicollinearity. There is a KMO statistic for each individual variable, and There is a KMO statistic for each individual variable, and their sum is the KMO overall statistic. KMO varies from 0 to their sum is the KMO overall statistic. KMO varies from 0 to 1.0. Overall KMO should be .50 or higher to proceed with factor 1.0. Overall KMO should be .50 or higher to proceed with factor analysis. If it is not, remove the variable with the lowest analysis. If it is not, remove the variable with the lowest individual KMO statistic value one at a time until KMO overall individual KMO statistic value one at a time until KMO overall rises above .50, and each individual variable KMO is above .50.rises above .50, and each individual variable KMO is above .50.

Rules of Thumb 3–2 Rules of Thumb 3–2

Testing Assumptions of Factor AnalysisTesting Assumptions of Factor Analysis

There must be a strong conceptual foundation to There must be a strong conceptual foundation to support the assumption that a structure does exist support the assumption that a structure does exist before the factor analysis is performed.before the factor analysis is performed.

A statistically significant Bartlett’s test of sphericity A statistically significant Bartlett’s test of sphericity (sig. > .05) indicates that sufficient correlations exist (sig. > .05) indicates that sufficient correlations exist among the variables to proceed.among the variables to proceed.

Measure of Sampling Adequacy (MSA) values must Measure of Sampling Adequacy (MSA) values must exceed .50 for both the overall test and each individual exceed .50 for both the overall test and each individual variable. Variables with values less than .50 should be variable. Variables with values less than .50 should be omitted from the factor analysis one at a time, with the omitted from the factor analysis one at a time, with the smallest one being omitted each time.smallest one being omitted each time.

Stage 4: Deriving Factors and Stage 4: Deriving Factors and Assessing Overall FitAssessing Overall Fit

• Selecting the factor extraction Selecting the factor extraction method – common vs. method – common vs. component analysis.component analysis.

• Determining the number of Determining the number of factors to represent the data.factors to represent the data.

Extraction Decisions:Extraction Decisions:

• Which method?Which method?o Principal Components Principal Components

Analysis.Analysis.o Common Factor Analysis.Common Factor Analysis.

• How to rotate?How to rotate?o Orthogonal or Oblique Orthogonal or Oblique

rotation.rotation.

Extraction Method Determines the Extraction Method Determines the Types of Variance Carried into the Factor Types of Variance Carried into the Factor

MatrixMatrix

Diagonal ValueDiagonal Value VarianceVariance

Unity (1)Unity (1)

CommunalityCommunality

Total VarianceTotal Variance

CommonCommon Specific and Specific and ErrorError

Variance Variance extractedextracted Variance not usedVariance not used

Principal Components vs. Common?Principal Components vs. Common?

Two CriteriaTwo Criteria:: • Objectives of the factor analysis.Objectives of the factor analysis.

• Amount of prior knowledge Amount of prior knowledge about about the variance in the variables.the variance in the variables.

Number of Factors?Number of Factors?

• A Priori Criterion.A Priori Criterion.

• Latent Root Criterion.Latent Root Criterion.

• Percentage of Variance.Percentage of Variance.

• Scree Test Criterion.Scree Test Criterion.

Eigenvalue Plot for Scree Test Eigenvalue Plot for Scree Test CriterionCriterion

Rules of Thumb 3–3 Rules of Thumb 3–3

Choosing Factor Models and Number of FactorsChoosing Factor Models and Number of Factors• Although both component and common factor analysis models yield similar Although both component and common factor analysis models yield similar

results in common research settings (30 or more variables or communalities results in common research settings (30 or more variables or communalities of .60 for most variables):of .60 for most variables):

the component analysis model is most appropriate when data reduction is the component analysis model is most appropriate when data reduction is paramount. paramount.

the common factor model is best in well-specified theoretical applications.the common factor model is best in well-specified theoretical applications.

• Any decision on the number of factors to be retained should be based on Any decision on the number of factors to be retained should be based on several considerations: several considerations:

use of several stopping criteria to determine the initial number of factors to retain. use of several stopping criteria to determine the initial number of factors to retain.

Factors With Eigenvalues greater than 1.0. Factors With Eigenvalues greater than 1.0. A pre-determined number of factors based on research objectives and/or prior A pre-determined number of factors based on research objectives and/or prior

research. research. Enough factors to meet a specified percentage of variance explained, usually 60% Enough factors to meet a specified percentage of variance explained, usually 60%

or higher. or higher. Factors shown by the scree test to have substantial amounts of common variance Factors shown by the scree test to have substantial amounts of common variance

(i.e., factors before inflection point). (i.e., factors before inflection point). More factors when there is heterogeneity among sample subgroups.More factors when there is heterogeneity among sample subgroups.

• Consideration of several alternative solutions (one more and one less factor Consideration of several alternative solutions (one more and one less factor than the initial solution) to ensure the best structure is identified.than the initial solution) to ensure the best structure is identified.

Processes of Factor InterpretationProcesses of Factor Interpretation

• Estimate the Factor Matrix.Estimate the Factor Matrix.

• Factor Rotation.Factor Rotation.

• Factor Interpretation.Factor Interpretation.

• Respecification of factor model, if needed, Respecification of factor model, if needed, may involve:may involve:o Deletion of variables from analysis.Deletion of variables from analysis.o Desire to use a different rotational Desire to use a different rotational

approach.approach.o Need to extract a different number of Need to extract a different number of

factors.factors.o Desire to change method of extraction.Desire to change method of extraction.

Rotation of Factors

• Factor rotation = the reference axes of the Factor rotation = the reference axes of the factors are tuned about the origin until factors are tuned about the origin until some other position has been reached. some other position has been reached. Since unrotated factor solutions extract Since unrotated factor solutions extract factors based on how much variance they factors based on how much variance they account for, with each subsequent factor account for, with each subsequent factor accounting for less variance, the ultimate accounting for less variance, the ultimate effect of rotating the factor matrix is to effect of rotating the factor matrix is to redistribute the variance from earlier redistribute the variance from earlier factors to later ones to achieve a simpler, factors to later ones to achieve a simpler, theoretically more meaningful factor theoretically more meaningful factor pattern.pattern.

Two Rotational Approaches:

1.1. Orthogonal = axes are Orthogonal = axes are maintained at 90 degrees.maintained at 90 degrees.

2.2. Oblique = axes are not Oblique = axes are not maintained at 90 degrees.maintained at 90 degrees.

Orthogonal Factor Orthogonal Factor RotationRotation Unrotated Unrotated Factor IIFactor II

Unrotated Unrotated Factor IFactor I

Rotated Rotated Factor IFactor I

Rotated Factor IIRotated Factor II

-1.0 -.50 0 +.50 +1.0

-.50

-1.0

+1.0

+.50

V1

V2

V3V4

V5

Unrotated Unrotated Factor IIFactor II

Unrotated Unrotated Factor IFactor I

Oblique Oblique Rotation: Rotation: Factor IFactor I

Orthogonal Orthogonal Rotation: Factor IIRotation: Factor II

-1.0 -.50 0 +.50 +1.0

-.50

-1.0

+1.0

+.50

V1

V2

V3

V4

V5

Orthogonal Orthogonal Rotation: Factor Rotation: Factor

II

Oblique Oblique Rotation: Factor Rotation: Factor

IIII

Oblique Factor RotationOblique Factor Rotation

Orthogonal Rotation Methods:

• Quartimax (simplify Quartimax (simplify rows).rows).

• Varimax (simplify Varimax (simplify columns).columns).

• Equimax (combination).Equimax (combination).

Rules of Thumb 3–4 Rules of Thumb 3–4

Choosing Factor Rotation MethodsChoosing Factor Rotation Methods

Orthogonal rotation methods: Orthogonal rotation methods:

o are the most widely used rotational methods. are the most widely used rotational methods.

o are The preferred method when the research goal is are The preferred method when the research goal is data reduction to either a smaller number of variables or data reduction to either a smaller number of variables or a set of uncorrelated measures for subsequent use in a set of uncorrelated measures for subsequent use in other multivariate techniques.other multivariate techniques.

Oblique rotation methods: Oblique rotation methods:

o best suited to the goal of obtaining several theoretically best suited to the goal of obtaining several theoretically meaningful factors or constructs because, meaningful factors or constructs because, realistically, very few constructs in the “real world” are realistically, very few constructs in the “real world” are uncorrelated.uncorrelated.

Which Factor Loadings Are Which Factor Loadings Are Significant?Significant?

• Customary Criteria = Practical Customary Criteria = Practical Significance.Significance.

• Sample Size & Statistical Significance.Sample Size & Statistical Significance.

• Number of Factors ( = >) and/or Variables Number of Factors ( = >) and/or Variables ( = <)( = <) ..

Guidelines for Identifying Significant Guidelines for Identifying Significant Factor Loadings Based on Sample SizeFactor Loadings Based on Sample Size

Factor LoadingFactor Loading Sample Size Sample Size Needed Needed for for SignificanceSignificance**

.30.30 350350

.35.35 250250

.40.40 200200

.45.45 150150

.50.50 120120

.55.55 100100

.60.60 85 85

.65.65 70 70

.70.70 60 60

.75.75 50 50

**Significance is based on a .05 significance level (a), a power level of 80 percent, Significance is based on a .05 significance level (a), a power level of 80 percent, and standard errors assumed to be twice those of conventional correlation and standard errors assumed to be twice those of conventional correlation coefficients.coefficients.

Rules of Thumb 3–5Rules of Thumb 3–5

Assessing Factor LoadingsAssessing Factor Loadings

• While factor loadings of While factor loadings of ++.30 to .30 to ++.40 are minimally acceptable, .40 are minimally acceptable, values greater than values greater than ++ .50 are considered necessary for practical .50 are considered necessary for practical significance. significance.

• To be considered significant: To be considered significant:

o A smaller loading is needed given either a larger sample size, or A smaller loading is needed given either a larger sample size, or a larger number of variables being analyzed.a larger number of variables being analyzed.

o A larger loading is needed given a factor solution with a larger A larger loading is needed given a factor solution with a larger number of factors, especially in evaluating the loadings on later number of factors, especially in evaluating the loadings on later factors.factors.

• Statistical tests of significance for factor loadings are generally Statistical tests of significance for factor loadings are generally very conservative and should be considered only as starting points very conservative and should be considered only as starting points needed for including a variable for further consideration. needed for including a variable for further consideration.

Stage 5: Interpreting the FactorsStage 5: Interpreting the Factors

• Selecting the factor extraction Selecting the factor extraction method – common vs. method – common vs. component analysis.component analysis.

• Determining the number of Determining the number of factors to represent the data.factors to represent the data.

Interpreting a Factor Matrix:Interpreting a Factor Matrix:

1.1. Examine the factor matrix of Examine the factor matrix of loadings.loadings.

2.2. Identify the highest loading Identify the highest loading across all factors for each across all factors for each variable.variable.

3.3. Assess communalities of the Assess communalities of the variables.variables.

4.4. Label the factors.Label the factors.

Rules of Thumb 3–6Rules of Thumb 3–6

Interpreting The FactorsInterpreting The Factors

An optimal structure exists when all variables have high loadings An optimal structure exists when all variables have high loadings only on a single factor.only on a single factor.

Variables that cross-load (load highly on two or more factors) are Variables that cross-load (load highly on two or more factors) are usually deleted unless theoretically justified or the objective is usually deleted unless theoretically justified or the objective is strictly data reduction.strictly data reduction.

Variables should generally have communalities of greater than .50 Variables should generally have communalities of greater than .50 to be retained in the analysis.to be retained in the analysis.

Respecification of a factor analysis can include options such as:Respecification of a factor analysis can include options such as:

o deleting a variable(s), deleting a variable(s),

o changing rotation methods, and/or changing rotation methods, and/or

o increasing or decreasing the number of factors.increasing or decreasing the number of factors.

Stage 6: Validation of Factor AnalysisStage 6: Validation of Factor Analysis

• Confirmatory Perspective.Confirmatory Perspective.• Assessing Factor Structure Assessing Factor Structure

Stability.Stability.• Detecting Influential Detecting Influential

Observations.Observations.

Stage 7: Additional Uses of Factor Stage 7: Additional Uses of Factor Analysis ResultsAnalysis Results

• Selecting Surrogate Selecting Surrogate Variables.Variables.

• Creating Summated Creating Summated Scales.Scales.

• Computing Factor Scores.Computing Factor Scores.

Rules of Thumb 3–7Rules of Thumb 3–7

Summated ScalesSummated Scales• A summated scale is only as good as the items used to represent the A summated scale is only as good as the items used to represent the

construct. While it may pass all empirical tests, it is useless without construct. While it may pass all empirical tests, it is useless without theoretical justification.theoretical justification.

• Never create a summated scale without first assessing its Never create a summated scale without first assessing its unidimensionality with exploratory or confirmatory factor analysis.unidimensionality with exploratory or confirmatory factor analysis.

• Once a scale is deemed unidimensional, its reliability score, as Once a scale is deemed unidimensional, its reliability score, as measured by Cronbach’s alpha: measured by Cronbach’s alpha:

o should exceed a threshold of .70, although a .60 level can be used in should exceed a threshold of .70, although a .60 level can be used in exploratory research. exploratory research.

o the threshold should be raised as the number of items increases, the threshold should be raised as the number of items increases, especially as the number of items approaches 10 or more. especially as the number of items approaches 10 or more.

• With reliability established, validity should be assessed in terms of:With reliability established, validity should be assessed in terms of:o convergent validity = scale correlates with other like scales.convergent validity = scale correlates with other like scales.o discriminant validity = scale is sufficiently different from other discriminant validity = scale is sufficiently different from other

related scales. related scales.o nomological validity = scale “predicts” as theoretically suggested.nomological validity = scale “predicts” as theoretically suggested.

Rules of Thumb 3–8Rules of Thumb 3–8

Representing Factor Analysis In Other AnalysesRepresenting Factor Analysis In Other Analyses

• The single surrogate variableThe single surrogate variable: : Advantages: simple to administer and interpret.Advantages: simple to administer and interpret. Disadvantages:Disadvantages:

1)1) does not represent all “facets” of a factor does not represent all “facets” of a factor 2)2) prone to measurement error.prone to measurement error.

• Factor scoresFactor scores: : Advantages:Advantages:

1)1) represents all variables loading on the factor,represents all variables loading on the factor,2)2) best method for complete data reduction. best method for complete data reduction. 3)3) Are by default orthogonal and can avoid Are by default orthogonal and can avoid

complications caused by multicollinearity.complications caused by multicollinearity. Disadvantages:Disadvantages:

1)1) interpretation more difficult since all variables interpretation more difficult since all variables contribute through loadings contribute through loadings

2)2) Difficult to replicate across studies.Difficult to replicate across studies.

Rules of Thumb 3–8 Rules of Thumb 3–8 Continued . . . Continued . . .

Representing Factor Analysis In Other AnalysesRepresenting Factor Analysis In Other Analyses

• Summated scalesSummated scales: : Advantages:Advantages:

1)1) compromise between the surrogate variable and compromise between the surrogate variable and factor score options.factor score options.

2)2) reduces measurement error.reduces measurement error.3)3) represents multiple facets of a concept.represents multiple facets of a concept.4)4) easily replicated across studies.easily replicated across studies.

Disadvantages:Disadvantages:1)1) includes only the variables that load highly on includes only the variables that load highly on

the factor and excludes those having little or the factor and excludes those having little or marginal impact.marginal impact.

2)2) not necessarily orthogonal.not necessarily orthogonal.3)3) Require extensive analysis of reliability and Require extensive analysis of reliability and

validity issues.validity issues.

Variable DescriptionVariable Description Variable TypeVariable TypeData Warehouse Classification VariablesData Warehouse Classification VariablesX1X1 Customer TypeCustomer Type nonmetric nonmetric X2X2 Industry TypeIndustry Type nonmetric nonmetric X3X3 Firm SizeFirm Size nonmetric nonmetric X4X4 RegionRegion nonmetricnonmetricX5X5 Distribution SystemDistribution System nonmetricnonmetricPerformance Perceptions VariablesPerformance Perceptions VariablesX6X6 Product QualityProduct Quality metricmetricX7X7 E-Commerce Activities/WebsiteE-Commerce Activities/Website metricmetricX8X8 Technical SupportTechnical Support metricmetricX9X9 Complaint ResolutionComplaint Resolution metricmetricX10X10 Advertising Advertising metricmetricX11X11 Product LineProduct Line metricmetricX12X12 Salesforce ImageSalesforce Image metricmetricX13X13 Competitive PricingCompetitive Pricing metricmetricX14X14 Warranty & ClaimsWarranty & Claims metricmetricX15X15 New ProductsNew Products metricmetricX16X16 Ordering & BillingOrdering & Billing metricmetricX17X17 Price FlexibilityPrice Flexibility metricmetricX18X18 Delivery SpeedDelivery Speed metricmetricOutcome/Relationship MeasuresOutcome/Relationship MeasuresX19X19 SatisfactionSatisfaction metric metric X20X20 Likelihood of RecommendationLikelihood of Recommendation metric metric X21X21 Likelihood of Future PurchaseLikelihood of Future Purchase metric metric X22X22 Current Purchase/Usage LevelCurrent Purchase/Usage Level metric metric X23X23 Consider Strategic Alliance/Partnership in FutureConsider Strategic Alliance/Partnership in Future nonmetricnonmetric

Description of HBAT Primary Database VariablesDescription of HBAT Primary Database Variables

Rotated Component Matrix Rotated Component Matrix ““Reduced Set” of HBAT Perceptions VariablesReduced Set” of HBAT Perceptions Variables

Component Communality 1 2 3 4

X9 – Complaint Resolution .933 .890X18 – Delivery Speed .931 .894X16 – Order & Billing .886 .806X12 – Salesforce Image .898 .860X7 – E-Commerce Activities .868 .780X10 – Advertising .743 .585X8 – Technical Support .940 .894X14 – Warranty & Claims .933 .891X6 – Product Quality .892 .798X13 – Competitive Pricing -.730 .661

Sum of Squares 2.589 2.216 1.846 1.406 8.057Percentage of Trace 25.893 22.161 18.457 14.061

80.572

Extraction Method: Principal Component Analysis. Rotation Method: Varimax.

Scree Test for HBAT Component Scree Test for HBAT Component AnalysisAnalysis

Factor Analysis Learning Factor Analysis Learning Checkpoint:Checkpoint:

1.1. What are the major uses of factor What are the major uses of factor analysis?analysis?

2.2. What is the difference between What is the difference between component analysis and common factor component analysis and common factor analysis?analysis?

3.3. Is rotation of factors necessary?Is rotation of factors necessary?4.4. How do you decide how many factors to How do you decide how many factors to

extract?extract?5.5. What is a significant factor loading?What is a significant factor loading?6.6. How and why do you name a factor?How and why do you name a factor?7.7. Should you use factor scores or Should you use factor scores or

summated ratings in follow-up summated ratings in follow-up analyses?analyses?