The Use of Explanations to Increase User Trust in a Recommendation Agent in Online Shopping

EXPLORATORY FACTORANALYSIS (EFA)Sahar Afshan1Learning ObjectivesUnderstand what is the factor analysis technique and its applications in research

Discuss exploratory factor analysis (EFA)

Run EFA with SPSS and interpret the resulted output

2 SCOPE of Factor Analysis todayFactor analysis and principal component analysis

Carrying out the analyses in SPSS

Deciding on the number of factors

Exploratory and confirmatory FA3Types of Measurement ModelsExploratory (EFA)Confirmatory (CFA)4EFA vs. CFAExploratory Factor Analysis is concerned with how many factors are necessary to explain the relations among a set of indicators and with estimation of factor loadings. It is associated with theory development.

Confirmatory Factor Analysis is concerned with determining if the number of factors conform to what is expected on the basis of pre-established theory. Do items load as predicted on the expected number of factors. Hypothesize beforehand the number of factors.5Factor AnalysisFactor Analysis is a method for identifying a structure (or factors, or dimensions) that underlies the relations among a set of observed variables. Factor analysis is a technique that transforms the correlations among a set of observed variables into smaller number of underlying factors, which contain all the essential information about the linear interrelationships among the original test scores.Factor analysis is a statistical procedure that involves the relationship between observed variables (measurements) and the underlying latent factors.

6Factor AnalysisFactor analysis is a fundamental component of Structural Equation modeling.Factor analysis explores the inter-relationships among variables to discover if those variables can be grouped into a smaller set of underlying factors.Many variables are reduced (grouped) into a smaller number of factorsThese variables reflect the causal impact of the latent underlying factors Statistical technique for dealing with multiple variables7

Explore data for patterns.Often a researcher is unclear if items or variables have a discernible patterns. Factor Analysis can be done in an Exploratory fashion to revealpatterns among the inter-relationships of the items.

Data Reduction. Factor analysis can be used to reduce a large number of variables into a smaller and more manageable number of factors. Factor analysis can create factor scores for each subject that represents these higher order variables.Factor Analysis can be used to reduce a large number of variables into a parsimonious set of few factors that account better for the underlying variance (causal impact) in the measured phenomenon.

Confirm Hypothesis of Factor Structure. Factor Analysis can be used to test whether a set of items designed to measure a certain variable(s) do, in fact, reveal the hypothesized factor structure (i.e. whether the underlying latent factor truly causes the variance in the observed variables and how certain we can be about it). In measurement research when a researcher wishes to validate a scale with a given or hypothesized factor structure, Confirmatory Factor Analysis is used.

Theory Testing.Factor Analysis can be used to test a priori hypotheses about the relations among a set of observed variables.Applications of Factor Analysis

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How would you group these Items?9In EFA, the researcheris attempting to explorethe relationships among items to determine if theitems can be groupedinto a smaller number of underlying factors.

In this analysis, all items are assumed to be related to all factors.V1V2V3V4Factor 1

Factor 1

Exploratory Factor Analysis10V1V2V3V4Factor 1

Factor 1

Exploratory Factor AnalysisFactor Loadings:

Measure the relationship between the items and the factors.

Factor loadings can be interpreted like correlation coefficients;ranging between -1.0 and +1.0.

The closer the value is to 1.0,positive or negative, the stronger the relationship between the factor and the item.

Loadings can be both positiveor negative.11Two statistics on the SPSS output allow you to look at some of the basic assumptions.Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy, and Bartlett's Test of SphericityKaiser-Meyer-Olkin Measure of Sampling Adequacy generally indicates whether or not the variables are able to be grouped into a smaller set of underlying factors. That is, will data factor well???KMO varies from 0 to 1 and should be .60 or higher to proceed (can us .50 more lenient cut-off)High values (close to 1.0) generally indicate that a factor analysis may be useful with your data. If the value is less than .50, the results of the factor analysis probably won't be very useful.

Tests for Basic Assumptions

12Kaiser-Meyer-Olkin (KMO)Marvelous - - - - - - .90sMeritorious - - - - - .80sMiddling - - - - - - - .70sMediocre - - - - - - - .60sMiserable - - - - - - .50sUnacceptable - - - below .50

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KMO Statistics: Interpreting the Output

In this example, the data support the use of factor analysis and suggest that the data may be grouped into a smaller set of underlying factors.

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Eigenvalues greater than 115Criteria For Retention Of FactorsEigenvalue greater than 1Single variable has variance equal to 1Plot of total variance - Scree plotGradual trailing off of variance accounted for is called the scree.Note cumulative % of variance of rotated factors

16Interpretation of Rotated MatrixLoadings of .40 or higher

Name each factor based on 3 or 4 variables with highest loadings.

Do not expect perfect conceptual fit of all variables.17Loading size based on sample (from Hair et al 2010 Table 3-2)Significant Factor Loadings based on Sample SizeSample SizeSufficient Factor Loading500.75600.70700.65850.601000.551200.501500.452000.402500.353500.30What else?How do you know when the factor structure is good?When it makes sense and has a (relatively) simple and clean structure.Total Variance Explained > .60How do you interpret factors?Good question, that is where the true art of this comes in.19Why EFA?20?Why EFA?21