research methology -factor analyses

FACTOR ANALYSESFACTOR ANALYSESWith InWith In

Research MethologyResearch Methology

ByBy

NEERAV SHIVHARENEERAV SHIVHARE

Factor AnalysisFactor Analysis Technique that serves to combine questions or Technique that serves to combine questions or

variables to create new factorsvariables to create new factors

PurposePurpose

To identify underlying constructs in the dataTo identify underlying constructs in the data

To reduce the number of variables to a more To reduce the number of variables to a more manageable setmanageable set

Factor Analysis (Contd.)Factor Analysis (Contd.)

MethodologyMethodology

Two commonly employed factor analytic proceduresTwo commonly employed factor analytic procedures

Principal Component AnalysisPrincipal Component Analysis Used when the need is to summarize information in a Used when the need is to summarize information in a

larger set of variables to a smaller set of factorslarger set of variables to a smaller set of factors

Common Factor AnalysisCommon Factor Analysis Used to uncover underlying dimensions surrounding Used to uncover underlying dimensions surrounding

the original variablesthe original variables

Factor Analysis (Contd.)Factor Analysis (Contd.)Principal Component AnalysisPrincipal Component Analysis The objective of factor analysis is to represent each of these variables as a The objective of factor analysis is to represent each of these variables as a

linear combination of a smaller set of factorslinear combination of a smaller set of factors This can be represented asThis can be represented as

XX11 = I = I1111FF11 + I + I1212FF22 + e + e11

XX22 = I = I2121FF11 + I + I2222FF22 + e + e22..

..

XXnn = i = in1n1ff11 + i + in2n2ff22 + e + enn

WhereWhere

XX11, ... x, ... xnn represent standardized scores represent standardized scores

FF11,F,F22 are the two standardized factor scores are the two standardized factor scores

II1111, i, i1212,....I,....I5252 are factor loadings are factor loadings

EE11,...E,...E55 are error variances are error variances

Factor Analysis (Contd.)Factor Analysis (Contd.)FactorFactor A variable or construct that is not directly observable A variable or construct that is not directly observable

but needs to be inferred from the input variablesbut needs to be inferred from the input variables

Eigenvalue CriteriaEigenvalue Criteria Represents the amount of variance in the original Represents the amount of variance in the original

variables that is associated with a factorvariables that is associated with a factor

Scree Plot CriteriaScree Plot Criteria A plot of the eigenvalues against the number of factors, A plot of the eigenvalues against the number of factors,

in order of extraction.in order of extraction.


Percentage of Variance CriteriaPercentage of Variance Criteria The number of factors extracted is determined so that The number of factors extracted is determined so that

the cumulative percentage of variance extracted by the the cumulative percentage of variance extracted by the factors reaches a satisfactory levelfactors reaches a satisfactory level

Significance Test CriteriaSignificance Test Criteria Statistical significance of the separate eigenvalues is Statistical significance of the separate eigenvalues is

determined, and only those factors that are statistically determined, and only those factors that are statistically significant are retainedsignificant are retained


Factor ScoresFactor Scores Values of each factor underlying the variablesValues of each factor underlying the variables

Factor LoadingsFactor Loadings Correlations between the factors and the Correlations between the factors and the

original variablesoriginal variables


CommunalityCommunality The amount of the variable variance that is explained The amount of the variable variance that is explained

by the factorby the factor

Factor RotationFactor Rotation Factor analysis can generate several solutions for any Factor analysis can generate several solutions for any

data set. Each solution is termed a particular factor data set. Each solution is termed a particular factor rotation and is generated by a particular factor rotation rotation and is generated by a particular factor rotation schemescheme

Factor Analysis (Contd.)Factor Analysis (Contd.)How Many Factors?How Many Factors? Rule of ThumbRule of Thumb

All included factors (prior to rotation) must explain at least as All included factors (prior to rotation) must explain at least as much variance as an "average variable"much variance as an "average variable"

Eigenvalues CriteriaEigenvalues Criteria Eigenvalue represents the amount of variance in the original Eigenvalue represents the amount of variance in the original

variables associated with a factorvariables associated with a factor

Sum of the square of the factor loadings of each variable on a Sum of the square of the factor loadings of each variable on a factor represents the eigen valuefactor represents the eigen value

Only factors with eigenvalues greater than 1.0 are retainedOnly factors with eigenvalues greater than 1.0 are retained


Scree Plot CriteriaScree Plot Criteria Plot of the eigenvalues against the number of factors in Plot of the eigenvalues against the number of factors in

order of extractionorder of extraction The shape of the plot determines the number of factorsThe shape of the plot determines the number of factors

Percentage of Variance CriteriaPercentage of Variance Criteria Number of factors extracted is determined when the Number of factors extracted is determined when the

cumulative percentage of variance extracted by the cumulative percentage of variance extracted by the factors reaches a satisfactory levelfactors reaches a satisfactory level


Common Factor AnalysisCommon Factor Analysis The factor extraction procedure is similar to that of The factor extraction procedure is similar to that of

principal component analysis except for the input principal component analysis except for the input correlation matrixcorrelation matrix

Communalities or shared variance is inserted in the Communalities or shared variance is inserted in the diagonal instead of unities in the original variable diagonal instead of unities in the original variable correlation matrixcorrelation matrix

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Cluster AnalysisCluster Analysis Technique that serves to combine objects to create new Technique that serves to combine objects to create new

groupsgroups Used to group variables, objects or peopleUsed to group variables, objects or people The input is any valid measure of correlations between The input is any valid measure of correlations between

objects, such asobjects, such as CorrelationsCorrelations Distance measures (Euclidean distance)Distance measures (Euclidean distance) Association coefficientsAssociation coefficients

Also, the number of clusters or the level of clustering can Also, the number of clusters or the level of clustering can be inputbe input


Cluster Analysis (Contd.)Cluster Analysis (Contd.)Hierarchical ClusteringHierarchical Clustering Can start with all objects in one cluster and divide Can start with all objects in one cluster and divide

and subdivide them until all objects are in their own and subdivide them until all objects are in their own single-object clustersingle-object cluster

Non-hierarchical ApproachNon-hierarchical Approach

Permits objects to leave one cluster and join another Permits objects to leave one cluster and join another as clusters are being formedas clusters are being formed


Hierarchical ClusteringHierarchical ClusteringSingle LinkageSingle Linkage Clustering criterion based on the shortest distanceClustering criterion based on the shortest distance

Complete LinkageComplete Linkage Clustering criterion based on the longest distanceClustering criterion based on the longest distance

Average LinkageAverage Linkage Clustering criterion based on the average distanceClustering criterion based on the average distance


Hierarchical Clustering (Contd.)Hierarchical Clustering (Contd.)

Ward's MethodWard's Method Based on the loss of information resulting from Based on the loss of information resulting from

grouping of the objects into clusters (minimize within grouping of the objects into clusters (minimize within cluster variation)cluster variation)

Centroid MethodCentroid Method Based on the distance between the group centroids (the Based on the distance between the group centroids (the

centroid is the point whose coordinates are the means centroid is the point whose coordinates are the means of all the observations in the cluster)of all the observations in the cluster)


Non-hierarchical ClusteringNon-hierarchical Clustering

Sequential ThresholdSequential Threshold Cluster center is selected and all objects within a prespecified Cluster center is selected and all objects within a prespecified

threshold is groupedthreshold is grouped

Parallel ThresholdParallel Threshold Several cluster centers are selected and objects within threshold Several cluster centers are selected and objects within threshold

level are assigned to the nearest centerlevel are assigned to the nearest center

OptimizingOptimizing Modifies the other two methods in that the objects can be later Modifies the other two methods in that the objects can be later

reassigned to clusters on the basis of optimizing some overall reassigned to clusters on the basis of optimizing some overall criterion measurecriterion measure

Number of ClustersNumber of ClustersDetermination of the appropriate number of clusters can be done Determination of the appropriate number of clusters can be done in one of the four waysin one of the four ways

The number of clusters can be specified by the analyst in The number of clusters can be specified by the analyst in advanceadvance

The levels of clustering can be specified by the analyst in The levels of clustering can be specified by the analyst in advanceadvance

The number of clusters can be determined from the pattern of The number of clusters can be determined from the pattern of clusters generated in the programclusters generated in the program

The ratio of within-group variance and the between-group The ratio of within-group variance and the between-group variance an be plotted against the number of clusters. The point variance an be plotted against the number of clusters. The point at which a sharp bend occurs indicates the number of clustersat which a sharp bend occurs indicates the number of clusters

THANK YOUTHANK YOU

SPECIAL THANKS TO SPECIAL THANKS TO

Prof.Pooja JainProf.Pooja Jain

FOR CORAL SUPPORT.FOR CORAL SUPPORT.

THANK YOU THANK YOU

research methology -factor analyses

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