Synopsis:
Ict: Data: (*)data_mining: Factor analysis:
42495745.pdf
63 4. 1 Principal components analysis...63 4. 2 Factor analysis...69 4. 3 Cronbach Coefficient Alpha...
89 6. 1 Weights based on principal components analysis or factor analysis...89 6. 2 Data envelopment analysis (DEA...
Maximisation EU European union EW Equal weighting FA Factor analysis GCI Growth Competitiveness Index GDP Gross domestic product GME Geometric aggregation HDI Human Development Index ICT Information
Factor analysis (FA) is similar to PCA, but is based on a particular statistical model. An alternative way to investigate the degree of correlation among a set of variables is to use the Cronbach coefficient alpha (c-alpha),
and weaknesses of multivariate analysis Strengths Weaknesses Principal Components/Factor analysis Can summarise a set of individual indicators while preserving the maximum possible proportion of the total variation in the original data set.
A number of weighting techniques exist (Table 4). Some are derived from statistical models, such as factor analysis, data envelopment analysis and unobserved components models (UCM
and cons. Statistical models such as principal components analysis (PCA) or factor analysis (FA) could be used to group individual indicators according to their degree of correlation.
It can be used for a broad range of problems, e g. variance component estimation or factor analysis.
and factor analysis, see Vermunt & Magidson 2005). 4. 1. Principal components analysis The objective is to explain the variance of the observed data through a few linear combinations of the original data. 15
Although social scientists may be attracted to factor analysis as a way of exploring data whose structure is unknown,
Principal component factor analysis (PFA), which is the most common variant of FA, is a linear procedure.
Note, however, that a variant of factor analysis, maximum likelihood factor analysis, does assume multivariate normality. The smaller the sample size, the more important it is to screen data for normality.
Moreover, as factor analysis is based on correlation (or sometimes covariance), both correlation and covariance will be attenuated when variables come from different underlying distributions (e g.,
, a normal vs. a bimodal variable will correlate less than 1. 0 even when both series are ordered perfectly co).
Factor analysis cannot create valid dimensions (factors) if none exist in the input data. In such cases, factors generated by the factor analysis algorithm will not be comprehensible.
Likewise, the inclusion of multiple definitionally-similar individual indicators representing essentially the same data will lead to tautological results.
but applying factor analysis to a correlation matrix with only low intercorrelations will require nearly as many factors as there are original variables,
thereby defeating the data reduction purposes of factor analysis. On the other hand, too high intercorrelations may indicate a multicollinearity problem
or otherwise eliminated prior to factor analysis. Notice also that PCA and Factor analysis (as well as Cronbach's alpha) assume uncorrelated measurement errors.
a) The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy is a statistic for comparing the magnitudes of the observed correlation coefficients to the magnitudes of the partial correlation coefficients.
if distinct factors are expected to emerge from factor analysis (Hutcheson & Sofroniou, 1999). A KMO statistic is computed for each individual indicator,
or higher to proceed with factor analysis (Kaiser & Rice, 1974), though realistically it should exceed 0. 80
and of how the interpretation of the components might be improved are addressed in the following section on Factor analysis. 4. 2. Factor analysis Factor analysis (FA) is similar to PCA.
Principal components factor analysis is preferred most in the development of composite indicators, e g. in the Product Market Regulation Index (Nicoletti et al.
This conclusion does not depend on the factor analysis method, as it has been confirmed by different methods (centroid method, principal axis method).
Note also that the factor analysis in the previous section had indicated university as the individual indicator that shared the least amount of common variance with the other individual indicators.
Although both factor analysis and the Cronbach coefficient alpha are based on correlations among individual indicators, their conceptual framework is different.
A method that combines k-means cluster analysis with aspects of Factor analysis and PCA is offered by Vichi & Kiers (2001.
unlike factor analysis. This technique finds scores for the rows and columns on a small number of dimensions which account for the greatest proportion of the 2 for association between the rows and columns,
However, while conventional factor analysis determines which variables cluster together (parametric approach), correspondence analysis determines which category values are close together (nonparametric approach).
When the dependent variable has more than two categories then it is a case of multiple Discriminant analysis (or also Discriminant Factor analysis or Canonical Discriminant analysis), e g. to discriminate countries on the basis of employment patterns in nine industries (predictors.
There are also conceptual similarities with Principal Components and Factor analysis but while PCA maximises the variance in all the variables HANDBOOK ON CONSTRUCTING COMPOSITE INDICATORS:
AND AGGREGATION WEIGHTING METHODS 6. 1. Weights based on principal components analysis or factor analysis Principal components analysis,
and more specifically factor analysis, groups together individual indicators which are collinear to form a composite indicator that captures as much as possible of the information common to individual indicators.
For a factor analysis only a subset of principal components is retained (m i e. those that account for the largest amount of the variance.
Rotation is a standard step in factor analysis it changes the factor loadings and hence the interpretation of the factors,
when dealing with environmental issues. 6. 9. Performance of the different weighting methods The weights for the TAI example are calculated using different weighting methods equal weighting (EW), factor analysis (FA), budget allocation (BAP
TAI weights based on different methods Equal weighting (EW), factor analysis (FA), budget allocation (BAP), analytic hierarchy process (AHP) Method Weights for the indicators (fixed for all countries) Patents Royalties Internet Tech exports Telephones Electricity Schooling University EW 0
In the 1970s factor analysis and latent variables enriched path analysis giving rise to the field of Structural Equation Modelling (SEM, see Kline, 1998.
Measurement techniques such as factor analysis and item response theory are used to relate latent variables to the observed indicators (the measurement model),
Similarly, Nicoletti and others make use of factor analysis in the analysis of, for example, product market regulation in OECD countries (Nicoletti et al.,
. and Yarnold P. R. 1995), Principal components analysis and exploratory and confirmatory factor analysis. In Grimm and Yarnold, Reading and understanding multivariate analysis.
in the 20th century, Journal of Computational and Applied mathematics, Vol. 123 (1-2). Gorsuch R. L. 1983), Factor analysis.
John Wiley & Sons, Inc. Hatcher L. 1994), A step-by-step approach to using the SAS system for factor analysis and structural equation modeling.
Kim, J.,Mueller, C. W. 1978), Factor analysis: Statistical methods and practical issues, Sage Publications, Beverly hills, California, pp. 88.
Covers confirmatory factor analysis using SEM techniques. See esp. Ch. 7. Knapp, T. R.,Swoyer, V. H. 1967), Some empirical results concerning the power of Bartlett's test of the significance of a correlation matrix.
Factor analysis as a statistical method, London: Butterworth and Co. 146 HANDBOOK ON CONSTRUCTING COMPOSITE INDICATORS:
METHODOLOGY AND USER GUIDE ISBN 978-92-64-04345-9-OECD 2008 Vermunt J. K. and Magidson J. 2005), Factor analysis with categorical indicators:
Entrepneurial Orientation and Network Ties_ innovative performance of SMEs in an emerging-economy manufacturing cluster.pdf
We derived multi-item variables using factor analysis, testing for their reliability and validity. We confirmed the reliability of these indicators by computing the Cronbach-alpha coefficient,
Entrrepreneurial and Innovative Behaviour in Spanish SMEs_ essays on .pdf
a single factor will emerge from the factor analysis or the majority of the covariance will be concentrated in one of the factors (Podsakoff et al.,
We applied the exploratory factor analysis to assess dimensionality and validity. Statisticians KMO of 0. 94 and Bartlett's sphericity test (p<.01) support the idea of the validity of the implementation of factorial analysis and allow us to check
we carried out a confirmatory factor analysis highlighting the existence of a multidimensional construct (see the path diagram for this construct as well as,
We applied the exploratory factor analysis to assess dimensionality and validity. Statisticians KMO of 0. 94 and Bartlett's sphericity test (p<0. 01) support the idea of the validity of the implementation of factorial analysis and allow us to check
we carried out a confirmatory factor analysis highlighting the existence of a multidimensional construct (see the path diagram for this construct,
we carried out an exploratory factor analysis to verify whether we could treat the information as a single construct.
SEM can be understood as a combination of confirmatory factor analysis (CFA) and multiple regression (Schreiber et al. 2006).
Reporting structural equation modeling and confirmatory factor analysis results: a review. The Journal of Education Research, 99,323-337.
Entrepreneurship Theory and Practice, 35,293-317.156 157 APPENDIX Appendix 1. Confirmatory factor analysis EO Model fit EO construct Recommended level CFA level CFI
EUR 21682 EN.pdf
. 1. 1 Principal Components Analysis 17 3. 1. 2 Factor analysis 21 3. 1. 3 Cronbach Coefficient Alpha 26 3. 2
and factor analysis 56 6. 1. 2 Data envelopment analysis and Benefit of the doubt 59 Benefit of the doubt approach 60 6. 1. 3 Regression approach
Factor analysis and Reliability/Item Analysis (e g. Coefficient Cronbach Alpha) can be used to group the information on the indicators.
such as 12 weighting schemes based on statistical models (e g. factor analysis, data envelopment analysis, unobserved components models), or on participatory methods (e g. budget allocation, analytic hierarchy processes).
Factor analysis and Reliability/Item Analysis can be used complementarily to explore whether the different dimensions of the phenomenon are balanced well-from a statistical viewpoint-in the composite indicator.
and how the interpretation of the components might be improved are addressed without further ado in the following section on Factor analysis. 3. 1. 2 Factor analysis Factor analysis (FA) has similar aims to PCA.
Principal components factor analysis is preferred most in the development of composite indicators (see Section 6), e g.
Assumptions in Principal Components Analysis and Factor analysis 1. Enough number of cases. The question of how many cases (or countries) are necessary to do PCA/FA has no scientific answer
Although social scientists may be attracted to factor analysis as a way of exploring data whose structure is unknown,
Principal components factor analysis (PFA), which is the most common variant of FA, is a linear procedure.
Note, however, that a variant of factor analysis, maximum likelihood factor analysis, does assume multivariate normality. The smaller the sample size, the more important it is to screen data for normality.
Moreover, as factor analysis is based on correlation (or sometimes covariance), both correlation and covariance will be attenuated when variables come from different underlying distributions (ex.,
a normal vs. a bimodal variable will correlate less than 1. 0 even when both series are ordered perfectly co).
Factor analysis cannot create valid dimensions (factors) if none exist in the input data. In such cases, factors generated by the factor analysis algorithm will not be comprehensible.
Likewise, the inclusion of multiple definitionally-similar sub-indicators representing essentially the same data will lead to tautological results. 8. Strong intercorrelations are required not mathematically,
but applying factor analysis to a correlation matrix with only low intercorrelations will require for solution nearly as many factors as there are original variables,
thereby defeating the data reduction purposes of factor analysis. On the other hand, too high inter-correlations may indicate a multi-collinearity problem
or otherwise eliminated prior to factor analysis. (a) The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy is a statistics for comparing the magnitudes of the observed correlation coefficients to the magnitudes of the partial correlation coefficients.
if one is to expect distinct factors to emerge from factor analysis (see Hutcheson and Sofroniou, 1999, p. 224).
or higher to proceed with factor analysis (Kaiser and Rice, 1974), though realistically it should exceed 0. 80
Note also, that the factor analysis in the previous section had indicated ENROLMENT as the sub-indicator that shares the least amount of common variance with the other sub-indicators.
Although both factor analysis and the Cronbach coefficient alpha are based on correlations among sub-indicators, their conceptual framework is different. 28 Table 3. 6. Cronbach coefficient alpha results for the 23 countries after deleting one subindicator (standardised values) at-a-time Deleted sub-indicator
Principal component analysis or Factor analysis) that summarize the common information in the data set by detecting non-observable dimensions.
A method that combines k-means cluster analysis with aspects of Factor analysis and PCA is presented by Vichi and Kiers (2001.
including Factor analysis, Coefficient Cronbach Alpha, Cluster analysis, is something of an art, and it is certainly not as objective as most statistical methods.
The advantage of the EM is its broadness (it can be used for a broad range of problems, e g. variance component estimation or factor analysis),
The summary indicators are obtained by means of factor analysis, in which each component of the regulatory framework is weighted according to its contribution to the overall variance in the data.
In this section a number of techniques are presented ranging from weighting schemes based on statistical models (such as factor analysis, data envelopment analysis, unobserved components models),
and factor analysis Principal component analysis (PCA) and more specifically factor analysis (FA)( Section 3) group together sub-indicators that are collinear to form a composite indicator capable of capturing as much of common information of those sub-indicators as possible.
For a factor analysis only a subset of principal components are retained (let's say m), the ones that account for the largest amount of the variance.
Rotation is a standard step in factor analysis, it changes the factor loadings and hence the interpretation of the factors leaving unchanged the analytical solutions obtained ex-ante and ex-post the rotation.
equal weighting (EW), factor analysis (FA), budget allocation (BAL), and analytic hierarchy process (AHP) Patents Royalties Internet Tech exports Telephones Electricity Schooling University EW 0. 13 0. 13 0. 13
and Factor analysis is employed usually as a supplementary method with a view to examine thoroughly the relationships among the subindicators.
Principal components analysis and exploratory and confirmatory factor analysis. In Grimm and Yarnold, Reading and understanding multivariate analysis.
Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4: 272-299.38. Fagerberg J. 2001) Europe at the crossroads:
Factor analysis. Hillsdale, NJ: Lawrence Erlbaum. Orig. ed. 1974.47. Gough C.,Castells, N, . and Funtowicz S.,(1998), Integrated Assessment:
A step-by-step approach to using the SAS system for factor analysis and structural equation modeling. Cary, NC:
Introduction to factor analysis: What it is and how to do it. Thousand Oaks, CA: Sage Publications, Quantitative Applications in the Social sciences Series, No. 13.63.
Factor analysis: Statistical methods and practical issues. Thousand Oaks, CA: Sage Publications, Quantitative Applications in the Social sciences Series, No. 14.64.
Covers confirmatory factor analysis using SEM techniques. See esp. Ch. 7. 77. Koedijk K, . and Kremers J.,(1996), Market opening, regulation and growth in Europe, Economic policy (0) 23.october 78.
Factor analysis as a statistical method. London: Butterworth and Co. 81. Levine, M. S.,(1977. Canonical analysis and factor comparison.
Making sense of factor analysis: The use of factor analysis for instrument development in health care research. Thousand Oaks, CA:
Sage Publications. 109. Pré Consultants (2000) The Eco-indicator 99. A damage oriented method for life cycle impact assessment. http://www. pre. nl/eco-indicator99/ei99-reports. htm 110.
Cited with regard to preference for PFA over PCA in confirmatory factor analysis in SEM. 144. World Economic Forum (2002) Environmental Sustainability Index http://www. ciesin org/indicators/ESI/index. html. 145.
Fueling innovation through information technology in smes.pdf
Analyses Structural equation modeling using LISREL 8. 52 was employed for validation of the scales through confirmatory factor analysis and for hypothesis testing.
For construct validation, a two-phase confirmatory factor analysis approach was conducted, as suggested by Anderson and Gerbing (1988).
Modern Factor analysis. Chicago, IL: University of chicago Press. Hax, A, . and N. Majluf (1991). The Strategy Concept and Process.
The Impact of Innovation in Romanian Small and Medium-Sized Enterprises on Economic Growth Development - Oncoiu.pdf
The constituents of the scoring variables was undertaken a factor analysis, and the resulting factors would the input of a cluster analysis.
The Relationship between innovation, knowledge, performance in family and non-family firms_ an analysis of SMEs.pdf
and factor analysis was used to reduce the number of items in some scales. Hierarchical linear regression analysis was utilized to analyze the relationships between the variables in the final model.
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