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Topic: Factor analysis

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	PA 765: Factor Analysis
		Factor analysis generates a table in which the rows are the observed raw indicator variables and the columns are the factors or latent variables which explain as much of the variance in these variables as possible.
		While factor analysis may demonstrate that a particular model with a given predicted number of latent variables is not inconsistent with the data by this technique, researchers should understand that other models with different numbers of latent variables may also have good fit by SEM techniques.
		Factor scores are coefficients of cases on the factors, whereas factor loadings are coefficients of variables on the factors.
	www2.chass.ncsu.edu /garson/pa765/factor.htm (8455 words)

	Factor Analysis
		Factor analysis was invented nearly 100 years ago by psychologist Charles Spearman, who hypothesized that the enormous variety of tests of mental ability--measures of mathematical skill, vocabulary, other verbal skills, artistic skills, logical reasoning ability, etc.--could all be explained by one underlying "factor" of general intelligence that he called g.
		Factor analysis is different; it is used to study the patterns of relationship among many dependent variables, with the goal of discovering something about the nature of the independent variables that affect them, even though those independent variables were not measured directly.
		Since factor loadings are among the most important pieces of output from a factor analysis, it seems natural to ask about the standard error of a factor loading, so that for instance we might test the significance of the difference between the factor loadings in two samples.
	www.psych.cornell.edu /Darlington/factor.htm (9606 words)

	APA Books (Site not responding. Last check: 2007-11-07)
		This volume presents the important concepts required for implementing two disciplines of factor analysis — exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) with an emphasis on EFA/CFA linkages.
		Variations of factor analysis, such as the factoring of people or time, have great potential to inform psychological research.
		Instructors or students who seek a clear and concise text about factor analysis will find this book to be an invaluable resource.
	www.apa.org /books/4316025.html (213 words)

	Exploratory Factor Analysis
		Factor analysis boils down a correlation matrix into a few major pieces so that the variables within the pieces are more highly correlated with each other than with variables in the other pieces.
		The factors are not observed, and are represented by circles.
		Factor analysis is sometimes called the psychometrician's Rorschach because it's something of an art form where lots of decisions have to be made.
	luna.cas.usf.edu /~mbrannic/files/pmet/factor1.htm (2772 words)

	FACTOR ANALYSIS
		Factor analysis can be applied in order to explore a content area, structure a domain, map unknown concepts, classify or reduce data, illuminate causal nexuses, screen or transform data, define relationships, test hypotheses, formulate theories, control variables, or make inferences.
		Factor analysis thus fulfills some functions of the laboratory and enables the scientist to untangle interrelationships, to separate different sources of variation, and to partial out or control for undesirable influences on the variables of concern.
		Factor analysis is a mathematical tool as is the calculus, and not a statistical technique like the chi-square, the analysis of variance, or sequential analysis.
	www.hawaii.edu /powerkills/UFA.HTM (13832 words)

	Factor Analysis SAS PROC FACTOR (Stat-53)
		Factor analysis is a generic term for a family of statistical techniques concerned with the reduction of a set of observable variables in terms of a small number of latent factors.
		The underlying assumption of factor analysis is that there exists a number of unobserved latent variables (or "factors") that account for the correlations among observed variables, such that if the latent variables are partialled out or held constant, the partial correlations among observed variables all become zero.
		A factor loading or factor structure matrix is a n by m matrix of correlations between the original variables and their factors, where n is the number of variables and m is the number of retained factors.
	www.utexas.edu /cc/docs/stat53.html (5851 words)

	FACTOR ANALYSIS
		Factor analysis is a data reduction technique for identifying the internal structure of a set of variables.
		FACTOR ROTATION: Given a cartesian coordinate system where the axes are the factors and the points are the variables, factor rotation is the process of holding the points constant and moving (rotating) the factor axes.
		The analysis is conducted to express the relationship between the factors that may or may not be orthogonal; rather than arbitrarily constraining the factor solution so that the factors are independent of each other.
	marketing.byu.edu /htmlpages/books/pcmds/FACTOR.html (2811 words)

	Exploratory Factor Analysis
		I recommend this article to those who are just learning about exploratory factor analysis as well as to those who have used it in their research for many years.
		If you wish to restrict the number of factors extracted to a particular number and specify particular patterns of relationship between measured variables and common factors, and this is done a priori (before seeing the data), then the confirmatory procedure is for you.
		Underfactoring is likely to lead to factors that are poorly estimated (poor correspondence between the structure of the true factors and that of the estimated factors), a more serious problem.
	core.ecu.edu /psyc/wuenschk/StatHelp/EFA.htm (1080 words)

	Information Technology Services
		A confirmatory factor analysis differs from exploratory (ordinary) factor analysis in that you specify the structure of three matrices a priori (in advance) of data analysis.
		The three matrices to be specified are 1) the factor loading matrix, 2) the factor intercorrelation matrix, and 3) the unique variance matrix.
		The chief advantage of confirmatory factor analysis is that it allows you to test hypotheses about specific factor structures.
	www.utexas.edu /cc/faqs/stat/sas/sas26.html (472 words)

	Inferring From Data
		Multivariate analysis is a branch of statistics involving the consideration of objects on each of which are observed the values of a number of variables.
		The probability distribution of the statistic upon which the the analysis is based is not dependent upon specific information or assumptions about the population(s) which the sample(s) are drawn, but only on general assumptions, such as a continuous and/or symmetric population distribution.
		By this definition, the distinction of nonparametric is accorded either because of the level of measurement used or required for the analysis, as in types 1 through 3; the type of inference, as in type 4 or the generality of the assumptions made about the population distribution, as in type 5.
	home.ubalt.edu /ntsbarsh/stat-data/Topics.htm (16064 words)

	Binary Data Factor Analysis and Multidimensional Latent Trait/Item Response Theory (IRT) Models
		Factor analysis of the tetrachoric correlations between all item pairs (Knol & Berger, 1991).
		This is potentially useful when (a) the assumption of latent multivariate normality is inappropriate; or (b) one wishes to consider the group (latent class) structure of cases as well as data dimensionality.
		Following are programs I know of for factor analysis of binary data and/or multidimensional latent trait modeling.
	ourworld.compuserve.com /homepages/jsuebersax/binary.htm (883 words)

	Exploratory Factor Analysis: A book manuscript by Ledyard
		We did not complete planned material on confirmatory factor analysis and a variety of advanced topics.
		In addition, the manuscript is incomplete in that there is no index or list of references, and appendices that are mentioned in the text are not available.
		Nevertheless, the completed material does provide an extensive technical treatment of the factor analysis model as well as methods for conducting exploratory factor analysis.
	www.unc.edu /~rcm/book/factornew.htm (224 words)

	Estimating a Latent Trait Model by Factor Analysis of Tetrachoric Correlations
		It is also useful--perhaps one of the best methods--for binary data factor analysis.
		If one uses iterated principal factor analysis or unweighted least-squares estimation, then the smoothing procedure is not required.
		The PROC FACTOR step requests estimation by the "PRINIT" (iterated principal factor analysis or IPFA) method, a two-factor model, varimax rotation, and a scree test of eigenvalues.
	ourworld.compuserve.com /homepages/jsuebersax/irt.htm (3247 words)

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