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FACTOR & MULTIVARIATE ANALYSES.
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Describes & compares theories & techniques of two approaches to analyzing research data.... More...
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Paper Abstract:
Describes & compares theories & techniques of two approaches to analyzing research data.
Paper Introduction:
FACTOR ANALYSIS AND MULTIVARIATE ANALYSIS
Introduction
This research presents an overview of factor analysis and multivariate analysis procedures. Additionally, the advantages and disadvantages of each set of procedure are identified.
Factor Analysis
Many research studies generate vast quantities of data. These data more often than not are multidimensional and are characterized by multicollinearity (Summers, Peters, and Armstrong, 1993, p. 555). In most instances, if the data are to be used effectively, it is necessary to reduce the number of explanatory variables to more manageable proportions.
Factor analysis is a general descriptor for a group of specific computational procedures (Emory, 1992, p. 559). Each of the pro
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Engleman, J. Special Applications of Multivariate Analysis For accuracy and power, multiple regression analysis depends upon alinear and additive relationship between independent and dependentvariables (Mallios, 1989, pp. Oliva. The main characteristic of the principal factormethod is that each factor accounts for the maximum possible amount of thevariance of the variables being factored. 2. Multivariateanalysis requires a researcher to consider fully the expectations of theresearch problem before undertaking a study. In mostsuch instances, however, some variant of multivariate analysis will beappropriate. The initial step involved in factor analysis is the construction of amatrix of correlation coefficients between all of the variables involved(Emory, 1992, p. Themaximum likelihood method of factor analysis is a procedure that obtainsthe best estimates of factor loadings from information provided by thecorrelation matrix, and is based on an assumption that the variable isexplained by the designated number of factors. Multivariate Analysis Multivariate analysis procedures includes those techniques that focuson the structure of simultaneous relationships among three or morevariables (Emory, 1992, p. Patterson. (1994). Statistical modeling: Applications in contemporary issues. In the common factor model, variables are estimated fromthe common factors by multiplying each factor by the appropriate weight,and summing across factors, common factors correlate zero with uniquefactors, unique factors correlate zero with one another, and all factorshave zero means and standard deviations of one. Through principal component analysis, the initial setof variables is transformed into a new set of composite variables, orprincipal components, which are referred to as factors. Factor analysis is a statistical procedure with data-reductioncapabilities that is used to determine the underlying pattern ofrelationships among a set of variables or conditions which may be taken assource variables, accounting for the observed interrelations in the data(Emory, 1992, p. These datamore often than not are multidimensional and are characterized bymulticollinearity (Summers, Peters, and Armstrong, 1993, p. 612-632). In mostinstances, if the data are to be used effectively, it is necessary toreduce the number of explanatory variables to more manageable proportions. Factor analytic techniques may be grouped into principal componentprocedures, and maximum likelihood procedures (Emory, 1992, p. Factor Analysis Many research studies generate vast quantities of data. FACTOR ANALYSIS AND MULTIVARIATE ANALYSIS Introduction This research presents an overview of factor analysis and multivariateanalysis procedures. I. (4th ed.). The interpretation of factor loadings is a largely subjective process(Emory, 1992, p. 555). 554). 577). Sampson. Frane, M. The second step requires the construction of a newset of variables, on the basis of the relationships identified in thematrix of correlations. The problem with the full component model is the mass of data andties required for its execution. The most frequently used of theseprocedures is principal component analysis (Frane, Jennrich, and Sampson,1994, pp. There are three instances wherein multivariate models of factoranalysis may not provide the best representation of the factor and variablerelationships (Emory, 1992, p. (1992). Although the multiplicative model is not linear in character,the character can be made to be linear through logit transformation. The choice among these techniquesdepends in part on the focus of the statistical analysis--dependence orindependence. (1993). J., M. It often represents an impracticalapproach to a solution to a problem. 555). 576). The full component model is based on the perfect calculation of thevariables from the components, while the common factor model also considerssources of variance which may not be attributable to common factors. A dichotomous variable is one wherein the classifications aremutually exclusive, such as the female and males classifications of genderas a variable. 1 8-11 ). Statistical methods for business and economics. Belmont, California" Wadsworth Publishing Company. Homewood, Illinois: Richard D. Principal componentprocedures are developed within the framework of the multivariate linearmodel. This methodextracts the maximum amount of variance possible by a given number offactors. Ames, Iowa: Iowa State University Press.Pfaffenberger, Roger C., & James H. If,however, the underlying bivariate relationship of a dichotomous variablecan be expected to take a known form, it is frequently possible to restatethe values of the variable to cause them to become linear. The mostfrequently used method used to make such a transformation of variablevalues is the log transformation. 552). Additionally, multivariateanalysis can identify causal variables relationships as opposed to simplyidentifying the existence of relationships. Choosing Multivariate or Factor Analysis When confronted with a mass of unrefined data, a researcher may noalternative other than factor analysis (Kaufman and Oliva, 1994, pp. There are two basic types of factor analysis, although there are anumber of different factor analysis procedures (Emory, 1992, p. Ineach instance--full component and common factor, the models may be furthersubdivided on the basis of the correlation or absence thereof of thefactors. Problems arise with respect tomultiple regression analysis, however, when a dependent variable isdichotomous. 879-88 ; Summers, Peters, and Armstrong, 1993, pp. 559). Even when it is essential to use factor analysis, however, the useof the multivariate variants of the procedure will strengthen the outcomes. 58 -599). 2 6-221). 58 ). A. In Dixon, W. Causal wins over casual in research. Academy of Management Journal, 37(1), 2 6-221.Mallios, William S. Factor analysis. Hill, R. Berkeley, California: University of California Press, pp. Thistransformation is performed by determining the best linear combination ofvariables which accounts for the total variance in the data set (Frane,Jennrich, and Sampson, 1994, pp. Brown, L. Thetwo basic types are R type analysis which involves the correlation of pairsof scale items, and Q type analysis which involves the correlation of pairsof individuals. When conditions do not demand the use of factor analysis, however, the useof multivariate analysis is preferable (Cook, 1992, pp. Irwin, Inc.Frane, J., Jennrich, R., & B. (1993). This method may be used with either the full component model orthe common factor model. Factor analysis attempts to summarize many variables in to afew factors. Additionally, the advantages and disadvantages ofeach set of procedure are identified. Basic statistics in business and economics. W. (5th ed.). Theapplication of the logit regression procedure is most appropriate formultivariate analysis. William. Irwin, Inc.Summers, George W., Peters, William S., & Armstrong, Charles P. Multivariate catastrophe model estimation. The assumptions required for the fullcomponents models are that the variables may be calculated from the factorsby multiplying each factor by the appropriate weight, and then summingacross all factors, and all factors have means of zero and standarddeviations of one. The full component model produces exact relationships (Emory, 1992, p.575). B. Jennrich, & J. 559). Nevertheless, there are instances wherefactor analysis of any type may be neither desirable nor feasible. Research methods. (1989). 3. The three general objectives of factoranalysis, as follows: 1. Homewood, Illinois: Richard D. 58 -599). (6th ed.). Journal of Advertising Research, 32(5), 7-8.Emory, C. Multivariate tests of independence includemultidimensional scaling, latent structure analysis, latent class analysis,cluster analysis, and two variants of factor analysis. Multivariate Variants of Factor Analysis There are several variants of the multivariate model of factoranalysis; however, these variants may be grouped into two principal classes--the full component model, and the common factor model (Emory, 1992, p.565). The second problem that arises in relation to regression analysis withrespect to dichotomous dependent variables is that the relationship betweenthe independent and dependent variables is not additive (Mallios, 1989, pp.1 8-11 ) A multiplicative model is more appropriate for use with suchvariables. (1992, September-October). BMDP statistical software manual. 581). These situations are whererelationships are nonlinear, where the relationship between the variableand the factor is not stable through all levels of the factor, and wherethe relationships of several factors to a single variable are virtuallyinterchangeable. In the common factor model, the factors are divided into two groups:the common factors themselves which consist of those factors whichcontribute to two or more of the variables; and non-common factors whichare summarized into what is called a unique factor that contains all of theremaining scores necessary to complete the prediction of a variable (Emory,1992, p. With a dichotomous variable such as gender, there is no way totransform the values to attain a linear character. (1994). Multivariate tests of dependence include multipleregression, discriminate analysis, canonical analysis, multipleclassification analysis, automatic interaction detection, and multivariateanalysis of variance. 57 ). In such instances, aspecial regression equation employing a dummy variable may be used or non-parametric statistical procedures may be used (Pfaffenberger and Patterson,1993, pp. ReferencesCook, William A. The first problem that arises in relation to regression analysis withrespect to dichotomous dependent variables is that the relationship betweenthe independent and dependent variables is non-linear (Mallion, 1989, pp.1 8-11 ). Toporek. 7-8). Each of the proceduresincluded in the group, however, are intended to reduce a large number ofmeasures to a smaller number which provides a more efficient and powerfulmeasure of the same thing. Factor loadings are the coefficients of factorsidentified in factor analysis, and are used as measures of the degree ofthe relationships between factors and variables. Factor analysis seeks to interpret each factor identifiedaccording the variables included in the factor. Within the variants of the multivariate model of factor analysis,any scores given weights and subsequently added together are defined asfactors of the resulting variables. 58O-599.Kaufman, Ralph G., & Terence A. There is a wide variety of mulitvariateprocedures available to the researcher. Factor analysis is a general descriptor for a group of specificcomputational procedures (Emory, 1992, p. The most widely used method of decomposition to identify factormatrices is principal factor analysis (Emory, 1992, p. The primary purpose of factoranalysis, thus, is exploration; an exploratory process to identifypotentially fruitful areas of research. Thus, when the interpretation of factor loadingscommences, factor analysis ceases to be a sophisticated mathematicalprocedure, and becomes, instead, an interpretative art. Factor analysis studies the correlations of a large numberof variables by clustering those variables into factors in a way that thevariables included in each factor are highly correlated. These weights are referred to asfactor coefficients, or factor loadings. Multivariate analysis, therefore, need not be an alternative to factoranalysis because two variants of factor analysis are multivariate incharacter (Emory, 1992, pp. 554). There are a number of procedures by which thesecond step may be accomplished. Factor meaningsmay not be calculated mathematically.
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