# Factor Scores This function computes factor scores by various methods. The function will acceptan an object of class `faMain` or, alternatively, user-input factor pattern (i.e., `Loadings`) and factor correlation (`Phi`) matrices. ```r faScores( X = NULL, faMainObject = NULL, Loadings = NULL, Phi = NULL, Method = "Thurstone" ) ``` ## Arguments - `X`: (Matrix) An N `x` variables data matrix. If X is a matrix of raw scores then `faScores` will convert the data to z scores. - `faMainObject`: (Object of class faMain ) The returned object from a call to faMain . Default = NULL - `Loadings`: (Matrix) A factor pattern matrix. Default = NULL. - `Phi`: (Matrix) A factor correlation matrix. Default = NULL. If a factor pattern is entered via the Loadings argument but Phi = NULL the program will set `Phi` to an identity matrix. - `Method`: (Character) Factor scoring method. Defaults to the Thurstone or regression based method. Available options include: * Thurstone Generates regression based factor score estimates. * Bartlett Generates Bartlett method factor score estimates. * tenBerge Generates factor score estimates with correlations identical to that found in Phi . * Anderson The Anderson Rubin method. Generates uncorrelated factor score estimates. This method is only appropriate for orthogonal factor models. * Harman Generates estimated factor scores by Harman's idealized variables method. * PCA Returns unrotated principal component scores. ## Returns * fscores A matrix om common factor score estimates. * Method The method used to create the factor score estimates. * W The factor scoring coefficient matrix. * Z A matrix of standardized data used to create the estimated factor scores. ## Details faScores can be used to calculate estimated factor scores by various methods. In general, to calculate score estimates, users must input a data matrix X and either (a) an object of class faMain or (b) a factor loadings matrix, Loadings and an optional (for oblique models) factor correlation matrix Phi . The one exception to this rule concerns scores for the principal components model. To calculate unrotated PCA scores (i.e., when Method = "PCA" ) users need only enter a data matrix, X . ## Examples ```r lambda.Pop <- matrix(c(.41, .00, .00, .45, .00, .00, .53, .00, .00, .00, .66, .00, .00, .38, .00, .00, .66, .00, .00, .00, .68, .00, .00, .56, .00, .00, .55), nrow = 9, ncol = 3, byrow = TRUE) NVar <- nrow(lambda.Pop) NFac <- 3 ## Factor correlation matrix Phi.Pop <- matrix(.50, nrow = 3, ncol = 3) diag(Phi.Pop) <- 1 #Model-implied correlation matrix R <- lambda.Pop %*% Phi.Pop %*% t(lambda.Pop) diag(R) <- 1 #Generate population data to perfectly reproduce pop R Out <- simFA( Model = list(Model = "oblique"), Loadings = list(FacPattern = lambda.Pop), Phi = list(PhiType = "user", UserPhi = Phi.Pop), FactorScores = list(FS = TRUE, CFSeed = 1, SFSeed = 2, EFSeed = 3, Population = TRUE, NFacScores = 100), Seed = 1) PopFactorScores <- Out$Scores$FactorScores X <- PopObservedScores <- Out$Scores$ObservedScores fout <- faMain(X = X, numFactors = 3, facMethod = "fals", rotate = "oblimin") print( round(fout$loadings, 2) ) print( round(fout$Phi,2) ) fload <- fout$loadings Phi <- fout$Phi fsOut <- faScores(X = X, faMainObject = fout, Method = "Thurstone") fscores <- fsOut$fscores print( round(cor(fscores), 2 )) print(round(Phi,2)) CommonFS <- PopFactorScores[,1:NFac] SpecificFS <-PopFactorScores[ ,(NFac+1):(NFac+NVar)] ErrorFS <- PopFactorScores[ , (NFac + NVar + 1):(NFac + 2*NVar) ] print( cor(fscores, CommonFS) ) ``` ## References * Bartlett, M. S. (1937). The statistical conception of mental factors.British Journal of Psychology, 28,97-104. * Grice, J. (2001). Computing and evaluating factor scores. Psychological Methods, 6(4), 430-450. * Harman, H. H. (1976). Modern factor analysis. University of Chicago press. * McDonald, R. P. and Burr, E. J. (1967). A Comparison of Four Methods of Constructing Factor Scores. Psychometrika, 32, 381-401. * Ten Berge, J. M. F., Krijnen, W. P., Wansbeek, T., and Shapiro, A. (1999). Some new results on correlation-preserving factor scores prediction methods. Linear Algebra and its Applications, 289(1-3), 311-318. * Tucker, L. (1971). Relations of factor score estimates to their use. Psychometrika, 36, 427-436. ## See Also Other Factor Analysis Routines: `BiFAD()`, `Box26`, `GenerateBoxData()`, `Ledermann()`, `SLi()`, `SchmidLeiman()`, `faAlign()`, `faEKC()`, `faIB()`, `faLocalMin()`, `faMB()`, `faMain()`, `faSort()`, `faStandardize()`, `faX()`, `fals()`, `fapa()`, `fareg()`, `fsIndeterminacy()`, `orderFactors()`, `print.faMB()`, `print.faMain()`, `promaxQ()`, `summary.faMB()`, `summary.faMain()` ## Author(s) Niels Waller

faScores function