# Generate a Factor Structure Matrix The `generateStructure` function returns a **mjc** factor structure matrix. The number of variables per major factor **pmjc** is equal for each factor. The argument **pmjc** must be divisible by **nVar**. The arguments are strongly inspired from Zick and Velicer (1986, p. 435-436) methodology. ```r generateStructure(var, mjc, pmjc, loadings, unique) ``` ## Arguments - `var`: numeric: number of variables - `mjc`: numeric: number of major factors (factors with practical significance) - `pmjc`: numeric: number of variables that load significantly on each major factor - `loadings`: numeric: loadings on the significant variables on each major factor - `unique`: numeric: loadings on the non significant variables on each major factor ## Returns values numeric matrix: factor structure ## Examples ```r # ....................................................... # Example inspired from Zwick and Velicer (1986, table 2, p. 437) ## ................................................................... unique=0.2; loadings=0.5 zwick1 <- generateStructure(var=36, mjc=6, pmjc= 6, loadings=loadings, unique=unique) zwick2 <- generateStructure(var=36, mjc=3, pmjc=12, loadings=loadings, unique=unique) zwick3 <- generateStructure(var=72, mjc=9, pmjc= 8, loadings=loadings, unique=unique) zwick4 <- generateStructure(var=72, mjc=6, pmjc=12, loadings=loadings, unique=unique) sat=0.8 ## ................................................................... zwick5 <- generateStructure(var=36, mjc=6, pmjc= 6, loadings=loadings, unique=unique) zwick6 <- generateStructure(var=36, mjc=3, pmjc=12, loadings=loadings, unique=unique) zwick7 <- generateStructure(var=72, mjc=9, pmjc= 8, loadings=loadings, unique=unique) zwick8 <- generateStructure(var=72, mjc=6, pmjc=12, loadings=loadings, unique=unique) ## ................................................................... # nsubjects <- c(72, 144, 180, 360) # require(psych) # Produce an usual correlation matrix from a congeneric model nsubjects <- 72 mzwick5 <- psych::sim.structure(fx=as.matrix(zwick5), n=nsubjects) mzwick5$r # Factor analysis: recovery of the factor structure iterativePrincipalAxis(mzwick5$model, nFactors=6, communalities="ginv")$loadings iterativePrincipalAxis(mzwick5$r , nFactors=6, communalities="ginv")$loadings factanal(covmat=mzwick5$model, factors=6) factanal(covmat=mzwick5$r , factors=6) # Number of components to retain eigenvalues <- eigen(mzwick5$r)$values aparallel <- parallel(var = length(eigenvalues), subject = nsubjects, rep = 30, quantile = 0.95, model="components")$eigen$qevpea results <- nScree(x = eigenvalues, aparallel = aparallel) results$Components plotnScree(results) # Number of factors to retain eigenvalues.fa <- eigen(corFA(mzwick5$r))$values aparallel.fa <- parallel(var = length(eigenvalues.fa), subject = nsubjects, rep = 30, quantile = 0.95, model="factors")$eigen$qevpea results.fa <- nScree(x = eigenvalues.fa, aparallel = aparallel.fa, model ="factors") results.fa$Components plotnScree(results.fa) # ...................................................... ``` ## References Raiche, G., Walls, T. A., Magis, D., Riopel, M. and Blais, J.-G. (2013). Non-graphical solutions for Cattell's scree test. Methodology, 9(1), 23-29. Zwick, W. R. and Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. **Psychological Bulletin, 99**, 432-442. ## See Also `principalComponents`, `iterativePrincipalAxis`, `rRecovery` ## Author(s) Gilles Raiche Centre sur les Applications des Modeles de Reponses aux Items (CAMRI) Universite du Quebec a Montreal raiche.gilles@uqam.ca David Magis Departement de mathematiques Universite de Liege David.Magis@ulg.ac.be

generateStructure function