ICLUST {psych} | R Documentation |
A common data reduction technique is to cluster cases (subjects). Less common, but particularly useful in psychological research, is to cluster items (variables). This may be thought of as an alternative to factor analysis, based upon a much simpler model. The cluster model is that the correlations between variables reflect that each item loads on at most one cluster, and that items that load on those clusters correlate as a function of their respective loadings on that cluster and items that define different clusters correlate as a function of their respective cluster loadings and the intercluster correlations.
Essentially, the cluster model is a Very Simple Structure factor model of complexity one (see VSS
).
This function applies the ICLUST algorithm to hierarchically cluster items to form composite scales. Clusters are combined if coefficients alpha and beta will increase in the new cluster.
Alpha, the mean split half correlation, and beta, the worst split half correlation, are estimates of the reliability and general factor saturation of the test. (See also the omega
function to estimate McDonald's coeffient omega.)
ICLUST(r.mat, nclusters=1, alpha=3, beta=1, beta.size=4, alpha.size=3, correct=TRUE, reverse=TRUE, beta.min=.5, output=1, digits=2,labels=NULL,cut=0, n.iterations = 0,title="ICLUST") #ICLUST(r.mat) #use all defaults #ICLUST(r.mat,nclusters =3) #use all defaults and if possible stop at 3 clusters #ICLUST(r.mat, output =3) #long output shows clustering history #ICLUST(r.mat, n.iterations =3) #clean up solution by item reassignment
r.mat |
A correlation matrix or data matrix/data.frame. (If r.mat is not square i.e, a correlation matrix, the data are correlated using pairwise deletion. |
nclusters |
Extract clusters until nclusters remain (default =1) |
alpha |
Apply the increase in alpha criterion (0) never or for (1) the smaller, 2) the average, or 3) the greater of the separate alphas. (default = 3) |
beta |
Apply the increase in beta criterion (0) never or for (1) the smaller, 2) the average, or 3) the greater of the separate betas. (default =1) |
beta.size |
Apply the beta criterion after clusters are of beta.size (default = 4) |
alpha.size |
Apply the alpha criterion after clusters are of size alpha.size (default =3) |
correct |
Correct correlations for reliability (default = TRUE) |
reverse |
Reverse negative keyed items (default = TRUE |
beta.min |
Stop clustering if the beta is not greater than beta.min (default = .5) |
output |
1) short, 2) medium, 3 ) long output (default =1) |
labels |
vector of item content or labels |
cut |
sort cluster loadings > absolute(cut) (default = 0) |
n.iterations |
|
digits |
Precision of digits of output (default = 2) |
title |
Title for this run |
Extensive documentation and justification of the algorithm is available in the original MBR 1979 http://personality-project.org/revelle/publications/iclust.pdf paper. Further discussion of the algorithm and sample output is available on the personality-project.org web page: http://personality-project.org/r/r.ICLUST.html
The results are best visualized using ICLUST.graph
, the results of which can be saved as a dot file for the Graphviz program. http://www.graphviz.org/
A common problem in the social sciences is to construct scales or composites of items to measure constructs of theoretical interest and practical importance. This process frequently involves administering a battery of items from which those that meet certain criteria are selected. These criteria might be rational, empirical,or factorial. A similar problem is to analyze the adequacy of scales that already have been formed and to decide whether the putative constructs are measured properly. Both of these problems have been discussed in numerous texts, as well as in myriad articles. Proponents of various methods have argued for the importance of face validity, discriminant validity, construct validity, factorial homogeneity, and theoretical importance.
Revelle (1979) proposed that hierachical cluster analysis could be used to estimate a new coefficient (beta) that was an estimate of the general factor saturation of a test. More recently, Zinbarg, Revelle, Yovel and Li (2005) compared McDonald's Omega to Chronbach's alpha and Revelle's beta. They conclude that omega is the best estimate. An algorithm for estimating omega
is available as part of this package.
This R version is a completely new version of ICLUST. Although early testing suggests it is stable, let me know if you have problems. Please email me if you want help with this version of ICLUST or if you desire more features.
The program currently has three primary functions: cluster, loadings, and graphics.
Clustering 24 tests of mental ability
A sample output using the 24 variable problem by Harman can be represented both graphically and in terms of the cluster order. Note that the graphic is created using GraphViz in the dot language. ICLUST.graph
produces the dot code for Graphviz. Somewhat lower resolution graphs with fewer options are available in the ICLUST.rgraph
function which requires Rgraphviz. Dot code can be viewed directly in Graphviz or can be tweaked using commercial software packages (e.g.,OmniGraffle)
Note that for this problem, with these parameters, the data formed one large cluster. (This is consistent with the Very Simple Structure (VSS
) output as well, which shows a clear one factor solution for complexity 1 data.) See below for an example with this same data set, but with more stringent parameter settings.
To see the graphic output go to http://personality-project.org/r/r.ICLUST.html or use ICLUST.rgraph
(requires Rgraphviz).
title |
Name of this run |
results |
A list containing |
clusters |
a matrix of -1,0, and 1 values to define cluster membership. |
corrected |
The raw and corrected for alpha reliability cluster intercorrelations. |
purified |
A list of the cluster definitions and cluster loadings of the purified solution |
William Revelle
Department of Psychology
Northwestern University
Evanston, Illinois
revelle@northwestern.edu
http://personality-project.org/revelle.html
Revelle, W. Hierarchical Cluster Analysis and the Internal Structure of Tests. Multivariate Behavioral Research, 1979, 14, 57-74.
http://personality-project.org/revelle/publications/iclust.pdf
See also more extensive documentation at
http://personality-project.org/r/r.ICLUST.html
ICLUST.graph
,ICLUST.cluster
, cluster.fit
, VSS
, omega
test.data <- Harman74.cor$cov ic.out <- ICLUST(test.data) if(require(Rgraphviz) ) {ICLUST.rgraph(ic.out,title="ICLUST of 24 mental tests") } ## Not run: test.data <- Harman74.cor$cov ic.out <- ICLUST(test.data) #use all defaults out.file <- file.choose(new=TRUE) #create a new file to write the plot commands to ICLUST.graph(ic.out,out.file,title = "ICLUST of Harman's 24 mental variables" ) ic.out <- ICLUST(test.data,nclusters =3) #use all defaults and if possible stop at 3 clusters ICLUST.graph(ic.out,out.file,title = "ICLUST of 24 mental variables with forced 3 cluster solution") ICLUST(test.data, output =3) #long output shows clustering history ic.out <- ICLUST(test.data,,nclusters=4, n.iterations =3) #clean up solution by item reassignment ICLUST.graph(ic.out,out.file,title = "ICLUST of 24 mental variables with forced 4 cluster solution") ic.out #shows the output on the console ## End(Not run) #produces this output #ICLUST(Harman74.cor$cov) #$title #[1] "ICLUST" # #$clusters # VisualPerception Cubes PaperFormBoard Flags GeneralInformation # 1 1 1 1 1 # PargraphComprehension SentenceCompletion WordClassification WordMeaning Addition # 1 1 1 1 1 # Code CountingDots StraightCurvedCapitals WordRecognition NumberRecognition # 1 1 1 1 1 # FigureRecognition ObjectNumber NumberFigure FigureWord Deduction # 1 1 1 1 1 # NumericalPuzzles ProblemReasoning SeriesCompletion ArithmeticProblems # 1 1 1 1 # #$corrected # [,1] #[1,] 1 # #$loadings # [,1] #VisualPerception 0.57 #Cubes 0.36 #PaperFormBoard 0.40 #Flags 0.46 #GeneralInformation 0.62 #PargraphComprehension 0.62 #SentenceCompletion 0.60 #WordClassification 0.63 #WordMeaning 0.62 #Addition 0.43 #Code 0.54 #CountingDots 0.44 #StraightCurvedCapitals 0.57 #WordRecognition 0.41 #NumberRecognition 0.38 #FigureRecognition 0.50 #ObjectNumber 0.45 #NumberFigure 0.51 #FigureWord 0.44 #Deduction 0.59 #NumericalPuzzles 0.58 #ProblemReasoning 0.58 #SeriesCompletion 0.66 #ArithmeticProblems 0.62 # #$fit #$fit$clusterfit #[1] 0.78 # #$fit$factorfit #[1] 0.78 # # #$results # Item/Cluster Item/Cluster similarity correlation alpha1 alpha2 beta1 beta2 size1 size2 rbar1 rbar2 r1 r2 alpha #C1 V23 V20 1.00 0.51 0.51 0.51 0.51 0.51 1 1 0.51 0.51 0.59 0.59 0.68 #C2 V9 V5 1.00 0.72 0.72 0.72 0.72 0.72 1 1 0.72 0.72 0.78 0.78 0.84 #C3 V7 V6 1.00 0.72 0.72 0.72 0.72 0.72 1 1 0.72 0.72 0.78 0.78 0.84 #C4 V12 V10 1.00 0.58 0.58 0.58 0.58 0.58 1 1 0.58 0.58 0.65 0.65 0.73 #C5 V13 V11 1.00 0.54 0.54 0.54 0.54 0.54 1 1 0.54 0.54 0.62 0.62 0.70 #C6 V18 V17 1.00 0.45 0.45 0.45 0.45 0.45 1 1 0.45 0.45 0.53 0.53 0.62 #C7 V4 V1 0.99 0.47 0.47 0.48 0.47 0.48 1 1 0.47 0.48 0.55 0.55 0.64 #C8 V16 V14 0.98 0.41 0.43 0.41 0.43 0.41 1 1 0.43 0.41 0.50 0.49 0.58 #C9 C2 C3 0.93 0.78 0.84 0.84 0.84 0.84 2 2 0.72 0.72 0.86 0.86 0.90 #C10 C1 V22 0.91 0.56 0.67 0.56 0.68 0.56 2 1 0.51 0.56 0.71 0.63 0.75 #C11 V21 V24 0.87 0.45 0.51 0.53 0.51 0.53 1 1 0.51 0.53 0.56 0.58 0.62 #C12 C10 C11 0.86 0.58 0.74 0.62 0.72 0.62 3 2 0.49 0.45 0.76 0.67 0.79 #C13 C9 V8 0.84 0.64 0.90 0.64 0.88 0.64 4 1 0.69 0.64 0.90 0.68 0.90 #C14 C8 V15 0.84 0.41 0.58 0.41 0.58 0.41 2 1 0.41 0.41 0.61 0.48 0.63 #C15 C5 C4 0.82 0.59 0.70 0.74 0.70 0.73 2 2 0.54 0.58 0.72 0.74 0.80 #C16 V3 V2 0.81 0.32 0.41 0.38 0.41 0.38 1 1 0.41 0.38 0.45 0.43 0.48 #C17 C16 C7 0.81 0.45 0.48 0.64 0.48 0.64 2 2 0.32 0.47 0.55 0.64 0.67 #C18 C12 C17 0.81 0.59 0.79 0.67 0.73 0.62 5 4 0.43 0.34 0.79 0.70 0.83 #C19 V19 C6 0.80 0.40 0.40 0.62 0.40 0.62 1 2 0.40 0.45 0.47 0.64 0.64 #C20 C19 C14 0.77 0.49 0.64 0.64 0.57 0.58 3 3 0.38 0.37 0.66 0.65 0.74 #C21 C18 C20 0.74 0.58 0.83 0.74 0.74 0.66 9 6 0.35 0.32 0.82 0.72 0.86 #C22 C21 C13 0.70 0.62 0.86 0.90 0.73 0.78 15 5 0.29 0.64 0.86 0.78 0.90 #C23 C22 C15 0.65 0.55 0.90 0.79 0.77 0.74 20 4 0.31 0.49 0.90 0.65 0.91 # beta rbar size #C1 0.68 0.51 2 #C2 0.84 0.72 2 #C3 0.84 0.72 2 #C4 0.73 0.58 2 #C5 0.70 0.54 2 #C6 0.62 0.45 2 #C7 0.64 0.47 2 #C8 0.58 0.41 2 #C9 0.88 0.69 4 #C10 0.72 0.49 3 #C11 0.62 0.45 2 #C12 0.73 0.43 5 #C13 0.78 0.64 5 #C14 0.58 0.37 3 #C15 0.74 0.49 4 #C16 0.48 0.32 2 #C17 0.62 0.34 4 #C18 0.74 0.35 9 #C19 0.57 0.38 3 #C20 0.66 0.32 6 #C21 0.73 0.29 15 #C22 0.77 0.31 20 #C23 0.71 0.30 24 # #$cor # [,1] #[1,] 1 # #$alpha #[1] 0.91 # #$size #[1] 24 # #$sorted #$sorted$sorted # item content cluster loadings #SeriesCompletion 23 SeriesCompletion 1 0.66 #WordClassification 8 WordClassification 1 0.63 #GeneralInformation 5 GeneralInformation 1 0.62 #PargraphComprehension 6 PargraphComprehension 1 0.62 #WordMeaning 9 WordMeaning 1 0.62 #ArithmeticProblems 24 ArithmeticProblems 1 0.62 #SentenceCompletion 7 SentenceCompletion 1 0.60 #Deduction 20 Deduction 1 0.59 #NumericalPuzzles 21 NumericalPuzzles 1 0.58 #ProblemReasoning 22 ProblemReasoning 1 0.58 #VisualPerception 1 VisualPerception 1 0.57 #StraightCurvedCapitals 13 StraightCurvedCapitals 1 0.57 #Code 11 Code 1 0.54 #NumberFigure 18 NumberFigure 1 0.51 #FigureRecognition 16 FigureRecognition 1 0.50 #Flags 4 Flags 1 0.46 #ObjectNumber 17 ObjectNumber 1 0.45 #CountingDots 12 CountingDots 1 0.44 #FigureWord 19 FigureWord 1 0.44 #Addition 10 Addition 1 0.43 #WordRecognition 14 WordRecognition 1 0.41 #PaperFormBoard 3 PaperFormBoard 1 0.40 #NumberRecognition 15 NumberRecognition 1 0.38 #Cubes 2 Cubes 1 0.36 # # #$p.fit #$p.fit$clusterfit #[1] 0.78 # #$p.fit$factorfit #[1] 0.78 # # #$p.sorted #$p.sorted$sorted # item content cluster loadings #SeriesCompletion 23 SeriesCompletion 1 0.66 #WordClassification 8 WordClassification 1 0.63 #GeneralInformation 5 GeneralInformation 1 0.62 #PargraphComprehension 6 PargraphComprehension 1 0.62 #WordMeaning 9 WordMeaning 1 0.62 #ArithmeticProblems 24 ArithmeticProblems 1 0.62 #SentenceCompletion 7 SentenceCompletion 1 0.60 #Deduction 20 Deduction 1 0.59 #NumericalPuzzles 21 NumericalPuzzles 1 0.58 #ProblemReasoning 22 ProblemReasoning 1 0.58 #VisualPerception 1 VisualPerception 1 0.57 #StraightCurvedCapitals 13 StraightCurvedCapitals 1 0.57 #Code 11 Code 1 0.54 #NumberFigure 18 NumberFigure 1 0.51 #FigureRecognition 16 FigureRecognition 1 0.50 #Flags 4 Flags 1 0.46 #ObjectNumber 17 ObjectNumber 1 0.45 #CountingDots 12 CountingDots 1 0.44 #FigureWord 19 FigureWord 1 0.44 #Addition 10 Addition 1 0.43 #WordRecognition 14 WordRecognition 1 0.41 #PaperFormBoard 3 PaperFormBoard 1 0.40 #NumberRecognition 15 NumberRecognition 1 0.38 #Cubes 2 Cubes 1 0.36 # # #$purified #$purified$cor # [,1] #[1,] 1 # #$purified$sd #[1] 13.79 # #$purified$corrected # [,1] #[1,] 0.91 # #$purified$size #[1] 24 # #