ICLUST                 package:psych                 R Documentation

_I_C_L_U_S_T: _I_t_e_m _C_l_u_s_t_e_r _A_n_a_l_y_s_i_s   - _H_i_e_r_a_r_c_h_i_c_a_l _c_l_u_s_t_e_r _a_n_a_l_y_s_i_s _u_s_i_n_g _p_s_y_c_h_o_m_e_t_r_i_c _p_r_i_n_c_i_p_l_e_s

_D_e_s_c_r_i_p_t_i_o_n:

     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.)

_U_s_a_g_e:

     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

_A_r_g_u_m_e_n_t_s:

   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 

_D_e_t_a_i_l_s:

     Extensive documentation and justification of the algorithm is
     available in the original MBR 1979 <URL:
     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: <URL:
     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. 
     <URL: 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 <URL:
     http://personality-project.org/r/r.ICLUST.html> or use
     'ICLUST.rgraph' (requires Rgraphviz).

_V_a_l_u_e:

  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

_A_u_t_h_o_r(_s):

     William Revelle 
      Department of Psychology 
      Northwestern University 
      Evanston, Illinois 
      revelle@northwestern.edu           
      <URL: http://personality-project.org/revelle.html>

_R_e_f_e_r_e_n_c_e_s:

     Revelle, W. Hierarchical Cluster Analysis and the Internal
     Structure of Tests. Multivariate Behavioral Research, 1979, 14,
     57-74.  <URL:
     http://personality-project.org/revelle/publications/iclust.pdf> 
      See also  more extensive documentation at  <URL:
     http://personality-project.org/r/r.ICLUST.html>

_S_e_e _A_l_s_o:

     'ICLUST.graph','ICLUST.cluster', 'cluster.fit ', 'VSS', 'omega'

_E_x_a_m_p_l_e_s:

     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
     #
     #
        

