1 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ + + + May 1990 G R O U P A L S 8 0 Version 2.0 + + + + GROUPALS80 is an adapted and enhanced version of + + GROUPALS V1.0 in which all output is rescaled to 80 + + columns. + + + + The computation of the initial configuration has been + + changed. The initial solution is not restricted by + + the cluster allocation anymore. + + + +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 G R O U P A L S 8 0 Cluster analysis for a fixed Stef van Buuren number of groups for discrete Dept. of Psychometrics Version 2.0 mixed measurement levels data University of Leiden Wassenaarseweg 52 May 1990 2333 AK Leiden The Netherlands Echo of parameter cards 2-6 GROUPALS wth test data jobrus 47 9 9 2 3 0 0 0 0 0 0 0 0.00E+00 0 0.00E+00 0 8 0 0 0 0 0 0 0 0 0 2 2 11 2 1 1 0 0 --------- Job nr. 1 --------- INPUT DATA SPECIFICATIONS: ------------------------- Title: GROUPALS wth test data jobrus * PROBLEM PARAMETERS * ------------------ Number of objects or individuals 47 Total number of variables in the data matrix 9 Number of analysis variables 9 Number of dimensions 2 Number of clusters 3 Number of categories for all variables 0 Measurement level for all variables 0 * STOP PARAMETERS * --------------- Maximum number of iterations for the initial solution 20 Convergence criterion for the initial solution 0.11E-02 Maximum number of iterations for the restricted solution 75 Convergence criterion for the restricted solution 0.50E-04 Maximum number of clustering sub iterations 24 * I/O UNITS * --------- Unit number for input of the data matrix 8 Unit number for input of the initial allocation 0 Unit number for output of the object scores 0 Unit number for output of the category coordinates 0 Unit number for output of the category quantifications 0 Unit number for output of the component loadings 0 Unit number for output of the cluster allocations 0 * PRINT/PLOT PARAMETERS * --------------------- Print data matrix 0 Output of the initial solution 2 Print object and category information 2 Print history of iterations 11 Print cluster allocations 2 Plot objects labeled by clusters 1 Plot silhouettes 1 Plot options parameter 0 1 Number of categories per variable: Number of Number of Number of Variable categories I Variable categories I Variable categories -------------------------------------------------------------------------- I I 1 6 I 4 8 I 7 3 2 5 I 5 5 I 8 5 3 5 I 6 6 I 9 3 0List of 10 rows of the data matrix: * * Variables * * * 1 2 3 4 5 6 7 8 9 Objects ************************************** 1 * 1 1 1 4 4 1 2 1 3 2 * 1 1 1 5 3 3 2 2 3 3 * 1 1 2 6 2 5 1 1 1 4 * 1 2 2 3 2 6 2 2 2 5 * 1 2 2 7 1 4 2 1 1 6 * 1 2 3 7 1 3 1 1 1 7 * 2 3 5 1 4 2 3 2 1 8 * 2 3 4 3 3 5 2 4 1 9 * 2 3 3 7 1 3 1 1 1 10 * 2 3 4 6 2 6 3 2 2 1 Measurement level per variable: Variable Level I Variable Level I Variable Level -------------------------------------------------------------------------- I I 1. single ordinal I 4. single numerical I 7. multiple nominal 2. single ordinal I 5. single ordinal I 8. single nominal 3. single numerical I 6. single ordinal I 9. multiple nominal 1 Marginal frequencies -------------------- * * Categories * * * Missing 1 2 3 4 5 6 7 8 Variables **************************************************** 1 * 0 6 7 7 12 11 4 2 * 0 3 3 10 6 25 3 * 3 2 11 17 7 7 4 * 0 3 5 9 9 5 9 6 1 5 * 0 10 11 14 11 1 6 * 0 3 2 3 4 22 13 7 * 0 6 28 13 8 * 0 18 15 5 6 3 9 * 0 16 12 19 1 The history of iterations to compute the initial configuration: Iteration Total Total Multiple Single number fit loss loss loss Difference 1 0.0752672 1.9247328 1.8235650 0.1011678 0.0752672 2 0.3744177 1.6255823 1.4246914 0.2008909 0.2991505 3 0.5512932 1.4487068 1.3040725 0.1446343 0.1768755 4 0.6022236 1.3977764 1.2588912 0.1388851 0.0509304 5 0.6150759 1.3849241 1.2461881 0.1387360 0.0128523 6 0.6188868 1.3811132 1.2423356 0.1387776 0.0038110 7 0.6205693 1.3794307 1.2404871 0.1389436 0.0016825 8 0.6217191 1.3782809 1.2393957 0.1388851 0.0011498 9 0.6229782 1.3770218 1.2384599 0.1385618 0.0012591 10 0.6250043 1.3749957 1.2372927 0.1377031 0.0020260 11 0.6287430 1.3712570 1.2352966 0.1359605 0.0037387 12 0.6353050 1.3646950 1.2318175 0.1328775 0.0065620 13 0.6445103 1.3554897 1.2267099 0.1287798 0.0092053 14 0.6549058 1.3450942 1.2215069 0.1235873 0.0103955 15 0.6655335 1.3344665 1.2168999 0.1175667 0.0106277 16 0.6750109 1.3249891 1.2129722 0.1120169 0.0094774 17 0.6819593 1.3180407 1.2097964 0.1082443 0.0069484 18 0.6861963 1.3138037 1.2076225 0.1061812 0.0042370 19 0.6886807 1.3113193 1.2067081 0.1046112 0.0024844 20 0.6902307 1.3097693 1.2063930 0.1033763 0.0015501 21 0.6912155 1.3087845 1.2063116 0.1024729 0.0009848 The iterative process stops because the maximum number of iterations is reached. 0Dimension Eigenvalue --------- ---------- 1 0.457 2 0.235 1 1 -------------------------------- Summary of initial configuration -------------------------------- Dimension : 1 2 Row sums Multiple fit ------------ 1 0.90 0.50 0.40 2 1.01 0.51 0.49 3 0.62 0.14 0.48 4 0.90 0.70 0.20 5 0.88 0.60 0.28 6 0.61 0.25 0.36 7 0.65 0.57 0.08 8 0.73 0.70 0.02 9 0.84 0.55 0.29 0Mean 0.79 0.50 0.29 0 Single fit ---------- 1 0.84 0.48 0.36 2 0.83 0.45 0.38 3 0.29 0.05 0.24 4 0.77 0.59 0.18 5 0.85 0.59 0.26 6 0.43 0.11 0.32 7 - - - 8 0.71 0.70 0.00 9 - - - 0Mean 0.73 0.43 0.30 0 Component loadings ------------------ 1 0.69 0.60 2 0.67 0.62 3 0.23 0.49 4 -0.77 0.42 5 0.77 -0.51 6 0.34 0.56 7 - - 8 0.84 -0.02 9 - - 0 Iteration Total Total Multiple Single number fit loss loss loss --------- ----- ----- -------- ------ 0 21 0.6912 1.3088 1.2063 0.1025 1 ** Cluster statistics ** Cluster Members Centroids 1 2 1 16 0.17 -0.09 2 16 0.09 -0.09 3 15 -0.27 0.20 1 The history of iterations to compute the restricted configuration: Iteration Total Total Multiple Single number fit loss loss loss Difference 1 0.4870309 1.5129691 1.3994448 0.1135243 0.2041846 2 0.5284893 1.4715107 1.3378914 0.1336193 0.0414584 3 0.5289046 1.4710954 1.3378938 0.1332016 0.0004153 4 0.5293014 1.4706986 1.3378943 0.1328043 0.0003968 5 0.5297068 1.4702932 1.3378940 0.1323992 0.0004054 6 0.5300829 1.4699171 1.3378943 0.1320228 0.0003761 7 0.5304030 1.4695970 1.3378940 0.1317030 0.0003201 8 0.5305659 1.4694341 1.3378940 0.1315401 0.0001629 9 0.5306117 1.4693883 1.3378940 0.1314943 0.0000458 The iterative process stops because the convergence test value is reached. 0Dimension Eigenvalue --------- ---------- 1 0.403 2 0.128 1 0 ------------ Variable 1. Type: single ordinal Missing: 0 ------------ Dimension : 1 2 Marginal Category Category frequency quantif. Single category coordinates -------- --------- -------- --------------------------- 1 6 -1.23 -0.80 -0.60 2 7 -1.23 -0.80 -0.60 3 7 -0.92 -0.59 -0.45 4 12 0.51 0.33 0.25 5 11 1.10 0.71 0.54 6 4 1.10 0.71 0.54 Multiple category coordinates ----------------------------- -0.94 -0.29 -0.70 -0.84 -0.51 -0.55 0.21 0.40 0.93 0.42 0.32 0.56 0------------------------------------------------------------------------------- 0 ------------ Variable 2. Type: single ordinal Missing: 0 ------------ Dimension : 1 2 Marginal Category Category frequency quantif. Single category coordinates -------- --------- -------- --------------------------- 1 3 -1.30 -0.86 -0.54 2 3 -1.23 -0.81 -0.52 3 10 -1.23 -0.81 -0.52 4 6 -0.46 -0.31 -0.19 5 25 0.91 0.61 0.38 Multiple category coordinates ----------------------------- -0.75 -0.71 -1.13 0.14 -0.83 -0.54 -0.13 -0.48 0.59 0.41 0------------------------------------------------------------------------------- 0 ------------ Variable 3. Type: single numerical Missing: 3 ------------ Dimension : 1 2 Marginal Category Category frequency quantif. Single category coordinates -------- --------- -------- --------------------------- 1 2 -2.10 -0.05 -0.74 2 11 -1.17 -0.03 -0.41 3 17 -0.23 -0.01 -0.08 4 7 0.70 0.02 0.25 5 7 1.64 0.04 0.58 Multiple category coordinates ----------------------------- -0.37 -1.57 -0.34 -0.74 0.36 0.56 0.03 -0.35 -0.30 0.38 0------------------------------------------------------------------------------- 0 ------------ Variable 4. Type: single numerical Missing: 0 ------------ Dimension : 1 2 Marginal Category Category frequency quantif. Single category coordinates -------- --------- -------- --------------------------- 1 3 -1.82 1.23 -0.47 2 5 -1.28 0.86 -0.33 3 9 -0.73 0.50 -0.19 4 9 -0.19 0.13 -0.05 5 5 0.35 -0.23 0.09 6 9 0.89 -0.60 0.23 7 6 1.43 -0.97 0.37 8 1 1.97 -1.33 0.51 Multiple category coordinates ----------------------------- 0.07 -0.91 0.67 0.02 0.64 -0.02 0.79 0.20 0.15 -0.77 -0.73 -0.21 -1.51 1.00 -1.51 1.00 0------------------------------------------------------------------------------- 0 ------------ Variable 5. Type: single ordinal Missing: 0 ------------ Dimension : 1 2 Marginal Category Category frequency quantif. Single category coordinates -------- --------- -------- --------------------------- 1 10 -1.86 -1.44 0.64 2 11 0.07 0.05 -0.02 3 14 0.68 0.52 -0.23 4 11 0.68 0.53 -0.23 5 1 0.81 0.63 -0.28 Multiple category coordinates ----------------------------- -1.40 0.74 -0.10 -0.38 0.56 -0.15 0.58 -0.12 0.93 0.42 0------------------------------------------------------------------------------- 0 ------------ Variable 6. Type: single ordinal Missing: 0 ------------ Dimension : 1 2 Marginal Category Category frequency quantif. Single category coordinates -------- --------- -------- --------------------------- 1 3 -2.85 -0.24 -1.14 2 2 -2.85 -0.24 -1.14 3 3 -0.26 -0.02 -0.11 4 4 0.40 0.03 0.16 5 22 0.40 0.03 0.16 6 13 0.40 0.03 0.16 Multiple category coordinates ----------------------------- 0.07 -0.91 -0.37 -1.57 -1.13 0.14 -0.29 0.71 -0.03 0.12 0.44 0.01 0------------------------------------------------------------------------------- 0 ------------ Variable 7. Type: multiple nominal Missing: 0 ------------ Dimension : 1 2 0 Marginal Category frequency Category quantifications -------- --------- ------------------------ 1 6 -1.51 1.00 2 28 -0.01 -0.26 3 13 0.73 0.11 0------------------------------------------------------------------------------- 0 ------------ Variable 8. Type: single nominal Missing: 0 ------------ Dimension : 1 2 Marginal Category Category frequency quantif. Single category coordinates -------- --------- -------- --------------------------- 1 18 -1.23 -1.00 -0.19 2 15 0.49 0.40 0.07 3 5 1.21 0.98 0.18 4 6 0.87 0.71 0.13 5 3 1.21 0.98 0.18 Multiple category coordinates ----------------------------- -1.00 -0.14 0.42 -0.07 0.93 0.42 0.72 0.09 0.93 0.42 0------------------------------------------------------------------------------- 0 ------------ Variable 9. Type: multiple nominal Missing: 0 ------------ Dimension : 1 2 0 Marginal Category frequency Category quantifications -------- --------- ------------------------ 1 16 -1.07 0.32 2 12 0.39 -0.41 3 19 0.66 0.00 0------------------------------------------------------------------------------- 1 ------------------- Summary of analysis ------------------- Dimension : 1 2 Row sums Multiple fit ------------ 1 0.72 0.45 0.27 2 0.66 0.45 0.22 3 0.48 0.09 0.39 4 0.97 0.69 0.28 5 0.77 0.61 0.16 6 0.36 0.15 0.21 7 0.61 0.44 0.17 8 0.70 0.66 0.04 9 0.68 0.61 0.08 0Mean 0.66 0.46 0.20 0 Single fit ---------- 1 0.65 0.42 0.24 2 0.61 0.44 0.18 3 0.13 0.00 0.12 4 0.52 0.46 0.07 5 0.72 0.60 0.12 6 0.17 0.01 0.16 7 - - - 8 0.68 0.66 0.02 9 - - - 0Mean 0.61 0.37 0.24 0 Component loadings ------------------ 1 0.64 0.49 2 0.66 0.42 3 0.03 0.35 4 -0.68 0.26 5 0.77 -0.34 6 0.09 0.40 7 - - 8 0.81 0.15 9 - - 0 Iteration Total Total Multiple Single number fit loss loss loss --------- ----- ----- -------- ------ 0 10 0.5306 1.4694 1.3379 0.1315 1Object scores ------------- * * Dimensions * * * 1 2 Objects ******************** 1 * -0.38 -1.51 2 * -0.09 -0.94 3 * -1.32 -0.02 4 * -0.06 -0.87 5 * -1.39 -0.20 6 * -1.74 0.33 7 * 0.00 -0.75 8 * -0.21 -0.37 9 * -1.74 0.33 10 * -0.13 -0.29 11 * -0.97 0.26 12 * -0.88 -0.57 13 * -0.52 -0.89 14 * -1.24 0.21 15 * -1.34 0.24 16 * -0.02 -1.02 17 * -0.92 -0.45 18 * 0.66 -0.32 19 * -0.87 -0.88 20 * 0.12 -0.82 21 * -0.89 0.70 22 * -0.92 0.62 23 * 0.53 -0.08 24 * 0.03 -0.16 25 * 0.94 0.14 26 * 0.63 -0.12 27 * 1.01 0.17 28 * 0.64 0.15 29 * -1.14 1.28 30 * 0.55 -0.15 31 * 0.92 0.57 32 * 0.82 0.10 33 * 0.61 0.48 34 * 0.11 0.62 35 * 0.77 0.17 36 * 0.80 0.07 37 * 0.87 0.23 38 * 1.08 0.36 39 * 0.77 0.45 40 * 0.94 0.32 41 * 1.05 0.20 42 * 0.88 0.44 43 * 0.76 -0.03 44 * 0.60 0.36 45 * -1.12 1.38 46 * 0.61 0.09 47 * 1.24 0.25 1 Cluster allocation for each object * 0 1 2 3 4 5 6 7 8 9 ****************************************************************** 00 * - 1 1 3 1 3 3 1 1 3 10 * 1 3 1 1 3 3 1 1 2 1 20 * 1 3 3 2 1 2 2 2 2 3 30 * 2 2 2 2 2 2 2 2 2 2 40 * 2 2 2 2 2 3 2 2 1 ** Cluster statistics ** Cluster Members Centroids 1 2 1 13 -0.30 -0.73 2 23 0.77 0.19 3 11 -1.25 0.47 1 Object scores, labeled by clusters +--+------+------+------+------+------+------+------+------+------+---+ 1.43 | 3 | 1.27 | 3 | 1.11 | | 0.95 | | 0.79 | | 0.64 | + 2 2 | 0.48 | 2 2 2 | 0.32 | + 3 2 2 2 2 | 0.16 | 3 3 22 2222 + | 0.00 | 3 22 | -0.15 | 3 1 + 2 | -0.31 | 1 1 2 | -0.47 | 1 | -0.63 | 1 | -0.78 | 1 1 | -0.94 | 1 1 +1 | -1.10 | | -1.26 | | -1.42 | | -1.57 | 1 | +--+------+------+------+------+------+------+------+------+------+---+ -1.74 -1.40 -1.06 -0.73 -0.39 -0.05 0.28 0.62 0.96 1.29 0 Summary of all cells (X,Y), marked : + in the plot containing more than 1 point identification Number of X Y points Point identification -0.92 0.64 2 33 -1.74 0.32 2 33 1.00 0.16 2 22 0.52 -0.15 2 22 -0.10 -0.94 2 11 1 ***************** * * * SILHOUETTES * * * ***************** 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0 0 1 1 2 2 2 3 3 4 4 4 5 5 6 6 6 7 7 8 8 8 9 9 0 0 4 8 2 6 0 4 8 2 6 0 4 8 2 6 0 4 8 2 6 0 4 8 2 6 0 Clu Neig S(I) I ++++++++++++++++++++++++++++++++++++++++++++++++++++ + + 1 3 0.87 13+******************************************* + 1 2 0.83 2+***************************************** + 1 2 0.82 4+***************************************** + 1 2 0.80 16+**************************************** + 1 2 0.78 1+*************************************** + 1 2 0.77 7+************************************** + 1 3 0.71 19+*********************************** + 1 2 0.70 20+*********************************** + 1 2 0.70 8+********************************** + 1 3 0.57 12+**************************** + 1 2 0.55 10+*************************** + 1 3 0.40 17+******************* + 1 2 0.05 24+** + + + 2 1 0.95 37+*********************************************** + 2 1 0.95 35+*********************************************** + 2 1 0.94 40+*********************************************** + 2 1 0.94 25+*********************************************** + 2 1 0.94 32+*********************************************** + 2 1 0.94 36+*********************************************** + 2 1 0.94 27+********************************************** + 2 1 0.94 42+********************************************** + 2 1 0.93 39+********************************************** + 2 1 0.93 41+********************************************** + 2 1 0.93 28+********************************************** + 2 1 0.93 38+********************************************** + 2 1 0.92 44+********************************************** + 2 1 0.92 31+********************************************* + 2 1 0.91 33+********************************************* + 2 1 0.91 46+********************************************* + 2 1 0.91 43+********************************************* + 2 1 0.90 47+********************************************* + 2 1 0.84 26+****************************************** + 2 1 0.81 23+**************************************** + 2 1 0.78 30+*************************************** + 2 1 0.70 18+********************************** + 2 3 0.65 34+******************************** + + + 3 1 0.83 15+***************************************** + 3 1 0.82 6+***************************************** + 3 1 0.82 9+***************************************** + 3 1 0.80 22+**************************************** + 3 1 0.80 14+**************************************** + 3 1 0.80 21+*************************************** + 3 2 0.78 29+*************************************** + 3 2 0.75 45+************************************* + 3 1 0.72 11+************************************ + 3 1 0.66 3+********************************* + 3 1 0.51 5+************************* + + + ++++++++++++++++++++++++++++++++++++++++++++++++++++ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0 0 1 1 2 2 2 3 3 4 4 4 5 5 6 6 6 7 7 8 8 8 9 9 0 0 4 8 2 6 0 4 8 2 6 0 4 8 2 6 0 4 8 2 6 0 4 8 2 6 0 Cluster 1 has average silhouette width 0.66 Cluster 2 has average silhouette width 0.89 Cluster 3 has average silhouette width 0.75 For the entire data set, the average silhouette width is 0.80 END OF ANALYSIS