pelora: Supervised Grouping of Predictor Variables

Description Usage Arguments Value Author(s) References See Also Examples

View source: R/pelora.R

Description

Performs selection and supervised grouping of predictor variables in large (microarray gene expression) datasets, with an option for simultaneous classification. Works in a greedy forward strategy and optimizes the binomial log-likelihood, based on estimated conditional probabilities from penalized logistic regression analysis.

Usage

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pelora(x, y, u = NULL, noc = 10, lambda = 1/32, flip = "pm",
       standardize = TRUE, trace = 1)

Arguments

x

Numeric matrix of explanatory variables (p variables in columns, n cases in rows). For example, these can be microarray gene expression data which should be grouped.

y

Numeric vector of length n containing the class labels of the individuals. These labels have to be coded by 0 and 1.

u

Numeric matrix of additional (clinical) explanatory variables (m variables in columns, n cases in rows) that are used in the (penalized logistic regression) prediction model, but neither grouped nor averaged. For example, these can be 'traditional' clinical variables.

noc

Integer, the number of clusters that should be searched for on the data.

lambda

Real, defaults to 1/32. Rescaled penalty parameter that should be in [0,1].

flip

Character string, describing a method how the x (gene expression) matrix should be sign-flipped. Possible are "pm" (the default) where the sign for each variable is determined upon its entering into the group, "cor" where the sign for each variable is determined a priori as the sign of the empirical correlation of that variable with the y-vector, and "none" where no sign-flipping is carried out.

standardize

Logical, defaults to TRUE. Is indicating whether the predictor variables (genes) should be standardized to zero mean and unit variance.

trace

Integer >= 0; when positive, the output of the internal loops is provided; trace >= 2 provides output even from the internal C routines.

Value

pelora returns an object of class "pelora". The functions print and summary are used to obtain an overview of the variables (genes) that have been selected and the groups that have been formed. The function plot yields a two-dimensional projection into the space of the first two group centroids that pelora found. The generic function fitted returns the fitted values, these are the cluster representatives. coef returns the penalized logistic regression coefficients θ_j for each of the predictors. Finally, predict is used for classifying test data with Pelora's internal penalized logistic regression classifier on the basis of the (gene) groups that have been found.

An object of class "pelora" is a list containing:

genes

A list of length noc, containing integer vectors consisting of the indices (column numbers) of the variables (genes) that have been clustered.

values

A numerical matrix with dimension n \times \code{noc}, containing the fitted values, i.e. the group centroids \tilde{x}_j.

y

Numeric vector of length n containing the class labels of the individuals. These labels are coded by 0 and 1.

steps

Numerical vector of length noc, showing the number of forward/backward cycles in the fitting process of each cluster.

lambda

The rescaled penalty parameter.

noc

The number of clusters that has been searched for on the data.

px

The number of columns (genes) in the x-matrix.

flip

The method that has been chosen for sign-flipping the x-matrix.

var.type

A factor with noc entries, describing whether the jth predictor is a group of predictors (genes) or a single (clinical) predictor variable.

crit

A list of length noc, containing numerical vectors that provide information about the development of the grouping criterion during the clustering.

signs

Numerical vector of length p, saying whether the ith variable (gene) should be sign-flipped (-1) or not (+1).

samp.names

The names of the samples (rows) in the x-matrix.

gene.names

The names of the variables (columns) in the x-matrix.

call

The function call.

Author(s)

Marcel Dettling, dettling@stat.math.ethz.ch

References

Marcel Dettling (2003) Finding Predictive Gene Groups from Microarray Data, see https://stat.ethz.ch/~dettling/supervised.html

Marcel Dettling and Peter Bühlmann (2002). Supervised Clustering of Genes. Genome Biology, 3(12): research0069.1-0069.15, doi: 10.1186/gb-2002-3-12-research0069.

Marcel Dettling and Peter Bühlmann (2004). Finding Predictive Gene Groups from Microarray Data. Journal of Multivariate Analysis 90, 106–131, doi: 10.1016/j.jmva.2004.02.012

See Also

wilma for another supervised clustering technique.

Examples

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## Working with a "real" microarray dataset
data(leukemia, package="supclust")

## Generating random test data: 3 observations and 250 variables (genes)
set.seed(724)
xN <- matrix(rnorm(750), nrow = 3, ncol = 250)

## Fitting Pelora
fit <- pelora(leukemia.x, leukemia.y, noc = 3)

## Working with the output
fit
summary(fit)
plot(fit)
fitted(fit)
coef(fit)

## Fitted values and class probabilities for the training data
predict(fit, type = "cla")
predict(fit, type = "prob")

## Predicting fitted values and class labels for the random test data
predict(fit, newdata = xN)
predict(fit, newdata = xN, type = "cla", noc = c(1,2,3))
predict(fit, newdata = xN, type = "pro", noc = c(1,3))

## Fitting Pelora such that the first 70 variables (genes) are not grouped
fit <- pelora(leukemia.x[, -(1:70)], leukemia.y, leukemia.x[,1:70])

## Working with the output
fit
summary(fit)
plot(fit)
fitted(fit)
coef(fit)

## Fitted values and class probabilities for the training data
predict(fit, type = "cla")
predict(fit, type = "prob")

## Predicting fitted values and class labels for the random test data
predict(fit, newdata = xN[, -(1:70)], newclin = xN[, 1:70])
predict(fit, newdata = xN[, -(1:70)], newclin = xN[, 1:70], "cla", noc  = 1:10)
predict(fit, newdata = xN[, -(1:70)], newclin = xN[, 1:70], type = "pro")

Example output

...................
Cluster 1 terminated 
.............
Cluster 2 terminated 
..............
Cluster 3 terminated 

Pelora called with lambda = 0.03125, 3 clusters fitted

Cluster 1 : Contains 18 genes, final criterion 8.967
Cluster 2 : Contains 11 genes, final criterion 6.157
Cluster 3 : Contains 13 genes, final criterion 4.870


Pelora called with lambda = 0.03125, 3 clusters fitted

Cluster 1 : Contains 18 genes, final criterion 8.967
Entry  1 : Gene  69          
Entry  2 : Gene 174          
Entry  3 : Gene 126 (flipped)
Entry  4 : Gene 183          
Entry  5 : Gene 161 (flipped)
Entry  6 : Gene 160          
Entry  7 : Gene 100          
Entry  8 : Gene 225          
Entry  9 : Gene 148          
Entry 10 : Gene 188 (flipped)
Entry 11 : Gene   7 (flipped)
Entry 12 : Gene 211          
Entry 13 : Gene  99          
Entry 14 : Gene 105          
Entry 15 : Gene 215          
Entry 16 : Gene 106          
Entry 17 : Gene  59          
Entry 18 : Gene 185          

Cluster 2 : Contains 11 genes, final criterion 6.157
Entry  1 : Gene 174          
Entry  2 : Gene 126 (flipped)
Entry  3 : Gene 183          
Entry  4 : Gene 160          
Entry  5 : Gene 219          
Entry  6 : Gene  75          
Entry  7 : Gene  82          
Entry  8 : Gene  96          
Entry  9 : Gene  30 (flipped)
Entry 10 : Gene 224          
Entry 11 : Gene  16 (flipped)

Cluster 3 : Contains 13 genes, final criterion 4.870
Entry  1 : Gene  69          
Entry  2 : Gene 183          
Entry  3 : Gene 126 (flipped)
Entry  4 : Gene 160          
Entry  5 : Gene 208          
Entry  6 : Gene 114          
Entry  7 : Gene 174          
Entry  8 : Gene  94          
Entry  9 : Gene  53          
Entry 10 : Gene  73          
Entry 11 : Gene 172 (flipped)
Entry 12 : Gene 120          
Entry 13 : Gene  66 (flipped)


   Predictor 1 Predictor 2 Predictor 3
1   -0.3067501  -0.2965628  -0.2807912
2   -0.2374449  -0.3131413  -0.2380897
3   -0.4191425  -0.3808118  -0.2312147
4   -0.3244100  -0.4359319  -0.3629393
5   -0.3349981  -0.2282353  -0.2410168
6   -0.3680656  -0.4578520  -0.1462987
7   -0.2662159  -0.2216154  -0.2543470
8   -0.2709801  -0.6160297  -0.2720166
9   -0.3497270  -0.2566270  -0.3303750
10  -0.2484176  -0.2943709  -0.2994681
11  -0.4637102  -0.3178805  -0.2984117
12  -0.3235507  -0.2917100  -0.3461716
13  -0.3366444  -0.3897017  -0.4069550
14  -0.2931148  -0.3388245  -0.3624948
15  -0.4169962  -0.2032941  -0.3515948
16  -0.4391570  -0.3784187  -0.2363739
17  -0.3128851  -0.3411971  -0.2828232
18  -0.2615623  -0.3756845  -0.2058427
19  -0.2831775  -0.2943629  -0.2397261
20  -0.3336864  -0.5069509  -0.2640107
21  -0.3837958  -0.3845756  -0.2993117
22  -0.3142992  -0.4328201  -0.1530615
23  -0.1996516  -0.4057742  -0.1693670
24  -0.2665744  -0.4606513  -0.1923565
25  -0.3142851  -0.3554785  -0.2537461
26  -0.3204541  -0.3454162  -0.1195990
27  -0.4312616  -0.2115664  -0.2837958
28   0.7438087   0.9335735   0.5623016
29   0.7871312   0.9655664   0.5585013
30   0.7860592   0.9352526   0.6519974
31   0.9007759   0.8123499   0.5657786
32   0.8102071   0.7373147   0.5826707
33   0.8063673   0.8564196   0.7031533
34   0.7725103   0.8871276   0.6922753
35   0.7453184   0.7902142   0.7821098
36   0.8641912   0.8211966   0.6916977
37   0.7685894   0.9798044   0.6990970
38   0.8359995   0.8166661   0.6326162
  Intercept Predictor 1 Predictor 2 Predictor 3 
  -1.393629    1.797641    1.636808    2.152874 
   3 Predictors
1             0
2             0
3             0
4             0
5             0
6             0
7             0
8             0
9             0
10            0
11            0
12            0
13            0
14            0
15            0
16            0
17            0
18            0
19            0
20            0
21            0
22            0
23            0
24            0
25            0
26            0
27            0
28            1
29            1
30            1
31            1
32            1
33            1
34            1
35            1
36            1
37            1
38            1
   3 Predictors
1    0.04587036
2    0.05490925
3    0.03667876
4    0.03012823
5    0.05273539
6    0.04230364
7    0.05827671
8    0.03004090
9    0.04094897
10   0.04895124
11   0.03261054
12   0.03924127
13   0.02895065
14   0.03712830
15   0.03794509
16   0.03518360
17   0.04215062
18   0.05108146
19   0.05212408
20   0.03255774
21   0.03365325
22   0.04758007
23   0.05834136
24   0.04560974
25   0.04365777
26   0.05772796
27   0.04204126
28   0.93596308
29   0.94290124
30   0.95044840
31   0.94121875
32   0.92581351
33   0.95127097
34   0.94966962
35   0.94899101
36   0.95226392
37   0.95676209
38   0.94309939
  Predictor 1 Predictor 2 Predictor 3
1  -0.4320335 -0.27838607 -0.02386751
2  -0.1053294 -0.01931307 -0.09584530
3  -0.1268362 -0.08248432 -0.14098159
  1 Predictors 2 Predictors 3 Predictors
1            0            0            0
2            0            0            0
3            0            0            0
  1 Predictors 3 Predictors
1    0.0386497   0.06432507
2    0.1397782   0.13932249
3    0.1290847   0.11302959
.
Cluster 1 terminated 
......................
Cluster 2 terminated 
.................
Cluster 3 terminated 
.............
Cluster 4 terminated 
...........
Cluster 5 terminated 
.................
Cluster 6 terminated 
......
Cluster 7 terminated 
.
Cluster 8 terminated 
.
Cluster 9 terminated 
............................
Cluster 10 terminated 

Pelora called with lambda = 0.03125,
7 clusters and 3 clinical variables fitted

Predictor  1 : Clinical variable 69, final criterion 12.146
Predictor  2 : Cluster with 20 genes, final criterion  6.805
Predictor  3 : Cluster with 16 genes, final criterion  5.154
Predictor  4 : Cluster with 12 genes, final criterion  4.285
Predictor  5 : Cluster with 10 genes, final criterion  3.739
Predictor  6 : Cluster with 16 genes, final criterion  3.348
Predictor  7 : Cluster with  5 genes, final criterion  3.077
Predictor  8 : Clinical variable 66, final criterion  2.959
Predictor  9 : Clinical variable 31, final criterion  2.867
Predictor 10 : Cluster with 26 genes, final criterion  2.662


Pelora called with lambda = 0.03125,
7 clusters and 3 clinical variables fitted

Predictor  1 : Clinical variable 69, final criterion 12.146

Predictor  2 : Cluster with 20 genes, final criterion  6.805
Entry  1 : Gene 104          
Entry  2 : Gene  56 (flipped)
Entry  3 : Gene 113          
Entry  4 : Gene 149          
Entry  5 : Gene  44          
Entry  6 : Gene  49          
Entry  7 : Gene  12          
Entry  8 : Gene  36          
Entry  9 : Gene  27          
Entry 10 : Gene 122          
Entry 11 : Gene 147 (flipped)
Entry 12 : Gene  90          
Entry 13 : Gene 152          
Entry 14 : Gene  76          
Entry 15 : Gene 138          
Entry 16 : Gene 129          
Entry 17 : Gene  26          
Entry 18 : Gene 128          
Entry 19 : Gene 170          
Entry 20 : Gene 109 (flipped)

Predictor  3 : Cluster with 16 genes, final criterion  5.154
Entry  1 : Gene 104          
Entry  2 : Gene 113          
Entry  3 : Gene  56 (flipped)
Entry  4 : Gene  90          
Entry  5 : Gene   5          
Entry  6 : Gene 149          
Entry  7 : Gene  12          
Entry  8 : Gene  26          
Entry  9 : Gene  76          
Entry 10 : Gene 131          
Entry 11 : Gene 122          
Entry 12 : Gene 155          
Entry 13 : Gene 100 (flipped)
Entry 14 : Gene  30          
Entry 15 : Gene  62          
Entry 16 : Gene  10 (flipped)

Predictor  4 : Cluster with 12 genes, final criterion  4.285
Entry  1 : Gene 104          
Entry  2 : Gene 113          
Entry  3 : Gene  56 (flipped)
Entry  4 : Gene  90          
Entry  5 : Gene   5          
Entry  6 : Gene 126          
Entry  7 : Gene 155          
Entry  8 : Gene  16          
Entry  9 : Gene 158          
Entry 10 : Gene  84          
Entry 11 : Gene 161 (flipped)
Entry 12 : Gene   3          

Predictor  5 : Cluster with 10 genes, final criterion  3.739
Entry  1 : Gene 104          
Entry  2 : Gene  91 (flipped)
Entry  3 : Gene 113          
Entry  4 : Gene  30          
Entry  5 : Gene 132          
Entry  6 : Gene 155          
Entry  7 : Gene 154          
Entry  8 : Gene  78          
Entry  9 : Gene 161 (flipped)
Entry 10 : Gene   9          

Predictor  6 : Cluster with 16 genes, final criterion  3.348
Entry  1 : Gene 104          
Entry  2 : Gene  91 (flipped)
Entry  3 : Gene 113          
Entry  4 : Gene  30          
Entry  5 : Gene 132          
Entry  6 : Gene 155          
Entry  7 : Gene 154          
Entry  8 : Gene   5          
Entry  9 : Gene 119          
Entry 10 : Gene  24          
Entry 11 : Gene 151 (flipped)
Entry 12 : Gene 149          
Entry 13 : Gene 140 (flipped)
Entry 14 : Gene  10 (flipped)
Entry 15 : Gene  71          
Entry 16 : Gene  50          

Predictor  7 : Cluster with  5 genes, final criterion  3.077
Entry 1 : Gene 104          
Entry 2 : Gene  91 (flipped)
Entry 3 : Gene 113          
Entry 4 : Gene  30          
Entry 5 : Gene 132          

Predictor  8 : Clinical variable 66, final criterion  2.959

Predictor  9 : Clinical variable 31, final criterion  2.867

Predictor 10 : Cluster with 26 genes, final criterion  2.662
Entry  1 : Gene 149          
Entry  2 : Gene  12          
Entry  3 : Gene 113          
Entry  4 : Gene  26          
Entry  5 : Gene  65          
Entry  6 : Gene 121          
Entry  7 : Gene 161 (flipped)
Entry  8 : Gene 132          
Entry  9 : Gene  44          
Entry 10 : Gene 170          
Entry 11 : Gene 137          
Entry 12 : Gene 133 (flipped)
Entry 13 : Gene 120          
Entry 14 : Gene  30          
Entry 15 : Gene  58          
Entry 16 : Gene 145          
Entry 17 : Gene 122          
Entry 18 : Gene 138          
Entry 19 : Gene 100 (flipped)
Entry 20 : Gene  76          
Entry 21 : Gene 177          
Entry 22 : Gene  63 (flipped)
Entry 23 : Gene 128          
Entry 24 : Gene 178          
Entry 25 : Gene  10 (flipped)
Entry 26 : Gene 147          


   Predictor 1 Predictor 2 Predictor 3 Predictor 4 Predictor 5 Predictor 6
1   -0.4060399  -0.1988190  -0.1764151  -0.5276747 -0.43261774  -0.2709890
2    0.9430274  -0.3024245  -0.3223401  -0.5329070 -0.30186209  -0.2857035
3   -0.6145205  -0.3365585  -0.3011438  -0.3601139 -0.42086686  -0.3006743
4   -1.3627031  -0.2594442  -0.2981212  -0.2832939 -0.38733884  -0.3447153
5   -1.3734152  -0.2692426  -0.2108856  -0.1628854 -0.25294441  -0.2564958
6    1.0657803  -0.3924563  -0.4329788  -0.5385678 -0.37081949  -0.2798448
7   -1.3374205  -0.2294537  -0.2833225  -0.2630923 -0.08457562  -0.2446500
8   -1.3354139  -0.2312732  -0.2094792  -0.3029268 -0.24043921  -0.1731558
9   -0.4067449  -0.3452204  -0.3282927  -0.4073596 -0.46628899  -0.1789397
10   0.2760965  -0.2621182  -0.3549939  -0.3327177 -0.44048202  -0.1903839
11  -1.2437437  -0.2228681  -0.2852932  -0.3878044 -0.58752197  -0.2115417
12  -0.9485866  -0.1954846  -0.2497780  -0.2519208 -0.40750018  -0.2963952
13  -1.3183164  -0.2929590  -0.1526353  -0.3588182 -0.49039866  -0.3520898
14   0.5652176  -0.4275906  -0.3407247  -0.2437327 -0.32728358  -0.3864132
15  -1.3396861  -0.2195409  -0.2474477  -0.3421138 -0.35555360  -0.2834904
16  -1.3573863  -0.3362329  -0.2724343  -0.3233672 -0.22479880  -0.2014709
17  -0.4053540  -0.2170572  -0.3454366  -0.3534689 -0.38016032  -0.1608026
18  -1.1799757  -0.2721089  -0.2945062  -0.3373299 -0.18761222  -0.3230994
19  -1.2076066  -0.2042550  -0.2828239  -0.1467543 -0.15759320  -0.2677612
20  -0.9575222  -0.3129403  -0.2710245  -0.3661953 -0.45554503  -0.2277328
21  -1.0457692  -0.2260243  -0.2695839  -0.1713213 -0.41803519  -0.2698210
22  -1.1115955  -0.1787175  -0.3100426  -0.2658555 -0.32307801  -0.2112505
23   0.1934126  -0.3300765  -0.4028228  -0.2141802 -0.33808943  -0.2949899
24  -1.4346453  -0.2309166  -0.3560609  -0.1628456 -0.29616359  -0.3641453
25  -1.2171742  -0.1839816  -0.2260751  -0.2935019 -0.39610751  -0.3254803
26  -1.2463141  -0.2101915  -0.1701988  -0.3030649 -0.46707433  -0.2582409
27  -1.2163623  -0.3313818  -0.2114892  -0.2873244 -0.40834397  -0.3068746
28   0.7410577   0.8644460   0.8123971   0.8030237  0.95358870   0.5416967
29   2.8713446   0.5091642   0.6323301   0.7137462  0.90306498   0.6968565
30   2.8404211   0.6085351   0.7190366   0.7471776  0.83533181   0.7134020
31   2.5610426   0.6083006   0.6731309   0.6143815  0.92147667   0.6234324
32   2.8598801   0.5794000   0.5498537   0.6949743  0.81219055   0.7228671
33   1.6246713   0.7242354   0.7266119   0.8285891  0.88759536   0.6110106
34   1.1566060   0.7456103   0.7304296   0.9371997  0.98673366   0.5910254
35   1.3758300   0.7578748   0.6902259   0.8781558  0.81929405   0.7543096
36   2.8477323   0.5502931   0.6184029   0.9061539  0.71769130   0.6763093
37   2.8649981   0.5469703   0.7333408   0.6684482  0.98778671   0.6531476
38   1.2206500   0.7245081   0.7205910   0.7292881  0.79434106   0.6830947
   Predictor 7 Predictor 8 Predictor 9 Predictor 10
1   -0.3377947 -0.54172399 -0.98103854  -0.24262700
2   -0.2598511 -1.32647301  0.21200654  -0.33026179
3   -0.6078839 -0.44441588 -0.79209596  -0.21531241
4   -0.1707361 -0.38894378 -1.36270310  -0.22026996
5   -0.4517779 -0.11559041 -0.26099616  -0.37148180
6   -0.4129790 -1.19283327 -0.55588074  -0.17041470
7   -0.4831630 -1.33742052 -1.33742052  -0.09763985
8   -0.2067421 -0.50767464 -1.16396233  -0.27696790
9   -0.6862245 -1.05639670 -1.22369368  -0.06686727
10  -0.3417866 -0.71879040 -0.27461021  -0.21466096
11  -0.7233215 -0.94330213 -1.24374365  -0.14290683
12  -0.5365463  0.00202941  0.06379095  -0.34423180
13  -0.4393363 -0.94953049 -1.31831643  -0.10417821
14  -0.5653535 -1.01678710 -0.27144455  -0.31414727
15  -0.2118393 -1.33968610 -1.12421926  -0.10603075
16  -0.3355517 -0.69925752 -1.09044682  -0.19459049
17  -0.4749806 -0.63182986 -1.51021939  -0.22101496
18  -0.3598141 -0.85163418 -1.17997570  -0.15392574
19  -0.5286960 -0.79177347 -1.20760661  -0.22561805
20  -0.3552274 -1.06203925 -1.53441337  -0.12800886
21  -0.8458994 -0.74633774 -0.83562242  -0.17875482
22  -0.1830584 -0.90968516 -1.11159548  -0.23687896
23  -0.4502238 -1.11368825 -1.18711813  -0.19449288
24  -0.3956765 -1.41634053 -0.90685483  -0.04129460
25  -0.5487348 -0.56720728 -1.21717418  -0.14357893
26  -0.3180278 -1.01980964 -1.24631406  -0.17155724
27  -0.3441807 -1.21636235 -0.92405624  -0.12719614
28   0.9471456 -0.35455408 -0.52250494   0.74819296
29   0.7868549  0.52584356  1.48838553   0.50876676
30   1.2425456  0.72995414  2.49675387   0.25958430
31   1.0185054  1.06700435  0.71014772   0.42509865
32   1.1924235  0.40793212 -0.30247047   0.53876303
33   1.2133198 -0.16927634  0.53393296   0.54281280
34   1.0705221  1.10391475  0.48085144   0.41491610
35   0.8002570  0.76088132  0.84562749   0.43643592
36   1.1476762  0.52069147  2.17426590   0.35226695
37   1.1229132 -0.11080491  1.80504585   0.44747837
38   1.0332438 -0.39202249  1.13339969   0.56059432
   Intercept  Predictor 1  Predictor 2  Predictor 3  Predictor 4  Predictor 5 
  -1.1716983    0.1842654    0.8385458    0.7976833    0.6847451    0.6067519 
 Predictor 6  Predictor 7  Predictor 8  Predictor 9 Predictor 10 
   0.8211166    0.4847442    0.2955851    0.1878370    1.2569333 
   10 Predictors
1              0
2              0
3              0
4              0
5              0
6              0
7              0
8              0
9              0
10             0
11             0
12             0
13             0
14             0
15             0
16             0
17             0
18             0
19             0
20             0
21             0
22             0
23             0
24             0
25             0
26             0
27             0
28             1
29             1
30             1
31             1
32             1
33             1
34             1
35             1
36             1
37             1
38             1
   10 Predictors
1     0.03866462
2     0.03974743
3     0.03224375
4     0.03486537
5     0.04463813
6     0.03406801
7     0.03653106
8     0.04346592
9     0.03030718
10    0.04857966
11    0.02524001
12    0.04508957
13    0.02969606
14    0.03226090
15    0.03469224
16    0.03685924
17    0.03601400
18    0.03544747
19    0.03887285
20    0.02999918
21    0.03312515
22    0.03956643
23    0.03412293
24    0.03433607
25    0.03619673
26    0.03483489
27    0.03233529
28    0.95720621
29    0.96622035
30    0.97474460
31    0.96496611
32    0.95933805
33    0.96241723
34    0.96869354
35    0.96463227
36    0.97012698
37    0.96790089
38    0.95607335
  Predictor 1 Predictor 2 Predictor 3 Predictor 4 Predictor 5 Predictor 6
1   0.4595198 -0.24995809 -0.13411424  -0.4149285  -0.6214466 -0.07272322
2   0.3588264 -0.01687939  0.13076628  -0.2711565   0.0143638  0.41795265
3  -1.4099869 -0.14563161 -0.06807276   0.2943940  -0.1881499 -0.01274870
  Predictor 7 Predictor 8 Predictor 9 Predictor 10
1  -0.5565468   0.8467976  -0.2796180 -0.187531434
2   0.2207801  -0.2882260   2.0823453  0.001349072
3   0.1095344   0.7402682   0.2787512 -0.112053556
  1 Predictors 2 Predictors 3 Predictors 4 Predictors 5 Predictors 6 Predictors
1            0            0            0            0            0            0
2            0            0            0            0            0            0
3            0            0            0            0            0            0
  7 Predictors 8 Predictors 9 Predictors 10 Predictors
1            0            0            0             0
2            0            0            0             0
3            0            0            0             0
  10 Predictors
1    0.08074821
2    0.39304527
3    0.20627144

supclust documentation built on Sept. 27, 2021, 5:11 p.m.