R Graphical Manual

Browse All

Last data update: 2014.03.03

R: ksIRT - kernel smoothing in Item Response Theory

ksIRT

R Documentation

ksIRT - kernel smoothing in Item Response Theory

Description

This function fits nonparametric item and options characteristic curves using kernel smoothing techniques. Within the KernSmoothIRT package, it provides the relevant data for the graphical analysis of multiple choice test and questionnaire data.

Usage

ksIRT(responses, key, format, kernel = c("gaussian","quadratic","uniform"), itemlabels,
weights,miss = c("option","omit","random.multinom","random.unif"), NAweight = 0, 
evalpoints, nevalpoints, bandwidth = c("Silverman","CV"), RankFun = "sum", SubRank, 
thetadist = list("norm",0,1), groups = FALSE)

## S3 method for class 'ksIRT'
print(x,...)

Arguments

`responses`	input data matrix with options selected from each individual for each item. Rows represent individuals, columns represent items. Alternatively, a data.frame or list can be specified. Missing values are inserted as `NA`.
`key`	a numeric vector or a scalar. If `key` is a vector, its length must match the number of items; if it is a scalar, its value is used for all items. If the items are multiple choice, `key` should contain the option that corresponds to the correct response. If the data are rating-scale, `key` should contain the largest option value for each item. In this case, the weight assigned to each option is equal to its option number. More complicated weighting schemes, such as partial credit, can be specified in the `weights` argument. If `weights` is specified, `key` must be left blank.
`format`	a numeric scalar or vector specifying the type of items. If all of the items are multiple choice, then `format = 1`. If all of the items are rating-scale or partial credit, then `format = 2`. If all of the items are nominal items, then `format = 3`. If the test has a mixture of items of different formats, then format is a vector with length equal to the number of items with entries of 1 for each multiple choice item and 2 for each rating-scale item. For more complicated weighting schemes use the `weights` argument.
`kernel`	a character string specifying the kernel function. `kernel` must be either `"gaussian"`, `"quadratic"` or `"uniform"`. The default is `"gaussian"`.
`itemlabels`	optional list of labels for each item. If omitted, each item will be labelled according to its numerical order. These labels will be used in plotting.
`weights`	optional list that may be used in lieu of including `key`. Specifying `weights` allows for more complicated weighting schemes than the default. Its length must be equal to the number of items and each entry must be a matrix with option numbers in the first row and option weights in the second row. If weights is omitted and `format=1`, then weights are given according to `key`. If `weights` is omitted and `format=2`, then an option weight equals the option number is given to each response. If `weights` is omitted and and `format=3`, then weights are set to zero.
`miss`	a character string specifying the method used to manage missing responses. The default value, `miss="option"`, considers the missing responses as a further option, labeled as `NA`, with zero weight. Such `NA` option will be added to the plot of the Option Characteristic Curves. Alternatively, a different weight for the `NA` option may be specified through the `NAweight` argument. `miss="random.unif"` substitutes `NA`s with options randomly chosen from the possible ones for the corresponding item. `miss="random.multinom"` does the same substitution as `miss="random.unif"` but each option has a probability of being selected proportional to its relative frequency. `miss="omit"` excludes from the analysis all the subjects with at least one omitted response.
`NAweight`	a scalar value that specifies the weight given to missing responses when `miss="option"`. The default is zero.
`evalpoints`	an optional numeric vector that specifies the quantiles at which to estimate the Option Characteristic Curves. If unspecified, the default is `nevalpoints` evenly spaced values with end points determined according to the number of subjects and the distribution specified with the `thetadist` argument.
`nevalpoints`	an optional scalar value that specifies the number of evenly spaced points at which curves are estimated. This value is used as an alternative to a user defined vector in the `evalpoints` argument. The default value is 51. The end points are determined according to the number of subjects and to the distribution specified for the `thetadist` argument. If both `nevalpoints` and `evalpoints` are specified, then `evalpoints` takes precedence.
`bandwidth`	either `"Silverman"`, `"CV"` or a numeric vector specifying, for each item, the bandwidth to use for kernel smoothing. The default value, `bandwidth="Silverman"`, is a numeric vector computed following the well-known Silverman's rule of thumb. If `bandwidth="CV"`, then the bandwidth is chosen for each item through cross-validation.
`RankFun`	a function that is used to rank subjects. The default value is `"sum"`. Another common choice is `"mean"`.
`SubRank`	a numeric vector specifying the rank of each of the subjects. If unspecified and `format=1` or `format= 2`, subjects will be ranked according to the function passed through the argument `RankFun`. When `format=3` this argument must be provided.
`thetadist`	a list specifying the distribution to be used to thetadist (see Ramsay, 1991, p. 615) the subjects. By default a standard normal distribution is used. A different distribution can be adopted by specifying the first element of the list as `"norm"`, `"beta"`, `"unif"`, `"gamma"`, etc. where the character string is the same as used in the subjscoresummary function `qnorm()`,`qbeta()`, `qunif()`, `qgamma()`. The other elements of the list should be the distribution parameters as required by the subjscoresummary function chosen.
`groups`	an optional vector of length equal to the number of subjects containing the group designation of each subject. Adding this option allows for comparisons between groups using the Differential Item Functioning tools (see details section).
`x`	a `ksIRT` object to be printed.
`...`	further parameters

Details

When bandwidth="Silverman", the rule of thumb of Silverman (1986, p. 45) is implemented with the formula: 1.06*sigma.hat*nsubj^(-.2), where nsubj is the number of subjects and sigma.hat is the standard deviation of the subjscoresummary associated to the subjects according to the distribution specified with thetadist. Note that when thetadist=list("norm",mean,sd), sigma.hat is the value specified for sd.

Printing the ksIRT object shows the point polyserial correlation correlation between each item and the overall test score.

Value

Returned from this function is a ksIRT object which is a list with the following components:

`nitem`	an integer indicating the number of items.
`nsubj`	an integer indicating the number of subjects.
`nevalpoints`	an integer indicating the number of points for curve estimation.
`binaryresp`	a matrix of binary responses. Each row corresponds to a single option. The first three columns specify the item, the option, and the corresponding weight. Each additional column is a binary indicator of whether a subject selected that option.
`OCC`	a matrix with the first 3 columns the same as `binaryresp` and an additional column for each quantile at which the option characteristic curves have been estimated. The additional columns contain the kernel smoothed probabilities of selecting each option.
`stderrs`	a matrix as `OCC` containing the standard errors of `OCC`.
`subjscore`	a vector containing the observed score of each subject.
`itemlabels`	a list containing the label for each item.
`thetadist`	a list indicating the distribution used to rank subjects (see `thetadist` in Arguments).
`subjtheta`	a vector of quantile ranks for each subject on the distribution specified in `thetadist`.
`evalpoints`	a vector with the subjscoresummary used in curve estimation.
`subjscoresummary`	a vector of subjscoresummary, of probabilities `.05`, `.25`, `.50`, `.75`, `.95`, for the observed overall scores.
`subjscoresummaryevalpoints`	a vector as `subjscoresummary` but computed on `subjtheta`.
`SmthWgts`	a matrix containing the kernel weights.
`scale`	a vector indicating whether each item is multiple-choice, rating-scale or nominal; `1` indicates multiple-choice, `0` indicates rating-scale, `3` indicates nominal.
`format`	returns the `format` argument passed at function call.
`bandwidth`	a vector containing the bandwidths for each item.
`DIF`	a list of `ksIRT` objects created for each of the subgroups specified by `groups`.
`groups`	returns the `groups` argument passed at function call.
`itemcor`	a vector containing the point polyserial correlation for each item.
`RCC`	a list of `nsubj` vectors containing the normalized likelihood for each value in `evalpoints`.
`subjthetaML`	the maximum likelihood estimate for the expected total score of each subject.

References

Mazza A, Punzo A, McGuire B. (2014). KernSmoothIRT: An R Package for Kernel Smoothing in Item Response Theory. Journal of Statistical Software, 58 6, 1-34. URL: http://www.jstatsoft.org/v58/i06/.

Ramsay, J.O. (2000). TestGraf: A program for the graphical analysis of multiple choice test and questionnaire data. http://www.psych.mcgill.ca/faculty/ramsay/ramsay.html.

Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis. Chapman & Hall, London.

Examples

 ## Psych101 data
data(Psych101)
Psych1 <- ksIRT(responses = Psychresponses[1:100,], key = Psychkey, format = 1)
Psych1
    
plot(Psych1,plottype="OCC", item=c(24,25,92,96))
plot(Psych1,plottype="EIS", item=c(24,25,92,96))
plot(Psych1, plottype="tetrahedron", items=c(24,92))
plot(Psych1, plottype="triangle", items=c(24,92))
plot(Psych1, plottype="PCA")
plot(Psych1,plottype="RCC", subjects=c(33,92))
 
PCA(Psych1)
subjEIS(Psych1)
subjETS(Psych1)
subjOCC(Psych1, stype="ObsScore")
subjscore(Psych1)
subjthetaML(Psych1)
subjscoreML(Psych1)
 
plot(Psych1, plottype="expected")
plot(Psych1, plottype="sd")
plot(Psych1, plottype="density")

## HIV data
data(HIV)
HIVsubset <- HIV[c(c(1:50),c(1508:1558),c(2934:2984)),]
gr2 <- as.character(HIVsubset$SITE)
DIF2 <- ksIRT(res=HIVsubset[,-(1:3)], key=HIVkey, format = 2, groups=gr2, miss="omit")

plot(DIF2, plottype="expectedDIF", lwd=2)
plot(DIF2, plottype="densityDIF", lwd=2)
plot(DIF2, plottype="EISDIF",  item=c(6,11))

### Ordinal Survey Data
data(BDI)
BDI1 <- ksIRT(responses=BDIresponses, key=BDIkey, format = 2, miss="omit")

plot(BDI1, plottype="OCC", items=1:4)
plot(BDI1, plottype="sd")
plot(BDI1, plottype="density", ylim=c(0,0.1))

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(KernSmoothIRT)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/KernSmoothIRT/ksIRT.Rd_%03d_medium.png", width=480, height=480)
> ### Name: ksIRT
> ### Title: ksIRT - kernel smoothing in Item Response Theory
> ### Aliases: ksIRT print.ksIRT
> 
> ### ** Examples
> 
>  ## Psych101 data
> data(Psych101)
> Psych1 <- ksIRT(responses = Psychresponses[1:100,], key = Psychkey, format = 1)
> Psych1
    Item Correlation
1      1  0.25649591
2      2  0.02677782
3      3  0.31383602
4      4  0.48082331
5      5  0.27337044
6      6  0.30066495
7      7  0.06094600
8      8  0.26786289
9      9  0.24416394
10    10  0.29036694
11    11 -0.09167675
12    12  0.11672180
13    13  0.35673809
14    14  0.38508561
15    15  0.21393572
16    16  0.37488562
17    17  0.31125237
18    18  0.20866377
19    19  0.10251262
20    20  0.17690514
21    21  0.36689552
22    22  0.05837302
23    23  0.40261936
24    24  0.18861821
25    25  0.42918758
26    26  0.31302205
27    27  0.29482179
28    28  0.24620279
29    29  0.40264614
30    30  0.32054662
31    31  0.35226408
32    32  0.48324792
33    33  0.36835729
34    34  0.25032496
35    35  0.22099327
36    36  0.14968733
37    37  0.33610537
38    38  0.22060420
39    39  0.13508245
40    40  0.26383227
41    41  0.25873834
42    42  0.15871280
43    43  0.41586999
44    44  0.24892583
45    45  0.29259704
46    46  0.23420217
47    47 -0.02784687
48    48  0.04140554
49    49  0.34749330
50    50  0.26970521
51    51 -0.01693182
52    52  0.28134781
53    53  0.25086885
54    54  0.57840217
55    55  0.17736880
56    56  0.34690274
57    57  0.06099389
58    58 -0.02441550
59    59  0.40810997
60    60  0.01820892
61    61  0.24745021
62    62  0.13531784
63    63  0.08247568
64    64  0.16807939
65    65  0.03894124
66    66  0.39106036
67    67  0.30230507
68    68  0.19942670
69    69  0.18529447
70    70  0.17712152
71    71  0.34539944
72    72  0.52002207
73    73  0.33429083
74    74  0.26113763
75    75  0.40930444
76    76  0.21587087
77    77  0.37827051
78    78  0.24961369
79    79  0.40543742
80    80  0.03268210
81    81  0.21256659
82    82  0.14123338
83    83  0.01494216
84    84  0.33480104
85    85  0.29491708
86    86  0.16582713
87    87  0.34420910
88    88  0.32577955
89    89  0.30076840
90    90  0.24745021
91    91  0.36872462
92    92  0.25965929
93    93  0.20863746
94    94  0.23990613
95    95  0.37610617
96    96 -0.09620540
97    97  0.37240652
98    98  0.40023911
99    99  0.07887368
100  100  0.18727827
>     
> plot(Psych1,plottype="OCC", item=c(24,25,92,96))
> plot(Psych1,plottype="EIS", item=c(24,25,92,96))
> plot(Psych1, plottype="tetrahedron", items=c(24,92))
Trait Levels
Red: Low
Green: Medium
Blue: High> plot(Psych1, plottype="triangle", items=c(24,92))
> plot(Psych1, plottype="PCA")
> plot(Psych1,plottype="RCC", subjects=c(33,92))
>  
> PCA(Psych1)
Standard deviations:
 [1] 188.1330945  65.0021475  40.4375029  28.6885735  19.8417874  16.3623210
 [7]   8.7884648   5.6172634   4.2990504   3.3942489   2.5450906   2.3091731
[13]   1.9658230   1.8166603   1.6497908   1.5686417   1.4936260   1.4271621
[19]   1.3363589   1.2468723   1.2156017   1.1513088   1.1470670   1.0446896
[25]   1.0272263   0.9297989   0.9110988   0.8656317   0.8608587   0.8203683
[31]   0.7595571   0.7177400   0.6936646   0.6492589   0.6325497   0.6046065
[37]   0.5842012   0.5286540   0.5246008   0.4972707   0.4622150   0.4281508
[43]   0.4171678   0.4074852   0.3799715   0.3521436   0.3283759   0.3180125
[49]   0.2984194   0.2599509   0.2337646

Rotation:
            PC1          PC2         PC3          PC4          PC5          PC6
 [1,] 0.1082737 -0.193149597  0.30904264  0.260330247 -0.222014643 -0.278243643
 [2,] 0.1140779 -0.209345017  0.28201479  0.234990754 -0.143811748 -0.172816598
 [3,] 0.1182882 -0.218918548  0.25419079  0.193584205 -0.094325375 -0.064784244
 [4,] 0.1227728 -0.221799685  0.22041306  0.144221508 -0.027138031  0.021068146
 [5,] 0.1265693 -0.220574499  0.18283540  0.086611608  0.018145988  0.114684458
 [6,] 0.1295555 -0.215577520  0.14928870  0.034207473  0.059927570  0.166706333
 [7,] 0.1321146 -0.209167622  0.11188932 -0.016036738  0.101977452  0.191813692
 [8,] 0.1342809 -0.199946785  0.08064541 -0.067979672  0.120690516  0.200451139
 [9,] 0.1366862 -0.185919958  0.04544238 -0.111480992  0.155359490  0.174913843
[10,] 0.1380823 -0.173918938  0.01931410 -0.144907496  0.170908044  0.154759317
[11,] 0.1407890 -0.151869907 -0.01062311 -0.172056789  0.176131378  0.091070041
[12,] 0.1415937 -0.142332722 -0.03458243 -0.191878870  0.159161723  0.039649276
[13,] 0.1431454 -0.126361668 -0.05716433 -0.199422012  0.122036076 -0.017687890
[14,] 0.1439990 -0.113665001 -0.07504217 -0.199675388  0.110868405 -0.068676463
[15,] 0.1451553 -0.099884474 -0.08822247 -0.194296560  0.072490315 -0.117973634
[16,] 0.1459000 -0.088466609 -0.09841604 -0.184264828  0.039165817 -0.170049194
[17,] 0.1470460 -0.073553868 -0.10447458 -0.169550097 -0.006747113 -0.190042530
[18,] 0.1478359 -0.061619471 -0.11240593 -0.149118472 -0.051049064 -0.192554850
[19,] 0.1483938 -0.051524387 -0.11704084 -0.127799998 -0.086206707 -0.194185443
[20,] 0.1487337 -0.044624805 -0.12151001 -0.097281020 -0.122531390 -0.194329986
[21,] 0.1492400 -0.037122173 -0.12176319 -0.072132644 -0.145191482 -0.168907878
[22,] 0.1493183 -0.030808492 -0.12815752 -0.045400868 -0.168022546 -0.138716596
[23,] 0.1494128 -0.022832552 -0.12890968 -0.013529243 -0.192483283 -0.098690262
[24,] 0.1494001 -0.011244101 -0.13472792  0.020528253 -0.208413406 -0.033807921
[25,] 0.1491766 -0.007443030 -0.13658124  0.041650985 -0.219837044  0.014965970
[26,] 0.1489893 -0.002380892 -0.13946286  0.063764498 -0.208588651  0.067286064
[27,] 0.1487086  0.005186689 -0.14068180  0.090392683 -0.191499157  0.105896323
[28,] 0.1484699  0.013595820 -0.14226926  0.111858857 -0.160138389  0.137040519
[29,] 0.1479977  0.021919968 -0.14451025  0.131973348 -0.131255313  0.159802865
[30,] 0.1474194  0.029600360 -0.14787440  0.151594857 -0.094330837  0.179439065
[31,] 0.1470451  0.037617834 -0.14658053  0.168618734 -0.038325567  0.184489134
[32,] 0.1467646  0.049919946 -0.14077034  0.173305428  0.015674417  0.181245077
[33,] 0.1466754  0.058455620 -0.13307681  0.175567033  0.066281009  0.148954014
[34,] 0.1463014  0.072674563 -0.12011126  0.174089038  0.121838204  0.092196327
[35,] 0.1460586  0.083986248 -0.09806163  0.171881110  0.172819141  0.034850653
[36,] 0.1454693  0.096411805 -0.07823676  0.163200749  0.205136114 -0.007118054
[37,] 0.1446126  0.112238986 -0.03644955  0.154185899  0.243964595 -0.047388187
[38,] 0.1441311  0.123727561 -0.00345335  0.136733775  0.232741429 -0.100684064
[39,] 0.1433568  0.133979540  0.02026252  0.122728011  0.207487544 -0.145747944
[40,] 0.1426842  0.143270117  0.04871434  0.091586105  0.189660829 -0.154140015
[41,] 0.1414467  0.152102401  0.07658860  0.075681249  0.155956136 -0.166190246
[42,] 0.1400209  0.163965229  0.10259758  0.035204547  0.112151656 -0.154548569
[43,] 0.1381542  0.174304032  0.12631308  0.003541409  0.070130492 -0.138447482
[44,] 0.1364835  0.182185357  0.14481532 -0.025819668  0.032297142 -0.103194968
[45,] 0.1351637  0.187052960  0.15788859 -0.059213832 -0.011272840 -0.048680108
[46,] 0.1338111  0.190307270  0.16609649 -0.090263562 -0.042954421  0.007116886
[47,] 0.1317884  0.193889775  0.17448301 -0.126420322 -0.081722282  0.064769940
[48,] 0.1299943  0.194038715  0.18439178 -0.151639105 -0.109944141  0.124087629
[49,] 0.1284848  0.194351238  0.18556269 -0.174286447 -0.133329970  0.162515978
[50,] 0.1272309  0.195872060  0.18512028 -0.188268326 -0.144951853  0.185206256
[51,] 0.1264536  0.195158505  0.18897006 -0.191489922 -0.157038492  0.194448667
               PC7         PC8          PC9         PC10          PC11
 [1,] -0.416779552 -0.12674084 -0.216822018  0.256987213 -4.062453e-01
 [2,] -0.189763374 -0.07875649 -0.049215305  0.013579418  1.506153e-01
 [3,] -0.001798105  0.07901832  0.085157858 -0.226861360  3.351098e-01
 [4,]  0.118468575  0.08591086  0.152404661 -0.183724374  2.231891e-01
 [5,]  0.173201282  0.10641702  0.197697619 -0.095306303  6.468844e-02
 [6,]  0.200390036  0.11949879  0.155028214 -0.002833697 -7.570445e-02
 [7,]  0.194301645  0.08855562  0.044985207 -0.026068037 -1.997594e-01
 [8,]  0.162420057  0.07645799 -0.012900834  0.077839527 -2.321593e-01
 [9,]  0.103393216  0.03399500 -0.148498527  0.168714347 -2.206950e-01
[10,]  0.029904876 -0.06995487 -0.230200867  0.272570387 -8.597791e-03
[11,] -0.058288775 -0.17887299 -0.203362763  0.204194427  1.490536e-01
[12,] -0.133734640 -0.18886876 -0.155135440  0.044088563  2.277756e-01
[13,] -0.177116001 -0.19147897 -0.088129727 -0.156285953  1.263070e-01
[14,] -0.188025063 -0.16816284  0.017398772 -0.244853140  4.229536e-02
[15,] -0.163937862 -0.12776103  0.151326914 -0.192483533  8.311196e-02
[16,] -0.127374662 -0.01202411  0.209179183 -0.147003044  2.627734e-03
[17,] -0.082009019  0.08709209  0.185985054 -0.042004193 -2.089603e-01
[18,] -0.035701307  0.12912131  0.191745713 -0.007448676 -1.854674e-01
[19,]  0.010912210  0.17928732  0.130623907  0.025246400 -1.643222e-01
[20,]  0.053530284  0.19143530  0.097430621  0.111869557 -4.894354e-02
[21,]  0.115456213  0.18584301 -0.011983018  0.125899918  5.024960e-02
[22,]  0.143576372  0.15242299 -0.088024626  0.180313227  1.354969e-01
[23,]  0.169258116  0.10658288 -0.224076146  0.142582286  1.846396e-01
[24,]  0.153254756  0.01400897 -0.218901745  0.042599234  1.734873e-01
[25,]  0.132719805 -0.03141849 -0.161571653 -0.047557700  7.165428e-02
[26,]  0.096048625 -0.10260019 -0.126666043 -0.112318589  1.219316e-05
[27,]  0.072808297 -0.16470814 -0.105631629 -0.135004541 -5.938254e-02
[28,]  0.039366722 -0.18718141  0.005045183 -0.134927039 -1.253170e-01
[29,]  0.010994144 -0.20381574  0.046995119 -0.144241805 -1.683363e-01
[30,] -0.033362986 -0.15703585  0.111625169 -0.052016983 -8.382335e-02
[31,] -0.093598757 -0.09176157  0.114657058  0.021792798 -2.099183e-02
[32,] -0.128319763 -0.05450673  0.169626448  0.106411854 -8.022108e-03
[33,] -0.177335798  0.02745271  0.149310204  0.138352530  3.892659e-02
[34,] -0.202983219  0.14454719  0.102473984  0.187119317  1.005770e-01
[35,] -0.184284516  0.18802578  0.051313156  0.126601722  1.139599e-01
[36,] -0.135297522  0.25566440 -0.033454424  0.093128683  1.427680e-01
[37,] -0.032380414  0.17027550 -0.083618530 -0.072354584  6.054100e-02
[38,]  0.028403923  0.11631800 -0.172313751 -0.190573783 -1.033093e-01
[39,]  0.071435378  0.08066680 -0.216548359 -0.199779879 -1.446608e-01
[40,]  0.129561871 -0.02860948 -0.135587917 -0.210288080 -1.914092e-01
[41,]  0.189017026 -0.08474885 -0.069154907 -0.072959864 -8.036885e-02
[42,]  0.158698346 -0.20006607 -0.042875941  0.043033496  7.435924e-02
[43,]  0.143078608 -0.24616842  0.085038558  0.101133889  9.224917e-02
[44,]  0.131516734 -0.19480514  0.166738108  0.150460304  6.570891e-02
[45,]  0.099022738 -0.15094995  0.170268881  0.154743475  2.604539e-02
[46,]  0.048874285 -0.10005777  0.215140570  0.136074824 -2.200362e-02
[47,]  0.007532774 -0.03192622  0.115108222  0.138346627  3.318489e-02
[48,] -0.032712325  0.02917439  0.024383849  0.040971088 -3.611710e-04
[49,] -0.138747585  0.11627008 -0.041439814 -0.064221998 -1.730291e-02
[50,] -0.161964228  0.19013379 -0.110453095 -0.152069906 -2.960465e-02
[51,] -0.189489676  0.23180659 -0.206232422 -0.189929925  3.144399e-02
             PC12         PC13         PC14         PC15         PC16
 [1,]  0.10917356 -0.166080490  0.049301066 -0.030769552  0.134296823
 [2,] -0.07450070  0.115018099  0.046923355 -0.005726306 -0.165413966
 [3,] -0.08512025  0.284957508 -0.108786518  0.153093313 -0.212859876
 [4,] -0.02160218  0.055385742 -0.059514165 -0.290090269  0.164509015
 [5,] -0.00447047 -0.131777100 -0.133404310  0.044627801  0.232441319
 [6,]  0.10281404 -0.154538536  0.181456066  0.236702336  0.079928385
 [7,]  0.02149564 -0.247323856  0.203311439  0.132735043 -0.212607899
 [8,] -0.03779575 -0.214564515  0.059747297 -0.188683821 -0.158302887
 [9,]  0.05888317  0.262793247 -0.227251344 -0.235911578  0.126749525
[10,]  0.07660987  0.389491027 -0.146991618  0.025837051  0.109064984
[11,] -0.21718492  0.110099239 -0.008611201  0.221368518 -0.088655378
[12,] -0.05545536 -0.109763124  0.014620941  0.140570321 -0.133761477
[13,] -0.01174028 -0.293710702  0.109154257  0.038320620  0.051198847
[14,]  0.07687171 -0.114947685  0.159549753 -0.242573520  0.109385372
[15,]  0.13052021 -0.009360762  0.018323354 -0.260747222  0.026286974
[16,]  0.07684383  0.118389049  0.007348184 -0.029222297 -0.080519302
[17,]  0.06224239  0.174792722 -0.166989617  0.120318402 -0.056826457
[18,] -0.02117380  0.136025151 -0.127877744  0.220487795  0.060595238
[19,] -0.08930655 -0.057259403 -0.038967747  0.232330864 -0.013696374
[20,] -0.14098247 -0.108199572 -0.066538535 -0.031174711  0.084243043
[21,] -0.17583724 -0.036160323  0.071088918 -0.175507667  0.048197737
[22,] -0.12906399  0.097198946  0.221083721 -0.096065780 -0.032335712
[23,] -0.01365470  0.048799289  0.308874677 -0.037639501 -0.052148803
[24,]  0.19638960 -0.165000545  0.080571854  0.017737529  0.032299783
[25,]  0.19415623 -0.061851541 -0.170088227 -0.042353144  0.130445917
[26,]  0.18784426 -0.121748783 -0.320983001 -0.053705421 -0.139887952
[27,]  0.06746499 -0.040553164 -0.221172960  0.039608498 -0.130266233
[28,]  0.06825902  0.061561199 -0.068333869  0.070086047 -0.214076392
[29,] -0.01741881  0.126599893  0.107386957  0.182054172  0.045193164
[30,] -0.09861640  0.127188354  0.187081360  0.052178592  0.222542076
[31,] -0.18829239  0.141929916  0.205785047 -0.054388416  0.267249651
[32,] -0.13933940  0.047250205  0.030494185 -0.131506476  0.002566345
[33,] -0.19954140 -0.108967383 -0.036474108 -0.104221680 -0.096363341
[34,] -0.09632613 -0.094581950 -0.108937539 -0.027692881 -0.213676282
[35,]  0.08514160 -0.138019475 -0.065241303  0.047345009 -0.105912949
[36,]  0.24962770 -0.114367428 -0.203916409  0.053967657  0.112014263
[37,]  0.36200365  0.093363406  0.124274464  0.080726316  0.222604617
[38,]  0.14643404  0.161806086  0.212777769  0.064381164 -0.025241435
[39,] -0.04246305  0.104747804  0.103638089 -0.049530086 -0.249833327
[40,] -0.20982945  0.013682040  0.021550071 -0.107411470 -0.069266563
[41,] -0.33733858 -0.074390180 -0.152778715 -0.197835115  0.035001644
[42,] -0.15763877 -0.163958925 -0.325232410  0.058771521  0.189114085
[43,] -0.02615208 -0.118348882  0.069245604  0.218590009  0.294516883
[44,]  0.07509461  0.047908606  0.039850546  0.231585522 -0.069505569
[45,]  0.11978023  0.010718616  0.077606679 -0.001127805 -0.212069754
[46,]  0.17152230  0.101275177  0.039210731 -0.192037671 -0.111956954
[47,]  0.17546468  0.116004966  0.035528738 -0.190815792 -0.008363987
[48,]  0.14331187 -0.056288336  0.088793117 -0.137517127 -0.090328752
[49,] -0.07380727 -0.064041630 -0.079454578  0.026426131 -0.062486913
[50,] -0.11457650 -0.042111806 -0.045406414  0.105583969  0.040033720
[51,] -0.18042563  0.065472951  0.012482525  0.096855987  0.190954321
              PC17        PC18         PC19         PC20         PC21
 [1,] -0.122536742  0.18588277 -0.040975555 -0.103710294  0.031083943
 [2,]  0.194881342 -0.47851063  0.005467244  0.297499893 -0.060580420
 [3,]  0.206804188  0.14265957  0.133406763 -0.270225957  0.136261263
 [4,] -0.126125296  0.18200110 -0.042896160 -0.063482933 -0.171371217
 [5,] -0.399414959  0.22747643  0.064061190  0.114442886  0.151304589
 [6,] -0.146481256 -0.26159669 -0.019175302  0.074335063 -0.145749370
 [7,]  0.109449282 -0.06674884 -0.215625248  0.048471605 -0.112736705
 [8,]  0.386891121  0.01100022  0.052066916 -0.085521547  0.180658024
 [9,]  0.211126284  0.02858743  0.035702025  0.019014490  0.079984454
[10,] -0.085458157  0.08710391 -0.172559288  0.078402047 -0.147654016
[11,] -0.236201137 -0.12304477  0.090888579 -0.133764882  0.139053169
[12,] -0.046639895  0.04576701  0.217964892  0.024795056 -0.013066542
[13,]  0.012791726  0.14315159  0.098386930 -0.134240752 -0.054591691
[14,] -0.010590459 -0.06169936  0.033689641 -0.072074847 -0.097222793
[15,]  0.057879291 -0.04030660 -0.181761343  0.261612427  0.025415572
[16,] -0.008387340 -0.02605424 -0.339779867  0.011504922  0.176393732
[17,]  0.022237616 -0.03444774 -0.036785466 -0.181140650  0.023715071
[18,] -0.006466264  0.07108435  0.149408259  0.014988159 -0.248041549
[19,] -0.029074435 -0.04056302  0.281070395  0.065965699 -0.187337297
[20,]  0.057343954  0.01255775  0.100371743  0.143867695  0.165672654
[21,] -0.001772274 -0.04765418 -0.073942942 -0.037904516  0.313446944
[22,] -0.076016881 -0.04048807 -0.029355846 -0.013991078  0.089623664
[23,] -0.104199657  0.02781547 -0.067522694  0.054412021 -0.258622463
[24,]  0.072734441  0.13367550 -0.090340822 -0.127783198  0.009196198
[25,]  0.223969906  0.01249581  0.011189192 -0.093303243 -0.119326717
[26,]  0.089913287 -0.01682142  0.174966889  0.011472698 -0.030242137
[27,] -0.218718638  0.04189247 -0.029454614  0.112578416 -0.034901153
[28,] -0.136686070 -0.13867176 -0.112728265  0.076311618  0.028297242
[29,] -0.032175077 -0.08401459 -0.113029553 -0.044993085  0.073925109
[30,] -0.008464087  0.02160052 -0.066685582 -0.044204383  0.350628998
[31,]  0.040155224 -0.05752157  0.099690617 -0.144898313 -0.045899596
[32,]  0.154209492  0.09932034  0.222630516  0.069265896 -0.227460879
[33,]  0.121313271  0.02121917  0.108285027  0.099543934 -0.098860595
[34,] -0.122432574  0.17627326 -0.094804522  0.076211910 -0.026934391
[35,] -0.036652222  0.12686233 -0.312209555  0.036598926  0.018077142
[36,] -0.027962577 -0.34293132 -0.111523437 -0.303044850  0.031490126
[37,]  0.051821810 -0.13359939  0.240925160  0.016472789  0.028025903
[38,]  0.046044628  0.09685656  0.165628696  0.240977306  0.185257521
[39,] -0.084134145  0.26773021  0.026703071  0.116348699  0.029588542
[40,] -0.107267239 -0.02665147  0.004572653 -0.245767010 -0.168910981
[41,] -0.115108559 -0.27259371 -0.130536740 -0.205493455 -0.134260466
[42,]  0.047121220 -0.07033361  0.021159100  0.378428704  0.170483329
[43,]  0.224332260  0.11222127 -0.061265806 -0.010831779 -0.034265185
[44,]  0.178407994  0.11380893 -0.154368886 -0.103625193 -0.018051610
[45,]  0.042457851  0.13941984 -0.021891248  0.003960551  0.052403921
[46,] -0.060904333  0.05042480  0.089787806 -0.102209921 -0.171571086
[47,] -0.169391517 -0.12509919  0.008366903  0.059804137 -0.076327032
[48,] -0.211533630 -0.13871064  0.319680532  0.030686988  0.218228118
[49,] -0.014040712 -0.03781891  0.061588515 -0.205463830  0.155718196
[50,]  0.060101013  0.01442008 -0.105612614 -0.027768858  0.005378029
[51,]  0.136609081  0.07167310 -0.195834466  0.216908321 -0.184155639
              PC22         PC23          PC24         PC25         PC26
 [1,]  0.015504474  0.043898956 -0.0708663078 -0.063640765 -0.044517285
 [2,] -0.156703894 -0.146943032  0.1156831846  0.100568029  0.103554794
 [3,]  0.383233793  0.045583926  0.0427581392  0.090375018 -0.025331320
 [4,] -0.203619900  0.323016282 -0.1796439242 -0.201348198 -0.116539991
 [5,] -0.142018889 -0.322609301  0.0895048970  0.002519688  0.113667470
 [6,] -0.026721251 -0.063476029  0.1253826159  0.056667334  0.011258097
 [7,]  0.088079365  0.096042583 -0.1289172765  0.108518640 -0.055021721
 [8,]  0.042504846  0.027455748 -0.2578163459 -0.078556359 -0.016495882
 [9,]  0.143887441 -0.130778018  0.3817020456 -0.149661190 -0.147906812
[10,]  0.022112703  0.128151673 -0.0582140717  0.107044949  0.367814354
[11,] -0.274117641  0.028774205 -0.0432668444 -0.017455639 -0.166261309
[12,] -0.084198578 -0.007666615 -0.0499209905  0.117832528 -0.208864330
[13,]  0.146781790  0.101222391 -0.0304010226  0.035546516  0.138892010
[14,]  0.157153980  0.038159688  0.2608781974  0.039187632  0.178266833
[15,]  0.012103335  0.030617957  0.0418481099 -0.131809549 -0.232437224
[16,] -0.210530233 -0.281809776 -0.1795932868 -0.086501677  0.146934657
[17,]  0.022236085 -0.175998670 -0.2780586625  0.023138176 -0.036821683
[18,]  0.177168439 -0.059417223 -0.0779160314 -0.044641513 -0.012643075
[19,] -0.016875994  0.134227437  0.1978706315 -0.010746930 -0.085179003
[20,] -0.112216184  0.225841143  0.0603346099  0.261591458  0.129427596
[21,] -0.154724114  0.220940530  0.1886969174  0.075051096 -0.092195244
[22,]  0.130021671  0.090249500  0.0104772735 -0.264761987  0.042675348
[23,]  0.194443611 -0.176148463 -0.2564793818 -0.186705583 -0.015136434
[24,]  0.018594766 -0.322064467  0.1263895486  0.184495916  0.085259867
[25,] -0.200626932 -0.161784653 -0.0028825594  0.112570193 -0.024287812
[26,] -0.156593760  0.067032507 -0.0560165614  0.107144970  0.013019137
[27,]  0.033285609  0.132886287  0.0081471519 -0.132074833 -0.095870555
[28,]  0.089270980  0.243720180  0.0271046795 -0.182338365  0.110012351
[29,]  0.078425621  0.042550211  0.1758672568 -0.079739007 -0.034894067
[30,]  0.082459091 -0.014908368 -0.0373864907  0.238763990 -0.066650428
[31,] -0.044866563 -0.003179996 -0.2381724183  0.170670822  0.003684003
[32,] -0.174285122 -0.104344828 -0.1014310272 -0.171643169 -0.071100260
[33,] -0.041039357 -0.186323441  0.0837713163 -0.123340582  0.110446380
[34,]  0.150284295 -0.005071038  0.1615939787  0.046716373  0.130145702
[35,]  0.157175252  0.019490288  0.0831427935  0.130038866 -0.114163383
[36,] -0.052926174  0.174355070 -0.0969443477 -0.089509984 -0.150803294
[37,] -0.018162250  0.042598571 -0.0213886556 -0.112495173  0.181594681
[38,] -0.074549210  0.087832991 -0.0729650731  0.055437029  0.056940391
[39,] -0.127002320 -0.140499298  0.0110834205  0.042187076 -0.178761561
[40,] -0.092296036 -0.026261355  0.1430755712  0.097669972 -0.081805064
[41,]  0.101760999 -0.114315741 -0.0008665913  0.016014542  0.200706335
[42,]  0.281316298 -0.009065930 -0.3178251457  0.031136422  0.008846686
[43,]  0.068744870  0.023790253  0.1194622570 -0.190540429 -0.106807532
[44,] -0.208975960 -0.006069447  0.1934127546 -0.207018819 -0.088593843
[45,] -0.186137166  0.150044790 -0.0527865461  0.013997624  0.271803148
[46,]  0.009858509  0.150431079  0.0174473996  0.319364824  0.137119986
[47,]  0.150318113 -0.114179189 -0.0555188779  0.298023652 -0.457017222
[48,]  0.176008853 -0.082844349  0.0123443090 -0.224269603  0.042818753
[49,] -0.044490229 -0.113576665 -0.0077382343 -0.186531618  0.147066527
[50,] -0.082023710 -0.044182150 -0.0380254085  0.007800706  0.020193458
[51,] -0.046005208  0.143124413  0.0309197319  0.042948727 -0.025954522
              PC27         PC28         PC29         PC30          PC31
 [1,]  0.148941378  0.008667280  0.004420128  0.114512891 -0.0288025157
 [2,] -0.308506567  0.005914901 -0.033685742 -0.212315030  0.0351478122
 [3,]  0.127200445  0.021733064  0.083534597  0.213429258 -0.0447317929
 [4,]  0.071970243 -0.187998013 -0.058947860 -0.233778392 -0.0216721574
 [5,] -0.231318369  0.042599490 -0.042084007  0.043636975  0.0204120078
 [6,]  0.368273664  0.195056768 -0.067619445  0.090280257  0.2420272998
 [7,] -0.088821577  0.038973046  0.252060254 -0.010346136 -0.3136086697
 [8,] -0.031571609 -0.104148746 -0.110265063 -0.007508282  0.0770439497
 [9,] -0.106251183 -0.042274380 -0.162012573  0.077002485  0.1328031799
[10,] -0.097123930  0.098341802  0.282482206 -0.050103162 -0.1422931985
[11,]  0.259055971 -0.287239419 -0.044671965 -0.078102346  0.0312414156
[12,] -0.027910026  0.110477933 -0.110723616  0.173668041  0.0080667594
[13,] -0.283162083  0.148726296 -0.274815192 -0.232452895 -0.1410934382
[14,]  0.140950611  0.106788119  0.202788003  0.037410212  0.2629266565
[15,]  0.057920057 -0.162666460  0.145357502  0.012310572  0.0198162481
[16,]  0.021780661  0.014176972 -0.034039439  0.312319002 -0.2312341991
[17,]  0.116557218  0.016260690 -0.015753771 -0.206722567  0.0584028015
[18,]  0.013952254  0.072149449 -0.053279584 -0.219253426  0.1352639474
[19,] -0.170069776 -0.216752451  0.062639619  0.071749505 -0.0449129566
[20,] -0.076935427 -0.142018903  0.080877987  0.120433698 -0.0644734503
[21,]  0.045750138  0.187614283  0.002564621 -0.003057360  0.0066961222
[22,]  0.039106347  0.392141458 -0.189817290 -0.018771050 -0.1516167113
[23,] -0.137002292 -0.296252034  0.079632970  0.081184258  0.1860767290
[24,]  0.059743496 -0.221266345 -0.009278998  0.070504346  0.0899949091
[25,]  0.171053837  0.214448884 -0.139885565 -0.297403947 -0.1753779627
[26,]  0.118001139 -0.057594828  0.282341215 -0.006102377  0.0308147791
[27,] -0.133378414  0.143112401  0.040802428  0.178326202 -0.0687403601
[28,]  0.012188642  0.034895926 -0.169421657  0.131273089  0.1867281874
[29,] -0.014752412 -0.205445412 -0.264224397 -0.114633848 -0.2041982658
[30,] -0.128181455 -0.164577340  0.151992238 -0.151926874  0.0570719324
[31,] -0.054076575  0.252880798  0.163154810  0.077622062  0.1875813107
[32,] -0.116980579  0.039709500 -0.029864069  0.109420280 -0.0004570027
[33,]  0.283762905 -0.008998648 -0.011595550  0.101388452 -0.1430285417
[34,]  0.162015126 -0.009354655  0.108662913 -0.132529652 -0.1845941581
[35,] -0.100666410 -0.091705372 -0.160252678 -0.230245694  0.2122428335
[36,] -0.196770985  0.075128117  0.099416180  0.124478930  0.1387697810
[37,] -0.018881257 -0.131154858 -0.124238807  0.151731605 -0.2619986943
[38,]  0.218114451 -0.015331727 -0.066520313 -0.129711119  0.0212530496
[39,] -0.114694340  0.201084401  0.114260012  0.017393604  0.1891235288
[40,] -0.104905954 -0.022816366  0.039627855  0.027995045 -0.1797987115
[41,]  0.124075136 -0.128141978 -0.037676532 -0.045542719 -0.0113412853
[42,]  0.044281201  0.071792302 -0.089131208  0.034739770  0.0843336858
[43,]  0.012461670 -0.055089822  0.159514949  0.127472774 -0.1202791410
[44,] -0.056329147  0.151164127  0.189882677 -0.180320615  0.0862132899
[45,]  0.007851301 -0.036807957 -0.160585112  0.020449862  0.1933956133
[46,] -0.057594178 -0.101241148 -0.217134929  0.148783211  0.0639820031
[47,]  0.033155568  0.090618958 -0.103965945  0.064057383 -0.2537051647
[48,]  0.039011884 -0.026005581  0.306983087 -0.311062658 -0.0912561572
[49,] -0.142593113  0.008703039  0.044000601  0.043096545  0.0641996597
[50,] -0.054377261 -0.002148825 -0.087373841  0.045685687  0.0151368315
[51,]  0.155314428 -0.026488485 -0.024824602  0.052364778  0.0396746985
              PC32         PC33          PC34         PC35         PC36
 [1,] -0.023350082 -0.039282693 -0.0813351880  0.004000823  0.009239389
 [2,]  0.062067764  0.026785891  0.1533612038  0.003898422  0.015112541
 [3,] -0.068999359  0.043543877 -0.1127334217  0.093403934  0.035153384
 [4,]  0.001308367 -0.012794674  0.0233638686 -0.223462746 -0.150263572
 [5,]  0.041339763  0.032154194  0.1082016918  0.081148818  0.181926187
 [6,]  0.023400380  0.025784547 -0.1969956713  0.031932091 -0.177627570
 [7,] -0.112619099 -0.240255329  0.0376773468  0.072132970  0.094621532
 [8,]  0.030464027  0.242806409  0.1591219678 -0.005698140  0.056388014
 [9,]  0.180303779 -0.222091956 -0.0053388790 -0.067745213 -0.065518994
[10,] -0.139618232  0.189577977 -0.1448431577 -0.073588243 -0.026331541
[11,] -0.008334918 -0.040953335  0.1793361768  0.274707546  0.176495397
[12,] -0.132401740 -0.072635338 -0.1114200715 -0.346528672 -0.136928554
[13,]  0.305637208  0.130839476 -0.1079892359  0.078415507 -0.136714835
[14,] -0.114283006  0.036137698  0.2098893443  0.146375052  0.020779587
[15,] -0.076514541 -0.166651157 -0.2662549022  0.053751819  0.185302937
[16,]  0.048255181 -0.073560259  0.1043668978 -0.122898414 -0.073775481
[17,] -0.054220449  0.209511149  0.0619929375 -0.030200382 -0.103505453
[18,]  0.114106383 -0.069082589  0.1241037341  0.180569027  0.204343586
[19,] -0.122122547 -0.137635757 -0.0800741204 -0.325759485 -0.137780706
[20,]  0.009291844  0.198725888 -0.1206346112  0.133221115 -0.098121952
[21,]  0.063260402  0.217790986  0.0052094819  0.010900991  0.149091000
[22,] -0.134286353 -0.316964384  0.0112613184  0.109059076 -0.008316449
[23,]  0.227198217  0.020126530  0.0379588506  0.019243305 -0.056222940
[24,] -0.173665830  0.099012629 -0.0555016118 -0.160639947  0.129859373
[25,] -0.216617604 -0.080800184  0.0762294583 -0.065402936 -0.031093609
[26,]  0.331782320 -0.211898598 -0.0771383777  0.160972386  0.025307513
[27,]  0.005830975  0.056234047  0.1411836005  0.217985103 -0.145784838
[28,]  0.039342400  0.313705917 -0.0245087496 -0.301528524  0.219789367
[29,] -0.106643914 -0.023094444  0.0256832300  0.064530230 -0.051404556
[30,] -0.029942144 -0.132981415 -0.0189869916  0.049381548 -0.330333683
[31,]  0.183360261 -0.145006660  0.0004726305 -0.244642391  0.238327501
[32,] -0.343301597  0.136457993 -0.2737087387  0.296173654  0.110236284
[33,]  0.092625936  0.128520924  0.1488687653 -0.091289738 -0.215051770
[34,]  0.246054909 -0.129537817  0.1085718584 -0.107087523  0.071391428
[35,] -0.175397042  0.007467030 -0.1003215967  0.020796788  0.107067132
[36,] -0.040834593 -0.035942499  0.1535104148  0.036194567 -0.117442319
[37,]  0.054413771  0.072419369 -0.0918629172  0.138736200  0.076255699
[38,]  0.132640291 -0.083551719 -0.0275059719 -0.136002233  0.053261854
[39,] -0.098341172  0.087322208  0.0802537908  0.119705366 -0.284313325
[40,] -0.029594787  0.010605118  0.0752863132 -0.135649057  0.340021356
[41,]  0.017715706 -0.007923916 -0.3134302911  0.087136073 -0.202938109
[42,] -0.157485082 -0.109491416  0.0478884114 -0.090012734  0.079556047
[43,]  0.061416159  0.101151307  0.2575341118  0.013224804  0.012429780
[4