1 Introduction

MMUPHin is an R package implementing meta-analysis methods for microbial community profiles. It has interfaces for: a) covariate-controlled batch and study effect adjustment, b) meta-analytic differential abundance testing, and meta-analytic discovery of c) discrete (cluster-based) or d) continuous unsupervised population structure.

Overall, MMUPHin enables the normalization and combination of multiple microbial community studies. It can then help in identifying microbes, genes, or pathways that are differential with respect to combined phenotypes. Finally, it can find clusters or gradients of sample types that reproduce consistently among studies.

2 Installation

MMUPHin is a Bioconductor package and can be installed via the following command.

if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
BiocManager::install("MMUPHin")

This vignette is intended to provide working examples for all four functionalities of MMUPHin.

MMUPHin can be loaded into R with the first library() command shown below. We also load some utility packages for data manipulation and visualization.

library(MMUPHin)
library(magrittr)
library(dplyr)
library(ggplot2)

3 Input data

As input, MMUPHin requires a properly formatted collection of microbial community studies, with both feature abundances and accompanying metadata. Here we use the five published colorectal cancer (CRC) stool metagenomic studies, incorporated in Thomas et al. (2019). Data for the studies are already conveniently packaged and accessible through the Biocondcutor package curatedMetagenomicData, though additional wranglings are needed to format input for MMUPHin.

Importantly, MMUPHin asks that feature abundances be provided as a feature-by-sample matrix, and the metadata be provided as a data frame. The two objects shoud agree on sample IDs, that is, rowname of the feature abundance matrix and colname of the metadata data frame must agree. Many popular ’omic data classes in R already enforce this standard, such as ExpressionSet from Biobase, or phyloseq from phyloseq.

To minimize users’ efforts in loading data to run the examples, we have properly formatted the five studies for easy access. The feature abundances and metadata can be loaded with the following code chunk. For the interested user, the commented out scripts were used for accessing data directly from curatedMetagenomicData and formatting. It might be worthwhile to read through these as they perform many of the common tasks for preprocessing microbial feature abundance data in R, including sample/feature subsetting, normalization, filtering, etc.

data("CRC_abd", "CRC_meta")
CRC_abd[1:5, 1, drop = FALSE]
##                                 FengQ_2015.metaphlan_bugs_list.stool:SID31004
## s__Faecalibacterium_prausnitzii                                    0.11110668
## s__Streptococcus_salivarius                                        0.09660736
## s__Ruminococcus_sp_5_1_39BFAA                                      0.09115385
## s__Subdoligranulum_unclassified                                    0.05806767
## s__Bacteroides_stercoris                                           0.05685503
CRC_meta[1, 1:5]
##                                               subjectID body_site
## FengQ_2015.metaphlan_bugs_list.stool:SID31004  SID31004     stool
##                                               study_condition
## FengQ_2015.metaphlan_bugs_list.stool:SID31004             CRC
##                                                                    disease
## FengQ_2015.metaphlan_bugs_list.stool:SID31004 CRC;fatty_liver;hypertension
##                                               age_category
## FengQ_2015.metaphlan_bugs_list.stool:SID31004        adult
table(CRC_meta$studyID)
## 
##      FengQ_2015.metaphlan_bugs_list.stool 
##                                       107 
## HanniganGD_2017.metaphlan_bugs_list.stool 
##                                        55 
##  VogtmannE_2016.metaphlan_bugs_list.stool 
##                                       104 
##        YuJ_2015.metaphlan_bugs_list.stool 
##                                       128 
##    ZellerG_2014.metaphlan_bugs_list.stool 
##                                       157

4 Performing batch (study) effect adjustment with adjust_batch

adjust_batch aims to correct for technical study/batch effects in microbial feature abundances. It takes as input the feature-by-sample abundance matrix, and performs batch effect adjustment given provided batch and optional covariate variables. It returns the batch-adjusted abundance matrix. Check help(adjust_batch) for additional details and options. This figure from the paper (figure 2b) shows the desired effect of the batch adjustment: batch effects are removed, making the effect of the biological variable of interest easier to detect.

Here we use adjust_batch to correct for differences in the five studies, while controlling for the effect of CRC versus control (variable study_condition in CRC_meta).

adjust_batch returns a list of multiple outputs. The part we are most interested in now is the adjusted abundance table, which we assign to CRC_abd_adj.

fit_adjust_batch <- adjust_batch(feature_abd = CRC_abd,
                                 batch = "studyID",
                                 covariates = "study_condition",
                                 data = CRC_meta,
                                 control = list(verbose = FALSE))

CRC_abd_adj <- fit_adjust_batch$feature_abd_adj

One way to evaluate the effect of batch adjustment is to assess the total variability in microbial profiles attributable to study differences, before and after adjustment. This is commonly known as a PERMANOVA test (Tang, Chen, and Alekseyenko 2016), and can be performed with the adonis function in vegan. The inputs to adonis() are indices of microbial compositional dissimilarity.

library(vegan, quietly = TRUE)
## This is vegan 2.6-2
D_before <- vegdist(t(CRC_abd))
D_after <- vegdist(t(CRC_abd_adj))

set.seed(1)
fit_adonis_before <- adonis(D_before ~ studyID, data = CRC_meta)
## 'adonis' will be deprecated: use 'adonis2' instead
fit_adonis_after <- adonis(D_after ~ studyID, data = CRC_meta)
## 'adonis' will be deprecated: use 'adonis2' instead
print(fit_adonis_before)
## $aov.tab
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##            Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## studyID     4     13.36  3.3400  11.855 0.07991  0.001 ***
## Residuals 546    153.82  0.2817         0.92009           
## Total     550    167.18                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $call
## adonis(formula = D_before ~ studyID, data = CRC_meta)
## 
## $coefficients
## NULL
## 
## $coef.sites
##                    [,1]        [,2]        [,3]        [,4]        [,5]
## (Intercept)  0.73079021  0.73169710  0.67250197  0.71605766  0.87336982
## studyID1    -0.04650105 -0.05934101 -0.06594520 -0.06916387 -0.04021647
## studyID2    -0.00960596 -0.01371390 -0.03127853 -0.04307342 -0.03532331
## studyID3     0.02492831  0.04299113  0.04968915  0.05007428  0.03897483
## studyID4     0.04102015  0.05598628  0.06354195  0.05829726  0.01373265
##                    [,6]        [,7]        [,8]        [,9]        [,10]
## (Intercept)  0.81329886  0.81982224  0.73286735  0.78795958  0.718324115
## studyID1    -0.06606706 -0.06650828 -0.06564355 -0.02205305 -0.046024930
## studyID2    -0.08502468 -0.03441529 -0.02623755  0.01814369 -0.003884227
## studyID3     0.06316730  0.05626508  0.05089622 -0.01825356  0.030691234
## studyID4     0.06503457  0.01587392  0.05786061  0.04961928  0.042904667
##                   [,11]       [,12]       [,13]       [,14]        [,15]
## (Intercept)  0.80541742  0.74132526  0.81710867  0.70795368  0.721987895
## studyID1    -0.04460555 -0.06188606 -0.07769478 -0.06250423 -0.068106124
## studyID2     0.01220036  0.01875803 -0.05734103 -0.02216895 -0.006623936
## studyID3     0.01853294  0.04324277  0.06442456  0.04787200  0.054217648
## studyID4     0.03508235  0.02154179  0.05558636  0.05359530  0.046021767
##                    [,16]        [,17]        [,18]       [,19]        [,20]
## (Intercept)  0.724763708  0.720709017  0.672344562  0.71879976  0.895069059
## studyID1    -0.041082155 -0.035945836 -0.018436077 -0.06847191 -0.026249117
## studyID2     0.020627539  0.029309877  0.026937828 -0.03286930 -0.008244704
## studyID3     0.009723736 -0.001863847 -0.007697855  0.05935282  0.019125882
## studyID4     0.046894057  0.040465859  0.039474956  0.05279717  0.015141685
##                   [,21]        [,22]       [,23]       [,24]       [,25]
## (Intercept)  0.70756159  0.859500463  0.73328228  0.87519251  0.78299716
## studyID1    -0.05207004 -0.040599238 -0.05130487 -0.06684140 -0.05570987
## studyID2    -0.03011202 -0.007236002 -0.05926688 -0.08763684 -0.08594157
## studyID3     0.02522928  0.036264028  0.05736280  0.06364694  0.07279483
## studyID4     0.06258455 -0.006517003  0.06319105  0.05981534  0.05848022
##                    [,26]         [,27]        [,28]       [,29]       [,30]
## (Intercept)  0.771194232  0.8417765012  0.708021213  0.74377429  0.80849317
## studyID1    -0.017877210 -0.0106373488 -0.056646978 -0.07045906 -0.06066943
## studyID2     0.006939035  0.0001720459 -0.008973142 -0.02893134 -0.05444733
## studyID3     0.008722146 -0.0009377920  0.037542927  0.06679191  0.06578068
## studyID4     0.010417212  0.0079291615  0.055077315  0.05305715  0.02607388
##                   [,31]       [,32]       [,33]       [,34]       [,35]
## (Intercept)  0.71096718  0.69937360  0.76646105  0.74107280  0.86080198
## studyID1    -0.08845056 -0.03262021 -0.07528971 -0.07232102 -0.07844225
## studyID2    -0.04830991 -0.03166673 -0.05595873 -0.07686114 -0.06609542
## studyID3     0.07345477  0.02174366  0.08403542  0.05670457  0.07321199
## studyID4     0.07208015  0.05820521  0.04970911  0.08259909  0.04108775
##                   [,36]        [,37]        [,38]       [,39]       [,40]
## (Intercept)  0.78485725  0.800353766  0.704317814  0.92518344  0.83096071
## studyID1    -0.07333451 -0.056877041 -0.059797497 -0.03717469 -0.09603239
## studyID2    -0.05788121  0.002084871 -0.002982447 -0.05980681 -0.06391249
## studyID3     0.07346187  0.046572844  0.032124676  0.03932895  0.08549132
## studyID4     0.04363908  0.035348179  0.042422987  0.02967674  0.04152928
##                   [,41]       [,42]         [,43]       [,44]       [,45]
## (Intercept)  0.86297220  0.72008343  0.7313460116  0.71515575  0.79402504
## studyID1    -0.02388482 -0.07173788 -0.0551093488 -0.07667420 -0.07120255
## studyID2    -0.01261734 -0.02623695  0.0003176773 -0.04030231 -0.07345587
## studyID3     0.02123076  0.05185719  0.0302679496  0.05886874  0.08452398
## studyID4     0.01485437  0.04856036  0.0486806985  0.07236564  0.04980713
##                   [,46]        [,47]       [,48]       [,49]       [,50]
## (Intercept)  0.79260432  0.726271016  0.83968414  0.73822097  0.76117565
## studyID1    -0.02275113 -0.018876038 -0.08818953 -0.09150021 -0.06949635
## studyID2    -0.02336605  0.033852323 -0.06934655 -0.06016353 -0.03795612
## studyID3     0.02077102 -0.003122252  0.07774874  0.08960851  0.05308874
## studyID4     0.03842737  0.007322358  0.04505643  0.05939020  0.05746601
##                    [,51]       [,52]       [,53]        [,54]       [,55]
## (Intercept)  0.749070788  0.72697936  0.70576051  0.731044308  0.71943910
## studyID1    -0.063512440  0.01976501 -0.03196234 -0.021915063  0.01711574
## studyID2    -0.007770849  0.08188655  0.03553587  0.057838550  0.07046869
## studyID3     0.051363240 -0.07090027 -0.01059085 -0.004548161 -0.06218881
## studyID4     0.036364110  0.01847215  0.04447515  0.004757544  0.02044711
##                    [,56]       [,57]        [,58]       [,59]        [,60]
## (Intercept)  0.694065903  0.81303818  0.772502057  0.73428510  0.768794266
## studyID1     0.005234712 -0.06509352 -0.005494334 -0.05623724  0.004823975
## studyID2     0.053840632 -0.02093313  0.057817276  0.01775326  0.060426824
## studyID3    -0.043458657  0.05468430 -0.016655197  0.03359785 -0.023974653
## studyID4     0.031578033  0.01309589  0.007840420  0.03530259 -0.013059033
##                   [,61]        [,62]       [,63]        [,64]       [,65]
## (Intercept)  0.75626581  0.722256668  0.79659272  0.685174699  0.86626059
## studyID1    -0.05678635 -0.024938712 -0.09783138 -0.045447647 -0.06679431
## studyID2    -0.01561288  0.009244992 -0.07768845  0.008441395 -0.06580121
## studyID3     0.03527453 -0.006813713  0.09050681  0.023880020  0.06123799
## studyID4     0.03703963  0.042379681  0.06036836  0.046491536  0.05473607
##                    [,66]       [,67]       [,68]       [,69]       [,70]
## (Intercept)  0.777973326  0.78532602  0.88617622  0.83138145  0.73208252
## studyID1    -0.040295795 -0.08423483 -0.04513834 -0.07048073 -0.04715621
## studyID2    -0.003152472 -0.04133572 -0.05296109 -0.06436904 -0.01543188
## studyID3     0.032365434  0.05571800  0.04345632  0.06168232  0.04105149
## studyID4     0.010984746  0.05486906  0.03720312  0.05352999  0.04101541
##                   [,71]       [,72]       [,73]       [,74]       [,75]
## (Intercept)  0.79628569  0.74564364  0.82963740  0.85648354  0.69383593
## studyID1    -0.07094938 -0.07820177 -0.06091010 -0.03302957 -0.08101647
## studyID2    -0.05341591 -0.01400483 -0.03722800 -0.07863538 -0.03510021
## studyID3     0.07510932  0.04600772  0.04419435  0.03720027  0.07220052
## studyID4     0.04982367  0.04899550  0.04269845  0.04971100  0.05154065
##                   [,76]       [,77]        [,78]       [,79]       [,80]
## (Intercept)  0.75828594  0.75491616  0.698578632  0.71157823  0.77634439
## studyID1    -0.03301151 -0.08926200 -0.038956950 -0.06451718 -0.07306696
## studyID2     0.01419652 -0.07095628 -0.004039631 -0.05402490 -0.09068076
## studyID3     0.01375530  0.08008457  0.021096937  0.04064663  0.06680122
## studyID4     0.03589495  0.05303716  0.054663702  0.06717357  0.07333525
##                    [,81]        [,82]       [,83]         [,84]       [,85]
## (Intercept)  0.777293438  0.707326451  0.77954551  0.7802628525  0.66377100
## studyID1    -0.022893174  0.007955915 -0.08892851 -0.0425010403 -0.03926263
## studyID2     0.009733795  0.032999077 -0.08597623 -0.0002989762  0.01150328
## studyID3     0.005883467 -0.043341692  0.08030758  0.0214859831  0.02283625
## studyID4     0.025757777  0.041900817  0.07176992  0.0288836445  0.03899032
##                   [,86]       [,87]        [,88]        [,89]        [,90]
## (Intercept)  0.73669370  0.68960159  0.794915405  0.950799505  0.681536133
## studyID1    -0.03100328 -0.05170864  0.011331421 -0.016988756 -0.006895492
## studyID2     0.03664492 -0.03463017  0.061178294  0.009956535  0.026448393
## studyID3    -0.01282797  0.04358591 -0.042648962  0.019935263 -0.019573161
## studyID4     0.03402930  0.06514813 -0.001067148 -0.025480966  0.035698698
##                   [,91]       [,92]       [,93]       [,94]        [,95]
## (Intercept)  0.77602797  0.75948032  0.74452823  0.82434660  0.766827710
## studyID1    -0.05309490 -0.05176798 -0.03932661  0.01497277 -0.001158024
## studyID2    -0.03280113 -0.07596665  0.03024806  0.05021643  0.053123917
## studyID3     0.05570932  0.04411548  0.01288461 -0.03264135 -0.022119364
## studyID4     0.03438912  0.07280730  0.03467307 -0.01740109  0.013140741
##                    [,96]       [,97]       [,98]       [,99]       [,100]
## (Intercept)  0.712164253  0.68855076  0.91005652  0.73466358  0.801902555
## studyID1    -0.027419866 -0.05033480  0.01390922 -0.02785560  0.033705550
## studyID2     0.034792148 -0.01435342  0.03792887  0.03455838  0.075986951
## studyID3    -0.001555805  0.03420867 -0.02364997  0.00511634 -0.055487366
## studyID4     0.023490094  0.05519212 -0.02176136  0.02956285 -0.009838992
##                   [,101]      [,102]       [,103]      [,104]       [,105]
## (Intercept)  0.781736304  0.78470581  0.752959053  0.71527754  0.685495223
## studyID1    -0.008643686 -0.06499234  0.004529713 -0.02264534 -0.015899240
## studyID2    -0.001231803 -0.04997590  0.060904611  0.04840013  0.035258528
## studyID3    -0.001193747  0.05255167 -0.057032177 -0.02385522 -0.008106758
## studyID4     0.018165833  0.04364129  0.033806568  0.03802453  0.034055285
##                  [,106]        [,107]      [,108]      [,109]      [,110]
## (Intercept)  0.79704542  0.7476354715  0.72111791  0.74695645  0.72165720
## studyID1    -0.05887184 -0.0356475247 -0.06389942 -0.05570215 -0.07781441
## studyID2    -0.04918143  0.0432040379 -0.09603090 -0.07286121 -0.07607202
## studyID3     0.04163504  0.0008598003  0.07388893  0.04790138  0.07363142
## studyID4     0.05266070  0.0313708648  0.07630438  0.07245070  0.07816349
##                  [,111]      [,112]      [,113]      [,114]      [,115]
## (Intercept)  0.80376501  0.76485120  0.81705387  0.82875081  0.80888621
## studyID1    -0.03805225 -0.02853643 -0.06342763 -0.02479917 -0.05067841
## studyID2    -0.09440377 -0.08578968 -0.10403666 -0.04264292 -0.07674822
## studyID3     0.04389452  0.03766355  0.07319994  0.04825242  0.05224949
## studyID4     0.06507869  0.05867997  0.05744107  0.02535254  0.05029131
##                  [,116]      [,117]      [,118]      [,119]       [,120]
## (Intercept)  0.76971559  0.80031381  0.67773592  0.73246771  0.920199444
## studyID1    -0.05726148 -0.01170429 -0.03978420 -0.05820645 -0.028635255
## studyID2    -0.09743218 -0.01860063 -0.02546947 -0.04608215 -0.014936005
## studyID3     0.06492941  0.00194482  0.03810171  0.04225766  0.030722022
## studyID4     0.07369688  0.04404772  0.05253060  0.05933272 -0.005775329
##                  [,121]      [,122]       [,123]      [,124]      [,125]
## (Intercept)  0.68638903  0.74277049  0.780366701  0.84852196  0.83508932
## studyID1    -0.04756543 -0.04507123  0.032484028 -0.01992758 -0.03278101
## studyID2    -0.06305348 -0.08707295  0.052365326 -0.04831042 -0.06898793
## studyID3     0.03784268  0.05214563 -0.049904528  0.04916471  0.05139544
## studyID4     0.07826084  0.06800002 -0.004362564  0.02194964  0.04074096
##                  [,126]      [,127]       [,128]      [,129]       [,130]
## (Intercept)  0.78281381  0.75122135  0.792906692  0.83061435  0.798174004
## studyID1    -0.08509840 -0.02563372 -0.006544456 -0.04042636 -0.016895820
## studyID2    -0.08089636 -0.06752592 -0.041371329 -0.09332218  0.008896812
## studyID3     0.07030577  0.04444490  0.020335893  0.05096549  0.022737650
## studyID4     0.07182748  0.03768099  0.029886048  0.05842652  0.001178961
##                  [,131]      [,132]      [,133]       [,134]      [,135]
## (Intercept)  0.83279134  0.77055119  0.79529298  0.770212949  0.72206627
## studyID1    -0.03249894 -0.05588641 -0.05984101 -0.007717136 -0.05108420
## studyID2    -0.05773611 -0.08000431 -0.12272278 -0.010835321 -0.03357562
## studyID3     0.05325093  0.05443385  0.07289155 -0.000998961  0.03014400
## studyID4     0.03028466  0.07123756  0.07880640  0.029770078  0.06290951
##                  [,136]      [,137]       [,138]      [,139]      [,140]
## (Intercept)  0.75355176  0.83987608  0.847922993  0.79849576  0.92122930
## studyID1    -0.06817237 -0.02073558 -0.002821352 -0.05508997 -0.02119358
## studyID2    -0.06984181 -0.08529225 -0.037713415 -0.11206922 -0.04029185
## studyID3     0.06816916  0.04050336  0.018295576  0.06339148  0.03103680
## studyID4     0.06584446  0.04657688  0.023198334  0.07648358  0.01416995
##                  [,141]      [,142]      [,143]        [,144]       [,145]
## (Intercept)  0.84593727  0.75386138  0.83072791  0.7803245723  0.686251922
## studyID1    -0.05232514 -0.05912919 -0.03626404 -0.0003778756 -0.033634340
## studyID2    -0.06891652 -0.09959083 -0.05574077 -0.0544661698 -0.006883302
## studyID3     0.06898300  0.07138559  0.04885793  0.0169098751  0.019621776
## studyID4     0.02641112  0.07453646  0.03060486  0.0398302336  0.047577855
##                   [,146]      [,147]       [,148]      [,149]      [,150]
## (Intercept)  0.994295658  0.75868056  0.736998188  0.80239349  0.83173664
## studyID1     0.003451089 -0.02898948 -0.008159385 -0.03713639 -0.02606258
## studyID2    -0.015622424 -0.02856729 -0.019327971 -0.08909527 -0.06267844
## studyID3     0.003596713  0.03142790  0.002786653  0.05194675  0.04593685
## studyID4     0.003970668  0.04048312  0.041452881  0.04941341  0.04592758
##                   [,151]      [,152]      [,153]      [,154]       [,155]
## (Intercept)  0.782046892  0.81196458  0.79575816  0.73825550  0.843025117
## studyID1    -0.043069017 -0.05438111 -0.02951726 -0.04254188 -0.009436994
## studyID2    -0.008739537 -0.09779982 -0.05008811 -0.06056540 -0.022774398
## studyID3     0.044882269  0.05155191  0.04039248  0.04223618  0.018865208
## studyID4     0.002232043  0.07168154  0.03369622  0.05826491  0.021294190
##                  [,156]      [,157]      [,158]      [,159]      [,160]
## (Intercept)  0.79523046  0.73211776  0.77865978  0.82731504  0.76432948
## studyID1    -0.06857357 -0.01804602 -0.02529721 -0.02367187 -0.07360264
## studyID2    -0.08933196 -0.02811177 -0.02488022 -0.06623715 -0.09670566
## studyID3     0.07264554  0.02356965  0.02124910  0.03947351  0.07008423
## studyID4     0.06070180  0.03608354  0.02148352  0.04059750  0.07288417
##                  [,161]      [,162]       [,163]      [,164]       [,165]
## (Intercept)  0.79564785  0.73324266  0.758657047  0.69862421  0.714064515
## studyID1    -0.06535233 -0.06967413  0.025088565  0.01481867  0.041141330
## studyID2    -0.06614586 -0.08815011  0.077507570  0.06935767  0.089172417
## studyID3     0.05231728  0.08371340 -0.045735613 -0.06501500 -0.084825904
## studyID4     0.06738471  0.07203452 -0.000632023  0.02831324  0.007365147
##                  [,166]      [,167]      [,168]       [,169]      [,170]
## (Intercept)  0.76206464  0.69860888  0.77912882  0.698783645  0.82970887
## studyID1     0.02741100  0.03114449 -0.00501328  0.026544742  0.04109193
## studyID2     0.04006648  0.08525124  0.02165157  0.073625804  0.08265927
## studyID3    -0.04632842 -0.07886944 -0.01017500 -0.067234723 -0.08154781
## studyID4     0.01071271  0.01472883  0.02621444  0.008789267 -0.01040782
##                   [,171]        [,172]       [,173]       [,174]       [,175]
## (Intercept)  0.764641487  0.7356837772  0.744862251  0.775706509  0.810909528
## studyID1     0.042384227  0.0356374376  0.009463761  0.015534162  0.011373870
## studyID2     0.082714735  0.0886933975  0.052189091  0.078354462  0.037722101
## studyID3    -0.083227855 -0.0764565172 -0.058018657 -0.054587554 -0.037483874
## studyID4     0.002158582 -0.0009766411  0.033569569  0.002091334  0.009965189
##                    [,176]      [,177]      [,178]       [,179]      [,180]
## (Intercept)  0.7775252965  0.70429697  0.73841259  0.819011698  0.79706231
## studyID1     0.0292088525  0.02380675  0.03737010  0.050111631  0.02285301
## studyID2     0.0724397253  0.06884931  0.04325429  0.071469049  0.06301956
## studyID3    -0.0633031869 -0.07361300 -0.05224203 -0.080042502 -0.06611550
## studyID4    -0.0002772396  0.02541665  0.00889166 -0.005854619  0.01108291
##                  [,181]      [,182]      [,183]      [,184]      [,185]
## (Intercept)  0.76555024  0.78894548  0.74058702  0.78033520  0.75240567
## studyID1     0.02782296  0.02334291  0.02485266  0.03419271 -0.01040240
## studyID2     0.04326448  0.07341098  0.07560952  0.07847625  0.03456229
## studyID3    -0.06362446 -0.04953065 -0.08095002 -0.05784425 -0.01802667
## studyID4     0.02773763 -0.01370129  0.02881716 -0.02204520  0.02404203
##                  [,186]      [,187]      [,188]      [,189]      [,190]
## (Intercept)  0.76184893  0.74562464  0.79481905  0.73666716  0.77699131
## studyID1     0.02316424  0.01300995  0.01311017  0.01990124  0.02250412
## studyID2     0.06645627  0.07078697  0.02896525  0.08232580  0.03360150
## studyID3    -0.07134436 -0.07239505 -0.04351122 -0.06967543 -0.06524106
## studyID4     0.01954875  0.03792472  0.02490085  0.01937233  0.03486877
##                   [,191]       [,192]      [,193]       [,194]      [,195]
## (Intercept)  0.775217415  0.775475775  0.82235502  0.758840329  0.70901594
## studyID1     0.038483677  0.020299882  0.02982408  0.036905538  0.02519451
## studyID2     0.077799503  0.050522053  0.04794190  0.097783611  0.04131071
## studyID3    -0.074604454 -0.041432545 -0.05485628 -0.087619834 -0.04996353
## studyID4    -0.002690892 -0.008773986 -0.00423774 -0.002482536  0.01642108
##                  [,196]      [,197]      [,198]       [,199]       [,200]
## (Intercept)  0.81903201  0.88524873  0.77016445  0.733025530  0.876775647
## studyID1     0.01679739  0.03130816  0.03748650  0.025141157  0.012671588
## studyID2     0.04569094  0.05653915  0.08188104  0.081038250  0.038936590
## studyID3    -0.04498943 -0.04887649 -0.07065736 -0.063241828 -0.031265910
## studyID4     0.01115081 -0.02015299 -0.01336101  0.003778427  0.003450027
##                   [,201]      [,202]       [,203]      [,204]      [,205]
## (Intercept)  0.773517426  0.76378802  0.951177126  0.76356473  0.78018506
## studyID1     0.007470932  0.02549457 -0.009162603  0.02662610  0.02868409
## studyID2     0.044019814  0.06914398  0.007089474  0.05552701  0.08186201
## studyID3    -0.036129778 -0.07139962  0.014998298 -0.07152779 -0.06400866
## studyID4     0.012241984  0.01577540 -0.025801599  0.02559676 -0.01136175
##                   [,206]       [,207]       [,208]      [,209]       [,210]
## (Intercept)  0.720112590  0.728136875  0.763896346  0.76201136  0.794435249
## studyID1     0.020681357  0.028010272  0.035473809  0.02173940  0.027908466
## studyID2     0.071999798  0.090634825  0.051681852  0.05765803  0.055201003
## studyID3    -0.058913382 -0.072371889 -0.055738167 -0.05997691 -0.054965426
## studyID4     0.008411493  0.000546931 -0.001679232  0.01984153 -0.008140277
##                  [,211]      [,212]       [,213]       [,214]       [,215]
## (Intercept)  0.81979395  0.77153796  0.865552537  0.743255122  0.733381736
## studyID1     0.03665432  0.04867535  0.008489117  0.040284248  0.030216863
## studyID2     0.04169193  0.09263218  0.006723492  0.082544495  0.089361305
## studyID3    -0.06357510 -0.08946286 -0.016496481 -0.077757416 -0.072474031
## studyID4     0.01163249 -0.00754092  0.004549845 -0.002194441  0.001945239
##                  [,216]      [,217]       [,218]       [,219]      [,220]
## (Intercept)  0.89719012  0.78089858  0.752672646  0.795408658  0.73734464
## studyID1     0.02948947  0.03385431  0.021925201  0.029604556  0.04290687
## studyID2     0.04953959  0.06988377  0.066726813  0.065357214  0.06669654
## studyID3    -0.04684169 -0.05833295 -0.050587143 -0.069257572 -0.07352216
## studyID4    -0.01720812 -0.01448554  0.000130078  0.007863647  0.01095949
##                   [,221]        [,222]        [,223]       [,224]      [,225]
## (Intercept)  0.919312099  0.8009581313  7.293674e-01  0.760452645  0.77283996
## studyID1    -0.004279109  0.0292589246 -3.939838e-02  0.030166421  0.04011954
## studyID2     0.004189207  0.0592186935  2.978391e-02  0.079133838  0.09499224
## studyID3    -0.003927197 -0.0655441570  9.741688e-05 -0.066293505 -0.07656536
## studyID4     0.002805455 -0.0006004025  2.969480e-02 -0.002267913 -0.01625933
##                   [,226]      [,227]       [,228]       [,229]      [,230]
## (Intercept)  0.837279815  0.76991515  0.740371580  0.818812436  0.72328916
## studyID1     0.046936537  0.01341897  0.025146752  0.028142488 -0.01659046
## studyID2     0.068395358  0.04532426  0.061559751  0.040986706  0.02871084
## studyID3    -0.078366067 -0.06224187 -0.047851959 -0.045138412 -0.01378762
## studyID4    -0.007069053  0.03482884 -0.001024127 -0.005709594  0.03752692
##                  [,231]      [,232]       [,233]      [,234]      [,235]
## (Intercept)  0.73155192  0.70949444  0.751551249  0.70939691  0.82038588
## studyID1     0.02268160  0.01036654  0.005348565  0.01811432  0.03047050
## studyID2     0.04645105  0.04777978  0.060524096  0.06999908  0.06160105
## studyID3    -0.06511525 -0.03777662 -0.048891561 -0.06363103 -0.07356698
## studyID4     0.02782818  0.01975608  0.026772364  0.01742128  0.01304736
##                   [,236]      [,237]      [,238]      [,239]      [,240]
## (Intercept)  0.763817622  0.78198513  0.77496846  0.80869258  0.71693752
## studyID1     0.009985327  0.00899530  0.03341714  0.03747458  0.02287115
## studyID2     0.039599920  0.02109572  0.06374854  0.07978300  0.05275479
## studyID3    -0.040113395 -0.02626988 -0.07214931 -0.06301681 -0.05257355
## studyID4     0.018923173  0.01282964  0.01494010 -0.01862391  0.01403267
##                   [,241]      [,242]       [,243]      [,244]       [,245]
## (Intercept)  0.830249142  0.80116258  0.752862537  0.70848136  0.929628042
## studyID1    -0.011841971  0.02201877  0.035653036  0.03041748  0.020699917
## studyID2     0.032503668  0.06345380  0.092280653  0.08154758  0.024617634
## studyID3    -0.005084079 -0.06542867 -0.084337759 -0.07872781 -0.029907594
## studyID4     0.004441175  0.02151126  0.008281907  0.01890732 -0.008424437
##                  [,246]       [,247]      [,248]       [,249]      [,250]
## (Intercept)  0.77095333  0.823750139  0.76646205  0.690308309  0.74595045
## studyID1     0.03064689  0.024172255  0.02638330  0.002955562  0.01863070
## studyID2     0.06320349  0.054321062  0.05383868  0.046553511  0.07422568
## studyID3    -0.07377868 -0.049669748 -0.06315695 -0.040819611 -0.05783279
## studyID4     0.01438112 -0.009076041  0.01328449  0.025042445  0.01820590
##                  [,251]       [,252]      [,253]       [,254]       [,255]
## (Intercept)  0.68211183  0.714891524  0.75577272  0.804446870  0.813340799
## studyID1    -0.02318971  0.009508865  0.02640145  0.034653687  0.012705617
## studyID2     0.06022882  0.068352138  0.04948395  0.069363901  0.052102025
## studyID3    -0.02166162 -0.057403790 -0.05508302 -0.072284814 -0.042003353
## studyID4     0.03161894  0.025058696  0.01107951  0.001291682  0.007612096
##                  [,256]      [,257]      [,258]       [,259]      [,260]
## (Intercept)  0.71431541  0.74343698  0.75913332  0.719306761  0.71682425
## studyID1     0.02829487  0.03159644  0.02816117  0.002432742  0.01855319
## studyID2     0.07311488  0.05627212  0.06921216  0.067960680  0.07827029
## studyID3    -0.06980319 -0.06556969 -0.07131701 -0.048902883 -0.06401136
## studyID4     0.01468102  0.02861709  0.01652813  0.018417019  0.01704000
##                  [,261]        [,262]      [,263]       [,264]       [,265]
## (Intercept)  0.84422405  0.6898202085  0.76157711  0.752370882  0.878952965
## studyID1     0.04569043  0.0002687865  0.02284337  0.010344882  0.003680280
## studyID2     0.08079096  0.0680696337  0.05088330  0.070107144  0.008995664
## studyID3    -0.07762354 -0.0431904470 -0.05163283 -0.056760973 -0.016680545
## studyID4    -0.02121520  0.0230005194  0.01441105  0.004976764  0.012146705
##                   [,266]       [,267]      [,268]      [,269]       [,270]
## (Intercept)  0.857285575  0.769614563  0.78851638  0.83388525  0.768343122
## studyID1     0.009194762 -0.006674724  0.03207236 -0.05609380 -0.015169156
## studyID2     0.007187361  0.012171909  0.04942985 -0.02356836  0.033808478
## studyID3    -0.025768620  0.005043750 -0.02880675  0.04708957  0.014449195
## studyID4     0.022094319  0.004764073 -0.02533376  0.02380204 -0.003291337
##                   [,271]      [,272]      [,273]      [,274]      [,275]
## (Intercept)  0.775097575  0.88864635  0.82427868  0.89875222  0.84139954
## studyID1     0.004143031  0.02145986 -0.02849903  0.03095694  0.03411916
## studyID2     0.049359465  0.03536371 -0.01609251  0.02193190  0.06888598
## studyID3    -0.018152645 -0.02532572  0.05915309 -0.01932814 -0.04810339
## studyID4    -0.014342458 -0.01589591 -0.01022578 -0.02436261 -0.03604400
##                  [,276]      [,277]      [,278]       [,279]      [,280]
## (Intercept)  0.81489939  0.83599043  0.82811115  0.800744411  0.78554751
## studyID1     0.02474405  0.01464060  0.03020380  0.003740254  0.02190307
## studyID2     0.04868097  0.05309238  0.07477849  0.063136280  0.03450770
## studyID3    -0.02581139 -0.01995640 -0.04240173 -0.020612076 -0.01226889
## studyID4    -0.03027584 -0.03579445 -0.03439616 -0.030614352 -0.03443260
##                  [,281]      [,282]       [,283]      [,284]      [,285]
## (Intercept)  0.87078112  0.80161103  0.819581286  0.90013419  0.81937970
## studyID1     0.03184734 -0.05699026  0.020635506  0.01236438  0.02559403
## studyID2     0.03463080 -0.02915175  0.029018972  0.03803109  0.05132595
## studyID3    -0.03070855  0.07110286 -0.024770864 -0.01055298 -0.02983041
## studyID4    -0.02502824  0.01476219 -0.006930657 -0.03325448 -0.03089382
##                  [,286]       [,287]       [,288]      [,289]       [,290]
## (Intercept)  0.88305230  0.833142203  0.829507137  0.85971400  0.892126683
## studyID1    -0.01018812 -0.000736515  0.006065787  0.03547778 -0.015216408
## studyID2    -0.02929212  0.035324935  0.026086503  0.05628617  0.008503198
## studyID3     0.02264146  0.012843149 -0.011251936 -0.03618365  0.022223667
## studyID4     0.01497964 -0.040627483 -0.016913956 -0.03648419 -0.021859625
##                  [,291]      [,292]       [,293]       [,294]      [,295]
## (Intercept)  0.77457812  0.83346289  0.774097674  0.790703726  0.80766938
## studyID1     0.02467280  0.03589345 -0.022816674 -0.024105622 -0.01666685
## studyID2     0.07570170  0.04770027  0.035220274  0.027070278 -0.05650662
## studyID3    -0.02891056 -0.04391389  0.013225757  0.015225074  0.03960652
## studyID4    -0.03618303 -0.02240439 -0.004531518 -0.005067104  0.02051915
##                  [,296]       [,297]       [,298]       [,299]       [,300]
## (Intercept)  0.86998797  0.751584083  0.793758231  0.783084750  0.731603029
## studyID1     0.04591000 -0.002705337 -0.024992885 -0.020913008  0.040611838
## studyID2     0.07468108  0.009191078  0.017003316  0.017862296  0.055511251
## studyID3    -0.05273826  0.009894345  0.018783055  0.017905819 -0.062774205
## studyID4    -0.05028962 -0.006737985 -0.004730267 -0.004767464  0.001779538
##                  [,301]      [,302]      [,303]       [,304]       [,305]
## (Intercept)  0.87016107  0.79058890  0.74879774  0.797481106  0.728822394
## studyID1     0.01730287  0.03691538 -0.02328578  0.022884189  0.008971865
## studyID2     0.03613738  0.06390194  0.02786126  0.035804964  0.061830036
## studyID3    -0.02140341 -0.04597544  0.01155486 -0.029526230 -0.025523167
## studyID4    -0.02473712 -0.03381870  0.01316431  0.001568224 -0.011301874
##                   [,306]      [,307]        [,308]      [,309]      [,310]
## (Intercept)  0.787528886  0.84031012  0.7706429751  0.79872583  0.71252781
## studyID1    -0.003607337  0.02401393  0.0009341721  0.03692195 -0.04813534
## studyID2    -0.011832843  0.06382851  0.0290290758  0.05459794  0.02807707
## studyID3     0.005065909 -0.03285835  0.0171577252 -0.04110413  0.03427317
## studyID4     0.011558535 -0.03408249 -0.0269871893 -0.02307477  0.01317112
##                   [,311]        [,312]      [,313]       [,314]      [,315]
## (Intercept)  0.779882526  0.7339964125  0.77745712  0.694296807  0.84766215
## studyID1    -0.025823266  0.0037988248  0.04080740 -0.012374933  0.01442969
## studyID2     0.007134511  0.0666071249  0.08290731  0.029006841  0.02367997
## studyID3     0.019111803 -0.0281344862 -0.05504365  0.001708666 -0.01677443
## studyID4     0.004397211  0.0007925347 -0.04218851  0.020623248 -0.02242491
##                   [,316]       [,317]      [,318]       [,319]       [,320]
## (Intercept)  0.945105260  0.718574497  0.81812601  0.902169610  0.794449303
## studyID1    -0.012583092  0.029363033  0.02351454  0.005904420 -0.016198969
## studyID2     0.008253078  0.065744599  0.05745321  0.013894874  0.033127377
## studyID3     0.021616989 -0.054113230 -0.03644015  0.005067076  0.004555850
## studyID4    -0.032086153 -0.002738664 -0.02822154 -0.031919290 -0.006932786
##                  [,321]      [,322]      [,323]      [,324]        [,325]
## (Intercept)  0.74783111  0.75247801  0.85395209  0.77455139  0.8958695359
## studyID1    -0.05706913  0.04179512  0.04276247 -0.01428122 -0.0035184493
## studyID2     0.01785964  0.08452324  0.06348240  0.04577113  0.0284474475
## studyID3     0.04274130 -0.06319505 -0.04843983  0.01665750  0.0004368222
## studyID4     0.01599446 -0.02837031 -0.04068804 -0.02600643 -0.0208833856
##                  [,326]       [,327]       [,328]        [,329]       [,330]
## (Intercept)  0.80434904  0.717536037  0.722218762  0.8189426312  0.722206578
## studyID1     0.01603516  0.005165708  0.014334102  0.0006278693  0.004701180
## studyID2     0.05039727  0.061868812  0.040524773  0.0372456852  0.052228871
## studyID3    -0.02269172 -0.009229701 -0.023251479 -0.0082735387 -0.020857193
## studyID4    -0.02047167 -0.012178876 -0.003506182 -0.0238203977 -0.006831181
##                  [,331]       [,332]       [,333]        [,334]       [,335]
## (Intercept)  0.81167785  0.786044405  0.796416828  0.7795027127  0.767715719
## studyID1     0.03149773  0.002308984  0.017955804  0.0002811639 -0.037951163
## studyID2     0.08221579  0.047295947  0.045537541  0.0489634309  0.011457508
## studyID3    -0.04984094 -0.016987897 -0.006474689  0.0108910357  0.043772614
## studyID4    -0.03194586 -0.005847084 -0.027033747 -0.0358620555  0.006349858
##                   [,336]       [,337]        [,338]        [,339]       [,340]
## (Intercept)  0.762183965  0.724952341  0.7451600506  0.6823345627  0.844520817
## studyID1    -0.040146220  0.024826961 -0.0078580478 -0.0158146493  0.001125325
## studyID2     0.027598441  0.069473080  0.0644824071  0.0113435811  0.042667603
## studyID3     0.030354234 -0.056157438  0.0007031798  0.0002872127  0.009926702
## studyID4     0.001197908  0.002072715 -0.0287077914  0.0288302158 -0.033992940
##                   [,341]      [,342]       [,343]      [,344]       [,345]
## (Intercept)  0.697107368  0.86865701  0.776067851  0.77718442  0.812484595
## studyID1     0.016231274  0.02877342  0.001547535  0.01633404  0.015818858
## studyID2     0.068937950  0.05385554  0.029319677  0.06999256  0.052880051
## studyID3    -0.036315572 -0.02249164 -0.005377371 -0.03581575 -0.008391383
## studyID4     0.004030687 -0.04148630 -0.007594990 -0.01736160 -0.047274683
##                    [,346]      [,347]       [,348]      [,349]       [,350]
## (Intercept)  0.7640295916  0.76795357  0.742150585  0.75644260  0.736912909
## studyID1     0.0002608535  0.04505554  0.006489672  0.01049444  0.027963380
## studyID2     0.0279280350  0.09670415  0.079823263  0.06777800  0.071836656
## studyID3    -0.0042255274 -0.06663694 -0.028394722 -0.02665025 -0.065071607
## studyID4    -0.0139760024 -0.03057568 -0.007665865 -0.01680212  0.006786251
##                   [,351]      [,352]       [,353]       [,354]      [,355]
## (Intercept)  0.765786442  0.80284316  0.871344367  0.732445406  0.74628071
## studyID1     0.017989790  0.02779058 -0.004602241  0.032957466  0.02265542
## studyID2     0.066309005  0.05105308  0.033620944  0.089602432  0.06713721
## studyID3    -0.035067633 -0.02579492  0.001622183 -0.060922425 -0.03465547
## studyID4    -0.005761592 -0.01969573 -0.032071156 -0.009892056 -0.01765999
##                   [,356]       [,357]       [,358]       [,359]      [,360]
## (Intercept)  0.779374577  0.733990731  0.752619521  0.803690593  0.71978303
## studyID1     0.046062210  0.019858529  0.053102310  0.011845249  0.01105676
## studyID2     0.067342009  0.064489047  0.076740133  0.045366535  0.02920423
## studyID3    -0.062485183 -0.046683079 -0.082881891 -0.006174756 -0.02174212
## studyID4    -0.006263496  0.002736641 -0.001590062 -0.031145890  0.01304749
##                   [,361]      [,362]        [,363]       [,364]       [,365]
## (Intercept)  0.946684988  0.79641311  0.7462432128  0.896724603  0.853845284
## studyID1     0.002061181  0.02704099 -0.0005650543  0.006848036 -0.010342500
## studyID2     0.010697255  0.03355325  0.0376795454  0.018645202 -0.006765324
## studyID3     0.008929256 -0.02027110 -0.0029862066 -0.006093542  0.018079234
## studyID4    -0.035624641 -0.02114129 -0.0008952213 -0.015860948 -0.012222357
##                  [,366]      [,367]      [,368]      [,369]       [,370]
## (Intercept)  0.77784791  0.80600209  0.73326246  0.81234166  0.810731431
## studyID1    -0.02226897  0.03894387  0.01141714 -0.03764754  0.016766465
## studyID2     0.01857757  0.08403722  0.06837759 -0.03484508  0.033155329
## studyID3     0.03328142 -0.06401881 -0.01734980  0.03774354 -0.018754923
## studyID4    -0.01727324 -0.02109436 -0.02232769  0.02538523 -0.003893008
##                  [,371]        [,372]       [,373]      [,374]       [,375]
## (Intercept)  0.81585951  0.7183436274  0.808581307  0.84935241  0.819413717
## studyID1     0.03240437  0.0273035124  0.001806393  0.03935983 -0.019104588
## studyID2     0.05984491  0.0666742105  0.032388669  0.06997074 -0.026080573
## studyID3    -0.03315300 -0.0520760552 -0.002206643 -0.04615545  0.042478897
## studyID4    -0.03959567  0.0003502657 -0.009950705 -0.03639585  0.009474868
##                    [,376]      [,377]       [,378]      [,379]       [,380]
## (Intercept)  0.7372641808  0.80873902  0.780909166  0.80344637  0.786785669
## studyID1    -0.0001873546  0.02840926  0.012095761  0.03393542 -0.017227932
## studyID2     0.0518379031  0.07443093  0.062490114  0.05646912 -0.009487205
## studyID3    -0.0250936218 -0.04623793 -0.038535002 -0.03349882  0.039150556
## studyID4     0.0023552335 -0.02706743 -0.009435946 -0.02583660  0.002509212
##                  [,381]      [,382]      [,383]      [,384]      [,385]
## (Intercept)  0.86456126  0.77952892  0.83895766  0.85298515  0.75242060
## studyID1     0.04286745  0.03296716  0.04430173  0.04303319  0.03577378
## studyID2     0.06351655  0.08378698  0.08032416  0.06912860  0.04496173
## studyID3    -0.05076778 -0.06484624 -0.06142179 -0.05220005 -0.03143618
## studyID4    -0.04029438 -0.02193542 -0.03055457 -0.03436416 -0.01696261
##                   [,386]      [,387]      [,388]       [,389]       [,390]
## (Intercept)  0.869957543  0.73345881  0.83130598  0.800292039  0.725299909
## studyID1     0.009169024  0.03618691  0.01576982 -0.040769943  0.003949265
## studyID2     0.040626596  0.07567538  0.04827505 -0.003528821 -0.002128863
## studyID3     0.009033573 -0.05017749 -0.02467715  0.043799146 -0.014455729
## studyID4    -0.043130457 -0.02357239 -0.02518621 -0.006386129  0.037671720
##                  [,391]      [,392]        [,393]       [,394]       [,395]
## (Intercept)  0.74988797  0.74457290  0.6893487482  0.832689905  0.702165812
## studyID1    -0.04628611  0.02122099 -0.0001088894 -0.035075780 -0.026030766
## studyID2    -0.02177168  0.07040471  0.0377090494 -0.001479279  0.019995404
## studyID3     0.05435280 -0.03500065 -0.0097536695  0.041888864 -0.004190248
## studyID4     0.02323767 -0.02306096  0.0184070054 -0.020470852  0.045735471
##                  [,396]       [,397]      [,398]       [,399]       [,400]
## (Intercept)  0.83945168  0.699291239  0.73873496  0.700851278  0.666148219
## studyID1     0.02953762 -0.009008707  0.03375150 -0.004950581 -0.020189608
## studyID2     0.07624022  0.028304814  0.05469864  0.032196106  0.031075043
## studyID3    -0.05092099 -0.005774625 -0.05951367 -0.002098953 -0.008624057
## studyID4    -0.01971329  0.033866949  0.02213125  0.026114609  0.047097304
##                    [,401]        [,402]       [,403]       [,404]       [,405]
## (Intercept)  7.897582e-01  0.6799091971  0.808830111  0.719070084  0.712003379
## studyID1     6.960577e-05 -0.0221009123 -0.008944344 -0.017312162  0.009786735
## studyID2     4.364252e-02  0.0292393421  0.036923980  0.004816913  0.071695105
## studyID3    -2.160660e-02 -0.0006298635  0.008451418 -0.003017418 -0.045063299
## studyID4     1.510567e-02  0.0271393432  0.004138461  0.049857442  0.018558514
##                   [,406]       [,407]       [,408]       [,409]       [,410]
## (Intercept)  0.771056824  0.744016336  0.777516506  0.692748755  0.678840276
## studyID1     0.003691062 -0.008090234  0.031896201  0.005781017 -0.025635881
## studyID2     0.044249828  0.058774459  0.052578284  0.046942151  0.015918233
## studyID3    -0.028795115 -0.020729974 -0.044964173 -0.033726646  0.007267168
## studyID4     0.016826971  0.004961282  0.004919753  0.023477624  0.050671552
##                   [,411]       [,412]       [,413]       [,414]       [,415]
## (Intercept)  0.728672367  0.801111862  0.813576233  0.806644881  0.740903094
## studyID1    -0.044676597  0.038917831 -0.007258932 -0.010598981 -0.003073551
## studyID2    -0.005354144  0.073670585  0.030766618  0.009120624  0.006477557
## studyID3     0.031695903 -0.068123569  0.006599163  0.017828427 -0.001293776
## studyID4     0.037792942 -0.000417097  0.009439595  0.015284037  0.022880126
##                  [,416]        [,417]       [,418]       [,419]       [,420]
## (Intercept)  0.76950758  0.9185513140  0.751561121  0.747173435  0.798888810
## studyID1     0.03232658  0.0032445671 -0.022081775 -0.005849462  0.005858569
## studyID2     0.08177263  0.0012902983  0.016637090  0.046509905  0.037803936
## studyID3    -0.06314948 -0.0006865415  0.001984645 -0.018523244 -0.015741226
## studyID4    -0.01251956  0.0033679152  0.026349067  0.006157306 -0.003505027
##                  [,421]       [,422]       [,423]       [,424]       [,425]
## (Intercept)  0.74588011  0.746285373  0.799650880  0.693350221  0.804108383
## studyID1     0.02039598 -0.053075413 -0.050593403 -0.008578326  0.004106392
## studyID2     0.07182336  0.006188479  0.001785762  0.036534607  0.049773928
## studyID3    -0.06385012  0.050310971  0.041615904 -0.017181800 -0.037256592
## studyID4     0.02191466  0.022001909  0.027813490  0.046679111  0.026289350
##                  [,426]        [,427]      [,428]       [,429]        [,430]
## (Intercept)  0.74425821  0.7850377645  0.77685758  0.874383280  7.427147e-01
## studyID1    -0.01788140 -0.0119133844 -0.05066339  0.028957523  2.965202e-05
## studyID2     0.02547895  0.0275229073 -0.02232381  0.029723611  5.802666e-02
## studyID3    -0.00854311  0.0009391663  0.05149927 -0.037223429 -2.177665e-02
## studyID4     0.03341306  0.0222272468  0.04870666 -0.001249419  2.058953e-02
##                  [,431]        [,432]      [,433]       [,434]       [,435]
## (Intercept)  0.84976749  0.8130781647  0.81216062  0.695340352  0.782637326
## studyID1    -0.03907588  0.0018977393 -0.04624368  0.004594381 -0.008692320
## studyID2    -0.02488543  0.0397615474 -0.05340917  0.054151741  0.042859193
## studyID3     0.05862850 -0.0002469969  0.04646356 -0.033917195 -0.005872164
## studyID4     0.01527157 -0.0133397578  0.04592951  0.035063499  0.016844135
##                   [,436]       [,437]       [,438]      [,439]       [,440]
## (Intercept)  0.830634027  0.724219460  0.803724443  0.76600424  0.837445683
## studyID1     0.003700076 -0.019729116  0.011749914 -0.05142296 -0.018938808
## studyID2     0.037174374  0.049707569  0.054836593 -0.02811180  0.014262789
## studyID3    -0.005178159  0.007270035 -0.033117921  0.05192527  0.011493413
## studyID4    -0.024382057  0.014085487  0.001731155  0.02479816  0.008621651
##                   [,441]      [,442]       [,443]        [,444]      [,445]
## (Intercept)  0.745950582  0.80923659  0.721182354  0.8180263766  0.72163765
## studyID1    -0.004252005  0.03917185 -0.024892574 -0.0007579445  0.01731538
## studyID2     0.052258895  0.06353784  0.010298725  0.0300111631  0.09418452
## studyID3    -0.022700005 -0.04675638  0.006192526 -0.0130079935 -0.06533619
## studyID4     0.029516559 -0.02564925  0.051186137  0.0020993686  0.01000201
##                   [,446]        [,447]       [,448]      [,449]       [,450]
## (Intercept)  0.688906548  0.8596210370  0.806981995  0.71336019  0.687788342
## studyID1    -0.014122469  0.0288074761 -0.018940143  0.01432311  0.014615230
## studyID2     0.017481112  0.0298559541  0.013598853  0.06538177  0.063671897
## studyID3     0.004430318 -0.0347233321  0.019462753 -0.03975677 -0.032377761
## studyID4     0.030144107 -0.0009961312 -0.005842216  0.02303492  0.008205139
##                   [,451]       [,452]      [,453]       [,454]       [,455]
## (Intercept)  0.810299106  0.865075277  0.70590504  0.757463907  0.701428554
## studyID1    -0.002154955  0.022420175 -0.02296554 -0.021502849  0.001793737
## studyID2     0.046637024  0.041800581  0.05865546  0.004006560  0.036078983
## studyID3    -0.015309191 -0.036887625 -0.01216706  0.001670128 -0.030049896
## studyID4     0.008501660 -0.005842737  0.02770816  0.034951070  0.040758429
##                   [,456]       [,457]       [,458]       [,459]       [,460]
## (Intercept)  0.708612894  0.761692434  0.676347407  0.764311134  0.729933745
## studyID1    -0.011694074  0.020907581 -0.004511749 -0.008774505  0.009124336
## studyID2     0.026309257  0.056037829  0.035835850  0.057594389  0.052696713
## studyID3     0.007375605 -0.046123713 -0.023412310 -0.030905548 -0.048129804
## studyID4     0.021158940  0.003715777  0.045841697  0.035237175  0.023650527
##                  [,461]      [,462]       [,463]       [,464]      [,465]
## (Intercept)  0.72764925  0.74633071  0.684111517  0.832710542  0.81067492
## studyID1     0.01444856 -0.02942660 -0.011951880  0.010197703 -0.05975306
## studyID2     0.08308315  0.01445299  0.044929584  0.018234345 -0.03946627
## studyID3    -0.05574226  0.01827845 -0.001895898 -0.012775365  0.05699626
## studyID4     0.01321512  0.03555220  0.024417938  0.001329241  0.05252579
##                   [,466]       [,467]      [,468]       [,469]       [,470]
## (Intercept)  0.758634026  0.715710894  0.74002245 0.9142019160  0.777863392
## studyID1    -0.003003013  0.013155696  0.01650803 0.0078506065  0.016593681
## studyID2     0.029412095  0.081928347  0.06204407 0.0095403354  0.072802645
## studyID3    -0.010443842 -0.040255512 -0.04100088 0.0005909371 -0.047498314
## studyID4     0.010677098  0.008049699  0.00704545 0.0002256434 -0.001468372
##                   [,471]      [,472]       [,473]        [,474]      [,475]
## (Intercept)  0.679874232  0.73634847  0.767809674  8.210647e-01  0.75121314
## studyID1    -0.029870873  0.02607450 -0.044601750  5.472864e-03  0.02738022
## studyID2     0.025909941  0.06796663 -0.003774917  1.277730e-02  0.05382670
## studyID3     0.009206168 -0.05549698  0.047920935 -4.550567e-04 -0.06861233
## studyID4     0.049141356  0.01476263  0.022744628 -6.533592e-05  0.03200722
##                   [,476]       [,477]       [,478]       [,479]       [,480]
## (Intercept)  0.683864616  0.875744510  0.736130803  0.729744486  0.753563344
## studyID1    -0.005605218  0.014602432 -0.005361074 -0.018669221  0.005502440
## studyID2     0.044617476  0.023465218  0.057120628  0.015083857  0.050842508
## studyID3    -0.018914048 -0.008454238 -0.012702306  0.006820543 -0.027417071
## studyID4     0.036662991 -0.009775050  0.010888696  0.036042771  0.008662072
##                   [,481]        [,482]      [,483]        [,484]      [,485]
## (Intercept)  0.744437030  7.425506e-01  0.73992176  0.7244169889  0.74050190
## studyID1    -0.018037874 -4.428348e-05  0.01244645 -0.0001935564 -0.02455606
## studyID2     0.050315685  5.104708e-02  0.06684344  0.0142263570  0.03162279
## studyID3     0.014884367 -2.566240e-02 -0.04833190 -0.0330110399  0.01527841
## studyID4     0.001217342  1.686975e-02  0.01795061  0.0487775489  0.01344153
##                  [,486]      [,487]      [,488]      [,489]       [,490]
## (Intercept)  0.73060590  0.72146498  0.76024346  0.75035138  0.749890332
## studyID1    -0.01318728 -0.04379858  0.02096242 -0.03268324  0.023204378
## studyID2     0.04924534 -0.03492104  0.07020008 -0.00793699  0.084149140
## studyID3    -0.01180934  0.04248216 -0.06366889  0.03432892 -0.061944500
## studyID4     0.02965500  0.05833628  0.03066558  0.04501529  0.001704515
##                   [,491]       [,492]      [,493]        [,494]      [,495]
## (Intercept)  0.752555830  0.853583542  0.75308582  8.541475e-01  0.83694979
## studyID1     0.003415827  0.027704938 -0.01331162  1.833433e-03  0.03537389
## studyID2     0.034048485  0.047558493  0.04237549  3.143937e-02  0.06815511
## studyID3    -0.024363299 -0.031885967 -0.01194291 -1.612792e-02 -0.05669406
## studyID4     0.010380754 -0.009852011  0.02949756  1.502877e-05 -0.01178907
##                  [,496]       [,497]       [,498]       [,499]      [,500]
## (Intercept)  0.78016942  0.733039781  0.718857227  0.742227258  0.75996062
## studyID1     0.01444723 -0.020785732 -0.052883563 -0.025002429  0.05250434
## studyID2     0.04297864  0.028703336 -0.005326699  0.037601657  0.10063151
## studyID3    -0.02439402  0.006397359  0.042369213  0.003827157 -0.07531051
## studyID4     0.01013984  0.012491046  0.039940684  0.017100753 -0.03207805
##                   [,501]      [,502]       [,503]       [,504]       [,505]
## (Intercept)  0.810746064  0.72048196  0.701067819  0.769044679  0.733514743
## studyID1    -0.006855010 -0.02560316 -0.016078825 -0.035896258 -0.042590469
## studyID2     0.011623086  0.04991596  0.033684624  0.005070562  0.009686297
## studyID3     0.019215360 -0.01113248  0.002774911  0.044597810  0.020055153
## studyID4     0.002483649  0.03828162  0.030069934  0.017120490  0.053394228
##                   [,506]       [,507]       [,508]      [,509]      [,510]
## (Intercept)  0.752173076  0.771915753  0.721945584  0.79685561  0.74492286
## studyID1     0.027390614  0.016357521 -0.016727514  0.01346359 -0.01858812
## studyID2     0.068276408  0.046238265  0.035383692  0.05686315  0.02219381
## studyID3    -0.053422087 -0.032240340 -0.002957782 -0.04647820  0.00277446
## studyID4     0.005780032  0.009595829  0.019192709  0.01397931  0.03113130
##                  [,511]       [,512]       [,513]      [,514]        [,515]
## (Intercept)  0.74071554  0.676658241  0.756324461  0.74800700  0.7770147356
## studyID1     0.02047680  0.008870223  0.009938951  0.03005037  0.0011948298
## studyID2     0.02568777  0.038956723  0.058327726  0.05357977  0.0580620059
## studyID3    -0.04189173 -0.017908047 -0.030205814 -0.06496324 -0.0163979198
## studyID4     0.03499053  0.023263217  0.002179003  0.02020251  0.0004167877
##                    [,516]       [,517]        [,518]      [,519]       [,520]
## (Intercept)  0.7311898484  0.754463485  0.7206435964  0.80566139  0.764521962
## studyID1    -0.0008093035 -0.004837788  0.0004121979  0.02752795  0.007802459
## studyID2     0.0442242280  0.058818438  0.0120918270  0.02637212  0.071750731
## studyID3    -0.0315420997 -0.023388977 -0.0159895344 -0.03517877 -0.038128789
## studyID4     0.0368351695  0.017869311  0.0403714813  0.01269520  0.004185801
##                  [,521]       [,522]       [,523]      [,524]       [,525]
## (Intercept)  0.75665251  0.699525659  0.856598972  0.72821245  0.730470037
## studyID1     0.01285632 -0.004518647  0.028842546 -0.01410605 -0.008636468
## studyID2     0.03069859  0.063560296  0.042470873  0.04228478  0.045706635
## studyID3    -0.03177858 -0.030878366 -0.036008162 -0.01998070 -0.028121033
## studyID4     0.01958731  0.019057777 -0.005984491  0.03216216  0.033086364
##                  [,526]      [,527]       [,528]       [,529]      [,530]
## (Intercept)  0.70223986  0.71244265  0.785678744  0.738176172  0.73641416
## studyID1    -0.01746276 -0.01933295  0.006692514  0.025239392 -0.00317709
## studyID2     0.05586032  0.04711987  0.040388643  0.095362831  0.01739013
## studyID3    -0.02224091 -0.01784792 -0.022131889 -0.060049701 -0.01385369
## studyID4     0.02695664  0.03526911 -0.002357003 -0.004435628  0.02894158
##                   [,531]       [,532]       [,533]       [,534]      [,535]
## (Intercept)  0.766110288  0.708200183  0.799015536  0.720706199  0.71481278
## studyID1     0.025297167  0.020358384  0.030659330 -0.009673549  0.02407470
## studyID2     0.053671506  0.076916056  0.069250917  0.024998278  0.07453381
## studyID3    -0.040286464 -0.049199193 -0.061427824 -0.003034226 -0.07994656
## studyID4     0.002392001  0.006873404  0.009165657  0.028791037  0.03979205
##                   [,536]       [,537]       [,538]       [,539]      [,540]
## (Intercept)  0.732889428  0.819792088  0.716107670  0.711549246  0.71134534
## studyID1     0.014441269  0.016273427  0.009606795 -0.024090188  0.01426914
## studyID2     0.052814121  0.009091139  0.071475948  0.056087135  0.04554835
## studyID3    -0.031631462 -0.029607341 -0.060334723 -0.009709743 -0.03473561
## studyID4    -0.001261994  0.022074805  0.026160277  0.021400033  0.01278058
##                   [,541]       [,542]      [,543]      [,544]      [,545]
## (Intercept)  0.783865478  0.805088814  0.71002602  0.74305595  0.71015300
## studyID1    -0.001919176  0.021251354  0.02755140  0.02763631  0.02920989
## studyID2     0.053990729  0.053802331  0.06720132  0.04506846  0.07266060
## studyID3    -0.033642488 -0.043198064 -0.06841275 -0.04864597 -0.06833452
## studyID4     0.025918273  0.005111637  0.02365552  0.01940027  0.02456472
##                    [,546]      [,547]       [,548]       [,549]      [,550]
## (Intercept)  0.8179097079  0.77110019  0.738174482  0.710568749  0.72194328
## studyID1     0.0008472454  0.01646614  0.005439632  0.009002755 -0.01806964
## studyID2     0.0334616464  0.05946702  0.059291991  0.027261000  0.05771934
## studyID3    -0.0202960144 -0.03340806 -0.028568432 -0.017373629 -0.02205352
## studyID4     0.0133352077 -0.01441851  0.005949941  0.028992099  0.01705428
##                  [,551]
## (Intercept)  0.72137640
## studyID1     0.02473271
## studyID2     0.06852849
## studyID3    -0.05749551
## studyID4     0.01167007
## 
## $f.perms
##              [,1]
##    [1,] 1.0057677
##    [2,] 0.8054855
##    [3,] 1.2880091
##    [4,] 0.9516901
##    [5,] 0.8671892
##    [6,] 0.9393818
##    [7,] 1.1256861
##    [8,] 0.9205191
##    [9,] 0.9421464
##   [10,] 1.1423109
##   [11,] 0.8785887
##   [12,] 1.2518957
##   [13,] 0.9010014
##   [14,] 1.1185882
##   [15,] 0.8978072
##   [16,] 0.8261698
##   [17,] 0.9386380
##   [18,] 1.1902188
##   [19,] 0.9101767
##   [20,] 0.8400449
##   [21,] 0.9142474
##   [22,] 0.8338681
##   [23,] 1.0588736
##   [24,] 1.0785844
##   [25,] 0.9819983
##   [26,] 0.9971145
##   [27,] 0.8187826
##   [28,] 1.0306712
##   [29,] 1.2330001
##   [30,] 1.0061338
##   [31,] 1.4765741
##   [32,] 1.1322350
##   [33,] 1.0526562
##   [34,] 1.1273373
##   [35,] 0.9908707
##   [36,] 0.8193011
##   [37,] 0.8410726
##   [38,] 1.2258908
##   [39,] 1.0439719
##   [40,] 1.1118988
##   [41,] 1.0431578
##   [42,] 0.8562478
##   [43,] 0.9322719
##   [44,] 0.9374564
##   [45,] 1.2229358
##   [46,] 1.0286734
##   [47,] 0.8582146
##   [48,] 0.8718764
##   [49,] 1.2059688
##   [50,] 1.2370903
##   [51,] 1.0895473
##   [52,] 0.9328736
##   [53,] 0.9603081
##   [54,] 0.8834607
##   [55,] 1.1544675
##   [56,] 1.2952392
##   [57,] 1.0046481
##   [58,] 0.7486102
##   [59,] 0.9908982
##   [60,] 1.1047352
##   [61,] 0.8096386
##   [62,] 0.8737925
##   [63,] 0.9239683
##   [64,] 0.8713885
##   [65,] 1.0589220
##   [66,] 1.0523460
##   [67,] 0.7752204
##   [68,] 1.0060593
##   [69,] 1.3320364
##   [70,] 1.0574317
##   [71,] 1.1007066
##   [72,] 0.9844744
##   [73,] 0.7834719
##   [74,] 1.0434946
##   [75,] 1.1744783
##   [76,] 0.7656137
##   [77,] 0.8232630
##   [78,] 0.8336811
##   [79,] 0.9986446
##   [80,] 0.8441916
##   [81,] 1.0489400
##   [82,] 1.0125192
##   [83,] 1.2472445
##   [84,] 0.9319356
##   [85,] 0.9237543
##   [86,] 0.8549696
##   [87,] 0.7949995
##   [88,] 0.8973508
##   [89,] 0.9672672
##   [90,] 1.0884042
##   [91,] 0.9147859
##   [92,] 0.9147594
##   [93,] 0.9433913
##   [94,] 0.8072336
##   [95,] 1.1709131
##   [96,] 1.3273902
##   [97,] 0.8824159
##   [98,] 1.2610347
##   [99,] 0.9304234
##  [100,] 0.8650460
##  [101,] 1.2221733
##  [102,] 0.9752177
##  [103,] 1.0703330
##  [104,] 1.0370546
##  [105,] 0.8736160
##  [106,] 1.0435974
##  [107,] 1.1495990
##  [108,] 1.0878816
##  [109,] 1.0900165
##  [110,] 1.2408095
##  [111,] 0.9326451
##  [112,] 0.9909310
##  [113,] 1.0616811
##  [114,] 0.9519169
##  [115,] 0.9453789
##  [116,] 1.3794359
##  [117,] 0.9648480
##  [118,] 0.8580348
##  [119,] 0.9840182
##  [120,] 0.8316406
##  [121,] 1.0943218
##  [122,] 1.1204978
##  [123,] 0.9561554
##  [124,] 1.1445973
##  [125,] 0.9791086
##  [126,] 1.0220879
##  [127,] 1.0592572
##  [128,] 0.9503271
##  [129,] 0.9268213
##  [130,] 1.1001522
##  [131,] 1.0042031
##  [132,] 0.9117230
##  [133,] 0.9151328
##  [134,] 1.1986574
##  [135,] 0.9593860
##  [136,] 0.9805369
##  [137,] 0.8138624
##  [138,] 0.8852184
##  [139,] 0.8940231
##  [140,] 1.0278942
##  [141,] 0.9479082
##  [142,] 1.1244463
##  [143,] 1.2760323
##  [144,] 0.8180291
##  [145,] 0.9223510
##  [146,] 0.8521388
##  [147,] 0.9325558
##  [148,] 1.0043096
##  [149,] 0.7838983
##  [150,] 1.0267904
##  [151,] 0.7655580
##  [152,] 1.0410955
##  [153,] 1.1629711
##  [154,] 1.3910954
##  [155,] 1.0182589
##  [156,] 0.9483630
##  [157,] 0.9226194
##  [158,] 1.0105687
##  [159,] 1.0095752
##  [160,] 1.2455401
##  [161,] 0.9887787
##  [162,] 0.9632079
##  [163,] 0.9355643
##  [164,] 0.7764766
##  [165,] 1.0062958
##  [166,] 0.8278105
##  [167,] 1.0221540
##  [168,] 0.7331007
##  [169,] 0.9627475
##  [170,] 0.8872246
##  [171,] 1.0994621
##  [172,] 0.8930284
##  [173,] 0.8139449
##  [174,] 1.1013466
##  [175,] 1.0719386
##  [176,] 1.1643872
##  [177,] 1.0702444
##  [178,] 0.9730500
##  [179,] 1.0673279
##  [180,] 0.9337136
##  [181,] 0.9551256
##  [182,] 0.8598886
##  [183,] 1.0093716
##  [184,] 0.9598812
##  [185,] 0.9611541
##  [186,] 1.1460788
##  [187,] 0.8818293
##  [188,] 0.7241664
##  [189,] 1.1201571
##  [190,] 1.1936506
##  [191,] 0.8898004
##  [192,] 1.0768724
##  [193,] 0.9965563
##  [194,] 0.7863649
##  [195,] 0.9169207
##  [196,] 1.0137220
##  [197,] 1.0143683
##  [198,] 1.3092549
##  [199,] 1.1151451
##  [200,] 0.9757986
##  [201,] 1.0795373
##  [202,] 0.9052430
##  [203,] 0.8359357
##  [204,] 1.0357265
##  [205,] 1.1063586
##  [206,] 0.8791732
##  [207,] 1.1003905
##  [208,] 1.2172796
##  [209,] 0.9944590
##  [210,] 1.1769217
##  [211,] 1.0789120
##  [212,] 1.1425743
##  [213,] 0.9680238
##  [214,] 0.9556957
##  [215,] 0.9160642
##  [216,] 1.1213818
##  [217,] 0.8423736
##  [218,] 1.2401752
##  [219,] 0.8235371
##  [220,] 0.9546518
##  [221,] 1.1722906
##  [222,] 0.9478580
##  [223,] 1.1210049
##  [224,] 0.9894733
##  [225,] 0.9598927
##  [226,] 0.9196027
##  [227,] 1.1243847
##  [228,] 0.9918667
##  [229,] 0.8292542
##  [230,] 0.8486948
##  [231,] 1.0760989
##  [232,] 0.9402021
##  [233,] 1.0489201
##  [234,] 0.9199816
##  [235,] 1.1716895
##  [236,] 0.7300406
##  [237,] 0.9326970
##  [238,] 1.0082821
##  [239,] 0.7141638
##  [240,] 0.9546923
##  [241,] 0.8750708
##  [242,] 0.9964654
##  [243,] 1.1834414
##  [244,] 1.0641101
##  [245,] 1.2041021
##  [246,] 0.9346416
##  [247,] 0.8891716
##  [248,] 0.9495524
##  [249,] 1.3030171
##  [250,] 1.1004610
##  [251,] 1.0467671
##  [252,] 1.4994375
##  [253,] 0.9076887
##  [254,] 0.8809941
##  [255,] 1.1443676
##  [256,] 1.1070069
##  [257,] 1.2768744
##  [258,] 1.0993731
##  [259,] 0.8579786
##  [260,] 0.8932666
##  [261,] 1.0215773
##  [262,] 0.8899308
##  [263,] 1.0433360
##  [264,] 0.8663038
##  [265,] 1.0072621
##  [266,] 1.0380542
##  [267,] 1.0250505
##  [268,] 0.8195956
##  [269,] 1.1313682
##  [270,] 0.9935256
##  [271,] 1.0503521
##  [272,] 1.0130874
##  [273,] 1.2690519
##  [274,] 0.9297655
##  [275,] 1.0382091
##  [276,] 0.9728987
##  [277,] 1.2906713
##  [278,] 0.8979663
##  [279,] 0.8482430
##  [280,] 0.9171609
##  [281,] 0.8967818
##  [282,] 0.8749586
##  [283,] 1.1735520
##  [284,] 1.1894364
##  [285,] 1.0803449
##  [286,] 1.1907701
##  [287,] 0.9894478
##  [288,] 1.0107978
##  [289,] 0.8896581
##  [290,] 0.9072616
##  [291,] 1.2832537
##  [292,] 0.8388576
##  [293,] 1.3753098
##  [294,] 1.1418231
##  [295,] 0.9778586
##  [296,] 1.0408258
##  [297,] 1.1646368
##  [298,] 0.9436626
##  [299,] 1.0556551
##  [300,] 0.8591318
##  [301,] 1.0279993
##  [302,] 1.0809903
##  [303,] 1.0483799
##  [304,] 0.7989740
##  [305,] 0.7371380
##  [306,] 0.8217847
##  [307,] 1.0253678
##  [308,] 1.0443407
##  [309,] 0.8060371
##  [310,] 1.0903621
##  [311,] 0.7571533
##  [312,] 1.0859188
##  [313,] 1.0846038
##  [314,] 0.8983626
##  [315,] 0.9518225
##  [316,] 0.9794251
##  [317,] 0.9397354
##  [318,] 1.1879428
##  [319,] 1.1690957
##  [320,] 0.9791667
##  [321,] 1.0419639
##  [322,] 1.0396738
##  [323,] 0.9319726
##  [324,] 1.1388824
##  [325,] 1.1316914
##  [326,] 1.0106999
##  [327,] 0.9262136
##  [328,] 1.0742525
##  [329,] 1.0056950
##  [330,] 1.0387218
##  [331,] 0.9081620
##  [332,] 1.0063055
##  [333,] 1.0477118
##  [334,] 0.9254562
##  [335,] 1.1115660
##  [336,] 1.0718197
##  [337,] 1.0076191
##  [338,] 0.9874576
##  [339,] 1.0258725
##  [340,] 1.0312838
##  [341,] 1.0677174
##  [342,] 1.2208183
##  [343,] 1.1992801
##  [344,] 0.8480485
##  [345,] 1.1711210
##  [346,] 0.9620710
##  [347,] 0.7659826
##  [348,] 1.0468687
##  [349,] 0.9982820
##  [350,] 1.0138102
##  [351,] 1.1619305
##  [352,] 1.0693308
##  [353,] 1.0682990
##  [354,] 0.8485005
##  [355,] 0.9834630
##  [356,] 1.2708412
##  [357,] 1.3392718
##  [358,] 0.8238553
##  [359,] 1.2671536
##  [360,] 0.7683870
##  [361,] 1.2406901
##  [362,] 0.9517103
##  [363,] 0.9168967
##  [364,] 1.3311283
##  [365,] 0.9420840
##  [366,] 1.0435787
##  [367,] 0.9956139
##  [368,] 1.1323327
##  [369,] 1.0209990
##  [370,] 1.0460093
##  [371,] 0.7245849
##  [372,] 1.1045393
##  [373,] 0.9137355
##  [374,] 1.1076446
##  [375,] 0.8171412
##  [376,] 0.9754921
##  [377,] 1.0042290
##  [378,] 0.9867396
##  [379,] 1.0454794
##  [380,] 1.0272019
##  [381,] 1.1425866
##  [382,] 0.9745924
##  [383,] 1.1439025
##  [384,] 0.8204210
##  [385,] 0.8472292
##  [386,] 1.0907443
##  [387,] 1.1549119
##  [388,] 1.0608485
##  [389,] 1.0177434
##  [390,] 0.8702281
##  [391,] 1.0876466
##  [392,] 0.9227873
##  [393,] 1.3401117
##  [394,] 0.9300789
##  [395,] 1.1443871
##  [396,] 1.2338538
##  [397,] 0.9145874
##  [398,] 1.0269385
##  [399,] 0.9937231
##  [400,] 1.0398929
##  [401,] 1.0122327
##  [402,] 0.9371223
##  [403,] 0.9471193
##  [404,] 0.8724570
##  [405,] 0.8634410
##  [406,] 0.8906423
##  [407,] 1.1588989
##  [408,] 1.0737534
##  [409,] 0.9437036
##  [410,] 0.8650850
##  [411,] 0.9349327
##  [412,] 1.1168684
##  [413,] 0.9534450
##  [414,] 0.9532923
##  [415,] 1.1333145
##  [416,] 1.0286770
##  [417,] 1.0204349
##  [418,] 1.0488385
##  [419,] 0.9540104
##  [420,] 0.8867504
##  [421,] 0.9362727
##  [422,] 0.9035327
##  [423,] 0.9801958
##  [424,] 0.9470115
##  [425,] 1.0979792
##  [426,] 1.0239136
##  [427,] 1.0654177
##  [428,] 0.9084966
##  [429,] 0.9764162
##  [430,] 0.9826489
##  [431,] 1.1120136
##  [432,] 1.0414235
##  [433,] 0.9198977
##  [434,] 0.9093840
##  [435,] 0.9641607
##  [436,] 1.1453378
##  [437,] 0.9402952
##  [438,] 0.9876412
##  [439,] 0.8875606
##  [440,] 0.9978687
##  [441,] 1.0441089
##  [442,] 1.2561540
##  [443,] 0.7970173
##  [444,] 0.9426588
##  [445,] 1.0476176
##  [446,] 1.1355309
##  [447,] 0.9108996
##  [448,] 0.8365207
##  [449,] 1.1109374
##  [450,] 0.8824727
##  [451,] 0.9008671
##  [452,] 0.9377730
##  [453,] 0.9277598
##  [454,] 1.0779849
##  [455,] 0.7287209
##  [456,] 0.8464505
##  [457,] 0.9415052
##  [458,] 1.0803030
##  [459,] 0.9337244
##  [460,] 0.9926997
##  [461,] 1.0293503
##  [462,] 1.1523193
##  [463,] 0.9186043
##  [464,] 0.7901459
##  [465,] 0.8912138
##  [466,] 0.9187359
##  [467,] 1.1384907
##  [468,] 0.9589068
##  [469,] 0.9820737
##  [470,] 1.1534132
##  [471,] 1.1783510
##  [472,] 1.1159536
##  [473,] 0.7697020
##  [474,] 1.1986120
##  [475,] 0.9037230
##  [476,] 0.9271909
##  [477,] 1.0351115
##  [478,] 0.9497060
##  [479,] 1.1357567
##  [480,] 0.8064949
##  [481,] 1.0005448
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##  [778,] 1.1476437
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##  [814,] 1.1578242
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##  [830,] 1.3648020
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##  [834,] 1.0417452
##  [835,] 0.8504412
##  [836,] 1.2292936
##  [837,] 1.1086572
##  [838,] 1.1779306
##  [839,] 0.9075120
##  [840,] 0.8576346
##  [841,] 1.0436219
##  [842,] 1.0560922
##  [843,] 1.0115656
##  [844,] 1.0373259
##  [845,] 1.1087209
##  [846,] 0.9809984
##  [847,] 0.9331121
##  [848,] 1.2779622
##  [849,] 0.9239388
##  [850,] 1.3836863
##  [851,] 0.8803244
##  [852,] 1.1214588
##  [853,] 0.9110840
##  [854,] 0.7311550
##  [855,] 0.9348233
##  [856,] 1.0440588
##  [857,] 1.0925039
##  [858,] 1.0735991
##  [859,] 1.0732437
##  [860,] 1.1096876
##  [861,] 1.0160602
##  [862,] 0.9854514
##  [863,] 1.2200049
##  [864,] 0.9999910
##  [865,] 0.9378808
##  [866,] 0.9574947
##  [867,] 0.9861551
##  [868,] 1.0032441
##  [869,] 1.1078525
##  [870,] 0.9158097
##  [871,] 0.9161758
##  [872,] 1.0269123
##  [873,] 0.8704544
##  [874,] 0.9288781
##  [875,] 0.8400335
##  [876,] 1.0700512
##  [877,] 0.9143019
##  [878,] 1.1596654
##  [879,] 0.8999799
##  [880,] 1.0328937
##  [881,] 1.0927493
##  [882,] 0.8331728
##  [883,] 1.2929742
##  [884,] 0.9993190
##  [885,] 1.1217456
##  [886,] 0.9729372
##  [887,] 1.1003481
##  [888,] 1.1845966
##  [889,] 1.1825130
##  [890,] 0.9474661
##  [891,] 0.8714856
##  [892,] 0.8367562
##  [893,] 0.8697242
##  [894,] 0.8290351
##  [895,] 1.1645174
##  [896,] 0.8130064
##  [897,] 0.9660601
##  [898,] 1.1665261
##  [899,] 0.8872230
##  [900,] 0.9259104
##  [901,] 1.0247238
##  [902,] 1.0220035
##  [903,] 1.0906704
##  [904,] 0.8026500
##  [905,] 0.8303402
##  [906,] 1.0165876
##  [907,] 1.0451235
##  [908,] 0.9797119
##  [909,] 0.9043218
##  [910,] 0.8080948
##  [911,] 0.9652555
##  [912,] 0.7896322
##  [913,] 1.3307560
##  [914,] 1.0028132
##  [915,] 0.7233279
##  [916,] 1.1356117
##  [917,] 0.8394916
##  [918,] 1.1054935
##  [919,] 0.8303645
##  [920,] 1.0987055
##  [921,] 1.0111098
##  [922,] 1.1777949
##  [923,] 1.1916271
##  [924,] 1.0585589
##  [925,] 1.3491950
##  [926,] 0.7684001
##  [927,] 0.8570969
##  [928,] 1.0550792
##  [929,] 0.9467386
##  [930,] 0.7908884
##  [931,] 1.0947918
##  [932,] 1.0607974
##  [933,] 1.0796516
##  [934,] 1.0865522
##  [935,] 0.9813184
##  [936,] 0.9300836
##  [937,] 1.1825470
##  [938,] 0.8671662
##  [939,] 0.9945184
##  [940,] 0.9551000
##  [941,] 0.8450715
##  [942,] 0.9051715
##  [943,] 0.8625268
##  [944,] 1.0164836
##  [945,] 0.8731855
##  [946,] 0.9175499
##  [947,] 0.8463470
##  [948,] 0.9308764
##  [949,] 0.9038918
##  [950,] 1.0479641
##  [951,] 0.9566081
##  [952,] 0.9028996
##  [953,] 1.0834673
##  [954,] 1.0932699
##  [955,] 0.9355111
##  [956,] 1.0053550
##  [957,] 0.6773795
##  [958,] 0.9766311
##  [959,] 0.9798689
##  [960,] 0.9889316
##  [961,] 0.7254926
##  [962,] 1.0189395
##  [963,] 0.9555691
##  [964,] 1.2441626
##  [965,] 1.1807358
##  [966,] 1.1107956
##  [967,] 1.1116892
##  [968,] 1.1244345
##  [969,] 0.8485504
##  [970,] 0.9348211
##  [971,] 0.8858040
##  [972,] 1.1979661
##  [973,] 0.8471685
##  [974,] 0.8656610
##  [975,] 1.0294702
##  [976,] 1.0542649
##  [977,] 0.8390960
##  [978,] 0.9979691
##  [979,] 0.9455027
##  [980,] 1.0932276
##  [981,] 0.9771701
##  [982,] 0.8736127
##  [983,] 0.9115851
##  [984,] 0.9220111
##  [985,] 1.0221142
##  [986,] 1.1954322
##  [987,] 0.9960520
##  [988,] 1.0386198
##  [989,] 0.8268104
##  [990,] 0.9219867
##  [991,] 0.7632419
##  [992,] 0.6925598
##  [993,] 1.0348600
##  [994,] 1.1277736
##  [995,] 0.7778288
##  [996,] 1.0088966
##  [997,] 1.0846182
##  [998,] 1.1396940
##  [999,] 0.9389285
## 
## $model.matrix
##                                                                (Intercept)
## FengQ_2015.metaphlan_bugs_list.stool:SID31004                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31009                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31021                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31071                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31112                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31129                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31159                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31160                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31188                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31219                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31223                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31236                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31237                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31267                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31276                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31285                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31300                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31328                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31333                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31343                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31360                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31367                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31379                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31416                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31428                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31446                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31450                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31452                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31489                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31493                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31512                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31519                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31537                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31549                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31557                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31637                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31685                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31700                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31711                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31714                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31723                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31749                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31750                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31766                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31865                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31866                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31868                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31870                            1
## FengQ_2015.metaphlan_bugs_list.stool:SID31871                            1
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## FengQ_2015.metaphlan_bugs_list.stool:SID532826                           1
## FengQ_2015.metaphlan_bugs_list.stool:SID532915                           1
## HanniganGD_2017.metaphlan_bugs_list.stool:MG100180                       1
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## HanniganGD_2017.metaphlan_bugs_list.stool:MG100125                       1
## VogtmannE_2016.metaphlan_bugs_list.stool:MMRS11288076ST-27-0-0           1
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## VogtmannE_2016.metaphlan_bugs_list.stool:MMRS99045180ST-27-0-0           1
## YuJ_2015.metaphlan_bugs_list.stool:SZAXPI003409-8                        1
## YuJ_2015.metaphlan_bugs_list.stool:SZAXPI003410-3                        1
## YuJ_2015.metaphlan_bugs_list.stool:SZAXPI003411-6                        1
## YuJ_2015.metaphlan_bugs_list.stool:SZAXPI003412-1                        1
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## YuJ_2015.metaphlan_bugs_list.stool:SZAXPI015230-16                       1
## YuJ_2015.metaphlan_bugs_list.stool:SZAXPI015231-17                       1
## YuJ_2015.metaphlan_bugs_list.stool:SZAXPI015232-18                       1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCIS00146684ST-4-0                1
## ZellerG_2014.metaphlan_bugs_list.stool:CCIS00281083ST-3-0                1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCIS05314658ST-4-0                1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCIS21126322ST-4-0                1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCIS87605453ST-4-0                1
## ZellerG_2014.metaphlan_bugs_list.stool:CCIS88007743ST-4-0                1
## ZellerG_2014.metaphlan_bugs_list.stool:CCIS88317640ST-4-0                1
## ZellerG_2014.metaphlan_bugs_list.stool:CCIS90164298ST-4-0                1
## ZellerG_2014.metaphlan_bugs_list.stool:CCIS91228662ST-4-0                1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCIS95409808ST-4-0                1
## ZellerG_2014.metaphlan_bugs_list.stool:CCIS98482370ST-3-0                1
## ZellerG_2014.metaphlan_bugs_list.stool:CCIS98512455ST-4-0                1
## ZellerG_2014.metaphlan_bugs_list.stool:CCIS98832363ST-4-0                1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCMD12232071ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD13071240ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD13934959ST-21-0               1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCMD18872694ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD19497912ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD23101338ST-21-0               1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCMD25963797ST-21-0               1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCMD35802077ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD40701343ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD42428553ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD45988061ST-21-0               1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCMD48236717ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD50071957ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD51864103ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD60079086ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD63399960ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD64503764ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD64776337ST-21-0               1
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## ZellerG_2014.metaphlan_bugs_list.stool:CCMD74930188ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD79987997ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD82866709ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD86114146ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD86707194ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD87156761ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD88272491ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD90311071ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD93344354ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD95433940ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:CCMD96553385ST-21-0               1
## ZellerG_2014.metaphlan_bugs_list.stool:MMPU29365221ST                    1
## ZellerG_2014.metaphlan_bugs_list.stool:MMPU68403337ST                    1
## ZellerG_2014.metaphlan_bugs_list.stool:MMPU72854103ST                    1
## ZellerG_2014.metaphlan_bugs_list.stool:MMPU84450604ST                    1
## ZellerG_2014.metaphlan_bugs_list.stool:MMPU99077057ST                    1
##                                                                studyID1
## FengQ_2015.metaphlan_bugs_list.stool:SID31004                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31009                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31021                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31071                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31112                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31129                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31159                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31160                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31188                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31219                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31223                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31236                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31237                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31267                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31276                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31285                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31300                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31328                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31333                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31343                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31360                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31367                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31379                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31416                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31428                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31446                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31450                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31452                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31489                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31493                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31512                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31519                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31537                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31549                         1
## FengQ_2015.metaphlan_bugs_list.stool:SID31557                         1
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## VogtmannE_2016.me