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  • Exploratory data analysis
  • Run udr
  • Plot sharing patterns

Last updated: 2022-09-20

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Knit directory: udr-data-application/

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Rmd 0f24122 yunqiyang0215 2022-09-20 wflow_publish("analysis/t2d_application.rmd")

Description: Apply udr to type 2 diabetes dataset from Dr.Udler.

  1. Data Description: In total, it contains 324 SNPs with 65 conditions. All SNPs are strong signals in at least one condition, meaning abs(z-score) >= 1.96. After remove SNPs with missing z-score, there are 305 SNPs.

  2. Initialization: I randomly initialized 20 unconstrained Us and 4 rank1 Us for fitting. I use nuclear norm regularization with λ (regularization strength) equals the number of conditions. V is set to be identity matrix.

library("readxl")
library(udr)
library(gridExtra)
dat = read_excel("./data/t2d.xlsx")
dat = data.frame(dat)
rownames(dat) = dat[,1]
dat = dat[,-1]

Exploratory data analysis

summary(dat)
 MAGIC_dv1_2hrG    ADIPOGen_dv1_Adiponectin BFpercent_dv1_BFP  
 Min.   :-4.7016   Min.   :-9.0448          Min.   :-6.708333  
 1st Qu.:-0.1263   1st Qu.:-1.4799          1st Qu.:-1.081263  
 Median : 0.6257   Median :-0.4483          Median :-0.098020  
 Mean   : 0.6327   Mean   :-0.6359          Mean   :-0.009601  
 3rd Qu.: 1.3767   3rd Qu.: 0.4888          3rd Qu.: 0.981013  
 Max.   : 4.6160   Max.   : 3.8193          Max.   : 9.941176  
 NA's   :3                                                     
 GiantUKBB_eu_dv1_BMI  MAGIC_dv1_FG     MAGIC_dv2_FI     MAGIC_eu_dv6_HBA1C
 Min.   :-8.4444      Min.   :-3.636   Min.   :-4.6341   Min.   :-1.737    
 1st Qu.:-2.0192      1st Qu.: 0.297   1st Qu.:-0.7466   1st Qu.: 0.460    
 Median : 0.1177      Median : 1.050   Median : 0.2190   Median : 1.307    
 Mean   : 1.3130      Mean   : 1.210   Mean   : 0.3513   Mean   : 1.528    
 3rd Qu.: 3.1202      3rd Qu.: 1.805   3rd Qu.: 1.3587   3rd Qu.: 2.250    
 Max.   :45.7647      Max.   :13.953   Max.   : 6.0000   Max.   :11.200    
 NA's   :5                                                                 
 GiantUKBB_eu_dv1_HEIGHT GIANT_eu_females_dv5_HIPCadjBMI
 Min.   :-40.7143        Min.   :-12.4000               
 1st Qu.: -2.9706        1st Qu.: -1.4341               
 Median : -0.5333        Median : -0.3509               
 Mean   : -0.8867        Mean   : -0.5513               
 3rd Qu.:  1.8333        3rd Qu.:  0.5429               
 Max.   : 24.9286        Max.   :  4.6296               
 NA's   :5               NA's   :1                      
 GIANT_eu_males_dv5_HIPCadjBMI MAGIC_dv1_HOMAB   MAGIC_dv1_HOMAIR 
 Min.   :-6.7308               Min.   :-7.8378   Min.   :-2.7660  
 1st Qu.:-1.2222               1st Qu.:-1.2320   1st Qu.:-0.5503  
 Median :-0.2778               Median :-0.3148   Median : 0.3604  
 Mean   :-0.4019               Mean   :-0.2984   Mean   : 0.4397  
 3rd Qu.: 0.6455               3rd Qu.: 0.8188   3rd Qu.: 1.3436  
 Max.   : 4.2708               Max.   : 3.1429   Max.   : 4.7500  
 NA's   :11                                                       
 MAGIC_dv4_ISIadjAgeSexBMI Leptin_eu_dv1_LEP Leptin_eu_dv1_LEPadjBMI
 Min.   :-6.4000           Min.   :-3.8600   Min.   :-4.2462        
 1st Qu.:-1.2121           1st Qu.:-0.5913   1st Qu.:-0.5949        
 Median :-0.2864           Median : 0.2083   Median : 0.2239        
 Mean   :-0.4544           Mean   : 0.1611   Mean   : 0.2489        
 3rd Qu.: 0.4023           3rd Qu.: 0.9278   3rd Qu.: 1.0478        
 Max.   : 2.9545           Max.   : 4.9796   Max.   : 5.2381        
 NA's   :2                 NA's   :1         NA's   :1              
  MAGIC_dv1_PI      GIANT_eu_females_dv5_WAIST GIANT_eu_males_dv5_WAIST
 Min.   :-13.0000   Min.   :-4.6000            Min.   :-7.08333        
 1st Qu.: -0.4571   1st Qu.:-0.6598            1st Qu.:-1.09240        
 Median :  0.3392   Median : 0.3239            Median :-0.07896        
 Mean   :  0.2867   Mean   : 0.5726            Mean   : 0.06923        
 3rd Qu.:  1.0064   3rd Qu.: 1.4706            3rd Qu.: 0.90079        
 Max.   :  8.4444   Max.   :15.7778            Max.   :16.38298        
                    NA's   :1                  NA's   :6               
 GIANT_eu_females_dv5_WAISTadjBMI GIANT_eu_males_dv5_WAISTadjBMI
 Min.   :-4.3182                  Min.   :-5.3846               
 1st Qu.:-0.3024                  1st Qu.:-1.0300               
 Median : 0.4615                  Median :-0.1132               
 Mean   : 0.6837                  Mean   :-0.1462               
 3rd Qu.: 1.4071                  3rd Qu.: 0.7696               
 Max.   :11.4286                  Max.   : 4.2466               
 NA's   :1                        NA's   :8                     
 GIANT_eu_females_dv5_WHR GIANT_eu_males_dv5_WHR GIANT_eu_females_dv5_WHRadjBMI
 Min.   :-5.40000         Min.   :-5.7143        Min.   :-4.1176               
 1st Qu.:-0.05289         1st Qu.:-0.5998        1st Qu.:-0.1176               
 Median : 0.72727         Median : 0.3158        Median : 0.6792               
 Mean   : 1.04842         Mean   : 0.3332        Mean   : 1.0237               
 3rd Qu.: 1.83667         3rd Qu.: 1.1396        3rd Qu.: 1.7165               
 Max.   :10.00000         Max.   :10.4167        Max.   :12.2000               
 NA's   :1                NA's   :9              NA's   :1                     
 GIANT_eu_males_dv5_WHRadjBMI MAGIC_dv5_CIR      MAGIC_dv5_DI    
 Min.   :-5.7143              Min.   :-6.8182   Min.   :-7.2727  
 1st Qu.:-0.6545              1st Qu.:-1.1805   1st Qu.:-1.1468  
 Median : 0.2600              Median :-0.3181   Median :-0.4317  
 Mean   : 0.2605              Mean   :-0.4284   Mean   :-0.4514  
 3rd Qu.: 1.0727              3rd Qu.: 0.4436   3rd Qu.: 0.3856  
 Max.   : 4.4000              Max.   : 2.6500   Max.   : 3.0938  
 NA's   :11                   NA's   :2         NA's   :2        
 UKBB_White.blood.cell..leukocyte..count_irnt_both
 Min.   :-18.2208                                 
 1st Qu.: -0.7697                                 
 Median :  0.6758                                 
 Mean   :  0.6271                                 
 3rd Qu.:  2.4026                                 
 Max.   : 15.3512                                 
                                                  
 UKBB_Red.blood.cell..erythrocyte..count_irnt_both
 Min.   :-14.7225                                 
 1st Qu.: -0.9043                                 
 Median :  0.5586                                 
 Mean   :  0.5325                                 
 3rd Qu.:  2.0537                                 
 Max.   : 14.1924                                 
                                                  
 UKBB_Haemoglobin.concentration_irnt_both
 Min.   :-16.5546                        
 1st Qu.: -1.1570                        
 Median :  0.2704                        
 Mean   :  0.2186                        
 3rd Qu.:  1.5898                        
 Max.   : 10.6601                        
                                         
 UKBB_Mean.corpuscular.volume_irnt_both
 Min.   :-21.6424                      
 1st Qu.: -2.0429                      
 Median : -0.5790                      
 Mean   : -0.6121                      
 3rd Qu.:  0.7729                      
 Max.   : 34.0513                      
                                       
 UKBB_Red.blood.cell..erythrocyte..distribution.width_irnt_both
 Min.   :-13.6756                                              
 1st Qu.: -1.6386                                              
 Median : -0.1589                                              
 Mean   :  0.1490                                              
 3rd Qu.:  1.2334                                              
 Max.   : 30.7538                                              
                                                               
 UKBB_Platelet.count_irnt_both
 Min.   :-16.9557             
 1st Qu.: -1.6401             
 Median : -0.3097             
 Mean   : -0.3738             
 3rd Qu.:  1.1401             
 Max.   : 12.3754             
                              
 UKBB_Mean.platelet..thrombocyte..volume_irnt_both
 Min.   :-12.5186                                 
 1st Qu.: -1.2068                                 
 Median :  0.1079                                 
 Mean   :  0.2361                                 
 3rd Qu.:  1.2998                                 
 Max.   : 22.8954                                 
                                                  
 UKBB_Platelet.distribution.width_irnt_both UKBB_Lymphocyte.count_irnt_both
 Min.   :-9.9613                            Min.   :-16.6525               
 1st Qu.:-0.6762                            1st Qu.: -0.7528               
 Median : 0.6511                            Median :  0.5302               
 Mean   : 0.7695                            Mean   :  0.6259               
 3rd Qu.: 1.8587                            3rd Qu.:  2.0755               
 Max.   :13.7195                            Max.   : 18.2743               
                                                                           
 UKBB_Monocyte.count_irnt_both UKBB_Eosinophill.count_irnt_both
 Min.   :-17.4017              Min.   :-9.2045                 
 1st Qu.: -0.9571              1st Qu.:-0.8276                 
 Median :  0.3107              Median : 0.3684                 
 Mean   :  0.1146              Mean   : 0.3035                 
 3rd Qu.:  1.5570              3rd Qu.: 1.4853                 
 Max.   :  6.8904              Max.   :11.6449                 
                                                               
 UKBB_Basophill.count_irnt_both UKBB_Mean.reticulocyte.volume_irnt_both
 Min.   :-4.78292               Min.   :-12.3778                       
 1st Qu.:-0.75775               1st Qu.: -1.7593                       
 Median : 0.05358               Median : -0.4256                       
 Mean   :-0.01316               Mean   : -0.2459                       
 3rd Qu.: 0.79590               3rd Qu.:  0.8440                       
 Max.   : 4.60448               Max.   : 35.6927                       
                                                                       
 UKBB_High.light.scatter.reticulocyte.count_irnt_both
 Min.   :-10.3262                                    
 1st Qu.: -0.1231                                    
 Median :  1.4324                                    
 Mean   :  1.5276                                    
 3rd Qu.:  3.0871                                    
 Max.   : 33.5552                                    
                                                     
 UKBB_Albumin..quantile._irnt_both
 Min.   :-22.2720                 
 1st Qu.: -1.1065                 
 Median :  0.5980                 
 Mean   :  0.5194                 
 3rd Qu.:  1.9410                 
 Max.   : 13.0821                 
                                  
 UKBB_Alkaline.phosphatase..quantile._irnt_both
 Min.   :-102.42449                            
 1st Qu.:  -1.08833                            
 Median :   0.28181                            
 Mean   :   0.02559                            
 3rd Qu.:   1.79791                            
 Max.   :  32.60653                            
                                               
 UKBB_Alanine.aminotransferase..quantile._irnt_both
 Min.   :-5.60888                                  
 1st Qu.:-0.02731                                  
 Median : 1.50262                                  
 Mean   : 1.91352                                  
 3rd Qu.: 3.31938                                  
 Max.   :36.65126                                  
                                                   
 UKBB_Apoliprotein.B..quantile._irnt_both
 Min.   :-62.2517                        
 1st Qu.: -1.2973                        
 Median : -0.2485                        
 Mean   : -0.3145                        
 3rd Qu.:  1.0240                        
 Max.   :  9.5859                        
                                         
 UKBB_Aspartate.aminotransferase..quantile._irnt_both
 Min.   :-14.4419                                    
 1st Qu.: -1.2424                                    
 Median :  0.3908                                    
 Mean   :  0.5634                                    
 3rd Qu.:  1.9606                                    
 Max.   : 36.1778                                    
                                                     
 UKBB_Direct.bilirubin..quantile._irnt_both UKBB_Urea..quantile._irnt_both
 Min.   :-6.76699                           Min.   :-11.9129              
 1st Qu.:-0.87599                           1st Qu.: -0.7853              
 Median :-0.03287                           Median :  0.4104              
 Mean   :-0.01376                           Mean   :  0.3251              
 3rd Qu.: 0.85249                           3rd Qu.:  1.5182              
 Max.   :12.96292                           Max.   :  7.2983              
                                                                          
 UKBB_Calcium..quantile._irnt_both UKBB_C.reactive.protein..quantile._irnt_both
 Min.   :-18.3632                  Min.   :-35.9112                            
 1st Qu.: -0.7259                  1st Qu.: -1.2164                            
 Median :  0.5552                  Median :  0.3625                            
 Mean   :  0.5275                  Mean   :  0.4326                            
 3rd Qu.:  1.8539                  3rd Qu.:  2.1565                            
 Max.   :  9.3335                  Max.   : 62.7113                            
                                                                               
 UKBB_Gamma.glutamyltransferase..quantile._irnt_both
 Min.   :-32.1167                                   
 1st Qu.: -0.2238                                   
 Median :  1.3074                                   
 Mean   :  1.2105                                   
 3rd Qu.:  2.8998                                   
 Max.   : 11.3009                                   
                                                    
 UKBB_Glucose..quantile._irnt_both UKBB_HDL.cholesterol..quantile._irnt_both
 Min.   :-8.193                    Min.   :-45.11552                        
 1st Qu.: 0.992                    1st Qu.: -3.47943                        
 Median : 2.388                    Median : -1.53624                        
 Mean   : 2.997                    Mean   : -2.31456                        
 3rd Qu.: 4.031                    3rd Qu.:  0.01377                        
 Max.   :31.513                    Max.   : 18.22511                        
                                                                            
 UKBB_IGF.1..quantile._irnt_both UKBB_Lipoprotein.A..quantile._irnt_both
 Min.   :-8.5869                 Min.   :-3.33277                       
 1st Qu.:-1.3329                 1st Qu.:-0.91386                       
 Median : 0.5221                 Median :-0.19555                       
 Mean   : 0.5547                 Mean   : 0.09755                       
 3rd Qu.: 2.0404                 3rd Qu.: 0.61855                       
 Max.   :24.6888                 Max.   :85.39116                       
                                                                        
 UKBB_Phosphate..quantile._irnt_both UKBB_SHBG..quantile._irnt_both
 Min.   :-8.51235                    Min.   :-90.5859              
 1st Qu.:-1.13720                    1st Qu.: -4.4009              
 Median :-0.00023                    Median : -2.2519              
 Mean   : 0.17706                    Mean   : -2.7702              
 3rd Qu.: 1.20004                    3rd Qu.: -0.8199              
 Max.   :32.00750                    Max.   : 28.2952              
                                                                   
 UKBB_Total.bilirubin..quantile._irnt_both
 Min.   :-8.5200                          
 1st Qu.:-1.2574                          
 Median :-0.2294                          
 Mean   :-0.3209                          
 3rd Qu.: 0.7218                          
 Max.   : 9.4678                          
                                          
 UKBB_Testosterone..quantile._irnt_female
 Min.   :-6.2869                         
 1st Qu.:-1.0626                         
 Median : 0.0296                         
 Mean   :-0.0496                         
 3rd Qu.: 0.9504                         
 Max.   : 8.3395                         
                                         
 UKBB_Total.protein..quantile._irnt_both
 Min.   :-16.4540                       
 1st Qu.: -0.9606                       
 Median :  0.4092                       
 Mean   :  0.3411                       
 3rd Qu.:  1.6455                       
 Max.   : 10.1773                       
                                        
 UKBB_Triglycerides..quantile._irnt_both UKBB_Urate..quantile._irnt_both
 Min.   :-42.23156                       Min.   :-22.2579               
 1st Qu.:  0.08495                       1st Qu.: -0.6106               
 Median :  1.56697                       Median :  0.9630               
 Mean   :  2.04582                       Mean   :  1.0268               
 3rd Qu.:  3.99707                       3rd Qu.:  2.6742               
 Max.   : 50.45309                       Max.   : 12.5405               
                                                                        
 UKBB_Vitamin.D..quantile._irnt_both
 Min.   :-6.2730                    
 1st Qu.:-1.5909                    
 Median :-0.5612                    
 Mean   :-0.5202                    
 3rd Qu.: 0.4173                    
 Max.   : 8.1506                    
                                    
 UKBB_Diastolic.blood.pressure..automated.reading_irnt_both
 Min.   :-6.1009                                           
 1st Qu.:-0.8588                                           
 Median : 0.3509                                           
 Mean   : 0.4356                                           
 3rd Qu.: 1.8728                                           
 Max.   : 5.6658                                           
                                                           
 UKBB_Systolic.blood.pressure..automated.reading_irnt_both
 Min.   :-5.2925                                          
 1st Qu.:-0.2404                                          
 Median : 0.9313                                          
 Mean   : 0.9694                                          
 3rd Qu.: 2.0875                                          
 Max.   : 7.4847                                          
                                                          
# Select strong signals
signals = apply(dat, 1, function(x) sum(abs(x) >= 1.96, na.rm = TRUE) != 0)
# Remove NAs
nas = apply(dat, 1, function(x) sum(is.na(x)) == 0)
dat2 = dat[nas, ]

Run udr

R = ncol(dat2)
K = 20
V = diag(R) # Use identity matrix for now
  
set.seed(999)
U.init = c()
for (k in 1:K){
  U.init[[k]] <- udr:::sim_unconstrained(R)
}
X = as.matrix(dat2)
f0 = ud_init(X = X, V = V, U_scaled = NULL, U_unconstrained = U.init)
set.seed(1)
fit1 = ud_fit(f0, control = list(unconstrained.update = "ted", rank1.update = "ted", resid.update = 'none', scaled.update = "fa", maxiter=1e3, tol = 1e-02, tol.lik = 1e-2, n0 = 0,
                                   lambda = R), verbose=TRUE)
control$scaled.update is ignored when no scaled covariances are included in U
Performing Ultimate Deconvolution on 305 x 64 matrix (udr 0.3-140, "R"):
data points are i.i.d. (same V)
prior covariances: 0 scaled, 4 rank-1, 20 unconstrained
prior covariance updates: scaled (none), rank-1 (ted), unconstrained (ted)
mixture weights update: em
residual covariance update: none
max 1000 updates, tol=1.0e-02, tol.lik=1.0e-02
iter          log-likelihood |w - w'| |U - U'| |V - V'|
   1 -4.1778734067387224e+04 1.02e-01 1.05e+02 0.00e+00
   2 -4.0097929195367360e+04 1.00e-01 2.38e+01 0.00e+00
   3 -3.9650548119978972e+04 9.23e-03 7.31e+00 0.00e+00
   4 -3.9436399991444137e+04 5.87e-03 2.35e+00 0.00e+00
   5 -3.9319671088311617e+04 5.15e-03 1.32e+00 0.00e+00
   6 -3.9225966249799269e+04 4.95e-03 1.71e+00 0.00e+00
   7 -3.9168599634440987e+04 6.21e-03 4.65e+00 0.00e+00
   8 -3.9141252687644723e+04 6.19e-03 2.95e+00 0.00e+00
   9 -3.9110363554430682e+04 5.91e-03 2.15e+00 0.00e+00
  10 -3.9099434787462196e+04 5.01e-03 1.41e+00 0.00e+00
  11 -3.9073233712234512e+04 6.10e-03 1.23e+00 0.00e+00
  12 -3.9021295382383149e+04 8.59e-03 1.69e+00 0.00e+00
  13 -3.8997402612334037e+04 1.06e-02 2.89e+00 0.00e+00
  14 -3.8968839870865981e+04 1.02e-02 2.15e+00 0.00e+00
  15 -3.8928392166238060e+04 1.26e-02 1.07e+00 0.00e+00
  16 -3.8894097402311178e+04 1.07e-02 1.07e+00 0.00e+00
  17 -3.8840403658758070e+04 1.05e-02 1.03e+00 0.00e+00
  18 -3.8802554338952163e+04 1.08e-02 1.01e+00 0.00e+00
  19 -3.8733749360556962e+04 1.30e-02 1.22e+00 0.00e+00
  20 -3.8663415318312036e+04 2.32e-02 1.03e+00 0.00e+00
  21 -3.8623502786072750e+04 1.60e-02 9.55e-01 0.00e+00
  22 -3.8590804570378175e+04 1.01e-02 9.42e-01 0.00e+00
  23 -3.8557701327752344e+04 1.11e-02 9.71e-01 0.00e+00
  24 -3.8536473589981557e+04 8.41e-03 9.18e-01 0.00e+00
  25 -3.8503138309166519e+04 1.03e-02 9.26e-01 0.00e+00
  26 -3.8453594678200003e+04 1.57e-02 1.39e+00 0.00e+00
  27 -3.8410236331832406e+04 1.22e-02 1.57e+00 0.00e+00
  28 -3.8375246079166420e+04 1.05e-02 9.99e-01 0.00e+00
  29 -3.8349628900093827e+04 8.58e-03 9.85e-01 0.00e+00
  30 -3.8317443475869019e+04 8.72e-03 9.80e-01 0.00e+00
  31 -3.8301454543905966e+04 6.42e-03 9.74e-01 0.00e+00
  32 -3.8287893103411290e+04 4.79e-03 9.69e-01 0.00e+00
  33 -3.8251799318154888e+04 9.47e-03 9.64e-01 0.00e+00
  34 -3.8224335041230632e+04 6.68e-03 1.42e+00 0.00e+00
  35 -3.8209130520324448e+04 3.18e-03 9.53e-01 0.00e+00
  36 -3.8164098426803852e+04 2.88e-03 9.47e-01 0.00e+00
  37 -3.8144488444736264e+04 4.72e-03 9.42e-01 0.00e+00
  38 -3.8144344114151128e+04 1.03e-03 9.36e-01 0.00e+00
  39 -3.8145369174200059e+04 7.06e-04 9.31e-01 0.00e+00
  40 -3.8140930576961939e+04 1.49e-03 9.25e-01 0.00e+00
  41 -3.8138894293064805e+04 1.35e-03 9.20e-01 0.00e+00
  42 -3.8140728444568107e+04 1.02e-03 9.14e-01 0.00e+00
  43 -3.8136507001351958e+04 8.94e-04 9.09e-01 0.00e+00
  44 -3.8125582730284084e+04 2.31e-03 1.77e+00 0.00e+00
  45 -3.8121084511540648e+04 2.21e-03 8.98e-01 0.00e+00
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 285 -3.7944689907153224e+04 1.03e-07 1.36e-01 0.00e+00
 286 -3.7944799415285837e+04 1.02e-07 1.35e-01 0.00e+00
 287 -3.7944907725775753e+04 1.01e-07 1.34e-01 0.00e+00
 288 -3.7945014857246162e+04 9.99e-08 1.33e-01 0.00e+00
 289 -3.7945120812850386e+04 9.88e-08 1.32e-01 0.00e+00
 290 -3.7945225613695111e+04 9.77e-08 1.30e-01 0.00e+00
 291 -3.7945329272849325e+04 9.67e-08 1.29e-01 0.00e+00
 292 -3.7945431774096323e+04 9.56e-08 1.28e-01 0.00e+00
 293 -3.7945533188433059e+04 9.45e-08 1.27e-01 0.00e+00
 294 -3.7945633502470999e+04 9.35e-08 1.26e-01 0.00e+00
 295 -3.7945732702341338e+04 9.24e-08 1.25e-01 0.00e+00
 296 -3.7945830845210650e+04 9.14e-08 1.24e-01 0.00e+00
 297 -3.7945927919075351e+04 9.03e-08 1.23e-01 0.00e+00
 298 -3.7946023944461216e+04 8.93e-08 1.22e-01 0.00e+00
 299 -3.7946118937044957e+04 8.83e-08 1.20e-01 0.00e+00
 300 -3.7946212901902116e+04 8.73e-08 1.19e-01 0.00e+00
 301 -3.7946305863633082e+04 8.62e-08 1.18e-01 0.00e+00
 302 -3.7946397816269055e+04 8.52e-08 1.17e-01 0.00e+00
 303 -3.7946488761930334e+04 8.42e-08 1.16e-01 0.00e+00
 304 -3.7946578752401023e+04 8.32e-08 1.15e-01 0.00e+00
 305 -3.7946667775270427e+04 8.22e-08 1.14e-01 0.00e+00
 306 -3.7946755837619588e+04 8.13e-08 1.13e-01 0.00e+00
 307 -3.7946842982856127e+04 8.01e-08 1.12e-01 0.00e+00
 308 -3.7946929169392730e+04 7.95e-08 1.11e-01 0.00e+00
 309 -3.7947014439760918e+04 7.84e-08 1.10e-01 0.00e+00
 310 -3.7947098801700580e+04 7.74e-08 1.09e-01 0.00e+00
 311 -3.7947182261426104e+04 7.65e-08 1.08e-01 0.00e+00
 312 -3.7947264833042165e+04 7.55e-08 1.07e-01 0.00e+00
 313 -3.7947346526456320e+04 7.46e-08 1.06e-01 0.00e+00
 314 -3.7947427347257522e+04 7.37e-08 1.05e-01 0.00e+00
 315 -3.7947507311017260e+04 7.28e-08 1.05e-01 0.00e+00
 316 -3.7947586425956171e+04 7.19e-08 1.04e-01 0.00e+00
 317 -3.7947664701895017e+04 7.10e-08 1.03e-01 0.00e+00
 318 -3.7947742148554884e+04 7.01e-08 1.02e-01 0.00e+00
 319 -3.7947818775523381e+04 6.92e-08 1.01e-01 0.00e+00
 320 -3.7947894592263467e+04 6.84e-08 1.00e-01 0.00e+00
 321 -3.7947969608114989e+04 6.75e-08 9.91e-02 0.00e+00
 322 -3.7948043832295931e+04 6.66e-08 9.83e-02 0.00e+00
 323 -3.7948117273903626e+04 6.58e-08 9.74e-02 0.00e+00
 324 -3.7948189941915756e+04 6.50e-08 9.65e-02 0.00e+00
 325 -3.7948261845191235e+04 6.41e-08 9.57e-02 0.00e+00
 326 -3.7948332992470911e+04 6.33e-08 9.48e-02 0.00e+00
 327 -3.7948403392378226e+04 6.25e-08 9.40e-02 0.00e+00
 328 -3.7948473057886222e+04 6.17e-08 9.31e-02 0.00e+00
 329 -3.7948541984601288e+04 6.09e-08 9.23e-02 0.00e+00
 330 -3.7948610181295153e+04 6.01e-08 9.15e-02 0.00e+00
 331 -3.7948677674539256e+04 5.92e-08 9.07e-02 0.00e+00

Plot sharing patterns

plot_sharing = function(X, to_cor=FALSE, title="", remove_names=F) {
        clrs <- colorRampPalette(rev(c("#D73027","#FC8D59","#FEE090","#FFFFBF",
                                       "#E0F3F8","#91BFDB","#4575B4")))(128)
        if (to_cor) lat <- cov2cor(X)
        else lat = X/max(diag(X))
        lat[lower.tri(lat)] <- NA
        n <- nrow(lat)
        if (remove_names) {
          colnames(lat) = NULL
          rownames(lat) = NULL
        }
        return(lattice::levelplot(lat[n:1,],col.regions = clrs,
                                xlab = "",ylab = "", main=title,
                                colorkey = TRUE,at = seq(-1,1,length.out = 128),
                                scales = list(cex = 0.2,x = list(rot = 45))))
    }
# Plot sharing patterns with w > 0.01 
tol = 1e-2
U <- lapply(fit1$U,function (e) "[["(e,"mat"))
n_component = sum(fit1$w > tol)
w = order(fit1$w, decreasing = TRUE)
indx = w[1:n_component]
plts = list()
for (i in 1:length(indx)){
  title = paste(names(U)[indx[i]], "w =", round(fit1$w[indx[i]], 6))
  plts[[i]] = plot_sharing(U[[indx[i]]], to_cor = TRUE, title = title)
}
unit = 4
n_col = 3
n_row = ceiling(n_component / n_col)
pdf('t2d_patterns.pdf', width = unit * n_col, height = unit * n_row)
do.call("grid.arrange", c(plts, list(ncol = n_col, nrow = n_row)))
dev.off()
quartz_off_screen 
                2 

sessionInfo()
R version 4.1.1 (2021-08-10)
Platform: x86_64-apple-darwin20.6.0 (64-bit)
Running under: macOS Monterey 12.0.1

Matrix products: default
BLAS:   /usr/local/Cellar/openblas/0.3.18/lib/libopenblasp-r0.3.18.dylib
LAPACK: /usr/local/Cellar/r/4.1.1_1/lib/R/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] gridExtra_2.3   udr_0.3-141     readxl_1.4.1    workflowr_1.6.2

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.8.3     pillar_1.6.4     compiler_4.1.1   cellranger_1.1.0
 [5] later_1.3.0      jquerylib_0.1.4  git2r_0.28.0     tools_4.1.1     
 [9] digest_0.6.28    lattice_0.20-44  gtable_0.3.0     evaluate_0.14   
[13] lifecycle_1.0.1  tibble_3.1.5     pkgconfig_2.0.3  rlang_0.4.12    
[17] yaml_2.2.1       mvtnorm_1.1-3    xfun_0.27        fastmap_1.1.0   
[21] stringr_1.4.0    knitr_1.36       fs_1.5.0         vctrs_0.3.8     
[25] rprojroot_2.0.2  grid_4.1.1       glue_1.4.2       R6_2.5.1        
[29] fansi_0.5.0      rmarkdown_2.11   magrittr_2.0.1   whisker_0.4     
[33] promises_1.2.0.1 ellipsis_0.3.2   htmltools_0.5.2  httpuv_1.6.3    
[37] utf8_1.2.2       stringi_1.7.5    crayon_1.4.1