sparse.mediation.old.RdFit a mediation model via penalized maximum likelihood and structural equation model. The regularization path is computed for the lasso or elasticnet penalty at a grid of values for the regularization parameter lambda. Currently, mediation analysis is developed based on gaussian assumption.
sparse.mediation.old(X, M, Y, tol = 10^(-10), max.iter = 100, lambda = log(1 + (1:50)/125), glmnet.penalty.factor = c(0, rep(1, 2 * V)), alpha = 1, tau = 1, verbose = FALSE)
| X | One-dimensional predictor |
|---|---|
| M | Multivariate mediator |
| Y | Outcome |
| tol | (default -10^(-10)) convergence criterion |
| max.iter | (default=100) maximum iteration |
| lambda | (default=log(1+(1:50)/125)) tuning parameter for L1 penalization |
| glmnet.penalty.factor | (default=c(0,rep(1,2*V))) give different weight of penalization for the 2V mediation paths. |
| alpha | (defult=1) tuning parameter for L2 penalization |
| tau | (default=1) tuning parameter for L1 penality weighting for paths a and b. |
| verbose | (default=FALSE) print progress |
c directeffect
hatb Path b (M->Y given X) estimates
hata Path a (X->M) estimates
medest Mediation estimates (a*b)
alpha
lambda
nump Number of selected mediation paths
Multiple Mediaton Model: (1) M = Xa + e1 (2) Y = Xc' + Mb + e2 And in the optimization, we do not regularize c', due to the assumption of partial mediation.
TBA
N=100 V=50 set.seed(1234) a = rbinom(V,1,0.1)*5;b<-a X = rnorm(N) M = X %*% t(a)+ matrix(rnorm(N*V),N,V) Y = X + M %*% b + rnorm(N) sparse.mediation.old(X,M,Y,tol=10^(-10), max.iter=100,lambda = log(1+(1:25)/50))#> $c #> [1] 0.04022092 0.03600612 0.03433900 0.03243881 0.03085479 0.02963070 #> [7] 0.02789994 0.02636909 0.02587669 0.02538428 0.02548996 0.02523398 #> [13] 0.02536482 0.02540086 0.02580411 0.02588929 0.02629656 0.02613293 #> [19] 0.02631453 0.02659668 0.02653930 0.02680362 0.02706866 0.02706577 #> [25] 0.02707630 #> #> $hatb #> [,1] [,2] [,3] [,4] [,5] #> [1,] -0.0008486792 0.000000000 0.000000000 0.000000000 0.000000000 #> [2,] -0.2276407745 -0.178476122 -0.157280695 -0.138957760 -0.117265113 #> [3,] 0.1242605695 0.101562788 0.080487407 0.055109273 0.029575482 #> [4,] 0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 #> [5,] -0.1708180479 -0.133037747 -0.115795287 -0.092549551 -0.065780271 #> [6,] -0.0077368105 0.000000000 0.000000000 0.000000000 0.000000000 #> [7,] 0.0743262602 0.050466575 0.027506278 0.014773473 0.000000000 #> [8,] -0.0198411043 -0.008123633 0.000000000 0.000000000 0.000000000 #> [9,] -0.0240009731 -0.036665997 -0.042265782 -0.035963528 -0.027850172 #> [10,] 0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 #> [11,] 0.0602117803 0.018528816 0.000000000 0.000000000 0.000000000 #> [12,] -0.2038213463 -0.151566324 -0.111915835 -0.077935894 -0.043435124 #> [13,] 0.0816750324 0.045378831 0.008601991 0.000000000 0.000000000 #> [14,] 5.1221367831 5.110657168 5.094139305 5.094910094 5.101041029 #> [15,] 0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 #> [16,] -0.0543430855 -0.006652661 0.000000000 0.000000000 0.000000000 #> [17,] -0.1412639379 -0.136303557 -0.128775910 -0.126761022 -0.120530938 #> [18,] 0.0819311317 0.007174270 0.000000000 0.000000000 0.000000000 #> [19,] -0.1676223477 -0.141432376 -0.130046202 -0.119070504 -0.105366700 #> [20,] 0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 #> [21,] -0.0205008301 -0.004695741 -0.001265497 0.000000000 0.000000000 #> [22,] 0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 #> [23,] -0.1506853704 -0.116434195 -0.096272028 -0.086018142 -0.079039868 #> [24,] -0.1096924147 -0.072887317 -0.048180022 -0.027534952 -0.008736537 #> [25,] 0.0181860359 0.006547161 0.004256775 0.000000000 0.000000000 #> [26,] 0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 #> [27,] 0.0702872349 0.042495104 0.019146740 0.001465286 0.000000000 #> [28,] 4.7811948292 4.823968958 4.842266440 4.854190025 4.864892548 #> [29,] -0.0673889073 -0.049639646 -0.025881641 -0.006914217 0.000000000 #> [30,] -0.0480967404 -0.029900507 -0.013954231 0.000000000 0.000000000 #> [31,] 0.0882210991 0.034063512 0.005072810 0.000000000 0.000000000 #> [32,] 0.1441720954 0.107659248 0.071461852 0.051234435 0.033859088 #> [33,] 0.0477368546 0.044058907 0.031202505 0.012520573 0.000000000 #> [34,] -0.0258833420 0.000000000 0.000000000 0.000000000 0.000000000 #> [35,] 0.1886374245 0.151999773 0.120738250 0.101166827 0.084773588 #> [36,] -0.0888157367 -0.036681879 -0.007368479 0.000000000 0.000000000 #> [37,] 0.0476724361 0.018407922 0.003399059 0.000000000 0.000000000 #> [38,] 0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 #> [39,] 4.6937331487 4.719880896 4.740183045 4.754512414 4.759395648 #> [40,] 0.1165837318 0.076609729 0.046729921 0.022859227 0.003967662 #> [41,] -0.2023502469 -0.158519700 -0.132725334 -0.100692592 -0.070585637 #> [42,] -0.1003168426 -0.066758372 -0.057102582 -0.045565709 -0.026519852 #> [43,] -0.1047137059 -0.064889373 -0.056161757 -0.044333816 -0.028280397 #> [44,] -0.0706958716 -0.026401012 0.000000000 0.000000000 0.000000000 #> [45,] 0.0981683564 0.068152714 0.047345551 0.023749452 0.000000000 #> [46,] 0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 #> [47,] -0.0746837684 -0.037493931 -0.011183582 0.000000000 0.000000000 #> [48,] 0.0228498761 0.000000000 0.000000000 0.000000000 0.000000000 #> [49,] -0.0552153461 -0.003864964 0.000000000 0.000000000 0.000000000 #> [50,] 0.0754632213 0.074751349 0.059875868 0.033237629 0.002208185 #> [,6] [,7] [,8] [,9] [,10] #> [1,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [2,] -0.086108127 -0.055619146 -0.03049181 -0.013949124 0.00000000 #> [3,] 0.008211179 0.000000000 0.00000000 0.000000000 0.00000000 #> [4,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [5,] -0.035793788 -0.013207816 0.00000000 0.000000000 0.00000000 #> [6,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [7,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [8,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [9,] -0.010210172 0.000000000 0.00000000 0.000000000 0.00000000 #> [10,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [11,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [12,] -0.015629647 0.000000000 0.00000000 0.000000000 0.00000000 #> [13,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [14,] 5.100193572 5.100941314 5.10174271 5.101590222 5.10140769 #> [15,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [16,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [17,] -0.113167428 -0.105958902 -0.09752567 -0.085816376 -0.07417618 #> [18,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [19,] -0.094415826 -0.084941812 -0.07491951 -0.061400309 -0.04825775 #> [20,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [21,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [22,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [23,] -0.062113900 -0.044192964 -0.02513273 -0.008364712 0.00000000 #> [24,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [25,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [26,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [27,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [28,] 4.876827891 4.886823121 4.89261173 4.892385032 4.89150591 #> [29,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [30,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [31,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [32,] 0.017039719 0.000000000 0.00000000 0.000000000 0.00000000 #> [33,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [34,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [35,] 0.070119636 0.057101815 0.04412478 0.032432340 0.01995194 #> [36,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [37,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [38,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [39,] 4.763658946 4.775984110 4.78941822 4.793695136 4.79842384 #> [40,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [41,] -0.042341576 -0.017295985 0.00000000 0.000000000 0.00000000 #> [42,] -0.017664555 -0.004312016 0.00000000 0.000000000 0.00000000 #> [43,] -0.003629897 0.000000000 0.00000000 0.000000000 0.00000000 #> [44,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [45,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [46,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [47,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [48,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [49,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [50,] 0.000000000 0.000000000 0.00000000 0.000000000 0.00000000 #> [,11] [,12] [,13] [,14] [,15] [,16] #> [1,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [2,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [3,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [4,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [5,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [6,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [7,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [8,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [9,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [10,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [11,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [12,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [13,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [14,] 5.100477159 5.10010076 5.09437951 5.09342987 5.091599121 5.090068 #> [15,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [16,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [17,] -0.060685586 -0.04747616 -0.04041737 -0.02427318 -0.008095172 0.000000 #> [18,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [19,] -0.035195058 -0.02197292 -0.01638827 0.00000000 0.000000000 0.000000 #> [20,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [21,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [22,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [23,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [24,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [25,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [26,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [27,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [28,] 4.889677318 4.88937584 4.88561241 4.88528314 4.881884615 4.880100 #> [29,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [30,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [31,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [32,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [33,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [34,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [35,] 0.008240951 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [36,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [37,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [38,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [39,] 4.795770089 4.79621402 4.79678217 4.79359557 4.789025559 4.787492 #> [40,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [41,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [42,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [43,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [44,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [45,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [46,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [47,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [48,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [49,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [50,] 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000 0.000000 #> [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] #> [1,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [2,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [3,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [4,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [5,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [6,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [7,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [8,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [9,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [10,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [11,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [12,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [13,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [14,] 5.087687 5.086617 5.084719 5.082613 5.081247 5.079110 5.076969 5.075442 #> [15,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [16,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [17,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [18,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [19,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [20,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [21,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [22,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [23,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [24,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [25,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [26,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [27,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [28,] 4.877219 4.876688 4.874735 4.872398 4.871415 4.869097 4.866781 4.865565 #> [29,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [30,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [31,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [32,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [33,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [34,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [35,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [36,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [37,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [38,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [39,] 4.783269 4.783975 4.781712 4.778538 4.778353 4.775389 4.772429 4.771761 #> [40,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [41,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [42,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [43,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [44,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [45,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [46,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [47,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [48,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [49,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [50,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 #> [,25] #> [1,] 0.000000 #> [2,] 0.000000 #> [3,] 0.000000 #> [4,] 0.000000 #> [5,] 0.000000 #> [6,] 0.000000 #> [7,] 0.000000 #> [8,] 0.000000 #> [9,] 0.000000 #> [10,] 0.000000 #> [11,] 0.000000 #> [12,] 0.000000 #> [13,] 0.000000 #> [14,] 5.073846 #> [15,] 0.000000 #> [16,] 0.000000 #> [17,] 0.000000 #> [18,] 0.000000 #> [19,] 0.000000 #> [20,] 0.000000 #> [21,] 0.000000 #> [22,] 0.000000 #> [23,] 0.000000 #> [24,] 0.000000 #> [25,] 0.000000 #> [26,] 0.000000 #> [27,] 0.000000 #> [28,] 4.864268 #> [29,] 0.000000 #> [30,] 0.000000 #> [31,] 0.000000 #> [32,] 0.000000 #> [33,] 0.000000 #> [34,] 0.000000 #> [35,] 0.000000 #> [36,] 0.000000 #> [37,] 0.000000 #> [38,] 0.000000 #> [39,] 4.770967 #> [40,] 0.000000 #> [41,] 0.000000 #> [42,] 0.000000 #> [43,] 0.000000 #> [44,] 0.000000 #> [45,] 0.000000 #> [46,] 0.000000 #> [47,] 0.000000 #> [48,] 0.000000 #> [49,] 0.000000 #> [50,] 0.000000 #> #> $hata #> [,1] [,2] [,3] [,4] [,5] #> [1,] 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 #> [2,] 0.069560562 0.0783505673 0.086684199 0.090633679 0.0881532413 #> [3,] 0.168871997 0.1587648907 0.144557381 0.130045354 0.1081551331 #> [4,] 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 #> [5,] 0.020418375 0.0111570940 0.005988069 0.000276387 0.0000000000 #> [6,] 0.157633825 0.1277533439 0.090735530 0.048359729 0.0000000000 #> [7,] 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 #> [8,] -0.126694378 -0.1194737865 -0.109341284 -0.097986299 -0.0827380153 #> [9,] 0.019346861 0.0027908869 0.000000000 0.000000000 0.0000000000 #> [10,] 0.104868961 0.0967618595 0.084186352 0.065731899 0.0420593686 #> [11,] -0.100956366 -0.0830150467 -0.070737267 -0.054242311 -0.0421637992 #> [12,] 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 #> [13,] -0.064664704 -0.0441438325 -0.020413200 0.000000000 0.0000000000 #> [14,] 4.912506847 4.8861550783 4.855505050 4.823788744 4.7882331487 #> [15,] -0.011856292 -0.0057763343 -0.001703663 0.000000000 0.0000000000 #> [16,] 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 #> [17,] 0.004479541 0.0000000000 0.000000000 0.000000000 0.0000000000 #> [18,] -0.237508538 -0.2359275616 -0.228840181 -0.213656388 -0.1943182496 #> [19,] 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 #> [20,] 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 #> [21,] 0.017177252 0.0001402115 0.000000000 0.000000000 0.0000000000 #> [22,] 0.009905589 0.0000000000 0.000000000 0.000000000 0.0000000000 #> [23,] 0.000000000 0.0000000000 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#> [25,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [26,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [27,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [28,] 23.4873531229 23.408537099 23.2427944605 23.06014 22.82337 22.49221 #> [29,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [30,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [31,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [32,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [33,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [34,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [35,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [36,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [37,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [38,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [39,] 22.7595529813 22.648361840 22.5028927394 22.32024 22.04874 21.67092 #> [40,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [41,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [42,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [43,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [44,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [45,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [46,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [47,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [48,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [49,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [50,] 0.0000000000 0.000000000 0.0000000000 0.00000 0.00000 0.00000 #> [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] #> [1,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [2,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [3,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [4,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [5,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [6,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [7,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [8,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [9,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [10,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [11,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [12,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [13,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [14,] 22.39514 0 0 0 0 0 0 0 0 0 0 #> [15,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [16,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [17,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [18,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [19,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [20,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [21,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [22,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [23,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [24,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [25,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [26,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [27,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [28,] 22.03891 0 0 0 0 0 0 0 0 0 0 #> [29,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [30,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [31,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [32,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [33,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [34,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [35,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [36,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [37,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [38,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [39,] 21.20067 0 0 0 0 0 0 0 0 0 0 #> [40,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [41,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [42,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [43,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [44,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [45,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [46,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [47,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [48,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [49,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [50,] 0.00000 0 0 0 0 0 0 0 0 0 0 #> [,23] [,24] [,25] #> [1,] 0 0 0 #> [2,] 0 0 0 #> [3,] 0 0 0 #> [4,] 0 0 0 #> [5,] 0 0 0 #> [6,] 0 0 0 #> [7,] 0 0 0 #> [8,] 0 0 0 #> [9,] 0 0 0 #> [10,] 0 0 0 #> [11,] 0 0 0 #> [12,] 0 0 0 #> [13,] 0 0 0 #> [14,] 0 0 0 #> [15,] 0 0 0 #> [16,] 0 0 0 #> [17,] 0 0 0 #> [18,] 0 0 0 #> [19,] 0 0 0 #> [20,] 0 0 0 #> [21,] 0 0 0 #> [22,] 0 0 0 #> [23,] 0 0 0 #> [24,] 0 0 0 #> [25,] 0 0 0 #> [26,] 0 0 0 #> [27,] 0 0 0 #> [28,] 0 0 0 #> [29,] 0 0 0 #> [30,] 0 0 0 #> [31,] 0 0 0 #> [32,] 0 0 0 #> [33,] 0 0 0 #> [34,] 0 0 0 #> [35,] 0 0 0 #> [36,] 0 0 0 #> [37,] 0 0 0 #> [38,] 0 0 0 #> [39,] 0 0 0 #> [40,] 0 0 0 #> [41,] 0 0 0 #> [42,] 0 0 0 #> [43,] 0 0 0 #> [44,] 0 0 0 #> [45,] 0 0 0 #> [46,] 0 0 0 #> [47,] 0 0 0 #> [48,] 0 0 0 #> [49,] 0 0 0 #> [50,] 0 0 0 #> #> $alpha #> [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 #> #> $tau #> [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 #> #> $lambda #> [1] 0.01980263 0.03922071 0.05826891 0.07696104 0.09531018 0.11332869 #> [7] 0.13102826 0.14842001 0.16551444 0.18232156 0.19885086 0.21511138 #> [13] 0.23111172 0.24686008 0.26236426 0.27763174 0.29266961 0.30748470 #> [19] 0.32208350 0.33647224 0.35065687 0.36464311 0.37843644 0.39204209 #> [25] 0.40546511 #> #> $nump #> [1] 78 70 58 47 39 31 24 18 14 12 10 9 6 5 5 4 4 4 4 4 4 4 4 4 4 #>