Jolly-Seber (POPAN) with individual covariates

posts related to the RMark library, which may not be of general interest to users of 'classic' MARK

Jolly-Seber (POPAN) with individual covariates

Postby markmiller » Wed Apr 04, 2018 3:48 pm

I have tried running a POPAN model with individual covariates. MARK and RMark return the same estimates if covariates vary among sampling occasions, but not among individuals. MARK and RMark do not return the same parameter estimates if covariates vary among sampling occasions and among individuals. Which is correct: MARK or RMark? Perhaps neither are correct. Perhaps both are correct. Perhaps I am simply failing to specify a required option in MARK or in RMark or in both?

I am aware from Chapter 12 of the MARK book that individual covariates are an area of active research. I can program a CJS model into SURVIV with individual covariates that vary among individuals and among sampling occasions, and I get the same parameter estimates from SURVIV that MARK returns.

However, I am having trouble writing code in any language for the Jolly Seber when individual covariates vary among individuals and among sampling occasions. My objective was to determine the correct parameter estimates from MARK and RMark and then try to reproduce those estimates with a different approach. However, that is when I discovered that I cannot get the same estimates from MARK and RMark. I also tried using the R package 'marked' which returned a third set of estimates. I almost surely made a mistake writing the marked code. However, I am more familiar with MARK and RMark.

Thank you for any advice regarding the use of MARK and/or RMark with the Jolly-Seber (POPAN or otherwise) when covariates vary among sampling occasions and among individuals. My RMark code and fake data set are below in case they are of any use in addressing my question.

Please let me know if I can provide additional information. Sorry if I am making a trivial silly mistake. I searched the archives and did not see this question raised earlier. Sorry if I overlooked it.

Here is my RMark code:

Code: Select all
setwd('C:/Users/mmiller/Documents/POPAN/')

library(RMark)
n.seasons <-  7
my.data = convert.inp("jstestApr4.inp",
           covariates = c(paste("mycov",   seq_along(1:n.seasons), sep="")))
head(my.data)
summary(my.data)
my.processed = process.data(my.data, model = "POPAN", time.intervals = c(1,1,1,1,1,1))
my.ddl = make.design.data(my.processed)
Phidot    = list(formula =~     1)
pmycov    = list(formula =~ mycov)
pentdot   = list(formula =~     1)
Ndot      = list(formula =~     1)
mod1 = mark(my.processed, my.ddl, model.parameters = list(Phi = Phidot, p = pmycov,
                                                          pent = pentdot, N = Ndot),
            invisible = FALSE, adjust = FALSE)


Here are the estimates from RMark when individual covariates differ among sampling occasions and among individuals:
Code: Select all
              PARM-SPECIFIC Link Function Parameters of { Phi(~1)p(~mycov)pent(~1)N(~1) }
                                                              95% Confidence Interval
 Parameter                    Beta         Standard Error      Lower           Upper
 -------------------------  --------------  --------------  --------------  --------------
    1:Phi:(Intercept)       2.9760378       0.3501626       2.2897191       3.6623566     
    2:p:(Intercept)         -1.2619440      0.0931833       -1.4445833      -1.0793046   
    3:p:mycov               1.0580120       0.1159514       0.8307473       1.2852767     
    4:pent:(Intercept)      -0.6108170      0.1797141       -0.9630567      -0.2585774   
    5:N:(Intercept)         5.5670076       0.0979087       5.3751066       5.7589086     


Here are the estimates from MARK when individual covariates differ among sampling occasions and among individuals:

Code: Select all
                 PARM-SPECIFIC Link Function Parameters of {phi(.) p(Var) pent(.) N(.)}
                                                              95% Confidence Interval
 Parameter                    Beta         Standard Error      Lower           Upper
 -------------------------  --------------  --------------  --------------  --------------
    1:                      2.8910850       0.3261802       2.2517717       3.5303982     
    2:                      -1.2735394      0.0975026       -1.4646445      -1.0824342   
    3:                      1.0924111       0.1304761       0.8366779       1.3481443     
    4:                      -0.3907057      0.1696304       -0.7231812      -0.0582301   
    5:                      5.8044715       0.0908512       5.6264031       5.9825398 


Here is the design matrix in Program MARK with the parameter specific links:

Code: Select all
  INPUT ---    design matrix constraints=20 covariates=5;
  INPUT ---              1 0 0 0 0;
  INPUT ---              1 0 0 0 0;
  INPUT ---              1 0 0 0 0;
  INPUT ---              1 0 0 0 0;
  INPUT ---              1 0 0 0 0;
  INPUT ---              1 0 0 0 0;
  INPUT ---              0 1 Var1 0 0;
  INPUT ---              0 1 Var2 0 0;
  INPUT ---              0 1 Var3 0 0;
  INPUT ---              0 1 Var4 0 0;
  INPUT ---              0 1 Var5 0 0;
  INPUT ---              0 1 Var6 0 0;
  INPUT ---              0 1 Var7 0 0;
  INPUT ---              0 0 0 1 0;
  INPUT ---              0 0 0 1 0;
  INPUT ---              0 0 0 1 0;
  INPUT ---              0 0 0 1 0;
  INPUT ---              0 0 0 1 0;
  INPUT ---              0 0 0 1 0;
  INPUT ---              0 0 0 0 1;
  INPUT ---    links=20;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    Logit;
  INPUT ---    MLogit(1);
  INPUT ---    MLogit(1);
  INPUT ---    MLogit(1);
  INPUT ---    MLogit(1);
  INPUT ---    MLogit(1);
  INPUT ---    MLogit(1);
  INPUT ---    Log;


Here is the fake data set (which is kind of big):

Code: Select all
0001101 1 0.11 0.477 0.919 0.499 0.107 0.247 0.533  ;
0000010 1 0.895 0.511 0.725 0.503 0.243 0.997 0.993  ;
0000001 1 0.969 0.769 0.06 0.227 0.958 0.486 0.479  ;
0000011 1 0.376 0.452 0.148 0.456 0.501 0.756 0.976  ;
0000100 1 0.046 0.862 0.534 0.007 0.181 0.771 0.085  ;
0000100 1 0.418 0.293 0.27 0.095 0.737 0.988 0.009  ;
0000001 1 0.098 0.957 0.082 0.761 0.842 0.628 0.378  ;
0000001 1 0.194 0.591 0.144 0.659 0.515 0.521 0.241  ;
0000010 1 0.038 0.198 0.808 0.548 0.095 0.383 0.684  ;
0001010 1 0.183 0.736 0.586 0.831 0.87 0.857 0.691  ;
0010110 1 0.332 0.285 0.502 0.069 0.652 0.723 0.465  ;
0000111 1 0.524 0.637 0.855 0.116 0.299 0.947 0.744  ;
0000001 1 0.952 0.627 0.382 0.849 0.899 0.123 0.816  ;
0100110 1 0.407 0.884 0.74 0.294 0.792 0.92 0.904  ;
0000100 1 0.533 0.936 0.611 0.776 0.694 0.05 0.064  ;
0001100 1 0.324 0.461 0.933 0.347 0.775 0.248 0.08  ;
0000111 1 0.746 0.24 0.541 0.129 0.238 0.098 0.518  ;
0010100 1 0.236 0.176 0.762 0.992 0.13 0.89 0.028  ;
0000010 1 0.573 0.839 0.522 0.493 0.882 0.492 0.26  ;
0000100 1 0.876 0.596 0.959 0.357 0.67 0.181 0.065  ;
0101001 1 0.764 0.919 0.071 0.257 0.12 0.431 0.214  ;
0001110 1 0.06 0.085 0.606 0.664 0.175 0.449 0.099  ;
0001000 1 0.249 0.836 0.104 0.88 0.488 0.947 0.357  ;
0110000 1 0.614 0.991 0.607 0.882 0.676 0.916 0.385  ;
0000011 1 0.708 0.865 0.677 0.564 0.197 0.315 0.477  ;
0001101 1 0.479 0.014 0.393 0.414 0.932 0.145 0.709  ;
0011110 1 0.482 0.31 0.533 0.206 0.756 0.692 0.822  ;
0000110 1 0.937 0.58 0.826 0.045 0.095 0.485 0.506  ;
0010010 1 0.202 0.439 0.905 0.367 0.098 0.705 0.649  ;
0000001 1 0.612 0.319 0.474 0.4 0.907 0.472 0.914  ;
0001001 1 0.069 0.711 0.946 0.35 0.409 0.377 0.746  ;
0000010 1 0.678 0.436 0.536 0.608 0.173 0.976 0.422  ;
0001100 1 0.266 0.179 0.382 0.345 0.244 0.812 0.36  ;
0000001 1 0.474 0.126 0.7 0.968 0.373 0.208 0.441  ;
0000010 1 0.797 0.622 0.94 0.408 0.344 0.807 0.281  ;
0011000 1 0.043 0.617 0.014 0.755 0.346 0.179 0.819  ;
1000111 1 0.883 0.458 0.087 0.353 0.797 0.675 0.82  ;
0001000 1 0.217 0.338 0.372 0.04 0.469 0.263 0.725  ;
0000011 1 0.235 0.687 0.636 0.232 0.624 0.285 0.52  ;
0001010 1 0.642 0.15 0.677 0.589 0.426 0.529 0.238  ;
0001100 1 0.823 0.425 0.014 0.926 0.844 0.178 0.108  ;
0001010 1 0.041 0.936 0.071 0.923 0.615 0.895 0.071  ;
1000110 1 0.566 0.622 0.13 0.522 0.618 0.535 0.344  ;
0010001 1 0.836 0.232 0.409 0.267 0.299 0.639 0.113  ;
0010010 1 0.243 0.906 0.714 0.919 0.277 0.527 0.475  ;
0001010 1 0.028 0.885 0.029 0.717 0.482 0.837 0.728  ;
0001101 1 0.417 0.049 0.447 0.827 0.809 0.539 0.808  ;
0000001 1 0.786 0.175 0.902 0.232 0.979 0.332 0.328  ;
0000010 1 0.892 0.139 0.659 0.048 0.575 0.808 0.929  ;
0000100 1 0.505 0.821 0.142 0.756 0.127 0.394 0.234  ;
1001100 1 0.675 0.17 0.528 0.99 0.655 0.093 0.827  ;
0000100 1 0.177 0.335 0.987 0.117 0.951 0.805 0.807  ;
0000011 1 0.831 0.597 0.186 0.54 0.976 0.82 0.715  ;
0000110 1 0.418 0.474 0.986 0.815 0.903 0.59 0.331  ;
0001110 1 0.122 0.803 0.444 0.753 0.526 0.361 0.639  ;
0000010 1 0.513 0.896 0.026 0.132 0.006 0.895 0.711  ;
0101000 1 0.507 0.558 0.549 0.952 0.021 0.737 0.005  ;
0010011 1 0.758 0.31 0.409 0.398 0.884 0.261 0.345  ;
1010100 1 0.879 0.378 0.331 0.267 0.452 0.758 0.019  ;
0100000 1 0.808 0.34 0.742 0.564 0.852 0.895 0.794  ;
0101010 1 0.514 0.999 0.46 0.968 0.772 0.496 0.867  ;
1000110 1 0.632 0.858 0.071 0.076 0.97 0.567 0.015  ;
0100000 1 0.248 0.674 0.244 0.304 0.638 0.993 0.597  ;
0000010 1 0.452 0.141 0.019 0.137 0.494 0.615 0.237  ;
0010100 1 0.399 0.274 0.657 0.998 0.539 0.514 0.992  ;
0001011 1 0.955 0.71 0.868 0.971 0.536 0.488 0.933  ;
0001000 1 0.903 0.081 0.234 0.923 0.19 0.029 0.808  ;
0001010 1 0.24 0.472 0.202 0.5 0.811 0.526 0.221  ;
0010001 1 0.029 0.755 0.418 0.206 0.085 0.165 0.856  ;
0010010 1 0.918 0.565 0.696 0.041 0.424 0.721 0.626  ;
0000011 1 0.69 0.643 0.177 0.66 0.521 0.563 0.082  ;
0000110 1 0.236 0.22 0.561 0.581 0.561 0.458 0.602  ;
1000100 1 0.465 0.398 0.273 0.895 0.389 0.48 0.274  ;
0100000 1 0.21 0.685 0.911 0.572 0.552 0.445 0.427  ;
0000100 1 0.208 0.826 0.289 0.012 0.823 0.575 0.815  ;
0000101 1 0.561 0.359 0.322 0.856 0.615 0.338 0.743  ;
0100011 1 0.539 0.228 0.89 0.528 0.373 0.723 0.973  ;
0000110 1 0.838 0.766 0.353 0.586 0.157 0.176 0.051  ;
0010000 1 0.159 0.654 0.605 0.176 0.731 0.674 0.45  ;
0010000 1 0.364 0.106 0.823 0.609 0.264 0.815 0.277  ;
0000001 1 0.207 0.99 0.493 0.301 0.797 0.87 0.588  ;
0001000 1 0.667 0.03 0.202 0.469 0.309 0.879 0.078  ;
0001000 1 0.152 0.323 0.772 0.161 0.913 0.404 0.121  ;
0100000 1 0.884 0.491 0.393 0.516 0.071 0.63 0.164  ;
0001000 1 0.106 0.421 0.697 0.511 0.375 0.718 0.849  ;
0000011 1 0.648 0.82 0.829 0.518 0.185 0.823 0.28  ;
0000100 1 0.425 0.862 0.561 0.251 0.56 0.644 0.683  ;
0000110 1 0.371 0.932 0.375 0.185 0.338 0.996 0.654  ;
0010000 1 0.958 0.253 0.566 0.087 0.305 0.06 0.978  ;
0000010 1 0.329 0.095 0.553 0.29 0.862 0.364 0.078  ;
0000100 1 0.03 0.094 0.606 0.42 0.986 0.448 0.034  ;
0001000 1 0.338 0.175 0.796 0.58 0.227 0.545 0.028  ;
0000111 1 0.75 0.606 0.958 0.634 0.822 0.795 0.718  ;
0101000 1 0.139 0.196 0.027 0.6 0.471 0.266 0.964  ;
0000001 1 0.31 0.719 0.407 0.613 0.916 0.91 0.594  ;
0000001 1 0.689 0.817 0.19 0.847 0.507 0.354 0.918  ;
0000110 1 0.774 0.192 0.563 0.275 0.823 0.601 0.27  ;
0001000 1 0.683 0.027 0.008 0.456 0.456 0.256 0.202  ;
0001010 1 0.314 0.8 0.533 0.766 0.26 0.431 0.431  ;
0001000 1 0.833 0.386 0.648 0.489 0.02 0.257 0.791  ;
0010100 1 0.403 0.308 0.599 0.807 0.655 0.347 0.412  ;
0011100 1 0.427 0.99 0.681 0.916 0.703 0.537 0.164  ;
0011100 1 0.418 0.772 0.28 0.716 0.892 0.492 0.463  ;
0000010 1 0.593 0.393 0.718 0.601 0.253 0.49 0.56  ;
1000010 1 0.918 0.051 0.971 0.508 0.975 0.441 0.702  ;
0010000 1 0.107 0.932 0.916 0.094 0.062 0.408 0.771  ;
0000100 1 0.95 0.215 0.798 0.064 0.863 0.137 0.502  ;
0001011 1 0.403 0.179 0.162 0.452 0.504 0.961 0.909  ;
0010101 1 0.407 0.817 0.357 0.465 0.444 0.123 0.5  ;
0000010 1 0.628 0.074 0.316 0.784 0.035 0.933 0.726  ;
0010000 1 0.631 0.591 0.987 0.901 0.017 0.364 0.506  ;
0001000 1 0.425 0.767 0.53 0.84 0.56 0.262 0.276  ;
0010100 1 0.601 0.369 0.547 0.336 0.935 0.085 0.524  ;
1000000 1 0.447 0.698 0.041 0.074 0.052 0.527 0.646  ;
0000100 1 0.905 0.719 0.82 0.61 0.749 0.617 0.225  ;
0001010 1 0.852 0.811 0.164 0.51 0.094 0.971 0.256  ;
0001000 1 0.925 0.731 0.361 0.838 0.461 0.885 0.735  ;
0100000 1 0.698 0.65 0.664 0.523 0.714 0.384 0.424  ;
0010111 1 0.653 0.076 0.909 0.04 0.716 0.744 0.849  ;
0000011 1 0.069 0.09 0.124 0.653 0.915 0.509 0.875  ;
0101001 1 0.451 0.734 0.106 0.679 0.706 0.389 0.155  ;
0000100 1 0.007 0.027 0.231 0.27 0.778 0.027 0.621  ;
0011000 1 0.07 0.906 0.801 0.834 0.576 0.806 0.561  ;
0000001 1 0.042 0.729 0.191 0.946 0.756 0.044 0.777  ;
0010000 1 0.795 0.547 0.856 0.433 0.102 0.377 0.785  ;
0000100 1 0.232 0.477 0.726 0.128 0.495 0.241 0.208  ;
0000011 1 0.811 0.425 0.799 0.914 0.351 0.645 0.9  ;
1000000 1 0.267 0.784 0.254 0.659 0.157 0.46 0.34  ;
0010100 1 0.228 0.141 0.657 0.955 0.292 0.33 0.412  ;
0011100 1 0.283 0.719 0.978 0.662 0.931 0.953 0.936  ;
0010111 1 0.177 0.109 0.234 0.114 0.888 0.625 0.308  ;
0000001 1 0.221 0.624 0.036 0.941 0.164 0.076 0.757  ;
1100010 1 0.355 0.059 0.49 0.86 0.941 0.613 0.199  ;
0000100 1 0.769 0.098 0.437 0.271 0.361 0.706 0.413  ;
0100000 1 0.422 0.915 0.99 0.371 0.144 0.256 0.112  ;
0011000 1 0.08 0.211 0.509 0.575 0.679 0.88 0.811  ;
1000000 1 0.594 0.392 0.531 0.076 0.19 0.53 0.763  ;
0010000 1 0.286 0.324 0.495 0.269 0.901 0.082 0.315  ;
0000100 1 0.685 0.434 0.534 0.652 0.383 0.491 0.266  ;
0101110 1 0.139 0.441 0.118 0.424 0.27 0.433 0.309  ;
0000010 1 0.678 0.937 0.657 0.478 0.138 0.67 0  ;
0000100 1 0.022 0.146 0.952 0.901 0.306 0.162 0.711  ;
0010100 1 0.507 0.483 0.754 0.321 0.376 0.129 0.591  ;
0000010 1 0.654 0.539 0.024 0.253 0.331 0.469 0.704  ;
0010101 1 0.806 0.75 0.963 0.895 0.501 0.651 0.635  ;
0011110 1 0.883 0.62 0.683 0.311 0.596 0.839 0.497  ;
0001000 1 0.056 0.038 0.809 0.791 0.139 0.155 0.543  ;
0000110 1 0.469 0.918 0.036 0.421 0.694 0.637 0.014  ;
0001010 1 0.441 0.91 0.712 0.706 0.479 0.541 0.921  ;
0100011 1 0.751 0.894 0.939 0.85 0.817 0.788 0.306  ;
0100100 1 0.911 0.422 0.334 0.387 0.389 0.623 0.478  ;
0001000 1 0.801 0.184 0.069 0.533 0.259 0.071 0.542  ;
0111001 1 0.665 0.507 0.461 0.866 0.792 0.082 0.843  ;
1000111 1 0.746 0.084 0.975 0.716 0.746 0.449 0.591  ;
0101000 1 0.344 0.649 0.682 0.431 0.163 0.325 0.265  ;
0010000 1 0.284 0.871 0.976 0.125 0.015 0.401 0.863  ;
0001010 1 0.21 0.416 0.229 0.865 0.206 0.966 0.131  ;
0000100 1 0.851 0.855 0.787 0.473 0.828 0.281 0.517  ;
0000101 1 0.934 0.309 0.637 0.094 0.704 0.196 0.407  ;
0011000 1 0.74 0.802 0.076 0.531 0.757 0.028 0.858  ;
0000110 1 0.695 0.34 0.467 0.341 0.331 0.908 0.283  ;
0100110 1 0.647 0.574 0.051 0.038 0.503 0.402 0.329  ;
0110000 1 0.487 0.394 0.736 0.112 0.452 0.867 0.046  ;
0000110 1 0.727 0.059 0.139 0.79 0.812 0.447 0.522  ;
0000001 1 0.723 0.542 0.843 0.19 0.11 0.782 0.592  ;
0001100 1 0.01 0.275 0.976 0.719 0.864 0.184 0.469  ;
1000000 1 0.988 0.981 0.634 0.936 0.413 0.629 0.267  ;
0101011 1 0.997 0.971 0.4 0.917 0.385 0.401 0.313  ;
0001000 1 0.316 0.694 0.019 0.62 0.844 0.287 0.29  ;
0000010 1 0.504 0.464 0.686 0.484 0.177 0.283 0.008  ;
0001010 1 0.831 0.026 0.898 0.699 0.143 0.625 0.701  ;
1000000 1 0.655 0.728 0.284 0.353 0.896 0.066 0.06  ;
1001100 1 0.332 0.898 0.803 0.45 0.593 0.164 0.609  ;
0010110 1 0.928 0.553 0.352 0.05 0.945 0.851 0.822  ;
0000101 1 0.075 0.732 0.213 0.016 0.444 0.787 0.438  ;
0000010 1 0.688 0.1 0.371 0.061 0.45 0.774 0.805  ;
0001011 1 0.484 0.684 0.335 0.789 0.364 0.816 0.086  ;
0001110 1 0.277 0.58 0.032 0.535 0.794 0.488 0.53  ;
0000100 1 0.163 0.468 0.149 0.278 0.104 0.402 0.828  ;
0001001 1 0.75 0.09 0.347 0.678 0.665 0.305 0.636  ;
0010110 1 0.273 0.965 0.933 0.829 0.761 0.496 0.19  ;
0000001 1 0.268 0.58 0.654 0.324 0.11 0.435 0.982  ;
0001000 1 0.313 0.361 0.313 0.907 0.494 0.596 0.839  ;
0101100 1 0.721 0.89 0.056 0.599 0.689 0.489 0.722  ;
0000110 1 0.134 0.86 0.19 0.3 0.864 0.777 0.553  ;
0100010 1 0.001 0.902 0.708 0.661 0.342 0.588 0.694  ;
0000010 1 0.602 0.565 0.88 0.724 0.036 0.492 0.695  ;
0000010 1 0.16 0.548 0.025 0.115 0.636 0.679 0.305  ;
0000010 1 0.441 0.038 0.015 0.095 0.751 0.785 0.058  ;
0001100 1 0.217 0.498 0.241 0.654 0.909 0.334 0.034  ;
0110100 1 0.317 0.748 0.32 0.637 0.315 0.273 0.093  ;
0000011 1 0.916 0.018 0.663 0.452 0.652 0.855 0.724  ;
0001111 1 0.775 0.664 0.225 0.402 0.661 0.766 0.974  ;
0001110 1 0.758 0.599 0.328 0.635 0.791 0.929 0.839  ;
0000011 1 0.039 0.589 0.664 0.317 0.678 0.664 0.356  ;
0100101 1 0.311 0.108 0.277 0.469 0.672 0.22 0.96  ;
0001010 1 0.207 0.408 0.737 0.88 0.663 0.976 0.511  ;
0010110 1 0.527 0.862 0.696 0.296 0.927 0.889 0.073  ;
0000100 1 0.973 0.809 0.461 0.644 0.877 0.363 0.875  ;
0101000 1 0.938 0.219 0.174 0.818 0.155 0.671 0.507  ;
0001100 1 0.829 0.577 0.163 0.622 0.39 0.16 0.367  ;
0010010 1 0.233 0.231 0.52 0.303 0.206 0.447 0.809  ;
1000000 1 0.423 0.502 0.894 0.078 0.744 0.476 0.67  ;
0001010 1 0.134 0.118 0.189 0.678 0.077 0.541 0.516  ;
0000010 1 0.023 0.145 0.246 0.279 0.931 0.317 0.327  ;
0011000 1 0.478 0.221 0.186 0.083 0.198 0.599 0.262  ;
0010100 1 0.875 0.939 0.803 0.043 0.22 0.837 0.914  ;
0000110 1 0.219 0.69 0.665 0.468 0.641 0.791 0.063  ;
0000010 1 0.112 0.776 0.978 0.382 0.134 0.116 0.319  ;
0000101 1 0.85 0.374 0.404 0.927 0.225 0.018 0.138  ;
0000010 1 0.249 0.311 0.929 0.218 0.229 0.608 0.063  ;
0000110 1 0.505 0.82 0.069 0.328 0.901 0.55 0.752  ;
0100111 1 0.566 0.468 0.434 0.138 0.744 0.653 0.832  ;
0001001 1 0.525 0.346 0.241 0.685 0.112 0.503 0.663  ;
0001010 1 0.333 0.106 0.268 0.538 0.652 0.871 0.206  ;
0001110 1 0.471 0.891 0.875 0.654 0.901 0.335 0.5  ;
0100000 1 0.195 0.556 0.097 0.539 0.189 0.46 0.306  ;
0000010 1 0.57 0.865 0.376 0.234 0.51 0.665 0.163  ;
0001100 1 0.34 0.342 0.576 0.661 0.926 0.176 0.42  ;
1000000 1 0.554 0.498 0.208 0.373 0.745 0.904 0.256  ;
0001010 1 0.135 0.293 0.044 0.28 0.253 0.986 0.303  ;
0000100 1 0.677 0.994 0.307 0.399 0.732 0.387 0.959  ;
0000110 1 0.822 0.88 0.055 0.122 0.906 0.705 0.182  ;
0010111 1 0.465 0.092 0.775 0.409 0.977 0.834 0.463  ;
0001110 1 0.3 0.426 0.566 0.978 0.584 0.95 0.247  ;
0001010 1 0.96 0.627 0.257 0.962 0.081 0.901 0.633  ;
0000010 1 0.636 0.32 0.363 0.614 0.082 0.447 0.874  ;
0001000 1 0.834 0.664 0.374 0.906 0.657 0.592 0.831  ;
0010000 1 0.579 0.33 0.768 0.114 0.742 0.642 0.846  ;
0000001 1 0.902 0.907 0.035 0.837 0.306 0.249 0.606  ;
0101100 1 0.378 0.44 0.243 0.841 0.749 0.28 0.295  ;
0001001 1 0.324 0.367 0.851 0.816 0.22 0.039 0.421  ;
0000111 1 0.062 0.04 0.81 0.344 0.873 0.357 0.769  ;
0000011 1 0.488 0.424 0.744 0.595 0.222 0.959 0.224  ;
0000001 1 0.234 0.085 0.243 0.632 0.84 0.168 0.424  ;
0000101 1 0.868 0.609 0.052 0.107 0.348 0.322 0.953  ;
0001000 1 0.668 0.398 0.608 0.878 0.443 0.938 0.397  ;
0010000 1 0.881 0.339 0.894 0.874 0.237 0.018 0.072  ;
0001001 1 0.003 0.465 0.187 0.403 0.126 0.301 0.98  ;
0000100 1 0.182 0.71 0.948 0.291 0.673 0.019 0.904  ;
0100100 1 0.352 0.305 0.472 0.216 0.264 0.29 0.538  ;
0001110 1 0.164 0.067 0.234 0.371 0.89 0.874 0.309  ;
1000001 1 0.413 0.14 0.975 0.321 0.367 0.787 0.781  ;
0000010 1 0.43 0.489 0.641 0.341 0.017 0.949 0.077  ;
1111010 1 0.403 0.7 0.226 0.7 0.477 0.618 0.935  ;
0001110 1 0.261 0.393 0.408 0.977 0.897 0.864 0.9  ;
1000010 1 0.146 0.038 0.922 0.03 0.416 0.769 0.553  ;
0001000 1 0.331 0.625 0.076 0.537 0.429 0.967 0.15  ;
1001001 1 0.495 0.429 0.529 0.357 0.365 0.232 0.974  ;
0010000 1 0.429 0.163 0.727 0.015 0.427 0.018 0.283  ;
0001000 1 0.721 0.14 0.34 0.964 0.333 0.263 0.055  ;
0000110 1 0.061 0.517 0.862 0.646 0.993 0.714 0.179  ;
0011100 1 0.043 0.713 0.92 0.261 0.705 0.369 0.772  ;
0001000 1 0.127 0.904 0.244 0.547 0.539 0.248 0.037  ;
0000110 1 0.955 0.881 0.288 0.854 0.726 0.853 0.631  ;
0011000 1 0.563 0.582 0.72 0.375 0.113 0.65 0.676  ;
0001011 1 0.273 0.187 0.665 0.8 0.545 0.462 0.583  ;
0100011 1 0.203 0.729 0.346 0.679 0.17 0.505 0.778  ;
0010011 1 0.706 0.239 0.395 0.172 0.101 0.762 0.595  ;
0001000 1 0.592 0.198 0.099 0.877 0.782 0.323 0.564  ;
1010000 1 0.98 0.267 0.933 0.262 0.82 0.512 0.442  ;
0000011 1 0.682 0.95 0.011 0.214 0.974 0.331 0.342  ;
0100010 1 0.427 0.273 0.226 0.792 0.95 0.948 0.658  ;
0010001 1 0.498 0.134 0.21 0.121 0.087 0.808 0.482  ;
1011100 1 0.457 0.041 0.845 0.604 0.708 0.371 0.016  ;
0000100 1 0.144 0.231 0.404 0.463 0.766 0.246 0.616  ;
0010010 1 0.432 0.896 0.97 0.136 0.909 0.089 0.314  ;
0010100 1 0.747 0.138 0.425 0.233 0.656 0.594 0.184  ;
0000011 1 0.139 0.376 0.301 0.145 0.173 0.582 0.839  ;
0100010 1 0.728 0.423 0.081 0.478 0.386 0.662 0.596  ;
0001010 1 0.306 0.844 0.118 0.631 0.733 0.843 0.394  ;
0001010 1 0.365 0.717 0.606 0.297 0.118 0.953 0.152  ;
0000100 1 0.62 0.843 0.235 0.043 0.525 0.489 0.504  ;
0000010 1 0.279 0.958 0.503 0.175 0.42 0.955 0.538  ;
0001000 1 0.553 0.138 0.279 0.677 0.717 0.303 0.342  ;
0011000 1 0.41 0.572 0.47 0.731 0.742 0.884 0.972  ;
0110000 1 0.7 0.72 0.815 0.277 0.79 0.624 0.504  ;
0010000 1 0.009 0.596 0.676 0.547 0.561 0.757 0.417  ;
0000100 1 0.363 0.703 0.01 0.078 0.887 0.192 0.244  ;
0001000 1 0.71 0.226 0.653 0.899 0.437 0.455 0.073  ;
0110000 1 0.327 0.595 0.32 0.111 0.281 0.488 0.859  ;
0000101 1 0.349 0.704 0.149 0.621 0.745 0.208 0.464  ;
0001110 1 0.744 0.213 0.048 0.749 0.825 0.409 0.011  ;
0000011 1 0.269 0.323 0.872 0.833 0.282 0.606 0.779  ;
0000100 1 0.492 0.929 0.709 0.618 0.869 0.619 0.607  ;
0101000 1 0.316 0.676 0.887 0.543 0.54 0.487 0.867  ;
0001000 1 0.714 0.57 0.035 0.847 0.551 0.953 0.375  ;
1000000 1 0.933 0.72 0.649 0.475 0.479 0.361 0.872  ;
0111100 1 0.35 0.911 0.553 0.295 0.266 0.326 0.115  ;
1000101 1 0.562 0.791 0.364 0.276 0.366 0.282 0.802  ;
0011010 1 0.111 0.391 0.714 0.434 0.101 0.678 0.002  ;
0010000 1 0.916 0.789 0.786 0.282 0.615 0.797 0.065  ;
0011000 1 0.701 0.478 0.659 0.552 0.364 0.705 0.522  ;
0000101 1 0.708 0.768 0.944 0.303 0.555 0.497 0.218  ;
0000101 1 0.095 0.217 0.031 0.474 0.714 0.401 0.941  ;
0100000 1 0.791 0.803 0.357 0.088 0.395 0.463 0.982  ;
0100000 1 0.545 0.116 0.226 0.846 0.18 0.129 0.282  ;
0000100 1 0.567 0.906 0.033 0.564 0.378 0.16 0.913  ;
0001100 1 0.707 0.571 0.192 0.838 0.885 0.981 0.197  ;
1110000 1 0.764 0.741 0.63 0.804 0.593 0.806 0.706  ;
0001000 1 0.4 0.257 0.531 0.96 0.443 0.5 0.236  ;
0100000 1 0.135 0.242 0.536 0.863 0.057 0.309 0.569  ;
0001011 1 0.087 0.459 0.127 0.832 0.795 0.735 0.883  ;
0000100 1 0.806 0.14 0.39 0.403 0.809 0.725 0.328  ;
0000010 1 0.398 0.897 0.37 0.067 0.866 0.217 0.854  ;
0101011 1 0.897 0.443 0.734 0.743 0.786 0.688 0.781  ;
0001010 1 0.157 0.303 0.233 0.688 0.065 0.533 0.493  ;
0000001 1 0.454 0.142 0.94 0.039 0.627 0.217 0.659  ;
0000010 1 0.627 0.847 0.118 0.678 0.589 0.803 0.741  ;
0000010 1 0.222 0.338 0.564 0.922 0.895 0.334 0.662  ;
0000010 1 0.587 0.414 0.426 0.577 0.142 0.847 0.93  ;
0001010 1 0.226 0.467 0.222 0.971 0.604 0.805 0.258  ;
0001100 1 0.81 0.031 0.899 0.623 0.87 0.028 0.288  ;
0000110 1 0.414 0.483 0.139 0.35 0.321 0.396 0.663  ;
0100100 1 0.168 0.805 0.288 0.987 0.34 0.819 0.453  ;
0001010 1 0.099 0.636 0.742 0.048 0.097 0.445 0.559  ;
1000000 1 0.473 0.651 0.339 0.535 0.007 0.406 0.904  ;
0001111 1 0.146 0.083 0.066 0.974 0.972 0.893 0.799  ;
0010010 1 0.184 0.748 0.37 0.371 0.912 0.627 0.136  ;
0010101 1 0.096 0.402 0.948 0.753 0.803 0.153 0.741  ;
0001000 1 0.525 0.867 0.243 0.974 0.109 0.354 0.36  ;
0010000 1 0.323 0.766 0.45 0.319 0.91 0.947 0.352  ;
0101010 1 0.08 0.691 0.653 0.878 0.084 0.907 0.358  ;
0000101 1 0.511 0.94 0.288 0.209 0.548 0.234 0.275  ;
0000010 1 0.841 0.382 0.169 0.047 0.824 0.865 0.567  ;
0010000 1 0.631 0.58 0.802 0.821 0.3 0.494 0.685  ;
0000100 1 0.555 0.84 0.797 0.588 0.163 0.195 0.327  ;
0001000 1 0.38 0.954 0.624 0.87 0.09 0.863 0.527  ;
0001001 1 0.709 0.141 0.222 0.993 0.658 0.047 0.668  ;
0011100 1 0.455 0.262 0.847 0.811 0.311 0.299 0.339  ;
0000110 1 0.905 0.47 0.878 0.923 0.858 0.249 0.163  ;
0001010 1 0.558 0.584 0.64 0.769 0.516 0.123 0.055  ;
0000110 1 0.56 0.874 0.823 0.686 0.957 0.156 0.468  ;
0001000 1 0.556 0.477 0.832 0.507 0.373 0.003 0.294  ;
0000100 1 0.983 0.129 0.089 0.166 0.422 0.042 0.634  ;
0000001 1 0.995 0.706 0.38 0.468 0.076 0.803 0.847  ;
1000110 1 0.694 0.817 0.955 0.316 0.134 0.849 0.185  ;
0001000 1 0.683 0.403 0.024 0.884 0.029 0.109 0.257  ;
0100000 1 0.819 0.367 0.284 0.488 0.026 0.58 0.721  ;
0010100 1 0.668 0.348 0.229 0.181 0.896 0.756 0.67  ;
0001100 1 0.709 0.456 0.397 0.245 0.404 0.314 0.326  ;
0000100 1 0.421 0.157 0.301 0.102 0.755 0.886 0.65  ;
1000000 1 0.094 0.866 0.148 0.508 0.042 0.13 0.969  ;
1001000 1 0.704 0.321 0.461 0.819 0.033 0.511 0.275  ;
0010000 1 0.594 0.739 0.774 0.606 0.702 0.944 0.307  ;
0100010 1 0.745 0.666 0.054 0.022 0.857 0.314 0.513  ;
0000010 1 0.542 0.247 0.426 0.982 0.389 0.481 0.206  ;
0000101 1 0.728 0.491 0.329 0.336 0.115 0.441 0.067  ;
0000010 1 0.199 0.369 0.673 0.277 0.067 0.261 0.841  ;
0100000 1 0.239 0.631 0.325 0.505 0.666 0.325 0.556  ;
0001100 1 0.139 0.652 0.138 0.893 0.785 0.984 0.292  ;
0000101 1 0.95 0.728 0.919 0.521 0.859 0.181 0.925  ;
0100100 1 0.389 0.798 0.857 0.226 0.673 0.523 0.257  ;
0100000 1 0.383 0.901 0.483 0.67 0.948 0.953 0.397  ;
0000010 1 0.174 0.721 0.809 0.328 0.049 0.606 0.059  ;
0011110 1 0.467 0.085 0.152 0.328 0.633 0.123 0.233  ;
0000110 1 0.313 0.357 0.303 0.403 0.714 0.732 0.585  ;
0000100 1 0.259 0.762 0.151 0.986 0.884 0.77 0.893  ;
0100100 1 0.983 0.846 0.826 0.938 0.302 0.668 0.957  ;
0000010 1 0.056 0.206 0.515 0.091 0.871 0.933 0.059  ;
0000010 1 0.049 0.451 0.796 0.136 0.378 0.711 0.306  ;
0000010 1 0.314 0.002 0.041 0.929 0.271 0.847 0.089  ;
0000010 1 0.77 0.273 0.548 0.126 0.221 0.257 0.901  ;
0000110 1 0.372 0.976 0.099 0.351 0.737 0.333 0.913  ;
0001010 1 0.055 0.112 0.818 0.117 0.209 0.485 0.343  ;
0010010 1 0.087 0.193 0.335 0.057 0.517 0.527 0.646  ;
0001100 1 0.121 0.874 0.172 0.776 0.651 0.519 0.574  ;
0101100 1 0.33 0.481 0.659 0.549 0.56 0.353 0.556  ;
0011100 1 0.401 0.269 0.392 0.992 0.772 0.146 0.259  ;
0000101 1 0.42 0.751 0.973 0.539 0.858 0.28 0.445  ;
0000010 1 0.695 0.253 0.177 0.123 0.093 0.446 0.465  ;
0010110 1 0.458 0.134 0.702 0.404 0.14 0.687 0.399  ;
0001101 1 0.98 0.997 0.628 0.913 0.789 0.782 0.45  ;
0000110 1 0.786 0.82 0.262 0.038 0.56 0.446 0.996  ;
0000001 1 0.977 0.713 0.834 0.224 0.405 0.377 0.982  ;
0011100 1 0.18 0.456 0.347 0.554 0.396 0.434 0.044  ;
0001000 1 0.036 0.628 0.07 0.992 0.173 0.118 0.721  ;
0000010 1 0.036 0.294 0.037 0.162 0.943 0.259 0.641  ;
0001110 1 0.297 0.556 0.023 0.37 0.386 0.916 0.481  ;
0000100 1 0.875 0.176 0.55 0.644 0.865 0.204 0.085  ;
0000010 1 0.871 0.147 0.382 0.188 0.063 0.746 0.791  ;
0010000 1 0.222 0.011 0.727 0.557 0.953 0.502 0.687  ;
0001000 1 0.28 0.254 0.528 0.539 0.772 0.159 0.004  ;
0001011 1 0.974 0.908 0.204 0.997 0.434 0.302 0.694  ;
1000010 1 0.301 0.556 0.642 0.313 0.073 0.941 0.501  ;
1000000 1 0.562 0.713 0.086 0.672 0.911 0.124 0.04  ;
0001100 1 0.585 0.609 0.203 0.268 0.412 0.377 0.047  ;
0000010 1 0.778 0.556 0.518 0.603 0.359 0.988 0.659  ;
1000010 1 0.137 0.865 0.367 0.344 0.922 0.113 0.71  ;
0010000 1 0.416 0.803 0.576 0.91 0.026 0.005 0.084  ;
0001010 1 0.052 0.321 0.793 0.454 0.422 0.59 0.208  ;
0001000 1 0.166 0.744 0.142 0.692 0.091 0.388 0.434  ;
0001100 1 0.556 0.334 0.367 0.271 0.478 0.704 0.627  ;
0001110 1 0.238 0.062 0.412 0.637 0.339 0.658 0.446  ;
0000110 1 0.08 0.176 0.002 0.434 0.151 0.203 0.822  ;
1000000 1 0.835 0.059 0.91 0.132 0.485 0.99 0.282  ;
0001000 1 0.477 0.63 0.539 0.847 0.503 0.578 0.653  ;
0000101 1 0.767 0.059 0.343 0.155 0.933 0.308 0.731  ;
0001010 1 0.761 0.141 0.983 0.637 0.78 0.418 0.921  ;
0011000 1 0.405 0.656 0.719 0.636 0.176 0.9 0.438  ;
0010110 1 0.063 0.483 0.5 0.814 0.769 0.432 0.206  ;
0000001 1 0.839 0.28 0.329 0.637 0.525 0.595 0.676  ;
0000100 1 0.437 0.248 0.565 0.193 0.665 0.137 0.032  ;
0010001 1 0.065 0.28 0.963 0.039 0.269 0.314 0.751  ;
0101010 1 0.59 0.993 0.197 0.729 0.125 0.361 0.498  ;
0000100 1 0.847 0.465 0.181 0.385 0.991 0.873 0.609  ;
0111110 1 0.909 0.834 0.637 0.665 0.676 0.533 0.54  ;
0010010 1 0.794 0.087 0.95 0.552 0.828 0.708 0.54  ;
0100000 1 0.446 0.942 0.578 0.146 0.371 0.349 0.968  ;
0110000 1 0.566 0.705 0.936 0.074 0.038 0.137 0.261  ;
1001101 1 0.836 0.475 0.621 0.542 0.754 0.359 0.835  ;
0001001 1 0.089 0.419 0.326 0.947 0.339 0.524 0.528  ;
0010100 1 0.121 0.168 0.842 0.919 0.764 0.948 0.343  ;
0000100 1 0.561 0.109 0.922 0.392 0.341 0.466 0.903  ;
0011001 1 0.148 0.235 0.925 0.641 0.153 0.176 0.464  ;
0011110 1 0.773 0.999 0.962 0.844 0.67 0.825 0.002  ;
0000010 1 0.587 0.157 0.635 0.391 0.796 0.584 0.751  ;
0000001 1 0.403 0.883 0.717 0.389 0.493 0.156 0.33  ;
0001100 1 0.661 0.816 0.276 0.748 0.43 0.538 0.646  ;
0000011 1 0.039 0.839 0.023 0.294 0.091 0.561 0.918  ;
0000111 1 0.169 0.035 0.37 0.776 0.648 0.536 0.996  ;
0000100 1 0.782 0.39 0.684 0.178 0.987 0.946 0.608  ;
0011001 1 0.934 0.46 0.516 0.862 0.162 0.704 1  ;
0001011 1 0.98 0.416 0.446 0.939 0.661 0.604 0.792  ;
0001100 1 0.526 0.913 0.243 0.61 0.473 0.724 0.947  ;
0011000 1 0.75 0.317 0.824 0.867 0.168 0.693 0.942  ;
0001100 1 0.732 0.454 0.092 0.891 0.971 0.74 0.504  ;
0010000 1 0.113 0.849 0.312 0.407 0.963 0.471 0.206  ;
0101111 1 0.552 0.485 0.412 0.906 0.78 0.907 0.228  ;
0010100 1 0.396 0.188 0.611 0.758 0.503 0.101 0.254  ;
0010000 1 0.238 0.455 0.429 0.003 0.49 0.069 0.188  ;
0100111 1 0.108 0.949 0.113 0.729 0.268 0.948 0.385  ;
0001010 1 0.539 0.7 0.071 0.841 0.063 0.239 0.687  ;
1011010 1 0.876 0.735 0.476 0.783 0.558 0.771 0.1  ;
0011010 1 0.077 0.27 0.63 0.275 0.038 0.998 0.021  ;
0001011 1 0.371 0.961 0.886 0.699 0.628 0.473 0.205  ;
0001100 1 0.024 0.254 0.279 0.816 0.633 0.345 0.246  ;
0010000 1 0.896 0.074 0.972 0.259 0.244 0.857 0.286  ;
0001110 1 0.189 0.908 0.676 0.713 0.936 0.648 0.443  ;
0101000 1 0.935 0.961 0.026 0.673 0.607 0.052 0.13  ;
0001001 1 0.406 0.304 0.727 0.319 0.324 0.165 0.933  ;
0001011 1 0.357 0.364 0.414 0.568 0.731 0.846 0.28  ;
1000010 1 0.552 0.331 0.426 0.186 0.819 0.896 0.723  ;
0011010 1 0.424 0.115 0.812 0.622 0.846 0.97 0.825  ;
0010000 1 0.038 0.411 0.776 0.141 0.199 0.938 0.63  ;
0011001 1 0.474 0.778 0.228 0.521 0.367 0.395 0.827  ;
1000000 1 0.777 0.707 0.064 0.177 0.741 0.447 0.092  ;
0010010 1 0.533 0.82 0.94 0.475 0.655 0.981 0.432  ;
0001011 1 0.621 0.456 0.769 0.824 0.789 0.955 0.819  ;
1000010 1 0.33 0.404 0.404 0.439 0.51 0.936 0.786  ;
0001111 1 0.611 0.352 0.06 0.494 0.898 0.384 0.98  ;
0000011 1 0.501 0.765 0.675 0.057 0.465 0.493 0.59  ;
0000010 1 0.065 0.073 0.312 0.499 0.402 0.664 0.775  ;
0101010 1 0.889 0.817 0.568 0.869 0.521 0.691 0.034  ;
0010010 1 0.563 0.666 0.903 0.578 0.375 0.833 0.824  ;
1011000 1 0.463 0.02 0.725 0.979 0.642 0.074 0.136  ;
0001001 1 0.348 0.752 0.765 0.885 0.769 0.14 0.816  ;
1001000 1 0.651 0.216 0.738 0.101 0.67 0.528 0.18  ;
0000010 1 0.793 0.629 0.233 0.296 0.28 0.974 0.123  ;
0001000 1 0.357 0.039 0.191 0.783 0.912 0.465 0.165  ;
0000001 1 0.933 0.099 0.918 0.372 0.695 0.446 0.497  ;
0000100 1 0.731 0.652 0.322 0.01 0.235 0.214 0.208  ;
0100000 1 0.113 0.621 0.026 0.351 0.616 0.161 0.76  ;
0000100 1 0.672 0.467 0.049 0.271 0.052 0.057 0.282  ;
0010010 1 0.159 0.942 0.74 0.814 0.985 0.68 0.288  ;
0001011 1 0.139 0.632 0.848 0.82 0.09 0.802 0.777  ;
1010000 1 0.948 0.492 0.381 0.641 0.302 0.54 0.222  ;
0001000 1 0.984 0.698 0.151 0.67 0.986 0.187 0.592  ;
0010011 1 0.74 0.396 0.991 0.316 0.232 0.85 0.547  ;
0001010 1 0.691 0.218 0.23 0.683 0.092 0.09 0.049  ;
0101010 1 0.034 0.765 0.115 0.776 0.385 0.947 0.181  ;
0001110 1 0.007 0.532 0.097 0.87 0.233 0.725 0.969  ;
0000011 1 0.195 0.88 0.684 0.866 0.771 0.941 0.847  ;
0100011 1 0.359 0.456 0.668 0.692 0.577 0.384 0.677  ;
0000101 1 0.999 0.161 0.384 0.063 0.058 0.533 0.529  ;
0000110 1 0.053 0.191 0.396 0.122 0.857 0.227 0.963  ;
0100111 1 0.959 0.773 0.918 0.228 0.596 0.559 0.623  ;
0100110 1 0.91 0.996 0.133 0.53 0.428 0.267 0.212  ;
0010101 1 0.19 0.397 0.766 0.188 0.792 0.164 0.245  ;
1011011 1 0.634 0.253 0.694 0.565 0.948 0.281 0.901  ;
0111000 1 0.189 0.676 0.787 0.556 0.365 0.045 0.231  ;
0000110 1 0.228 0.806 0.393 0.579 0.581 0.982 0.084  ;
1001100 1 0.837 0.46 0.699 0.394 0.93 0.544 0.699  ;
0001000 1 0.177 0.541 0.313 0.969 0.333 0.539 0.451  ;
0000011 1 0.259 0.999 0.848 0.281 0.292 0.108 0.463  ;
0110000 1 0.78 0.982 0.999 0.169 0.04 0.014 0.301  ;
0011111 1 0.511 0.181 0.936 0.865 0.487 0.377 0.69  ;
0001101 1 0.575 0.779 0.408 0.301 0.751 0.13 0.662  ;
0000010 1 0.559 0.171 0.603 0.642 0.094 0.524 0.767  ;
0000010 1 0.869 0.895 0.063 0.963 0.983 0.811 0.338  ;
0011100 1 0.816 0.358 0.728 0.977 0.989 0.667 0.785  ;
0100100 1 0.77 0.879 0.857 0.507 0.522 0.359 0.348  ;
0000100 1 0.859 0.522 0.258 0.852 0.806 0.01 0.04  ;
0001110 1 0.692 0.696 0.089 0.471 0.212 0.947 0.312  ;
0001010 1 0.37 0.604 0.034 0.812 0.437 0.66 0.201  ;
1010000 1 0.463 0.59 0.464 0.844 0.411 0.629 0.976  ;
0000010 1 0.54 0.655 0.253 0.819 0.267 0.915 0.525  ;
0000010 1 0.266 0.897 0.043 0.527 0.78 0.649 0.024  ;
0000110 1 0.767 0.641 0.242 0.111 0.414 0.79 0.101  ;
0001000 1 0.205 0.784 0.331 0.663 0.075 0.116 0.019  ;
0010111 1 0.959 0.023 0.601 0.506 0.513 0.842 0.536  ;
0000011 1 0.995 0.384 0.515 0.301 0.534 0.6 0.494  ;
0001111 1 0.768 0.993 0.215 0.704 0.828 0.595 0.653  ;
0010010 1 0.391 0.779 0.441 0.638 0.487 0.145 0.166  ;
1000100 1 0.911 0.899 0.036 0.097 0.322 0.189 0.136  ;
0110100 1 0.236 0.38 0.799 0.996 0.731 0.102 0.334  ;
0001100 1 0.077 0.82 0.581 0.718 0.609 0.445 0.514  ;
0011000 1 0.913 0.775 0.559 0.986 0.466 0.805 0.036  ;
0001110 1 0.764 0.495 0.831 0.921 0.72 0.661 0.763  ;
1000001 1 0.777 0.033 0.152 0.35 0.043 0.1 0.377  ;
0000110 1 0.588 0.739 0.375 0.756 0.89 0.89 0.434  ;
0000101 1 0.147 0.519 0.77 0.821 0.66 0.408 0.351  ;
0001000 1 0.842 0.783 0.227 0.708 0.516 0.211 0.869  ;
0000010 1 0.895 0.46 0.007 0.089 0.307 0.435 0.082  ;
0100010 1 0.188 0.911 0.223 0.163 0.97 0.878 0.941  ;
0000100 1 0.885 0.36 0.156 0.302 0.908 0.743 0.374  ;
0001000 1 0.598 0.542 0.369 0.633 0.024 0.17 0.986  ;
0001011 1 0.693 0.821 0.365 0.61 0.084 0.874 0.79  ;
0100110 1 0.254 0.903 0.143 0.085 0.494 0.532 0.939  ;
0001011 1 0.769 0.198 0.086 0.407 0.081 0.929 0.926  ;
0000110 1 0.082 0.777 0.969 0.195 0.383 0.122 0.325  ;
0000100 1 0.896 0.018 0.21 0.201 0.377 0.101 0.313  ;
0001000 1 0.604 0.491 0.078 0.568 0.59 0.715 0.388  ;
0100000 1 0.435 0.501 0.129 0.051 0.736 0.871 0.167  ;
0001100 1 0.007 0.951 0.392 0.953 0.573 0.606 0.382  ;
0000110 1 0.089 0.795 0.669 0.199 0.759 0.556 0.831  ;
0001000 1 0.695 0.099 0.268 0.81 0.349 0.795 0.693  ;
0001010 1 0.346 0.58 0.958 0.631 0.666 0.842 0.17  ;
0001000 1 0.834 0.21 0.425 0.618 0.057 0.939 0.412  ;
0001110 1 0.244 0.82 0.113 0.73 0.561 0.603 0.101  ;
1000000 1 0.701 0.846 0.611 0.257 0.487 0.332 0.771  ;
1000000 1 0.561 0.614 0.892 0.352 0.538 0.069 0.513  ;
0010000 1 0.724 0.033 0.151 0.233 0.434 0.437 0.755  ;
0010100 1 0.112 0.233 0.853 0.059 0.99 0.108 0.701  ;
0010000 1 0.928 0.519 0.883 0.307 0.125 0.896 0.196  ;
0001000 1 0.117 0.982 0.279 0.913 0.312 0.42 0.938  ;
0000100 1 0.415 0.907 0.739 0.163 0.607 0.352 0.69  ;
1001001 1 0.959 0.926 0.795 0.895 0.872 0.656 0.91  ;
0000010 1 0.867 0.028 0.389 0.64 0.755 0.942 0.601  ;
0001110 1 0.065 0.216 0.225 0.899 0.896 0.726 0.12  ;
0011101 1 0.295 0.815 0.791 0.528 0.696 0.849 0.546  ;
0100000 1 0.141 0.398 0.508 0.627 0.595 0.297 0.563  ;
0011010 1 0.239 0.225 0.517 0.88 0.971 0.907 0.689  ;
0001100 1 0.905 0.219 0.637 0.487 0.999 0.422 0.309  ;
0001010 1 0.63 0.694 0.008 0.445 0.306 0.63 0.631  ;
0000010 1 0.106 0.908 0.026 0.703 0.048 0.441 0.297  ;
0000011 1 0.193 0.42 0.621 0.382 0.718 0.6 0.606  ;
0001000 1 0.119 0.623 0.968 0.294 0.272 0.105 0.379  ;
0100010 1 0.491 0.834 0.97 0.158 0.086 0.245 0.903  ;
0001110 1 0.825 0.526 0.034 0.861 0.599 0.153 0.737  ;
0000100 1 0.823 0.653 0.006 0.103 0.96 0.229 0.384  ;
0000010 1 0.416 0.72 0.364 0.753 0.381 0.882 0.754  ;
0011001 1 0.437 0.343 0.244 0.743 0.651 0.207 0.256  ;
0000011 1 0.774 0.825 0.264 0.994 0.062 0.489 0.541  ;
0010000 1 0.576 0.726 0.088 0.457 0.23 0.34 0.594  ;
0001001 1 0.784 0.266 0.505 0.581 0.281 0.523 0.867  ;
0001100 1 0.056 0.7 0.116 0.143 0.9 0.272 0.108  ;
0001001 1 0.103 0.379 0.564 0.876 0.077 0.576 0.994  ;
0010100 1 0.421 0.611 0.61 0.249 0.615 0.063 0.261  ;
0001100 1 0.838 0.033 0.28 0.376 0.485 0.542 0.625  ;
0101100 1 0.168 0.359 0.458 0.274 0.621 0.008 0.112  ;
0010000 1 0.306 0.339 0.738 0.192 0.606 0.143 0.32  ;
0001000 1 0.688 0.9 0.268 0.837 0.029 0.129 0.444  ;
0000100 1 0.414 0.021 0.296 0.413 0.848 0.675 0.117  ;
0010000 1 0.215 0.644 0.969 0.512 0.009 0.25 0.146  ;
0001000 1 0.775 0.331 0.474 0.559 0.323 0.367 0.27  ;
0010110 1 0.762 0.854 0.596 0.007 0.89 0.632 0.749  ;
0010001 1 0.867 0.656 0.419 0.215 0.349 0.062 0.881  ;
0000100 1 0.241 0.484 0.275 0.671 0.942 0.977 0.571  ;
0001110 1 0.189 0.133 0.98 0.294 0.787 0.599 0.105  ;
0001111 1 0.301 0.769 0.497 0.556 0.647 0.149 0.784  ;
0001100 1 0.976 0.685 0.992 0.931 0.611 0.042 0.137  ;
0010000 1 0.454 0.372 0.072 0.957 0.785 0.311 0.21  ;
0000010 1 0.126 0.868 0.234 0.111 0.52 0.87 0.748  ;
0010100 1 0.368 0.048 0.939 0.047 0.64 0.438 0.027  ;
0000111 1 0.229 0.235 0.54 0.396 0.895 0.558 0.376  ;
0001010 1 0.382 0.332 0.602 0.876 0.163 0.951 0.589  ;
0010110 1 0.072 0.45 0.89 0.072 0.387 0.974 0.66  ;
0000100 1 0.617 0.281 0.195 0.775 0.871 0.479 0.362  ;
0010111 1 0.128 0.156 0.522 0.297 0.864 0.704 0.789  ;
0001110 1 0.65 0.334 0.195 0.404 0.787 0.791 0.073  ;
0001000 1 0.432 0.13 0.967 0.604 0.997 0.018 0.185  ;
0010101 1 0.682 0.28 0.756 0.485 0.124 0.354 0.972  ;
0000100 1 0.582 0.762 0.911 0.354 0.897 0.109 0.342  ;
0000001 1 0.554 0.592 0.658 0.81 0.595 0.713 0.788  ;
0000110 1 0.127 0.811 0.033 0.044 0.796 0.615 0.943  ;
0010010 1 0.033 0.094 0.345 0.074 0.84 0.812 0.955  ;
0001000 1 0.595 0.561 0.742 0.838 0.939 0.717 0.093  ;
0001000 1 0.173 0.158 0.697 0.602 0.784 0.89 0.134  ;
0000001 1 0.149 0.62 0.216 0.394 0.577 0.625 0.812  ;
0001010 1 0.921 0.079 0.246 0.103 0.355 0.405 0.596  ;
0001000 1 0.623 0.916 0.775 0.911 0.04 0.624 0.77  ;
0001001 1 0.164 0.52 0.176 0.966 0.587 0.309 0.921  ;
0000100 1 0.638 0.615 0.648 0.038 0.981 0.234 0.227  ;
0000001 1 0.146 0.532 0.452 0.289 0.083 0.16 0.47  ;
0000110 1 0.452 0.315 0.822 0.128 0.916 0.939 0.042  ;
0000011 1 0.925 0.619 0.3 0.232 0.397 0.358 0.555  ;
0000100 1 0.824 0.633 0.913 0.914 0.707 0.053 0.946  ;
0000100 1 0.466 0.956 0.877 0.945 0.656 0.114 0.686  ;
0000110 1 0.557 0.749 0.814 0.443 0.991 0.437 0.638  ;
0001100 1 0.375 0.217 0.387 0.719 0.261 0.903 0.207  ;
0001011 1 0.58 0.84 0.609 0.686 0.84 0.307 0.901  ;
0000100 1 0.593 0.548 0.729 0.494 0.996 0.978 0.953  ;
0000010 1 0.315 0.244 0.781 0.494 0.253 0.338 0.9  ;
0001010 1 0.395 0.852 0.013 0.958 0.782 0.979 0.683  ;
0000110 1 0.539 0.84 0.72 0.051 0.298 0.667 0.879  ;
0001001 1 0.132 0.991 0.788 0.957 0.639 0.148 0.47  ;
0001110 1 0.354 0.037 0.63 0.726 0.656 0.206 0.282  ;
0001010 1 0.675 0.694 0.456 0.118 0.763 0.694 0.99  ;
0001010 1 0.355 0.95 0.234 0.713 0.647 0.4 0.299  ;
0001000 1 0.493 0.916 0.589 0.839 0.256 0.911 0.137  ;
0000011 1 0.217 0.962 0.975 0.946 0.046 0.917 0.814  ;
0001000 1 0.541 0.058 0.094 0.787 0.376 0.602 0.753  ;
0001001 1 0.9 0.699 0.928 0.356 0.454 0.05 0.374  ;
0000100 1 0.504 0.644 0.975 0.407 0.718 0.856 0.151  ;
0000010 1 0.008 0.535 0.667 0.601 0.309 0.937 0.22  ;
0001110 1 0.057 0.094 0.739 0.624 0.917 0.863 0.618  ;
0000010 1 0.147 0.272 0.038 0.082 0.506 0.694 0.006  ;
0001000 1 0.475 0.376 0.828 0.898 0.94 0.006 0.992  ;
0000110 1 0.482 0.211 0.753 0.476 0.765 0.246 0.035  ;
0001010 1 0.986 0.985 0.983 0.679 0.009 0.508 0.886  ;
0000110 1 0.304 0.518 0.111 0.5 0.237 0.481 0.341  ;
0000100 1 0.378 0.753 0.764 0.941 0.628 0.528 0.292  ;
0000010 1 0.316 0.172 0.967 0.344 0.475 0.639 0.222  ;
0000100 1 0.143 0.996 0.395 0.457 0.643 0.976 0.395  ;
0001010 1 0.091 0.376 0.013 0.198 0.306 0.918 0.199  ;
0000111 1 0.583 0.272 0.618 0.17 0.435 0.798 0.576  ;
0001011 1 0.919 0.11 0.463 0.994 0.475 0.611 0.772  ;
0000100 1 0.507 0.935 0.49 0.317 0.291 0.924 0.517  ;
0001000 1 0.919 0.967 0.001 0.532 0.398 0.998 0.889  ;
0000010 1 0.457 0.736 0.758 0.897 0.184 0.907 0.351  ;
0001001 1 0.31 0.813 0.845 0.85 0.361 0.35 0.313  ;
0001000 1 0.818 0.163 0.823 0.967 0.784 0.957 0.45  ;
0000010 1 0.392 0.14 0.079 0.296 0.111 0.551 0.945  ;
0001100 1 0.621 0.687 0.774 0.427 0.823 0.032 0.745  ;
0000011 1 0.802 0.943 0.062 0.412 0.061 0.096 0.418  ;
0000011 1 0.428 0.919 0.305 0.478 0.856 0.315 0.989  ;
0000011 1 0.603 0.745 0.499 0.305 0.94 0.85 0.775  ;
0000100 1 0.841 0.705 0.655 0.54 0.571 0.778 0.778  ;
0000010 1 0.27 0.392 0.184 0.625 0.693 0.535 0.594  ;
0000010 1 0.437 0.82 0.02 0.788 0.601 0.617 0.854  ;
0000010 1 0.291 0.144 0.014 0.677 0.81 0.76 0.045  ;
0000110 1 0.924 0.978 0.344 0.936 0.752 0.908 0.145  ;
0000110 1 0.959 0.368 0.24 0.105 0.539 0.854 0.118  ;
0000011 1 0.97 0.671 0.567 0.526 0.752 0.854 0.585  ;
0000100 1 0.996 0.138 0.373 0.96 0.784 0.859 0.021  ;
0000001 1 0.814 0.317 0.959 0.428 0.371 0.12 0.661  ;
0000100 1 0.456 0.108 0.914 0.521 0.967 0.35 0.637  ;
0000101 1 0.782 0.299 0.387 0.892 0.693 0.839 0.076  ;
0000101 1 0.074 0.984 0.076 0.084 0.95 0.497 0.797  ;
0000100 1 0.877 0.799 0.576 0.505 0.269 0.372 0.339  ;
0000111 1 0.352 0.99 0.262 0.595 0.918 0.572 0.25  ;
0000010 1 0.158 0.355 0.825 0.119 0.387 0.927 0.81  ;
0000110 1 0.397 0.003 0.436 0.889 0.207 0.824 0.208  ;
0000100 1 0.155 0.114 0.275 0.551 0.811 0.293 0.714  ;
0000010 1 0.112 0.762 0.495 0.712 0.101 0.938 0.236  ;
0000010 1 0.815 0.496 0.267 0.288 0.137 0.455 0.025  ;
0000011 1 0.578 0.782 0.543 0.405 0.608 0.873 0.973  ;
0000110 1 0.456 0.305 0.359 0.143 0.735 0.292 0.251  ;
0000010 1 0.22 0.297 0.644 0.914 0.115 0.06 0.051  ;
0000100 1 0.177 0.143 0.324 0.562 0.632 0.46 0.413  ;
0000110 1 0.226 0.277 0.093 0.611 0.623 0.274 0.968  ;
0000010 1 0.389 0.297 0.806 0.45 0.436 0.212 0.509  ;
0000010 1 0.323 0.568 0.419 0.249 0.681 0.963 0.766  ;
0000110 1 0.106 0.161 0.366 0.728 0.727 0.786 0.651  ;
0000100 1 0.986 0.212 0.28 0.258 0.618 0.318 0.271  ;
0000011 1 0.899 0.423 0.992 0.783 0.287 0.452 0.878  ;
0000001 1 0.318 0.183 0.417 0.212 0.629 0.517 0.777  ;
0000010 1 0.546 0.51 0.999 0 0.853 0.942 0.633  ;
0000010 1 0.224 0.252 0.39 0.576 0.953 0.861 0.35  ;
0000010 1 0.479 0.472 0.454 0.977 0.374 0.805 0.323  ;
0000001 1 0.95 0.095 0.101 0.255 0.649 0.583 0.482  ;
0000010 1 0.398 0.112 0.114 0.606 0.816 0.649 0.89  ;
0000010 1 0.28 0.362 0.346 0.186 0.556 0.835 0.095  ;
0000010 1 0.133 0.622 0.273 0.15 0.351 0.443 0.377  ;
0000011 1 0.095 0.065 0.907 0.604 0.521 0.669 0.938  ;
0000010 1 0.215 0.338 0.126 0.681 0.569 0.438 0.367  ;
0000010 1 0.911 0.628 0.249 0.756 0.021 0.816 0.639  ;
0000011 1 0.823 0.924 0.134 0.619 0.597 0.712 0.991  ;
0000010 1 0.861 0.004 0.777 0.334 0.707 0.916 0.206  ;
0000001 1 0.197 0.155 0.225 0.363 0.366 0.144 0.875  ;
0000010 1 0.901 0.568 0.942 0.669 0.744 0.855 0.176  ;
0000001 1 0.265 0.057 0.717 0.657 0.519 0.142 0.137  ;
0000010 1 0.454 0.533 0.46 0.47 0.805 0.967 0.764  ;
0000010 1 0.154 0.749 0.61 0.061 0.471 0.649 0.012  ;
0000010 1 0.852 0.993 0.057 0.806 0.634 0.792 0.14  ;
0000010 1 0.56 0.016 0.574 0.604 0.738 0.503 0.99  ;
0000001 1 0.113 0.199 0.525 0.176 0.434 0.848 0.243  ;
0000001 1 0.308 0.994 0.096 0.382 0.334 0.26 0.663  ;
0000001 1 0.136 0.101 0.939 0.744 0.219 0.489 0.381  ;
0000001 1 0.935 0.933 0.998 0.722 0.261 0.433 0.936  ;
0000001 1 0.531 0.136 0.858 0.634 0.322 0.334 0.701  ;
markmiller
 
Posts: 39
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Re: Jolly-Seber (POPAN) with individual covariates

Postby jlaake » Wed Apr 04, 2018 4:35 pm

Please read the sticky post on this subject. Unless you use popan.derived, RMark doesn't calculate estimates of N. MARK does all of the estimation. So either you have different data, links or design matrix. Export the RMark model, import into MARK and run it to convince yourself that you'll get the same result as when you ran from RMark interface. If you don't (I'd be shocked) then you can report a bug.

With regard to individual covariates and POPAN, it is probably not a good idea because you don't know the covariate values for the ones that are never seen and unlike CJS they are part of the likelihood in JS models. To do it correctly you would need to develop a likelihood that includes a distribution for the covariate in the population because if as shown p depends on the covariate
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Re: Jolly-Seber (POPAN) with individual covariates

Postby markmiller » Wed Apr 04, 2018 7:27 pm

Thank you, Jeff. That was very helpful. I have been running my Jolly-Seber models using my own code and was not familiar with the popan.derived option in RMark. Nor was I aware that models could be exported from RMark and imported into MARK.

When I exported the example JS model (with the data set in which covariates differ by sampling occasion and by individual) from RMark and imported the .Rinp file into MARK then the parameter estimates for the sole model that immediately appears in the AIC table do indeed match the parameter estimates that RMark returned.

However, if I retrieve that model and run it again in MARK with a new model name then the parameter estimates change to match those that MARK returned originally. I am not sure what I am doing incorrectly. I can try to explore this some more. Regardless, the popan.derived option and the export / import options between RMark and MARK are very helpful.

Someone suggested when using covariates that vary among individuals and among sampling occasions in the Jolly-Seber I should consider a multi-state approach. I am not sure whether that approach is possible in MARK or RMark. I should look into that as well.
markmiller
 
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Re: Jolly-Seber (POPAN) with individual covariates

Postby jlaake » Wed Apr 04, 2018 10:04 pm

Not sure what is going on there. That should not happen, if I'm understanding you correctly. Please send me the MARK .dbf and .fpt files for the imported runs and I'll look at it. (jefflaake@gmail.com).

The standard multistate models in MARK are supported by RMark but they are based on CJS approach. That approach works for time-varying covariates where you only know the value of the time varying covariate when it is seen. However, you have to discretize the covariate as those discrete values become the states, as I understand it. I don't know of anyway to do that in a JS framework other than what I suggested previously.
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Re: Jolly-Seber (POPAN) with individual covariates

Postby jlaake » Thu Apr 05, 2018 12:44 pm

Congratulations. You are now just one of 2 people that have found a true difference between MARK and RMark runs. Exporting/importing and re-running is the only way to truly document it.

No need to send files. I used your example and replicated your results. It turns out Gary added a switch called "pentfirst" to control whether the first pent or last is computed by subtraction. I was unaware of it. if you looked at the files from the 2 runs in MARK you would have seen that the one run from RMark did not have the "pentfirst" switch and the one run from MARK did. Other than that the files were essentially identical. A few versions back Gary changed which pent was computed by subtraction from the first to the last. I had falsely assumed that MARK handled these differences via the model type. That was a bad assumption apparently.

I'm working out this issue with Gary. However it is not clear which is the best approach here in this case. The run without the switch from RMark actually was a better fit via -2lnl. However, as I pointed out there is a fundamental problem using individual covariates with POPAN models. The switch didn't matter when the covariates were static but when they were time varying it mattered because it changed the set of covariates being used from the last 6 to the first 6. One set isn't used because the pent is computed by subtraction.
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Re: Jolly-Seber (POPAN) with individual covariates

Postby markmiller » Thu Apr 05, 2018 3:12 pm

Thank you, Jeff. I was going to send the files first thing this morning, but will not send them now.

All I really need for now is to run models in which the covariates vary by sampling occasion (and by group: such as males versus females or Region A vs Region B). It sounds like those kinds of models should be fine using the existing versions of MARK / RMark.

For now I was just interested in exploring time-varying individual covariates (that differ by sampling occasion and individual) and that is when I discovered the differing estimates between MARK and RMark. If I am really interested in that topic I guess I might need to convert the models to a Bayesian framework.
markmiller
 
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Re: Jolly-Seber (POPAN) with individual covariates

Postby jlaake » Thu Apr 05, 2018 3:40 pm

For those following this, the discrepancy between MARK and RMark only occurred with the release of ver 9 of MARK that came out earlier this week. I'll make the changes necessary and will post on CRAN soon. That new post will also contain the Hidden Markov model that Gary added recently.

For POPAN, group covariates are fine as long as you use N~group (that is the default formula) so you estimate N by group. Occasion specific covariates are fine also. It is individual covariates that are problematic with POPAN because you don't know the covariate value for those never seen and they are part of the likelihood. Time-varying individual covariates are even worse as demonstrated by the fact that the results depend on whether the first or last pent is computed by subtraction.

It is not necessary to use a Bayesian approach. It would only require specifying a flexible form for the distribution of the individual covariate and including the distribution and its parameters in the likelihood formulation and optimization. If the covariate was time varying, you would either need a transition function (eg growth) for the covariate over time or a covariate distribution for each time.
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Re: Jolly-Seber (POPAN) with individual covariates

Postby gwhite » Fri Apr 06, 2018 4:00 pm

Although MARK will allow you to use individual covariates on p with the POPAN data type, you should not. Just as is the case with the full-likelihood closed captures models, you do not have individual covariate values for the animals never captured. As a result the population estimates and likelihood values are incorrect.

The reason that RMark and MARK were giving different answers was because MARK does not sort the encounter history file when the model is run. In contrast, RMark sorts the histories. The likelihood was being computed on the values of the individual covariates in the first encounter history, so different first histories produced different likelihoods. This difference in behavior explains the discrepancy between RMark and MARK, and not the PENTFIRST option that Jeff thought.

In summary, individual covariates on phi in POPAN models would be okay, because the likelihood is conditional on first capture for estimation of phi. However, individual covariates should never be used on p or pent because these parameters are not conditional on first capture.
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