Phi estimate of nearly 1 with lcl 0 and ucl 1

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Phi estimate of nearly 1 with lcl 0 and ucl 1

Postby Toad_aly » Wed Apr 27, 2022 8:37 pm

Hi everyone!

I’m a pretty new user to RMark. For my bachelor thesis, I am using a ten year data set (2010, 2013, 2016, 2020) with 2 capture events each year in an open CJS model to estimate survival and capture probabilities and as well the population size of a toad population.

Everything worked out well expect for the survival estimation on the second date in 2016.
t5 has an estimate of nearly 1 and the lcl is 0 and the ucl 1.
The phitable:

Code: Select all
> phitable
                all.diff.index par.index  estimate        se           lcl
Phi g1 c1 a0 t1              1         1 0.8667496 0.0454135  7.506031e-01
Phi g1 c1 a1 t2              2         2 0.3533644 0.0181798  3.185974e-01
Phi g1 c1 a2 t3              3         3 0.8257282 0.0392040  7.352984e-01
Phi g1 c1 a3 t4              4         4 0.4642861 0.0396758  3.879939e-01
Phi g1 c1 a4 t5              5         5 0.9998393 0.0906375 3.461938e-305
Phi g1 c1 a5 t6              6         6 0.0441878 0.0111267  2.684490e-02
Phi g1 c1 a6 t7              7         7 0.3190024 0.0000000  3.190024e-01
Phi g1 c2 a0 t2              8         2 0.3533644 0.0181798  3.185974e-01
Phi g1 c2 a1 t3              9         3 0.8257282 0.0392040  7.352984e-01
Phi g1 c2 a2 t4             10         4 0.4642861 0.0396758  3.879939e-01
Phi g1 c2 a3 t5             11         5 0.9998393 0.0906375 3.461938e-305
Phi g1 c2 a4 t6             12         6 0.0441878 0.0111267  2.684490e-02
Phi g1 c2 a5 t7             13         7 0.3190024 0.0000000  3.190024e-01
Phi g1 c3 a0 t3             14         3 0.8257282 0.0392040  7.352984e-01
Phi g1 c3 a1 t4             15         4 0.4642861 0.0396758  3.879939e-01
Phi g1 c3 a2 t5             16         5 0.9998393 0.0906375 3.461938e-305
Phi g1 c3 a3 t6             17         6 0.0441878 0.0111267  2.684490e-02
Phi g1 c3 a4 t7             18         7 0.3190024 0.0000000  3.190024e-01
Phi g1 c4 a0 t4             19         4 0.4642861 0.0396758  3.879939e-01
Phi g1 c4 a1 t5             20         5 0.9998393 0.0906375 3.461938e-305
Phi g1 c4 a2 t6             21         6 0.0441878 0.0111267  2.684490e-02
Phi g1 c4 a3 t7             22         7 0.3190024 0.0000000  3.190024e-01
Phi g1 c5 a0 t5             23         5 0.9998393 0.0906375 3.461938e-305
Phi g1 c5 a1 t6             24         6 0.0441878 0.0111267  2.684490e-02
Phi g1 c5 a2 t7             25         7 0.3190024 0.0000000  3.190024e-01
Phi g1 c6 a0 t6             26         6 0.0441878 0.0111267  2.684490e-02
Phi g1 c6 a1 t7             27         7 0.3190024 0.0000000  3.190024e-01
Phi g1 c7 a0 t7             28         7 0.3190024 0.0000000  3.190024e-01
                      ucl fixed note group cohort age time occ.cohort Cohort
Phi g1 c1 a0 t1 0.9335911                1      1   0    1          1      0
Phi g1 c1 a1 t2 0.3897553                1      1   1    2          1      0
Phi g1 c1 a2 t3 0.8898908                1      1   2    3          1      0
Phi g1 c1 a3 t4 0.5422873                1      1   3    4          1      0
Phi g1 c1 a4 t5 1.0000000                1      1   4    5          1      0
Phi g1 c1 a5 t6 0.0719071                1      1   5    6          1      0
Phi g1 c1 a6 t7 0.3190024                1      1   6    7          1      0
Phi g1 c2 a0 t2 0.3897553                1      2   0    2          2      1
Phi g1 c2 a1 t3 0.8898908                1      2   1    3          2      1
Phi g1 c2 a2 t4 0.5422873                1      2   2    4          2      1
Phi g1 c2 a3 t5 1.0000000                1      2   3    5          2      1
Phi g1 c2 a4 t6 0.0719071                1      2   4    6          2      1
Phi g1 c2 a5 t7 0.3190024                1      2   5    7          2      1
Phi g1 c3 a0 t3 0.8898908                1      3   0    3          3      2
Phi g1 c3 a1 t4 0.5422873                1      3   1    4          3      2
Phi g1 c3 a2 t5 1.0000000                1      3   2    5          3      2
Phi g1 c3 a3 t6 0.0719071                1      3   3    6          3      2
Phi g1 c3 a4 t7 0.3190024                1      3   4    7          3      2
Phi g1 c4 a0 t4 0.5422873                1      4   0    4          4      3
Phi g1 c4 a1 t5 1.0000000                1      4   1    5          4      3
Phi g1 c4 a2 t6 0.0719071                1      4   2    6          4      3
Phi g1 c4 a3 t7 0.3190024                1      4   3    7          4      3
Phi g1 c5 a0 t5 1.0000000                1      5   0    5          5      4
Phi g1 c5 a1 t6 0.0719071                1      5   1    6          5      4
Phi g1 c5 a2 t7 0.3190024                1      5   2    7          5      4
Phi g1 c6 a0 t6 0.0719071                1      6   0    6          6      5
Phi g1 c6 a1 t7 0.3190024                1      6   1    7          6      5
Phi g1 c7 a0 t7 0.3190024                1      7   0    7          7      6


Let me walk you through what I have done:
Code: Select all
str(Rmarkgbu)
'data.frame':   2321 obs. of  2 variables:
 $ ch  : chr  "00100100" "01000000" "10000000" "00000001" ...
 $ freq: num  1 1 1 1 1 1 1 1 1 1 ...
> summary(Rmarkgbu)
      ch                 freq 
 Length:2321        Min.   :1 
 Class :character   1st Qu.:1 
 Mode  :character   Median :1 
                    Mean   :1 
                    3rd Qu.:1 
                    Max.   :1 
> hw.proc <- process.data(Rmarkgbu, model="CJS")
> hw.ddl = make.design.data(hw.proc)
> release.gof(hw.proc)
RELEASE NORMAL TERMINATION
      Chi.square df      P
TEST2     0.9482  5 0.9666
TEST3    17.2108 11 0.1018
Total    18.1590 16 0.3147
> ###BUILDING MODELS
> # survival process
> Phi.ct = list(formula=~1) # constant
> Phi.time = list(formula=~time) # year effect
>
> # detection process
> p.ct = list(formula=~1) # constant
> p.time = list(formula=~time) # year effect
> # constant survival, constant recapture
  Model.1 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.ct,p=p.ct),output = FALSE,delete=T)
  # constant survival, time-dependent recapture
  Model.2 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.ct,p=p.time),output = FALSE,delete=T)
  # time-dependent survival, constant recapture
  Model.3 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.time,p=p.ct),output = FALSE,delete=T)
  # time-dependent survival, time-dependent recapture
  Model.4 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.time,p=p.time),output = FALSE,delete=T)


Due to the low AICs, only the 4 model follows:
Code: Select all
> # time-dependent survival, time-dependent recapture
> Model.4 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.time,p=p.time),output = FALSE,delete=T)
  The file is mark013.inp on unit 4.
  Welcome to MARK monah on machine DESKTOP-0F4CH6H in subdirectory "C:\Dokumente\Uni\Institut Zoologie\Wildbook\Data Anaylse\2010-2020_Liekwegen" running file "mark013.inp".
  INPUT --- proc title ;

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc chmatrix occasions= 8 groups= 1 etype= Live Nodes= 101
  INPUT --- ICMeans NoHist hist= 69 ;
  INPUT ---    time interval 1 1 1 1 1 1 1 ;
  INPUT ---    glabel(1)=Group 1;
   Number of unique encounter histories read was 69.
   Number of individual covariates read was 0.
   Time interval lengths are all equal to 1.

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc estimate link=Logit NOLOOP varest=2ndPart    ;
   Model is { Phi(~time)p(~time) }
  INPUT --- model={ Phi(~time)p(~time) };
  INPUT ---    group=1 Phi    rows=7 cols=7 Triang ;
  INPUT ---        1 2 3 4 5 6 7 ;
  INPUT ---        2 3 4 5 6 7 ;
  INPUT ---        3 4 5 6 7 ;
  INPUT ---        4 5 6 7 ;
  INPUT ---        5 6 7 ;
  INPUT ---        6 7 ;
  INPUT ---        7 ;
  INPUT ---    group=1 p    rows=7 cols=7 Triang ;
  INPUT ---        8 9 10 11 12 13 14 ;
  INPUT ---        9 10 11 12 13 14 ;
  INPUT ---        10 11 12 13 14 ;
  INPUT ---        11 12 13 14 ;
  INPUT ---        12 13 14 ;
  INPUT ---        13 14 ;
  INPUT ---        14 ;
  INPUT ---    design matrix constraints=14 covariates=14;
  INPUT ---        1 0 0 0 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 1 0 0 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 1 0 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 1 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 0 1 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 0 0 1 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 0 0 0 1 0 0 0 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 1 0 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 1 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 1 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 1 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 0 1 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 0 0 1;
  INPUT ---       blabel(1)=Phi:(Intercept);
  INPUT ---       blabel(2)=Phi:time2;
  INPUT ---       blabel(3)=Phi:time3;
  INPUT ---       blabel(4)=Phi:time4;
  INPUT ---       blabel(5)=Phi:time5;
  INPUT ---       blabel(6)=Phi:time6;
  INPUT ---       blabel(7)=Phi:time7;
  INPUT ---       blabel(8)=p:(Intercept);
  INPUT ---       blabel(9)=p:time3;
  INPUT ---       blabel(10)=p:time4;
  INPUT ---       blabel(11)=p:time5;
  INPUT ---       blabel(12)=p:time6;
  INPUT ---       blabel(13)=p:time7;
  INPUT ---       blabel(14)=p:time8;
  INPUT ---       rlabel(1)=Phi g1 c1 a0 t1;
  INPUT ---       rlabel(2)=Phi g1 c1 a1 t2;
  INPUT ---       rlabel(3)=Phi g1 c1 a2 t3;
  INPUT ---       rlabel(4)=Phi g1 c1 a3 t4;
  INPUT ---       rlabel(5)=Phi g1 c1 a4 t5;
  INPUT ---       rlabel(6)=Phi g1 c1 a5 t6;
  INPUT ---       rlabel(7)=Phi g1 c1 a6 t7;
  INPUT ---       rlabel(8)=p g1 c1 a1 t2;
  INPUT ---       rlabel(9)=p g1 c1 a2 t3;
  INPUT ---       rlabel(10)=p g1 c1 a3 t4;
  INPUT ---       rlabel(11)=p g1 c1 a4 t5;
  INPUT ---       rlabel(12)=p g1 c1 a5 t6;
  INPUT ---       rlabel(13)=p g1 c1 a6 t7;
  INPUT ---       rlabel(14)=p g1 c1 a7 t8;
   Model is { Ph{ Phi(~time)p(~time) } Iteration 138                                                                                                                                           
   CPU Time for numerical optimization was 0.28 seconds.     
   -2logL { Phi(~time)p(~time) } = 5420.4504     
   Penalty { Phi(~time)p(~time) } = 0.0000000     
   Gradient { Phi(~time)p(~time) }:
  0.2124795E-04  0.1755496E-04   0.000000     -0.2023967E-04   0.000000   
 { Phi(~time)p(~time) } VC Matrix: 100% done.  CPU Time to compute VC matrix was 0.01 seconds.                                         
 CPU Time to invert VC matrix was 0.01 seconds.     
 Gap Method for Num. of Estimated Parameters { Phi(~time)p(~time) } = 12         
 Numerical Threshold Method for Num. of Estimated Parameters { Phi(~time)p(~time) } = 12         
 Number of Estimated Parameters { Phi(~time)p(~time) } = 12         
   DEVIANCE { Phi(~time)p(~time) } = 115.45050               
 DEVIANCE Degrees of Freedom { Phi(~time)p(~time) } = 49         
   c-hat { Phi(~time)p(~time) } = 2.3561326     
   AIC { Phi(~time)p(~time) } = 5444.4504     
   AICc { Phi(~time)p(~time) } = 5444.5394     
   BIC { Phi(~time)p(~time) } = 5518.4313     
   Pearson Chisquare { Phi(~time)p(~time) } = 219.02696     
   Possible Encounter Histories { Phi(~time)p(~time) } = 254         
   Pearson Chisquare df { Phi(~time)p(~time) } = 235         
   Pearson chat { Phi(~time)p(~time) } = 0.9320296     
   Sum(Observed/Expected) { Phi(~time)p(~time) } = 225.45989     
   s-bar { Phi(~time)p(~time) } = -0.1155470   
   Fletcher chat { Phi(~time)p(~time) } = 1.0537922     
 Beta number 5 is a singular value.

Note: only 12 parameters counted of 14 specified parameters
AICc and parameter count have been adjusted upward
42 Warnings
>







> summary(Model.1)$AICc
[1] 5971.911
> summary(Model.2)$AICc
[1] 5701.434
> summary(Model.3)$AICc
[1] 5481.055
> summary(Model.4)$AICc
[1] 5448.57


> PIMS(Model.4, "Phi")
group = Group 1
   1  2  3  4  5  6  7
1  1  2  3  4  5  6  7
2     2  3  4  5  6  7
3        3  4  5  6  7
4           4  5  6  7
5              5  6  7
6                 6  7
7                    7
> PIMS(Model.4,"p")
group = Group 1
   2  3  4  5  6  7  8
1  8  9 10 11 12 13 14
2     9 10 11 12 13 14
3       10 11 12 13 14
4          11 12 13 14
5             12 13 14
6                13 14
7                   14
>
> #dimensions of design matrix
> dim(Model.4$design.matrix)
[1] 14 14
>
> #Design matrix for Phi portion
> Model.4$design.matrix[1:7,1:7]
                Phi:(Intercept) Phi:time2 Phi:time3 Phi:time4 Phi:time5
Phi g1 c1 a0 t1 "1"             "0"       "0"       "0"       "0"     
Phi g1 c1 a1 t2 "1"             "1"       "0"       "0"       "0"     
Phi g1 c1 a2 t3 "1"             "0"       "1"       "0"       "0"     
Phi g1 c1 a3 t4 "1"             "0"       "0"       "1"       "0"     
Phi g1 c1 a4 t5 "1"             "0"       "0"       "0"       "1"     
Phi g1 c1 a5 t6 "1"             "0"       "0"       "0"       "0"     
Phi g1 c1 a6 t7 "1"             "0"       "0"       "0"       "0"     
                Phi:time6 Phi:time7
Phi g1 c1 a0 t1 "0"       "0"     
Phi g1 c1 a1 t2 "0"       "0"     
Phi g1 c1 a2 t3 "0"       "0"     
Phi g1 c1 a3 t4 "0"       "0"     
Phi g1 c1 a4 t5 "0"       "0"     
Phi g1 c1 a5 t6 "1"       "0"     
Phi g1 c1 a6 t7 "0"       "1"     
>
> #display estimates for this model and real parameter estimates.
> Model.4$results$beta
                  estimate          se           lcl          ucl
Phi:(Intercept)  1.8725197   0.3932083     1.1018314    2.6432080
Phi:time2       -2.4768027   0.4308168    -3.3212036   -1.6324019
Phi:time3       -0.3168699   0.4783669    -1.2544690    0.6207291
Phi:time4       -2.0156188   0.4243319    -2.8473093   -1.1839283
Phi:time5        6.8635684 564.2640100 -1099.0939000 1112.8211000
Phi:time6       -4.9466326   0.4732863    -5.8742738   -4.0189914
Phi:time7       -2.6308800   0.0000000    -2.6308800   -2.6308800
p:(Intercept)    0.2916342   0.1500662    -0.0024956    0.5857639
p:time3          0.9746740   0.2167973     0.5497512    1.3995968
p:time4          0.2753713   0.2098636    -0.1359613    0.6867039
p:time5          0.1030551   0.2490068    -0.3849983    0.5911086
p:time6         -1.4341179   0.2151147    -1.8557428   -1.0124931
p:time7          0.1104052   0.5759449    -1.0184469    1.2392573
p:time8          1.4588605   0.0000000     1.4588605    1.4588605
> Model.4$results$real
                 estimate        se           lcl       ucl fixed note
Phi g1 c1 a0 t1 0.8667496 0.0454135  7.506031e-01 0.9335911           
Phi g1 c1 a1 t2 0.3533644 0.0181798  3.185974e-01 0.3897553           
Phi g1 c1 a2 t3 0.8257282 0.0392040  7.352984e-01 0.8898908           
Phi g1 c1 a3 t4 0.4642861 0.0396758  3.879939e-01 0.5422873           
Phi g1 c1 a4 t5 0.9998393 0.0906375 3.461938e-305 1.0000000           
Phi g1 c1 a5 t6 0.0441878 0.0111267  2.684490e-02 0.0719071           
Phi g1 c1 a6 t7 0.3190024 0.0000000  3.190024e-01 0.3190024           
p g1 c1 a1 t2   0.5723962 0.0367300  4.993761e-01 0.6423926           
p g1 c1 a2 t3   0.7801101 0.0268397  7.230492e-01 0.8282079           
p g1 c1 a3 t4   0.6380719 0.0338799  5.694139e-01 0.7015208           
p g1 c1 a4 t5   0.5974110 0.0477915  5.013054e-01 0.6865754           
p g1 c1 a5 t6   0.2418646 0.0282568  1.908463e-01 0.3014407           
p g1 c1 a6 t7   0.5991775 0.1335434  3.345179e-01 0.8163633           
p g1 c1 a7 t8   0.8520152 0.0000000  8.520152e-01 0.8520152     












>run.gbu=function()
  {
    hw.proc <- process.data(Rmarkgbu, model="CJS")
    hw.ddl = make.design.data(hw.proc)
    Phi.ct = list(formula=~1)
    Phi.time = list(formula=~time)
    p.ct = list(formula=~1)
    p.time = list(formula=~time)
    model.list<-create.model.list("CJS")
    results<-mark.wrapper(model.list,data=hw.proc,ddl=hw.ddl)
    return(results )
  }
> gbu.results<-run.gbu()








Phi.ct.p.ct

  The file is mark013.inp on unit 4.
  Welcome to MARK monah on machine DESKTOP-0F4CH6H in subdirectory "C:\Dokumente\Uni\Institut Zoologie\Wildbook\Data Anaylse\2010-2020_Liekwegen" running file "mark013.inp".
  INPUT --- proc title ;

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc chmatrix occasions= 8 groups= 1 etype= Live Nodes= 101
  INPUT --- ICMeans NoHist hist= 69 ;
  INPUT ---    time interval 1 1 1 1 1 1 1 ;
  INPUT ---    glabel(1)=Group 1;
   Number of unique encounter histories read was 69.
   Number of individual covariates read was 0.
   Time interval lengths are all equal to 1.

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc estimate link=Logit NOLOOP varest=2ndPart    ;
   Model is { Phi(~1)p(~1) }
  INPUT --- model={ Phi(~1)p(~1) };
  INPUT ---    group=1 Phi    rows=7 cols=7 Triang ;
  INPUT ---        1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 ;
  INPUT ---        1 1 1 1 ;
  INPUT ---        1 1 1 ;
  INPUT ---        1 1 ;
  INPUT ---        1 ;
  INPUT ---    group=1 p    rows=7 cols=7 Triang ;
  INPUT ---        2 2 2 2 2 2 2 ;
  INPUT ---        2 2 2 2 2 2 ;
  INPUT ---        2 2 2 2 2 ;
  INPUT ---        2 2 2 2 ;
  INPUT ---        2 2 2 ;
  INPUT ---        2 2 ;
  INPUT ---        2 ;
  INPUT ---    design matrix constraints=2 covariates=2 identity;
  INPUT ---       blabel(1)=Phi:(Intercept);
  INPUT ---       blabel(2)=p:(Intercept);
  INPUT ---       rlabel(1)=Phi g1 c1 a0 t1;
  INPUT ---       rlabel(2)=p g1 c1 a1 t2;
   Model is { Phi(~1)p(~1) }
   Link Function Used is LOGIT       
   Variance Estimation Procedure Used is 2ndPart
   -2logL(saturated) = 5304.999{ Phi(~1)p(~1) } Iteration 7       
   CPU Time for numerical optimization was 0.01 seconds.     
   -2logL { Phi(~1)p(~1) } = 5967.9078     
   Penalty { Phi(~1)p(~1) } = 0.0000000     
   Gradient { Phi(~1){ Phi(~1)p(~1) } VC Matrix: 100% done.  CPU Time to compute VC matrix was 0.01 seconds.     
 CPU Time to invert VC matrix was 0.01 seconds.     
 Gap Method for Num. of Estimated Parameters { Phi(~1)p(~1) } = 2         
 Numerical Threshold Method for Num. of Estimated Parameters { Phi(~1)p(~1) } = 2         
 Number of Estimated Parameters { Phi(~1)p(~1) } = 2         
   DEVIANCE { Phi(~1)p(~1) } = 662.90794               
 DEVIANCE Degrees of Freedom { Phi(~1)p(~1) } = 59         
   c-hat { Phi(~1)p(~1) } = 11.235728     
   AIC { Phi(~1)p(~1) } = 5971.9078     
   AICc { Phi(~1)p(~1) } = 5971.9112     
   BIC { Phi(~1)p(~1) } = 5984.2380     
   Pearson Chisquare { Phi(~1)p(~1) } = 704.57224     
   Possible Encounter Histories { Phi(~1)p(~1) } = 254         
   Pearson Chisquare df { Phi(~1)p(~1) } = 245         
   Pearson chat { Phi(~1)p(~1) } = 2.8758051     
   Sum(Observed/Expected) { Phi(~1)p(~1) } = 187.88856     
   s-bar { Phi(~1)p(~1) } = -0.2676577   
   Fletcher chat { Phi(~1)p(~1) } = 3.9268590     

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc stop;

     CPU Time in minutes for this job was 0.00

     Time Start = 02:03:22.188   Time End = 02:03:22.209

     Wall Clock Time in minutes for this job was 0.00
STOP NORMAL EXIT

Output summary for CJS model
Name : Phi(~1)p(~1)

Npar :  2
-2lnL:  5967.908
AICc :  5971.911

Beta
                  estimate        se        lcl       ucl
Phi:(Intercept) -0.0481868 0.0381038 -0.1228703 0.0264967
p:(Intercept)    0.6853685 0.0749680  0.5384312 0.8323058


Real Parameter Phi
 
          1         2         3         4         5         6         7
1 0.4879556 0.4879556 0.4879556 0.4879556 0.4879556 0.4879556 0.4879556
2           0.4879556 0.4879556 0.4879556 0.4879556 0.4879556 0.4879556
3                     0.4879556 0.4879556 0.4879556 0.4879556 0.4879556
4                               0.4879556 0.4879556 0.4879556 0.4879556
5                                         0.4879556 0.4879556 0.4879556
6                                                   0.4879556 0.4879556
7                                                             0.4879556


Real Parameter p
 
          2         3         4         5         6         7         8
1 0.6649358 0.6649358 0.6649358 0.6649358 0.6649358 0.6649358 0.6649358
2           0.6649358 0.6649358 0.6649358 0.6649358 0.6649358 0.6649358
3                     0.6649358 0.6649358 0.6649358 0.6649358 0.6649358
4                               0.6649358 0.6649358 0.6649358 0.6649358
5                                         0.6649358 0.6649358 0.6649358
6                                                   0.6649358 0.6649358
7                                                             0.6649358

Phi.time.p.ct

  The file is mark014.inp on unit 4.
  Welcome to MARK monah on machine DESKTOP-0F4CH6H in subdirectory "C:\Dokumente\Uni\Institut Zoologie\Wildbook\Data Anaylse\2010-2020_Liekwegen" running file "mark014.inp".
  INPUT --- proc title ;

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc chmatrix occasions= 8 groups= 1 etype= Live Nodes= 101
  INPUT --- ICMeans NoHist hist= 69 ;
  INPUT ---    time interval 1 1 1 1 1 1 1 ;
  INPUT ---    glabel(1)=Group 1;
   Number of unique encounter histories read was 69.
   Number of individual covariates read was 0.
   Time interval lengths are all equal to 1.

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc estimate link=Logit NOLOOP varest=2ndPart    ;
   Model is { Phi(~time)p(~1) }
  INPUT --- model={ Phi(~time)p(~1) };
  INPUT ---    group=1 Phi    rows=7 cols=7 Triang ;
  INPUT ---        1 2 3 4 5 6 7 ;
  INPUT ---        2 3 4 5 6 7 ;
  INPUT ---        3 4 5 6 7 ;
  INPUT ---        4 5 6 7 ;
  INPUT ---        5 6 7 ;
  INPUT ---        6 7 ;
  INPUT ---        7 ;
  INPUT ---    group=1 p    rows=7 cols=7 Triang ;
  INPUT ---        8 8 8 8 8 8 8 ;
  INPUT ---        8 8 8 8 8 8 ;
  INPUT ---        8 8 8 8 8 ;
  INPUT ---        8 8 8 8 ;
  INPUT ---        8 8 8 ;
  INPUT ---        8 8 ;
  INPUT ---        8 ;
  INPUT ---    design matrix constraints=8 covariates=8;
  INPUT ---        1 0 0 0 0 0 0 0;
  INPUT ---        1 1 0 0 0 0 0 0;
  INPUT ---        1 0 1 0 0 0 0 0;
  INPUT ---        1 0 0 1 0 0 0 0;
  INPUT ---        1 0 0 0 1 0 0 0;
  INPUT ---        1 0 0 0 0 1 0 0;
  INPUT ---        1 0 0 0 0 0 1 0;
  INPUT ---        0 0 0 0 0 0 0 1;
  INPUT ---       blabel(1)=Phi:(Intercept);
  INPUT ---       blabel(2)=Phi:time2;
  INPUT ---       blabel(3)=Phi:time3;
  INPUT ---       blabel(4)=Phi:time4;
  INPUT ---       blabel(5)=Phi:time5;
  INPUT ---       blabel(6)=Phi:time6;
  INPUT ---       blabel(7)=Phi:time7;
  INPUT ---       blabel(8)=p:(Intercept);
  INPUT ---       rlabel(1)=Phi g1 c1 a0 t1;
  INPUT ---       rlabel(2)=Phi g1 c1 a1 t2;
  INPUT ---       rlabel(3)=Phi g1 c1 a2 t3;
  INPUT ---       rlabel(4)=Phi g1 c1 a3 t4;
  INPUT ---       rlabel(5)=Phi g1 c1 a4 t5;
  INPUT ---       rlabel(6)=Phi g1 c1 a5 t6;
  INPUT ---       rlabel(7)=Phi g1 c1 a6 t7;
  INPUT ---       rlabel(8)=p g1 c1 a1 t2;
   Model is { Phi(~time)p(~1) }
   Link Function Used is LOGIT       
   Variance Estimation Procedure Used is 2ndPart
   -2logL(sa{ Phi(~time)p(~1) } Iteration 22                       
   CPU Time for numerical optimization was 0.02 seconds.     
   -2logL { Phi(~time)p(~1) } = 5465.0139     
   Penalty { Phi(~time)p(~1) } = 0.0000000     
   Gradient { Phi(~time)p(~1) }:
   0.000000       0.000000       0.000000       0.00{ Phi(~time)p(~1) } VC Matrix: 100% done.  CPU Time to compute VC matrix was 0.01 seconds.     
 CPU Time to invert VC matrix was 0.01 seconds.     
 Gap Method for Num. of Estimated Parameters { Phi(~time)p(~1) } = 8         
 Numerical Threshold Method for Num. of Estimated Parameters { Phi(~time)p(~1) } = 8         
 Number of Estimated Parameters { Phi(~time)p(~1) } = 8         
   DEVIANCE { Phi(~time)p(~1) } = 160.01401               
 DEVIANCE Degrees of Freedom { Phi(~time)p(~1) } = 53         
   c-hat { Phi(~time)p(~1) } = 3.0191322     
   AIC { Phi(~time)p(~1) } = 5481.0139     
   AICc { Phi(~time)p(~1) } = 5481.0549     
   BIC { Phi(~time)p(~1) } = 5530.3345     
   Pearson Chisquare { Phi(~time)p(~1) } = 443.00722     
   Possible Encounter Histories { Phi(~time)p(~1) } = 254         
   Pearson Chisquare df { Phi(~time)p(~1) } = 239         
   Pearson chat { Phi(~time)p(~1) } = 1.8535867     
   Sum(Observed/Expected) { Phi(~time)p(~1) } = 404.85811     
   s-bar { Phi(~time)p(~1) } = 0.6107616     
   Fletcher chat { Phi(~time)p(~1) } = 1.1507518     

   CPU Time for the last procedure was 0.02 seconds.     
  INPUT --- proc stop;

     CPU Time in minutes for this job was 0.00

     Time Start = 02:03:22.686   Time End = 02:03:22.799

     Wall Clock Time in minutes for this job was 0.00
STOP NORMAL EXIT

Output summary for CJS model
Name : Phi(~time)p(~1)

Npar :  8
-2lnL:  5465.014
AICc :  5481.055

Beta
                  estimate        se        lcl        ucl
Phi:(Intercept)  1.4073833 0.1980270  1.0192504  1.7955163
Phi:time2       -1.8603346 0.2232116 -2.2978293 -1.4228399
Phi:time3       -0.0859399 0.2408633 -0.5580320  0.3861522
Phi:time4       -1.6354728 0.2226990 -2.0719629 -1.1989827
Phi:time5       -1.7875486 0.2185353 -2.2158777 -1.3592194
Phi:time6       -3.8190833 0.2879576 -4.3834802 -3.2546864
Phi:time7       -1.7221837 0.2703487 -2.2520671 -1.1923002
p:(Intercept)    0.6186704 0.0765595  0.4686138  0.7687271


Real Parameter Phi
 
          1         2         3         4        5         6         7
1 0.8033529 0.3886593 0.7894218 0.4432236 0.406087 0.0822849 0.4219435
2           0.3886593 0.7894218 0.4432236 0.406087 0.0822849 0.4219435
3                     0.7894218 0.4432236 0.406087 0.0822849 0.4219435
4                               0.4432236 0.406087 0.0822849 0.4219435
5                                         0.406087 0.0822849 0.4219435
6                                                  0.0822849 0.4219435
7                                                            0.4219435


Real Parameter p
 
          2         3         4         5         6         7         8
1 0.6499161 0.6499161 0.6499161 0.6499161 0.6499161 0.6499161 0.6499161
2           0.6499161 0.6499161 0.6499161 0.6499161 0.6499161 0.6499161
3                     0.6499161 0.6499161 0.6499161 0.6499161 0.6499161
4                               0.6499161 0.6499161 0.6499161 0.6499161
5                                         0.6499161 0.6499161 0.6499161
6                                                   0.6499161 0.6499161
7                                                             0.6499161

Phi.ct.p.time

  The file is mark015.inp on unit 4.
  Welcome to MARK monah on machine DESKTOP-0F4CH6H in subdirectory "C:\Dokumente\Uni\Institut Zoologie\Wildbook\Data Anaylse\2010-2020_Liekwegen" running file "mark015.inp".
  INPUT --- proc title ;

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc chmatrix occasions= 8 groups= 1 etype= Live Nodes= 101
  INPUT --- ICMeans NoHist hist= 69 ;
  INPUT ---    time interval 1 1 1 1 1 1 1 ;
  INPUT ---    glabel(1)=Group 1;
   Number of unique encounter histories read was 69.
   Number of individual covariates read was 0.
   Time interval lengths are all equal to 1.

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc estimate link=Logit NOLOOP varest=2ndPart    ;
   Model is { Phi(~1)p(~time) }
  INPUT --- model={ Phi(~1)p(~time) };
  INPUT ---    group=1 Phi    rows=7 cols=7 Triang ;
  INPUT ---        1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 ;
  INPUT ---        1 1 1 1 ;
  INPUT ---        1 1 1 ;
  INPUT ---        1 1 ;
  INPUT ---        1 ;
  INPUT ---    group=1 p    rows=7 cols=7 Triang ;
  INPUT ---        2 3 4 5 6 7 8 ;
  INPUT ---        3 4 5 6 7 8 ;
  INPUT ---        4 5 6 7 8 ;
  INPUT ---        5 6 7 8 ;
  INPUT ---        6 7 8 ;
  INPUT ---        7 8 ;
  INPUT ---        8 ;
  INPUT ---    design matrix constraints=8 covariates=8;
  INPUT ---        1 0 0 0 0 0 0 0;
  INPUT ---        0 1 0 0 0 0 0 0;
  INPUT ---        0 1 1 0 0 0 0 0;
  INPUT ---        0 1 0 1 0 0 0 0;
  INPUT ---        0 1 0 0 1 0 0 0;
  INPUT ---        0 1 0 0 0 1 0 0;
  INPUT ---        0 1 0 0 0 0 1 0;
  INPUT ---        0 1 0 0 0 0 0 1;
  INPUT ---       blabel(1)=Phi:(Intercept);
  INPUT ---       blabel(2)=p:(Intercept);
  INPUT ---       blabel(3)=p:time3;
  INPUT ---       blabel(4)=p:time4;
  INPUT ---       blabel(5)=p:time5;
  INPUT ---       blabel(6)=p:time6;
  INPUT ---       blabel(7)=p:time7;
  INPUT ---       blabel(8)=p:time8;
  INPUT ---       rlabel(1)=Phi g1 c1 a0 t1;
  INPUT ---       rlabel(2)=p g1 c1 a1 t2;
  INPUT ---       rlabel(3)=p g1 c1 a2 t3;
  INPUT ---       rlabel(4)=p g1 c1 a3 t4;
  INPUT ---       rlabel(5)=p g1 c1 a4 t5;
  INPUT ---       rlabel(6)=p g1 c1 a5 t6;
  INPUT ---       rlabel(7)=p g1 c1 a6 t7;
  INPUT ---       rlabel(8)=p g1 c1 a7 t8;
   Model is { Phi(~1)p(~time) }
   Link Function Used is LOGIT       
   Variance Estimation Procedure Used is 2ndPart
   -2logL(sa{ Phi(~1)p(~time) } Iteration 22                       
   CPU Time for numerical optimization was 0.02 seconds.     
   -2logL { Phi(~1)p(~time) } = 5685.3929     
   Penalty { Phi(~1)p(~time) } = 0.0000000     
   Gradient { Phi(~1)p(~time) }:
 -0.4764727E-04 -0.3050278E-04   0.000000     -0.588{ Phi(~1)p(~time) } VC Matrix: 100% done.  CPU Time to compute VC matrix was 0.01 seconds.     
 CPU Time to invert VC matrix was 0.01 seconds.     
 Gap Method for Num. of Estimated Parameters { Phi(~1)p(~time) } = 8         
 Numerical Threshold Method for Num. of Estimated Parameters { Phi(~1)p(~time) } = 8         
 Number of Estimated Parameters { Phi(~1)p(~time) } = 8         
   DEVIANCE { Phi(~1)p(~time) } = 380.39306               
 DEVIANCE Degrees of Freedom { Phi(~1)p(~time) } = 53         
   c-hat { Phi(~1)p(~time) } = 7.1772275     
   AIC { Phi(~1)p(~time) } = 5701.3929     
   AICc { Phi(~1)p(~time) } = 5701.4340     
   BIC { Phi(~1)p(~time) } = 5750.7136     
   Pearson Chisquare { Phi(~1)p(~time) } = 624.51674     
   Possible Encounter Histories { Phi(~1)p(~time) } = 254         
   Pearson Chisquare df { Phi(~1)p(~time) } = 239         
   Pearson chat { Phi(~1)p(~time) } = 2.6130408     
   Sum(Observed/Expected) { Phi(~1)p(~time) } = 368.46712     
   s-bar { Phi(~1)p(~time) } = 0.4634296     
   Fletcher chat { Phi(~1)p(~time) } = 1.7855595     

   CPU Time for the last procedure was 0.03 seconds.     
  INPUT --- proc stop;

     CPU Time in minutes for this job was 0.00

     Time Start = 02:03:23.075   Time End = 02:03:23.181

     Wall Clock Time in minutes for this job was 0.00
STOP NORMAL EXIT

Output summary for CJS model
Name : Phi(~1)p(~time)

Npar :  8
-2lnL:  5685.393
AICc :  5701.434

Beta
                  estimate        se        lcl        ucl
Phi:(Intercept)  0.2809791 0.0471769  0.1885125  0.3734458
p:(Intercept)    1.0009703 0.1361386  0.7341386  1.2678020
p:time3         -0.5151322 0.1786958 -0.8653759 -0.1648885
p:time4          0.0368232 0.1836453 -0.3231216  0.3967681
p:time5         -0.7418467 0.1957555 -1.1255276 -0.3581659
p:time6         -1.3233191 0.1863139 -1.6884944 -0.9581438
p:time7         -3.5195783 0.2676317 -4.0441365 -2.9950202
p:time8         -2.3035386 0.2176624 -2.7301570 -1.8769202


Real Parameter Phi
 
          1         2         3         4         5         6         7
1 0.5697863 0.5697863 0.5697863 0.5697863 0.5697863 0.5697863 0.5697863
2           0.5697863 0.5697863 0.5697863 0.5697863 0.5697863 0.5697863
3                     0.5697863 0.5697863 0.5697863 0.5697863 0.5697863
4                               0.5697863 0.5697863 0.5697863 0.5697863
5                                         0.5697863 0.5697863 0.5697863
6                                                   0.5697863 0.5697863
7                                                             0.5697863


Real Parameter p
 
          2         3        4         5         6         7         8
1 0.7312493 0.6191255 0.738424 0.5644208 0.4201034 0.0745639 0.2137331
2           0.6191255 0.738424 0.5644208 0.4201034 0.0745639 0.2137331
3                     0.738424 0.5644208 0.4201034 0.0745639 0.2137331
4                              0.5644208 0.4201034 0.0745639 0.2137331
5                                        0.4201034 0.0745639 0.2137331
6                                                  0.0745639 0.2137331
7                                                            0.2137331








Phi.time.p.tim

  The file is mark016.inp on unit 4.
  Welcome to MARK monah on machine DESKTOP-0F4CH6H in subdirectory "C:\Dokumente\Uni\Institut Zoologie\Wildbook\Data Anaylse\2010-2020_Liekwegen" running file "mark016.inp".
  INPUT --- proc title ;

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc chmatrix occasions= 8 groups= 1 etype= Live Nodes= 101
  INPUT --- ICMeans NoHist hist= 69 ;
  INPUT ---    time interval 1 1 1 1 1 1 1 ;
  INPUT ---    glabel(1)=Group 1;
   Number of unique encounter histories read was 69.
   Number of individual covariates read was 0.
   Time interval lengths are all equal to 1.

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc estimate link=Logit NOLOOP varest=2ndPart    ;
   Model is { Phi(~time)p(~time) }
  INPUT --- model={ Phi(~time)p(~time) };
  INPUT ---    group=1 Phi    rows=7 cols=7 Triang ;
  INPUT ---        1 2 3 4 5 6 7 ;
  INPUT ---        2 3 4 5 6 7 ;
  INPUT ---        3 4 5 6 7 ;
  INPUT ---        4 5 6 7 ;
  INPUT ---        5 6 7 ;
  INPUT ---        6 7 ;
  INPUT ---        7 ;
  INPUT ---    group=1 p    rows=7 cols=7 Triang ;
  INPUT ---        8 9 10 11 12 13 14 ;
  INPUT ---        9 10 11 12 13 14 ;
  INPUT ---        10 11 12 13 14 ;
  INPUT ---        11 12 13 14 ;
  INPUT ---        12 13 14 ;
  INPUT ---        13 14 ;
  INPUT ---        14 ;
  INPUT ---    design matrix constraints=14 covariates=14;
  INPUT ---        1 0 0 0 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 1 0 0 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 1 0 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 1 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 0 1 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 0 0 1 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 0 0 0 1 0 0 0 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 1 0 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 1 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 1 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 1 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 0 1 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 0 0 1;
  INPUT ---       blabel(1)=Phi:(Intercept);
  INPUT ---       blabel(2)=Phi:time2;
  INPUT ---       blabel(3)=Phi:time3;
  INPUT ---       blabel(4)=Phi:time4;
  INPUT ---       blabel(5)=Phi:time5;
  INPUT ---       blabel(6)=Phi:time6;
  INPUT ---       blabel(7)=Phi:time7;
  INPUT ---       blabel(8)=p:(Intercept);
  INPUT ---       blabel(9)=p:time3;
  INPUT ---       blabel(10)=p:time4;
  INPUT ---       blabel(11)=p:time5;
  INPUT ---       blabel(12)=p:time6;
  INPUT ---       blabel(13)=p:time7;
  INPUT ---       blabel(14)=p:time8;
  INPUT ---       rlabel(1)=Phi g1 c1 a0 t1;
  INPUT ---       rlabel(2)=Phi g1 c1 a1 t2;
  INPUT ---       rlabel(3)=Phi g1 c1 a2 t3;
  INPUT ---       rlabel(4)=Phi g1 c1 a3 t4;
  INPUT ---       rlabel(5)=Phi g1 c1 a4 t5;
  INPUT ---       rlabel(6)=Phi g1 c1 a5 t6;
  INPUT ---       rlabel(7)=Phi g1 c1 a6 t7;
  INPUT ---       rlabel(8)=p g1 c1 a1 t2;
  INPUT ---       rlabel(9)=p g1 c1 a2 t3;
  INPUT ---       rlabel(10)=p g1 c1 a3 t4;
  INPUT ---       rlabel(11)=p g1 c1 a4 t5;
  INPUT ---       rlabel(12)=p g1 c1 a5 t6;
  INPUT ---       rlabel(13)=p g1 c1 a6 t7;
  INPUT ---       rlabel(14)=p g1 c1 a7 t8;
   Model is { Ph{ Phi(~time)p(~time) } Iteration 138                                                                                                                                           
   CPU Time for numerical optimization was 0.27 seconds.     
   -2logL { Phi(~time)p(~time) } = 5420.4504     
   Penalty { Phi(~time)p(~time) } = 0.0000000     
   Gradient { Phi(~time)p(~time) }:
  0.2124795E-04  0.1755496E-04   0.000000     -0.2023967E-04   0.000000   
 { Phi(~time)p(~time) } VC Matrix: 100% done.  CPU Time to compute VC matrix was 0.08 seconds.                                         
 CPU Time to invert VC matrix was 0.01 seconds.     
 Gap Method for Num. of Estimated Parameters { Phi(~time)p(~time) } = 12         
 Numerical Threshold Method for Num. of Estimated Parameters { Phi(~time)p(~time) } = 12         
 Number of Estimated Parameters { Phi(~time)p(~time) } = 12         
   DEVIANCE { Phi(~time)p(~time) } = 115.45050               
 DEVIANCE Degrees of Freedom { Phi(~time)p(~time) } = 49         
   c-hat { Phi(~time)p(~time) } = 2.3561326     
   AIC { Phi(~time)p(~time) } = 5444.4504     
   AICc { Phi(~time)p(~time) } = 5444.5394     
   BIC { Phi(~time)p(~time) } = 5518.4313     
   Pearson Chisquare { Phi(~time)p(~time) } = 219.02696     
   Possible Encounter Histories { Phi(~time)p(~time) } = 254         
   Pearson Chisquare df { Phi(~time)p(~time) } = 235         
   Pearson chat { Phi(~time)p(~time) } = 0.9320296     
   Sum(Observed/Expected) { Phi(~time)p(~time) } = 225.45989     
   s-bar { Phi(~time)p(~time) } = -0.1155470   
   Fletcher chat { Phi(~time)p(~time) } = 1.0537922     
 Beta number 5 is a singular value.

   CPU Time for the last procedure was 0.34 seconds.     
  INPUT --- proc stop;

     CPU Time in minutes for this job was 0.01

     Time Start = 02:03:23.513   Time End = 02:03:23.839

     Wall Clock Time in minutes for this job was 0.01
STOP NORMAL EXIT

Note: only 12 parameters counted of 14 specified parameters

AICc and parameter count have been adjusted upward





Output summary for CJS model
Name : Phi(~time)p(~time

Npar :  14  (unadjusted=12)
-2lnL:  5420.45
AICc :  5448.57  (unadjusted=5444.5394)

Beta
                  estimate          se           lcl          ucl
Phi:(Intercept)  1.8725197   0.3932083     1.1018314    2.6432080
Phi:time2       -2.4768027   0.4308168    -3.3212036   -1.6324019
Phi:time3       -0.3168699   0.4783669    -1.2544690    0.6207291
Phi:time4       -2.0156188   0.4243319    -2.8473093   -1.1839283
Phi:time5        6.8635684 564.2640100 -1099.0939000 1112.8211000
Phi:time6       -4.9466326   0.4732863    -5.8742738   -4.0189914
Phi:time7       -2.6308800   0.0000000    -2.6308800   -2.6308800
p:(Intercept)    0.2916342   0.1500662    -0.0024956    0.5857639
p:time3          0.9746740   0.2167973     0.5497512    1.3995968
p:time4          0.2753713   0.2098636    -0.1359613    0.6867039
p:time5          0.1030551   0.2490068    -0.3849983    0.5911086
p:time6         -1.4341179   0.2151147    -1.8557428   -1.0124931
p:time7          0.1104052   0.5759449    -1.0184469    1.2392573
p:time8          1.4588605   0.0000000     1.4588605    1.4588605


Real Parameter Phi
 
          1         2         3         4         5         6         7
1 0.8667496 0.3533644 0.8257282 0.4642861 0.9998393 0.0441878 0.3190024
2           0.3533644 0.8257282 0.4642861 0.9998393 0.0441878 0.3190024
3                     0.8257282 0.4642861 0.9998393 0.0441878 0.3190024
4                               0.4642861 0.9998393 0.0441878 0.3190024
5                                         0.9998393 0.0441878 0.3190024
6                                                   0.0441878 0.3190024
7                                                             0.3190024


Real Parameter p
 
          2         3         4        5         6         7         8
1 0.5723962 0.7801101 0.6380719 0.597411 0.2418646 0.5991775 0.8520152
2           0.7801101 0.6380719 0.597411 0.2418646 0.5991775 0.8520152
3                     0.6380719 0.597411 0.2418646 0.5991775 0.8520152
4                               0.597411 0.2418646 0.5991775 0.8520152
5                                        0.2418646 0.5991775 0.8520152
6                                                  0.5991775 0.8520152
7                                                            0.8520152
Es gab 50 oder mehr Warnungen (Anzeige der ersten 50 mit warnings())
     





> gbu.results
               model npar     AICc DeltaAICc       weight Deviance
4 Phi(~time)p(~time)   14 5448.570    0.0000 9.999999e-01 115.4505
3    Phi(~time)p(~1)    8 5481.055   32.4846 8.832015e-08 160.0140
2    Phi(~1)p(~time)    8 5701.434  252.8636 0.000000e+00 380.3931
1       Phi(~1)p(~1)    2 5971.911  523.3409 0.000000e+00 662.9079




> summary(gbu.results)
                Length Class      Mode
Phi.ct.p.ct     25     mark       list
Phi.ct.p.time   25     mark       list
Phi.time.p.ct   25     mark       list
Phi.time.p.time 25     mark       list
model.table      8     data.frame list
>
> gbu.results$Model.4$results$real
NULL
  ###TABLE OF ESTIMATES                                 
  #get real estimates under Phi p model
 > phitable = get.real(Model.4,"Phi", se= TRUE)
 > phitable
>  phitable[c("estimate","se","lcl","ucl")]


I know that Beta number 5 is a singular value and the estimation of phi 5 is weird. As well as there just have been 12 parameters out of 14 been taken into account. I have already tried to adjust the parameters, but always fail. I don't know how to code it.

I am not sure what I can do, to get reliable results for the survival probability of the individuals from the first date to the second monitoring date in 2016.

I have read all the articles and papers and also the guide, but unfortunately I am getting nowhere and have no one to ask.

Any information and help is greatly appreciated!
Toad_aly
 
Posts: 3
Joined: Wed Apr 27, 2022 7:29 pm

Re: Phi estimate of nearly 1 with lcl 0 and ucl 1

Postby jlaake » Wed Apr 27, 2022 9:35 pm

You need to specify the time.intervals between the occasions. The years you specify aren't consecutive so those are clearly not a unit interval and you said you have 2 occasions per year. Are they close together? Thus you have some intervals that are very short and others that are several years long. No surprise some survivals aren't coming out correctly.
jlaake
 
Posts: 1417
Joined: Fri May 12, 2006 12:50 pm
Location: Escondido, CA

Re: Phi estimate of nearly 1 with lcl 0 and ucl 1

Postby Toad_aly » Thu Apr 28, 2022 2:48 am

Oh okay, I see! That absolutely makes sense.

Excatly, so the monitoring dates within the years are approximateley 1 to 2 months apart:
    16 May 2010, 01 Aug 2010
    12 June 2013, 31 July 2013
    06 June 2016, 10 Aug 2016
    19 June 2020, 03 Aug 2020

Thank you very much for your help! Could you offer some adivce on how to specify the time.intervals between the occasions?
Toad_aly
 
Posts: 3
Joined: Wed Apr 27, 2022 7:29 pm

Re: Phi estimate of nearly 1 with lcl 0 and ucl 1

Postby jlaake » Thu Apr 28, 2022 9:12 am

Compute number of days between each occasion and then divide by 365.25 to get the proportion of a year. Some will obviously be close to 1/12th and others around 3 or more. Then use those values in time.intervals argument of process.data. This will make your survival rates be annual values and I'll be surprised if any are close to 1 with toads and it will be less likely that you will get survival varying by time.
jlaake
 
Posts: 1417
Joined: Fri May 12, 2006 12:50 pm
Location: Escondido, CA

Re: Phi estimate of nearly 1 with lcl 0 and ucl 1

Postby Toad_aly » Sun May 01, 2022 12:59 pm

Hi, thank you for your advice! I have been trying for the last few days, but I still have the same results, even after adjusting the interval time as you suggested.

Code: Select all
> #set time.inervals
>hw.proc <- process.data(Rmarkgbu, model="CJS",begin.time=2010,time.intervals=c(0.21,2.87,0.13,2.85,0.18,3.86,0.12))
>
> #define design data
> hw.ddl = make.design.data(hw.proc)
> release.gof(hw.proc)
RELEASE NORMAL TERMINATION
      Chi.square df      P
TEST2     0.9482  5 0.9666
TEST3    17.2108 11 0.1018
Total    18.1590 16 0.3147

###BUILDING MODELS
  # survival process
  Phi.ct = list(formula=~1) # constant
  Phi.time = list(formula=~time) # year effect
 
  # detection process
  p.ct = list(formula=~1) # constant
  p.time = list(formula=~time) # year effect
  # constant survival, constant recapture
  Model.1 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.ct,p=p.ct),output = FALSE,delete=T)
  # constant survival, time-dependent recapture
  Model.2 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.ct,p=p.time),output = FALSE,delete=T)
  # time-dependent survival, constant recapture
  Model.3 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.time,p=p.ct),output = FALSE,delete=T)
  # time-dependent survival, time-dependent recapture
  Model.4 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.time,p=p.time),output = FALSE,delete=T)
 

Code: Select all
> Model.1 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.ct,p=p.ct),output = FALSE,delete=T)
  The file is mark022.inp on unit 4.
  Welcome to MARK monah on machine DESKTOP-0F4CH6H in subdirectory "C:\Dokumente\Uni\Institut Zoologie\Wildbook\Data Anaylse\2010-2020_Liekwegen" running file "mark022.inp".
  INPUT --- proc title ;

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc chmatrix occasions= 8 groups= 1 etype= Live Nodes= 101
  INPUT --- ICMeans NoHist hist= 69 ;
  INPUT ---    time interval 0.21 2.87 0.13 2.85 0.18 3.86 0.12 ;
  INPUT ---    glabel(1)=Group 1;
   Number of unique encounter histories read was 69.
   Number of individual covariates read was 0.
   Time interval lengths vary and/or not equal to 1.

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc estimate link=Logit NOLOOP varest=2ndPart    ;
   Model is { Phi(~1)p(~1) }
  INPUT --- model={ Phi(~1)p(~1) };
  INPUT ---    group=1 Phi    rows=7 cols=7 Triang ;
  INPUT ---        1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 ;
  INPUT ---        1 1 1 1 ;
  INPUT ---        1 1 1 ;
  INPUT ---        1 1 ;
  INPUT ---        1 ;
  INPUT ---    group=1 p    rows=7 cols=7 Triang ;
  INPUT ---        2 2 2 2 2 2 2 ;
  INPUT ---        2 2 2 2 2 2 ;
  INPUT ---        2 2 2 2 2 ;
  INPUT ---        2 2 2 2 ;
  INPUT ---        2 2 2 ;
  INPUT ---        2 2 ;
  INPUT ---        2 ;
  INPUT ---    design matrix constraints=2 covariates=2 identity;
  INPUT ---       blabel(1)=Phi:(Intercept);
  INPUT ---       blabel(2)=p:(Intercept);
  INPUT ---       rlabel(1)=Phi g1 c2010 a0 t2010;
  INPUT ---       rlabel(2)=p g1 c2010 a0.21 t2010.21;
   Model is { Phi(~1)p(~1) }
   Link Function Used is LOGIT       
   Variance Estimation Procedure Used is 2ndPart
   -2logL(saturated) = 5304.99{ Phi(~1)p(~1) } Iteration 8         
   CPU Time for numerical optimization was 0.01 seconds.     
   -2logL { Phi(~1)p(~1) } = 5856.4354     
   Penalty { Phi(~1)p(~1) } = 0.0000000     
   Gradient { Phi(~1){ Phi(~1)p(~1) } VC Matrix: 100% done.  CPU Time to compute VC matrix was 0.01 seconds.     
 CPU Time to invert VC matrix was 0.01 seconds.     
 Gap Method for Num. of Estimated Parameters { Phi(~1)p(~1) } = 2         
 Numerical Threshold Method for Num. of Estimated Parameters { Phi(~1)p(~1) } = 2         
 Number of Estimated Parameters { Phi(~1)p(~1) } = 2         
   DEVIANCE { Phi(~1)p(~1) } = 551.43549               
 DEVIANCE Degrees of Freedom { Phi(~1)p(~1) } = 59         
   c-hat { Phi(~1)p(~1) } = 9.3463643     
   AIC { Phi(~1)p(~1) } = 5860.4354     
   AICc { Phi(~1)p(~1) } = 5860.4388     
   BIC { Phi(~1)p(~1) } = 5872.7655     
   Pearson Chisquare { Phi(~1)p(~1) } = 637.98609     
   Possible Encounter Histories { Phi(~1)p(~1) } = 254         
   Pearson Chisquare df { Phi(~1)p(~1) } = 245         
   Pearson chat { Phi(~1)p(~1) } = 2.6040249     
   Sum(Observed/Expected) { Phi(~1)p(~1) } = 124.52597     
   s-bar { Phi(~1)p(~1) } = -0.5241864   
   Fletcher chat { Phi(~1)p(~1) } = 5.4727833     

   CPU Time for the last procedure was 0.02 seconds.     
  INPUT --- proc stop;

     CPU Time in minutes for this job was 0.00

     Time Start = 18:44:35.417   Time End = 18:44:35.430

     Wall Clock Time in minutes for this job was 0.00
STOP NORMAL EXIT
Es gab 18 Warnungen (Anzeige mit warnings())
> # constant survival, time-dependent recapture
> Model.2 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.ct,p=p.time),output = FALSE,delete=T)
  The file is mark022.inp on unit 4.
  Welcome to MARK monah on machine DESKTOP-0F4CH6H in subdirectory "C:\Dokumente\Uni\Institut Zoologie\Wildbook\Data Anaylse\2010-2020_Liekwegen" running file "mark022.inp".
  INPUT --- proc title ;

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc chmatrix occasions= 8 groups= 1 etype= Live Nodes= 101
  INPUT --- ICMeans NoHist hist= 69 ;
  INPUT ---    time interval 0.21 2.87 0.13 2.85 0.18 3.86 0.12 ;
  INPUT ---    glabel(1)=Group 1;
   Number of unique encounter histories read was 69.
   Number of individual covariates read was 0.
   Time interval lengths vary and/or not equal to 1.

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc estimate link=Logit NOLOOP varest=2ndPart    ;
   Model is { Phi(~1)p(~time) }
  INPUT --- model={ Phi(~1)p(~time) };
  INPUT ---    group=1 Phi    rows=7 cols=7 Triang ;
  INPUT ---        1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 ;
  INPUT ---        1 1 1 1 ;
  INPUT ---        1 1 1 ;
  INPUT ---        1 1 ;
  INPUT ---        1 ;
  INPUT ---    group=1 p    rows=7 cols=7 Triang ;
  INPUT ---        2 3 4 5 6 7 8 ;
  INPUT ---        3 4 5 6 7 8 ;
  INPUT ---        4 5 6 7 8 ;
  INPUT ---        5 6 7 8 ;
  INPUT ---        6 7 8 ;
  INPUT ---        7 8 ;
  INPUT ---        8 ;
  INPUT ---    design matrix constraints=8 covariates=8;
  INPUT ---        1 0 0 0 0 0 0 0;
  INPUT ---        0 1 0 0 0 0 0 0;
  INPUT ---        0 1 1 0 0 0 0 0;
  INPUT ---        0 1 0 1 0 0 0 0;
  INPUT ---        0 1 0 0 1 0 0 0;
  INPUT ---        0 1 0 0 0 1 0 0;
  INPUT ---        0 1 0 0 0 0 1 0;
  INPUT ---        0 1 0 0 0 0 0 1;
  INPUT ---       blabel(1)=Phi:(Intercept);
  INPUT ---       blabel(2)=p:(Intercept);
  INPUT ---       blabel(3)=p:time2013.08;
  INPUT ---       blabel(4)=p:time2013.21;
  INPUT ---       blabel(5)=p:time2016.06;
  INPUT ---       blabel(6)=p:time2016.24;
  INPUT ---       blabel(7)=p:time2020.1;
  INPUT ---       blabel(8)=p:time2020.22;
  INPUT ---       rlabel(1)=Phi g1 c2010 a0 t2010;
  INPUT ---       rlabel(2)=p g1 c2010 a0.21 t2010.21;
  INPUT ---       rlabel(3)=p g1 c2010 a3.08 t2013.08;
  INPUT ---       rlabel(4)=p g1 c2010 a3.21 t2013.21;
  INPUT ---       rlabel(5)=p g1 c2010 a6.06 t2016.06;
  INPUT ---       rlabel(6)=p g1 c2010 a6.24 t2016.24;
  INPUT ---       rlabel(7)=p g1 c2010 a10.1 t2020.1;
  INPUT ---       rlabel(8)=p g1 c2010 a10.22 t2020.22;
   Model is { Phi(~1)p(~time) }
   Link Function Used is LOGIT       
   Variance Estimation Procedure Used is 2ndPart
   -2logL(saturate{ Phi(~1)p(~time) } Iteration 16                 
   CPU Time for numerical optimization was 0.01 seconds.     
   -2logL { Phi(~1)p(~time) } = 5478.4235     
   Penalty { Phi(~1)p(~time) } = 0.0000000     
   Gradient { Phi(~1)p(~time) }:
  0.3450809E-04   0.000000       0.000000       0.00{ Phi(~1)p(~time) } VC Matrix: 100% done.  CPU Time to compute VC matrix was 0.01 seconds.     
 CPU Time to invert VC matrix was 0.01 seconds.     
 Gap Method for Num. of Estimated Parameters { Phi(~1)p(~time) } = 8         
 Numerical Threshold Method for Num. of Estimated Parameters { Phi(~1)p(~time) } = 8         
 Number of Estimated Parameters { Phi(~1)p(~time) } = 8         
   DEVIANCE { Phi(~1)p(~time) } = 173.42362               
 DEVIANCE Degrees of Freedom { Phi(~1)p(~time) } = 53         
   c-hat { Phi(~1)p(~time) } = 3.2721439     
   AIC { Phi(~1)p(~time) } = 5494.4235     
   AICc { Phi(~1)p(~time) } = 5494.4646     
   BIC { Phi(~1)p(~time) } = 5543.7441     
   Pearson Chisquare { Phi(~1)p(~time) } = 336.54040     
   Possible Encounter Histories { Phi(~1)p(~time) } = 254         
   Pearson Chisquare df { Phi(~1)p(~time) } = 239         
   Pearson chat { Phi(~1)p(~time) } = 1.4081188     
   Sum(Observed/Expected) { Phi(~1)p(~time) } = 288.96754     
   s-bar { Phi(~1)p(~time) } = 0.1415690     
   Fletcher chat { Phi(~1)p(~time) } = 1.2334943     

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc stop;

     CPU Time in minutes for this job was 0.00

     Time Start = 18:44:35.818   Time End = 18:44:35.926

     Wall Clock Time in minutes for this job was 0.00
STOP NORMAL EXIT
Es gab 30 Warnungen (Anzeige mit warnings())
> # time-dependent survival, constant recapture
> Model.3 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.time,p=p.ct),output = FALSE,delete=T)
  The file is mark022.inp on unit 4.
  Welcome to MARK monah on machine DESKTOP-0F4CH6H in subdirectory "C:\Dokumente\Uni\Institut Zoologie\Wildbook\Data Anaylse\2010-2020_Liekwegen" running file "mark022.inp".
  INPUT --- proc title ;

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc chmatrix occasions= 8 groups= 1 etype= Live Nodes= 101
  INPUT --- ICMeans NoHist hist= 69 ;
  INPUT ---    time interval 0.21 2.87 0.13 2.85 0.18 3.86 0.12 ;
  INPUT ---    glabel(1)=Group 1;
   Number of unique encounter histories read was 69.
   Number of individual covariates read was 0.
   Time interval lengths vary and/or not equal to 1.

   CPU Time for the last procedure was 0.02 seconds.     
  INPUT --- proc estimate link=Logit NOLOOP varest=2ndPart    ;
   Model is { Phi(~time)p(~1) }
  INPUT --- model={ Phi(~time)p(~1) };
  INPUT ---    group=1 Phi    rows=7 cols=7 Triang ;
  INPUT ---        1 2 3 4 5 6 7 ;
  INPUT ---        2 3 4 5 6 7 ;
  INPUT ---        3 4 5 6 7 ;
  INPUT ---        4 5 6 7 ;
  INPUT ---        5 6 7 ;
  INPUT ---        6 7 ;
  INPUT ---        7 ;
  INPUT ---    group=1 p    rows=7 cols=7 Triang ;
  INPUT ---        8 8 8 8 8 8 8 ;
  INPUT ---        8 8 8 8 8 8 ;
  INPUT ---        8 8 8 8 8 ;
  INPUT ---        8 8 8 8 ;
  INPUT ---        8 8 8 ;
  INPUT ---        8 8 ;
  INPUT ---        8 ;
  INPUT ---    design matrix constraints=8 covariates=8;
  INPUT ---        1 0 0 0 0 0 0 0;
  INPUT ---        1 1 0 0 0 0 0 0;
  INPUT ---        1 0 1 0 0 0 0 0;
  INPUT ---        1 0 0 1 0 0 0 0;
  INPUT ---        1 0 0 0 1 0 0 0;
  INPUT ---        1 0 0 0 0 1 0 0;
  INPUT ---        1 0 0 0 0 0 1 0;
  INPUT ---        0 0 0 0 0 0 0 1;
  INPUT ---       blabel(1)=Phi:(Intercept);
  INPUT ---       blabel(2)=Phi:time2010.21;
  INPUT ---       blabel(3)=Phi:time2013.08;
  INPUT ---       blabel(4)=Phi:time2013.21;
  INPUT ---       blabel(5)=Phi:time2016.06;
  INPUT ---       blabel(6)=Phi:time2016.24;
  INPUT ---       blabel(7)=Phi:time2020.1;
  INPUT ---       blabel(8)=p:(Intercept);
  INPUT ---       rlabel(1)=Phi g1 c2010 a0 t2010;
  INPUT ---       rlabel(2)=Phi g1 c2010 a0.21 t2010.21;
  INPUT ---       rlabel(3)=Phi g1 c2010 a3.08 t2013.08;
  INPUT ---       rlabel(4)=Phi g1 c2010 a3.21 t2013.21;
  INPUT ---       rlabel(5)=Phi g1 c2010 a6.06 t2016.06;
  INPUT ---       rlabel(6)=Phi g1 c2010 a6.24 t2016.24;
  INPUT ---       rlabel(7)=Phi g1 c2010 a10.1 t2020.1;
  INPUT ---       rlabel(8)=p g1 c2010 a0.21 t2010.21;
   Model is { Phi(~time)p(~1) }
   Link Function Used is LOGIT       
   Variance Estimation Procedure Used is 2ndPart
   -2logL(sat{ Phi(~time)p(~1) } Iteration 21                     
   CPU Time for numerical optimization was 0.01 seconds.     
   -2logL { Phi(~time)p(~1) } = 5465.0139     
   Penalty { Phi(~time)p(~1) } = 0.0000000     
   Gradient { Phi(~time)p(~1) }:
   0.000000     -0.2393829E-04   0.000000       0.00{ Phi(~time)p(~1) } VC Matrix: 100% done.  CPU Time to compute VC matrix was 0.03 seconds.     
 CPU Time to invert VC matrix was 0.01 seconds.     
 Gap Method for Num. of Estimated Parameters { Phi(~time)p(~1) } = 8         
 Numerical Threshold Method for Num. of Estimated Parameters { Phi(~time)p(~1) } = 8         
 Number of Estimated Parameters { Phi(~time)p(~1) } = 8         
   DEVIANCE { Phi(~time)p(~1) } = 160.01401               
 DEVIANCE Degrees of Freedom { Phi(~time)p(~1) } = 53         
   c-hat { Phi(~time)p(~1) } = 3.0191322     
   AIC { Phi(~time)p(~1) } = 5481.0139     
   AICc { Phi(~time)p(~1) } = 5481.0549     
   BIC { Phi(~time)p(~1) } = 5530.3345     
   Pearson Chisquare { Phi(~time)p(~1) } = 443.00712     
   Possible Encounter Histories { Phi(~time)p(~1) } = 254         
   Pearson Chisquare df { Phi(~time)p(~1) } = 239         
   Pearson chat { Phi(~time)p(~1) } = 1.8535863     
   Sum(Observed/Expected) { Phi(~time)p(~1) } = 404.85801     
   s-bar { Phi(~time)p(~1) } = 0.6107612     
   Fletcher chat { Phi(~time)p(~1) } = 1.1507518     

   CPU Time for the last procedure was 0.03 seconds.     
  INPUT --- proc stop;

     CPU Time in minutes for this job was 0.00

     Time Start = 18:44:36.091   Time End = 18:44:36.208

     Wall Clock Time in minutes for this job was 0.00
STOP NORMAL EXIT
Es gab 30 Warnungen (Anzeige mit warnings())
> # time-dependent survival, time-dependent recapture
> Model.4 = mark(hw.proc,hw.ddl,model.parameters=list(Phi=Phi.time,p=p.time),output = FALSE,delete=T)
  The file is mark022.inp on unit 4.
  Welcome to MARK monah on machine DESKTOP-0F4CH6H in subdirectory "C:\Dokumente\Uni\Institut Zoologie\Wildbook\Data Anaylse\2010-2020_Liekwegen" running file "mark022.inp".
  INPUT --- proc title ;

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc chmatrix occasions= 8 groups= 1 etype= Live Nodes= 101
  INPUT --- ICMeans NoHist hist= 69 ;
  INPUT ---    time interval 0.21 2.87 0.13 2.85 0.18 3.86 0.12 ;
  INPUT ---    glabel(1)=Group 1;
   Number of unique encounter histories read was 69.
   Number of individual covariates read was 0.
   Time interval lengths vary and/or not equal to 1.

   CPU Time for the last procedure was 0.01 seconds.     
  INPUT --- proc estimate link=Logit NOLOOP varest=2ndPart    ;
   Model is { Phi(~time)p(~time) }
  INPUT --- model={ Phi(~time)p(~time) };
  INPUT ---    group=1 Phi    rows=7 cols=7 Triang ;
  INPUT ---        1 2 3 4 5 6 7 ;
  INPUT ---        2 3 4 5 6 7 ;
  INPUT ---        3 4 5 6 7 ;
  INPUT ---        4 5 6 7 ;
  INPUT ---        5 6 7 ;
  INPUT ---        6 7 ;
  INPUT ---        7 ;
  INPUT ---    group=1 p    rows=7 cols=7 Triang ;
  INPUT ---        8 9 10 11 12 13 14 ;
  INPUT ---        9 10 11 12 13 14 ;
  INPUT ---        10 11 12 13 14 ;
  INPUT ---        11 12 13 14 ;
  INPUT ---        12 13 14 ;
  INPUT ---        13 14 ;
  INPUT ---        14 ;
  INPUT ---    design matrix constraints=14 covariates=14;
  INPUT ---        1 0 0 0 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 1 0 0 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 1 0 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 1 0 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 0 1 0 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 0 0 1 0 0 0 0 0 0 0 0;
  INPUT ---        1 0 0 0 0 0 1 0 0 0 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 1 0 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 1 0 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 1 0 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 1 0 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 0 1 0;
  INPUT ---        0 0 0 0 0 0 0 1 0 0 0 0 0 1;
  INPUT ---       blabel(1)=Phi:(Intercept);
  INPUT ---       blabel(2)=Phi:time2010.21;
  INPUT ---       blabel(3)=Phi:time2013.08;
  INPUT ---       blabel(4)=Phi:time2013.21;
  INPUT ---       blabel(5)=Phi:time2016.06;
  INPUT ---       blabel(6)=Phi:time2016.24;
  INPUT ---       blabel(7)=Phi:time2020.1;
  INPUT ---       blabel(8)=p:(Intercept);
  INPUT ---       blabel(9)=p:time2013.08;
  INPUT ---       blabel(10)=p:time2013.21;
  INPUT ---       blabel(11)=p:time2016.06;
  INPUT ---       blabel(12)=p:time2016.24;
  INPUT ---       blabel(13)=p:time2020.1;
  INPUT ---       blabel(14)=p:time2020.22;
  INPUT ---       rlabel(1)=Phi g1 c2010 a0 t2010;
  INPUT ---       rlabel(2)=Phi g1 c2010 a0.21 t2010.21;
  INPUT ---       rlabel(3)=Phi g1 c2010 a3.08 t2013.08;
  INPUT ---       rlabel(4)=Phi g1 c2010 a3.21 t2013.21;
  INPUT ---       rlabel(5)=Phi g1 c2010 a6.06 t2016.06;
  INPUT ---       rlabel(6)=Phi g1 c2010 a6.24 t2016.24;
  INPUT ---       rlabel(7)=Phi g1 c2010 a10.1 t2020.1;
  INPUT ---       rlabel(8)=p g1 c2010 a0.21 t2010.21;
  INPUT ---       rlabel(9)=p g1 c2010 a3.08 t2013.08;
  INPUT ---       rlabel(10)=p g1 c2010 a3.21 t2013.21;
  INPUT ---       rlabel(11)=p g1 c2010 a6.06 t2016.06;
  INPUT ---       rlabel(12)=p g1 c2010 a6.24 t2016.24;
  INPUT ---       rlabel(13)=p g1 c2010 a10.1 t2020.1;
  INPUT ---       rlabel(14)=p g1 c2010 a10.22 t2020.22;
   Model is { Phi(~time)p(~time) }
   Link Function Used is LOGIT       
   Variance Estimatio{ Phi(~time)p(~time) } Iteration 60                                                             
   CPU Time for numerical optimization was 0.08 seconds.     
   -2logL { Phi(~time)p(~time) } = 5420.4504     
   Penalty { Phi(~time)p(~time) } = 0.0000000     
   Gradient { Phi(~time)p(~time) }:
 -0.5957602E-03  0.3383968E-04 -0.1091318E-03 -0.2270930E-03   0.000000   
 { Phi(~time)p(~time) } VC Matrix: 100% done.  CPU Time to compute VC matrix was 0.03 seconds.                                         
 CPU Time to invert VC matrix was 0.01 seconds.     
 Gap Method for Num. of Estimated Parameters { Phi(~time)p(~time) } = 12         
 Numerical Threshold Method for Num. of Estimated Parameters { Phi(~time)p(~time) } = 12         
 Number of Estimated Parameters { Phi(~time)p(~time) } = 12         
   DEVIANCE { Phi(~time)p(~time) } = 115.45050               
 DEVIANCE Degrees of Freedom { Phi(~time)p(~time) } = 49         
   c-hat { Phi(~time)p(~time) } = 2.3561326     
   AIC { Phi(~time)p(~time) } = 5444.4504     
   AICc { Phi(~time)p(~time) } = 5444.5394     
   BIC { Phi(~time)p(~time) } = 5518.4313     
   Pearson Chisquare { Phi(~time)p(~time) } = 219.02606     
   Possible Encounter Histories { Phi(~time)p(~time) } = 254         
   Pearson Chisquare df { Phi(~time)p(~time) } = 235         
   Pearson chat { Phi(~time)p(~time) } = 0.9320258     
   Sum(Observed/Expected) { Phi(~time)p(~time) } = 225.45936     
   s-bar { Phi(~time)p(~time) } = -0.1155492   
   Fletcher chat { Phi(~time)p(~time) } = 1.0537904     
 Beta number 5 is a singular value.

   CPU Time for the last procedure was 0.11 seconds.     
  INPUT --- proc stop;

     CPU Time in minutes for this job was 0.00

     Time Start = 18:44:36.454   Time End = 18:44:36.707

     Wall Clock Time in minutes for this job was 0.00
STOP NORMAL EXIT

Note: only 12 parameters counted of 14 specified parameters

AICc and parameter count have been adjusted upward

Es gab 42 Warnungen (Anzeige mit warnings())
>


The summary ended up to be exactly the same as before:
Code: Select all
> summary(Model.1)$AICc
[1] 5860.439
> summary(Model.2)$AICc
[1] 5494.465
> summary(Model.3)$AICc
[1] 5481.055
> summary(Model.4)$AICc
[1] 5448.57
>


Code: Select all
> # get PIM table
> PIMS(Model.4, "Phi")
group = Group 1
        2010 2010.21 2013.08 2013.21 2016.06 2016.24 2020.1
2010       1       2       3       4       5       6      7
2010.21            2       3       4       5       6      7
2013.08                    3       4       5       6      7
2013.21                            4       5       6      7
2016.06                                    5       6      7
2016.24                                            6      7
2020.1                                                    7
> PIMS(Model.4,"p")
group = Group 1
        2010.21 2013.08 2013.21 2016.06 2016.24 2020.1 2020.22
2010          8       9      10      11      12     13      14
2010.21               9      10      11      12     13      14
2013.08                      10      11      12     13      14
2013.21                              11      12     13      14
2016.06                                      12     13      14
2016.24                                             13      14
2020.1                                                      14
> #dimensions of design matrix
> dim(Model.4$design.matrix)
[1] 14 14
>
> Model.4$design.matrix[1:7,1:7]
                            Phi:(Intercept) Phi:time2010.21 Phi:time2013.08 Phi:time2013.21
Phi g1 c2010 a0 t2010       "1"             "0"             "0"             "0"           
Phi g1 c2010 a0.21 t2010.21 "1"             "1"             "0"             "0"           
Phi g1 c2010 a3.08 t2013.08 "1"             "0"             "1"             "0"           
Phi g1 c2010 a3.21 t2013.21 "1"             "0"             "0"             "1"           
Phi g1 c2010 a6.06 t2016.06 "1"             "0"             "0"             "0"           
Phi g1 c2010 a6.24 t2016.24 "1"             "0"             "0"             "0"           
Phi g1 c2010 a10.1 t2020.1  "1"             "0"             "0"             "0"           
                            Phi:time2016.06 Phi:time2016.24 Phi:time2020.1
Phi g1 c2010 a0 t2010       "0"             "0"             "0"           
Phi g1 c2010 a0.21 t2010.21 "0"             "0"             "0"           
Phi g1 c2010 a3.08 t2013.08 "0"             "0"             "0"           
Phi g1 c2010 a3.21 t2013.21 "0"             "0"             "0"           
Phi g1 c2010 a6.06 t2016.06 "1"             "0"             "0"           
Phi g1 c2010 a6.24 t2016.24 "0"             "1"             "0"           
Phi g1 c2010 a10.1 t2020.1  "0"             "0"             "1"           
> Model.4$results$beta
                  estimate          se           lcl          ucl
Phi:(Intercept)  0.0244920   0.5051895    -0.9656794    1.0146635
Phi:time2010.21  0.8036567   0.5311985    -0.2374924    1.8448057
Phi:time2013.08 -1.2371178   0.6926303    -2.5946733    0.1204377
Phi:time2013.21  1.1501377   0.5209135     0.1291473    2.1711281
Phi:time2016.06  7.6722362 733.0930500 -1429.1902000 1444.5346000
Phi:time2016.24 -0.2425850   0.5180859    -1.2580334    0.7728635
Phi:time2020.1  -0.7469449 259.3873400  -509.1461400  507.6522500
p:(Intercept)    0.2916346   0.1500665    -0.0024956    0.5857649
p:time2013.08    0.9746732   0.2167976     0.5497499    1.3995965
p:time2013.21    0.2753706   0.2098635    -0.1359618    0.6867030
p:time2016.06    0.1030587   0.2489796    -0.3849414    0.5910588
p:time2016.24   -1.4342258   0.1959169    -1.8182228   -1.0502287
p:time2020.1     0.1103995   0.5759433    -1.0184493    1.2392483
p:time2020.22   -1.0878934  30.4034110   -60.6785800   58.5027930
> Model.4$results$real
                             estimate         se           lcl       ucl fixed note
Phi g1 c2010 a0 t2010       0.5061227  0.1262784  2.757425e-01 0.7339318           
Phi g1 c2010 a0.21 t2010.21 0.6959633  0.0124759  6.709725e-01 0.7198486           
Phi g1 c2010 a3.08 t2013.08 0.2292368  0.0837208  1.051429e-01 0.4294961           
Phi g1 c2010 a3.21 t2013.21 0.7639808  0.0229039  7.161953e-01 0.8059011           
Phi g1 c2010 a6.06 t2016.06 0.9995459  0.3327498 1.224422e-305 1.0000000           
Phi g1 c2010 a6.24 t2016.24 0.4456919  0.0283832  3.909612e-01 0.5017719           
Phi g1 c2010 a10.1 t2020.1  0.3268531 57.0703500 7.791593e-222 1.0000000           
p g1 c2010 a0.21 t2010.21   0.5723963  0.0367301  4.993761e-01 0.6423928           
p g1 c2010 a3.08 t2013.08   0.7801101  0.0268397  7.230491e-01 0.8282078           
p g1 c2010 a3.21 t2013.21   0.6380719  0.0338798  5.694140e-01 0.7015207           
p g1 c2010 a6.06 t2016.06   0.5974120  0.0477830  5.013236e-01 0.6865614           
p g1 c2010 a6.24 t2016.24   0.2418449  0.0230938  1.994949e-01 0.2899292           
p g1 c2010 a10.1 t2020.1    0.5991763  0.1335431  3.345176e-01 0.8163620           
p g1 c2010 a10.22 t2020.22  0.3108264  6.5127380  5.951052e-27 1.0000000           
> #display estimates for this model and real parameter estimates.
> Model.4$results$beta
                  estimate          se           lcl          ucl
Phi:(Intercept)  0.0244920   0.5051895    -0.9656794    1.0146635
Phi:time2010.21  0.8036567   0.5311985    -0.2374924    1.8448057
Phi:time2013.08 -1.2371178   0.6926303    -2.5946733    0.1204377
Phi:time2013.21  1.1501377   0.5209135     0.1291473    2.1711281
Phi:time2016.06  7.6722362 733.0930500 -1429.1902000 1444.5346000
Phi:time2016.24 -0.2425850   0.5180859    -1.2580334    0.7728635
Phi:time2020.1  -0.7469449 259.3873400  -509.1461400  507.6522500
p:(Intercept)    0.2916346   0.1500665    -0.0024956    0.5857649
p:time2013.08    0.9746732   0.2167976     0.5497499    1.3995965
p:time2013.21    0.2753706   0.2098635    -0.1359618    0.6867030
p:time2016.06    0.1030587   0.2489796    -0.3849414    0.5910588
p:time2016.24   -1.4342258   0.1959169    -1.8182228   -1.0502287
p:time2020.1     0.1103995   0.5759433    -1.0184493    1.2392483
p:time2020.22   -1.0878934  30.4034110   -60.6785800   58.5027930
> Model.4$results$real
                             estimate         se           lcl       ucl fixed note
Phi g1 c2010 a0 t2010       0.5061227  0.1262784  2.757425e-01 0.7339318           
Phi g1 c2010 a0.21 t2010.21 0.6959633  0.0124759  6.709725e-01 0.7198486           
Phi g1 c2010 a3.08 t2013.08 0.2292368  0.0837208  1.051429e-01 0.4294961           
Phi g1 c2010 a3.21 t2013.21 0.7639808  0.0229039  7.161953e-01 0.8059011           
Phi g1 c2010 a6.06 t2016.06 0.9995459  0.3327498 1.224422e-305 1.0000000           
Phi g1 c2010 a6.24 t2016.24 0.4456919  0.0283832  3.909612e-01 0.5017719           
Phi g1 c2010 a10.1 t2020.1  0.3268531 57.0703500 7.791593e-222 1.0000000           
p g1 c2010 a0.21 t2010.21   0.5723963  0.0367301  4.993761e-01 0.6423928           
p g1 c2010 a3.08 t2013.08   0.7801101  0.0268397  7.230491e-01 0.8282078           
p g1 c2010 a3.21 t2013.21   0.6380719  0.0338798  5.694140e-01 0.7015207           
p g1 c2010 a6.06 t2016.06   0.5974120  0.0477830  5.013236e-01 0.6865614           
p g1 c2010 a6.24 t2016.24   0.2418449  0.0230938  1.994949e-01 0.2899292           
p g1 c2010 a10.1 t2020.1    0.5991763  0.1335431  3.345176e-01 0.8163620           
p g1 c2010 a10.22 t2020.22  0.3108264  6.5127380  5.951052e-27 1.0000000


With the weird Phi g1 c2010 a6.06 t2016.06 0.9995459 0.3327498 1.224422e-305 1.0000000.

Have I made a mistake? Or do you have another suggestion?
I would appreciate it very much if you could help me again.
Toad_aly
 
Posts: 3
Joined: Wed Apr 27, 2022 7:29 pm

Re: Phi estimate of nearly 1 with lcl 0 and ucl 1

Postby jlaake » Mon May 02, 2022 11:45 am

Two posts below your post is one that discusses this exact problem. When parameters are at boundary the confidence interval is not reliable. Because you are not using individual covariates you can use the sun link. Read that post and look at help for make.design.data.
jlaake
 
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