Rapport Capture-Marquage-R

===================

La méthode Capture-Marque-Recapture, abrégée CMR est utilisé pour estimer le taux de survie et de capture des populations étudiées.

Librarie & import des données

Librarie

#### Pour le formatage des données
#install.packages("tidyverse", dependencies = TRUE)
library(tidyverse)

## Warning: package 'ggplot2' was built under R version 4.3.2

#install.packages("tidyr")
library(tidyr)
#install.packages("dplyr")
library(dplyr)
#install.packages("xtable")
library(xtable)
#install.packages("RMark")
library(kableExtra)
#install.packages("webshot")
library(webshot)
# Install PhantomJS
#webshot::install_phantomjs()

#### Pour le formatage spécifique à RMarkdown
#install.packages("knitr")
library(knitr)

#### Pour la CMR
#install.packages("RMark")
library(RMark)
#install.packages("R2ucare")
library(R2ucare)

#### Pour les statistiques
#install.packages("rstatix")
library(rstatix)
#install.packages("car")
library(car)
#install.packages("rcompanion")
library(rcompanion)

#### Pour les représentation graphiques
#install.packages("ggplot2")
library(ggplot2)
#install.packages("ggpubr")
library(ggpubr)

Import et visualisation des données de CMR des colonnies 1 et 2

#### Import
col1.2 <- import.chdata("/Users/Lj/Desktop/Master_EEE_S2/EFE - Ecologie fonctionnelle et évolutive/RAPPORT_Annalyse_de_données_CMR/Data/Devoir_EFE_colony.txt", header=T, field.types=c("f"))

#### Visualisation brute
head(col1.2) ; tail(col1.2)

str(col1.2)

## 'data.frame':    128 obs. of  2 variables:
##  $ ch    : chr  "11100000" "11100000" "11001000" "11000000" ...
##  $ colony: Factor w/ 2 levels "1","2": 1 1 1 1 1 1 1 1 1 1 ...

summary(col1.2)

##       ch            colony
##  Length:128         1:35  
##  Class :character   2:93  
##  Mode  :character

Méthode Co…-J…-S… (CJS)

Process avec le modèle CJS

#### Traitement des données d'analyse de CMR, préparation pour l'utilisation du modèle CJS  
colonie_data.process <- process.data(col1.2, model="CJS", groups="colony")

#### Résumé des données préparées pour le modèle CJS
summary(colonie_data.process)

##                  Length Class      Mode     
## data             3      data.frame list     
## model            1      -none-     character
## mixtures         1      -none-     numeric  
## freq             2      data.frame list     
## nocc             1      -none-     numeric  
## nocc.secondary   0      -none-     NULL     
## time.intervals   7      -none-     numeric  
## begin.time       1      -none-     numeric  
## age.unit         1      -none-     numeric  
## initial.ages     2      -none-     numeric  
## group.covariates 1      data.frame list     
## nstrata          1      -none-     numeric  
## strata.labels    0      -none-     NULL     
## counts           0      -none-     NULL     
## reverse          1      -none-     logical  
## areas            0      -none-     NULL     
## events           0      -none-     NULL

#### Conception des "design data", données pour la modélisation
colonie_data.ddl <- 
make.design.data(colonie_data.process)
colonie_data.ddl

## $Phi
##    par.index model.index group cohort age time occ.cohort Cohort Age Time
## 1          1           1     1      1   0    1          1      0   0    0
## 2          2           2     1      1   1    2          1      0   1    1
## 3          3           3     1      1   2    3          1      0   2    2
## 4          4           4     1      1   3    4          1      0   3    3
## 5          5           5     1      1   4    5          1      0   4    4
## 6          6           6     1      1   5    6          1      0   5    5
## 7          7           7     1      1   6    7          1      0   6    6
## 8          8           8     1      2   0    2          2      1   0    1
## 9          9           9     1      2   1    3          2      1   1    2
## 10        10          10     1      2   2    4          2      1   2    3
## 11        11          11     1      2   3    5          2      1   3    4
## 12        12          12     1      2   4    6          2      1   4    5
## 13        13          13     1      2   5    7          2      1   5    6
## 14        14          14     1      3   0    3          3      2   0    2
## 15        15          15     1      3   1    4          3      2   1    3
## 16        16          16     1      3   2    5          3      2   2    4
## 17        17          17     1      3   3    6          3      2   3    5
## 18        18          18     1      3   4    7          3      2   4    6
## 19        19          19     1      4   0    4          4      3   0    3
## 20        20          20     1      4   1    5          4      3   1    4
## 21        21          21     1      4   2    6          4      3   2    5
## 22        22          22     1      4   3    7          4      3   3    6
## 23        23          23     1      5   0    5          5      4   0    4
## 24        24          24     1      5   1    6          5      4   1    5
## 25        25          25     1      5   2    7          5      4   2    6
## 26        26          26     1      6   0    6          6      5   0    5
## 27        27          27     1      6   1    7          6      5   1    6
## 28        28          28     1      7   0    7          7      6   0    6
## 29        29          29     2      1   0    1          1      0   0    0
## 30        30          30     2      1   1    2          1      0   1    1
## 31        31          31     2      1   2    3          1      0   2    2
## 32        32          32     2      1   3    4          1      0   3    3
## 33        33          33     2      1   4    5          1      0   4    4
## 34        34          34     2      1   5    6          1      0   5    5
## 35        35          35     2      1   6    7          1      0   6    6
## 36        36          36     2      2   0    2          2      1   0    1
## 37        37          37     2      2   1    3          2      1   1    2
## 38        38          38     2      2   2    4          2      1   2    3
## 39        39          39     2      2   3    5          2      1   3    4
## 40        40          40     2      2   4    6          2      1   4    5
## 41        41          41     2      2   5    7          2      1   5    6
## 42        42          42     2      3   0    3          3      2   0    2
## 43        43          43     2      3   1    4          3      2   1    3
## 44        44          44     2      3   2    5          3      2   2    4
## 45        45          45     2      3   3    6          3      2   3    5
## 46        46          46     2      3   4    7          3      2   4    6
## 47        47          47     2      4   0    4          4      3   0    3
## 48        48          48     2      4   1    5          4      3   1    4
## 49        49          49     2      4   2    6          4      3   2    5
## 50        50          50     2      4   3    7          4      3   3    6
## 51        51          51     2      5   0    5          5      4   0    4
## 52        52          52     2      5   1    6          5      4   1    5
## 53        53          53     2      5   2    7          5      4   2    6
## 54        54          54     2      6   0    6          6      5   0    5
## 55        55          55     2      6   1    7          6      5   1    6
## 56        56          56     2      7   0    7          7      6   0    6
##    colony
## 1       1
## 2       1
## 3       1
## 4       1
## 5       1
## 6       1
## 7       1
## 8       1
## 9       1
## 10      1
## 11      1
## 12      1
## 13      1
## 14      1
## 15      1
## 16      1
## 17      1
## 18      1
## 19      1
## 20      1
## 21      1
## 22      1
## 23      1
## 24      1
## 25      1
## 26      1
## 27      1
## 28      1
## 29      2
## 30      2
## 31      2
## 32      2
## 33      2
## 34      2
## 35      2
## 36      2
## 37      2
## 38      2
## 39      2
## 40      2
## 41      2
## 42      2
## 43      2
## 44      2
## 45      2
## 46      2
## 47      2
## 48      2
## 49      2
## 50      2
## 51      2
## 52      2
## 53      2
## 54      2
## 55      2
## 56      2
## 
## $p
##    par.index model.index group cohort age time occ.cohort Cohort Age Time
## 1          1          57     1      1   1    2          1      0   1    0
## 2          2          58     1      1   2    3          1      0   2    1
## 3          3          59     1      1   3    4          1      0   3    2
## 4          4          60     1      1   4    5          1      0   4    3
## 5          5          61     1      1   5    6          1      0   5    4
## 6          6          62     1      1   6    7          1      0   6    5
## 7          7          63     1      1   7    8          1      0   7    6
## 8          8          64     1      2   1    3          2      1   1    1
## 9          9          65     1      2   2    4          2      1   2    2
## 10        10          66     1      2   3    5          2      1   3    3
## 11        11          67     1      2   4    6          2      1   4    4
## 12        12          68     1      2   5    7          2      1   5    5
## 13        13          69     1      2   6    8          2      1   6    6
## 14        14          70     1      3   1    4          3      2   1    2
## 15        15          71     1      3   2    5          3      2   2    3
## 16        16          72     1      3   3    6          3      2   3    4
## 17        17          73     1      3   4    7          3      2   4    5
## 18        18          74     1      3   5    8          3      2   5    6
## 19        19          75     1      4   1    5          4      3   1    3
## 20        20          76     1      4   2    6          4      3   2    4
## 21        21          77     1      4   3    7          4      3   3    5
## 22        22          78     1      4   4    8          4      3   4    6
## 23        23          79     1      5   1    6          5      4   1    4
## 24        24          80     1      5   2    7          5      4   2    5
## 25        25          81     1      5   3    8          5      4   3    6
## 26        26          82     1      6   1    7          6      5   1    5
## 27        27          83     1      6   2    8          6      5   2    6
## 28        28          84     1      7   1    8          7      6   1    6
## 29        29          85     2      1   1    2          1      0   1    0
## 30        30          86     2      1   2    3          1      0   2    1
## 31        31          87     2      1   3    4          1      0   3    2
## 32        32          88     2      1   4    5          1      0   4    3
## 33        33          89     2      1   5    6          1      0   5    4
## 34        34          90     2      1   6    7          1      0   6    5
## 35        35          91     2      1   7    8          1      0   7    6
## 36        36          92     2      2   1    3          2      1   1    1
## 37        37          93     2      2   2    4          2      1   2    2
## 38        38          94     2      2   3    5          2      1   3    3
## 39        39          95     2      2   4    6          2      1   4    4
## 40        40          96     2      2   5    7          2      1   5    5
## 41        41          97     2      2   6    8          2      1   6    6
## 42        42          98     2      3   1    4          3      2   1    2
## 43        43          99     2      3   2    5          3      2   2    3
## 44        44         100     2      3   3    6          3      2   3    4
## 45        45         101     2      3   4    7          3      2   4    5
## 46        46         102     2      3   5    8          3      2   5    6
## 47        47         103     2      4   1    5          4      3   1    3
## 48        48         104     2      4   2    6          4      3   2    4
## 49        49         105     2      4   3    7          4      3   3    5
## 50        50         106     2      4   4    8          4      3   4    6
## 51        51         107     2      5   1    6          5      4   1    4
## 52        52         108     2      5   2    7          5      4   2    5
## 53        53         109     2      5   3    8          5      4   3    6
## 54        54         110     2      6   1    7          6      5   1    5
## 55        55         111     2      6   2    8          6      5   2    6
## 56        56         112     2      7   1    8          7      6   1    6
##    colony
## 1       1
## 2       1
## 3       1
## 4       1
## 5       1
## 6       1
## 7       1
## 8       1
## 9       1
## 10      1
## 11      1
## 12      1
## 13      1
## 14      1
## 15      1
## 16      1
## 17      1
## 18      1
## 19      1
## 20      1
## 21      1
## 22      1
## 23      1
## 24      1
## 25      1
## 26      1
## 27      1
## 28      1
## 29      2
## 30      2
## 31      2
## 32      2
## 33      2
## 34      2
## 35      2
## 36      2
## 37      2
## 38      2
## 39      2
## 40      2
## 41      2
## 42      2
## 43      2
## 44      2
## 45      2
## 46      2
## 47      2
## 48      2
## 49      2
## 50      2
## 51      2
## 52      2
## 53      2
## 54      2
## 55      2
## 56      2
## 
## $pimtypes
## $pimtypes$Phi
## $pimtypes$Phi$pim.type
## [1] "all"
## 
## 
## $pimtypes$p
## $pimtypes$p$pim.type
## [1] "all"

#### Exploration du "design data" créé  
colonie_data.ddl$pimtypes

## $Phi
## $Phi$pim.type
## [1] "all"
## 
## 
## $p
## $p$pim.type
## [1] "all"

class(colonie_data.ddl$Phi)

## [1] "data.frame"

head(colonie_data.ddl$Phi)

Les modèles à comparer

Il faut toujours calculer le modèle du plus complexe au plus simple.

Partie ### 1

Phi(colonyt) p(.)
p(t)
p(colonie)
p(temps + colonie)
p(temps colonie)

Partie ### 2

Phi(.) p(.)
Phi(temps) p(.)
Phi(colonie) p(.)
Phi(temps + colonie) p(.)
Phi(temps * colonie) p(.)

1. Commencer par le modèle Phi() le plus complexe pour choisir le modèle p()

Modèle 1 - Effet du temps et de la colonie sur la survie (M. le plus simple)

#modèle phi(t*colony)p(.):
  
# specifier les formules
p.constant <- list(formula = ~1)  

Phi.time.colony <- list(formula = ~time*colony)

mod_phitc_pc <- mark(colonie_data.process, colonie_data.ddl, model.parameters = list(Phi = Phi.time.colony, p = p.constant))

## 
## Output summary for CJS model
## Name : Phi(~time * colony)p(~1) 
## 
## Npar :  15
## -2lnL:  353.9155
## AICc :  386.4962
## 
## Beta
##                     estimate        se         lcl        ucl
## Phi:(Intercept)    1.2070034 1.2744529  -1.2909243  3.7049311
## Phi:time2         -0.9779385 1.5339857  -3.9845505  2.0286735
## Phi:time3         -1.1893652 1.5902422  -4.3062400  1.9275096
## Phi:time4         -1.4147120 1.5273360  -4.4082905  1.5788666
## Phi:time5         -0.7913678 1.6399046  -4.0055809  2.4228453
## Phi:time6          0.9132993 3.4316443  -5.8127236  7.6393222
## Phi:time7         -2.3111286 1.5326346  -5.3150924  0.6928352
## Phi:colony2        2.8141120 6.3862767  -9.7029907 15.3312150
## Phi:time2:colony2 -2.0453372 6.6050831 -14.9913000 10.9006260
## Phi:time3:colony2 -1.8446664 6.4812431 -14.5479030 10.8585700
## Phi:time4:colony2 -1.0608478 6.4756873 -13.7531950 11.6314990
## Phi:time5:colony2 -2.1010278 6.4910165 -14.8234200 10.6213650
## Phi:time6:colony2 -3.7172660 7.2023979 -17.8339660 10.3994340
## Phi:time7:colony2 -1.7795010 6.4522797 -14.4259690 10.8669680
## p:(Intercept)      1.0702370 0.2539345   0.5725254  1.5679486
## 
## 
## Real Parameter Phi
## Group:colony1 
##           1         2         3         4         5         6         7
## 1 0.7697683 0.5570171 0.5044094 0.4482587 0.6024384 0.8928609 0.2489678
## 2           0.5570171 0.5044094 0.4482587 0.6024384 0.8928609 0.2489678
## 3                     0.5044094 0.4482587 0.6024384 0.8928609 0.2489678
## 4                               0.4482587 0.6024384 0.8928609 0.2489678
## 5                                         0.6024384 0.8928609 0.2489678
## 6                                                   0.8928609 0.2489678
## 7                                                             0.2489678
## 
## Group:colony2 
##          1         2         3         4         5         6         7
## 1 0.982383 0.7306336 0.7285115 0.8242709 0.7556026 0.7715614 0.4826284
## 2          0.7306336 0.7285115 0.8242709 0.7556026 0.7715614 0.4826284
## 3                    0.7285115 0.8242709 0.7556026 0.7715614 0.4826284
## 4                              0.8242709 0.7556026 0.7715614 0.4826284
## 5                                        0.7556026 0.7715614 0.4826284
## 6                                                  0.7715614 0.4826284
## 7                                                            0.4826284
## 
## 
## Real Parameter p
## Group:colony1 
##          2        3        4        5        6        7        8
## 1 0.744642 0.744642 0.744642 0.744642 0.744642 0.744642 0.744642
## 2          0.744642 0.744642 0.744642 0.744642 0.744642 0.744642
## 3                   0.744642 0.744642 0.744642 0.744642 0.744642
## 4                            0.744642 0.744642 0.744642 0.744642
## 5                                     0.744642 0.744642 0.744642
## 6                                              0.744642 0.744642
## 7                                                       0.744642
## 
## Group:colony2 
##          2        3        4        5        6        7        8
## 1 0.744642 0.744642 0.744642 0.744642 0.744642 0.744642 0.744642
## 2          0.744642 0.744642 0.744642 0.744642 0.744642 0.744642
## 3                   0.744642 0.744642 0.744642 0.744642 0.744642
## 4                            0.744642 0.744642 0.744642 0.744642
## 5                                     0.744642 0.744642 0.744642
## 6                                              0.744642 0.744642
## 7                                                       0.744642

####  ~~~~~~  Les AIC, nombres de paramètres par modèle  ~~~~~~  ####

#mod_phitc_pc$results # TOUS LES RESULTATS

cat("Le modèle calculé est :", mod_phitc_pc$model.name, "\n")

## Le modèle calculé est : Phi(~time * colony)p(~1)

cat("Le modèle a", mod_phitc_pc$results[["npar"]][1], "paramètres", "\n")

## Le modèle a 15 paramètres

cat("-2lnL :", mod_phitc_pc$results[["lnl"]][1], "\n")

## -2lnL : 353.9155

cat("Le modèle a", mod_phitc_pc$results[["AICc"]][1], "pour AIC", "\n")

## Le modèle a 386.4962 pour AIC

Phi(~time * colony)p(~1) :
• Npar : 15
• -2lnL: 353.9155
• AICc : 386.4962

Modèle 2

p.time <- list(formula=~time)  

Phi.time.colony <- list(formula=~time*colony)

mod_phitc_pc <- mark(colonie_data.process,colonie_data.ddl,
                model.parameters=list(Phi = Phi.time.colony, p = p.time))

## 
## Note: only 20 parameters counted of 21 specified parameters

## AICc and parameter count have been adjusted upward

## 
## Output summary for CJS model
## Name : Phi(~time * colony)p(~time) 
## 
## Npar :  21  (unadjusted=20)
## -2lnL:  346.7694
## AICc :  393.9027  (unadjusted=391.41029)
## 
## Beta
##                     estimate          se           lcl         ucl
## Phi:(Intercept)    0.8920740    1.016612    -1.1004858    2.884634
## Phi:time2         -0.5723019    1.304972    -3.1300478    1.985444
## Phi:time3         -0.4649351    1.647430    -3.6938986    2.764029
## Phi:time4         -1.2126353    1.344061    -3.8469957    1.421725
## Phi:time5         -0.6259153    1.403332    -3.3764458    2.124615
## Phi:time6          0.5731718    2.027436    -3.4006038    4.546947
## Phi:time7         -1.7755302 2230.284900 -4373.1341000 4369.583000
## Phi:colony2        1.7682737    1.937002    -2.0282493    5.564797
## Phi:time2:colony2 -0.9922945    2.215302    -5.3342863    3.349697
## Phi:time3:colony2 -0.8966463    2.420496    -5.6408193    3.847527
## Phi:time4:colony2 -0.0736321    2.246609    -4.4769852    4.329721
## Phi:time5:colony2 -1.1602891    2.217577    -5.5067411    3.186163
## Phi:time6:colony2 -2.2518355    2.616943    -7.3810444    2.877374
## Phi:time7:colony2 -0.6081198 1428.759600 -2800.9769000 2799.760700
## p:(Intercept)      2.0134249    1.049825    -0.0442319    4.071082
## p:time3           -1.0096340    1.198441    -3.3585795    1.339311
## p:time4           -1.9040429    1.162948    -4.1834209    0.375335
## p:time5           -1.2090461    1.175206    -3.5124498    1.094358
## p:time6           -0.0983434    1.291915    -2.6304966    2.433810
## p:time7           -0.0687108    1.480362    -2.9702208    2.832799
## p:time8           -1.3431204 4662.758700 -9140.3503000 9137.664000
## 
## 
## Real Parameter Phi
## Group:colony1 
##          1         2         3        4         5         6         7
## 1 0.709318 0.5792687 0.6051903 0.420539 0.5661496 0.8123337 0.2924621
## 2          0.5792687 0.6051903 0.420539 0.5661496 0.8123337 0.2924621
## 3                    0.6051903 0.420539 0.5661496 0.8123337 0.2924621
## 4                              0.420539 0.5661496 0.8123337 0.2924621
## 5                                       0.5661496 0.8123337 0.2924621
## 6                                                 0.8123337 0.2924621
## 7                                                           0.2924621
## 
## Group:colony2 
##           1         2         3         4         5         6         7
## 1 0.9346459 0.7494632 0.7856273 0.7980386 0.7056071 0.7274422 0.5687364
## 2           0.7494632 0.7856273 0.7980386 0.7056071 0.7274422 0.5687364
## 3                     0.7856273 0.7980386 0.7056071 0.7274422 0.5687364
## 4                               0.7980386 0.7056071 0.7274422 0.5687364
## 5                                         0.7056071 0.7274422 0.5687364
## 6                                                   0.7274422 0.5687364
## 7                                                             0.5687364
## 
## 
## Real Parameter p
## Group:colony1 
##           2         3         4         5         6         7         8
## 1 0.8821994 0.7318032 0.5273182 0.6909104 0.8715889 0.8748691 0.6615713
## 2           0.7318032 0.5273182 0.6909104 0.8715889 0.8748691 0.6615713
## 3                     0.5273182 0.6909104 0.8715889 0.8748691 0.6615713
## 4                               0.6909104 0.8715889 0.8748691 0.6615713
## 5                                         0.8715889 0.8748691 0.6615713
## 6                                                   0.8748691 0.6615713
## 7                                                             0.6615713
## 
## Group:colony2 
##           2         3         4         5         6         7         8
## 1 0.8821994 0.7318032 0.5273182 0.6909104 0.8715889 0.8748691 0.6615713
## 2           0.7318032 0.5273182 0.6909104 0.8715889 0.8748691 0.6615713
## 3                     0.5273182 0.6909104 0.8715889 0.8748691 0.6615713
## 4                               0.6909104 0.8715889 0.8748691 0.6615713
## 5                                         0.8715889 0.8748691 0.6615713
## 6                                                   0.8748691 0.6615713
## 7                                                             0.6615713

####  ~~~~~~  Les AIC, nombres de paramètres par modèle  ~~~~~~  ####

#mod_phitc_pc$results # TOUS LES RESULTATS

cat("Le modèle calculé est :", mod_phitc_pc$model.name, "\n")

## Le modèle calculé est : Phi(~time * colony)p(~time)

cat("Le modèle a", mod_phitc_pc$results[["npar.unadjusted"]][1], "paramètres non ajustés et", mod_phitc_pc$results[["npar"]][1], "paramètres ajustés", "\n")

## Le modèle a 20 paramètres non ajustés et 21 paramètres ajustés

cat("-2lnL :", mod_phitc_pc$results[["lnl"]][1], "\n")

## -2lnL : 346.7694

cat("L'AIC non ajusté du modèle est de", mod_phitc_pc$results[["AICc.unadjusted"]][1], "et de", mod_phitc_pc$results[["AICc"]][1], "pour l'AIC ajusté", "\n")

## L'AIC non ajusté du modèle est de 391.4103 et de 393.9027 pour l'AIC ajusté

Modèle 3

# specifier les formules
p.col <- list(formula=~colony)  

Phi.time.colony <- list(formula=~time*colony)

mod_phitc_pcol <- mark(colonie_data.process,colonie_data.ddl,
                model.parameters=list(Phi = Phi.time.colony, p = p.col))

## 
## Note: only 15 parameters counted of 16 specified parameters

## AICc and parameter count have been adjusted upward

## 
## Output summary for CJS model
## Name : Phi(~time * colony)p(~colony) 
## 
## Npar :  16  (unadjusted=15)
## -2lnL:  351.9678
## AICc :  386.9084  (unadjusted=384.54848)
## 
## Beta
##                      estimate        se         lcl        ucl
## Phi:(Intercept)     1.8319100 2.2861599  -2.6489634   6.312784
## Phi:time2          -1.3514326 2.5711509  -6.3908884   3.688023
## Phi:time3          -1.8358931 2.5252865  -6.7854548   3.113669
## Phi:time4          -1.9740845 2.4512873  -6.7786077   2.830439
## Phi:time5          -1.3869838 2.5192060  -6.3246276   3.550660
## Phi:time6          15.0694730 0.0000000  15.0694730  15.069473
## Phi:time7          -2.6894371 2.3981164  -7.3897453   2.010871
## Phi:colony2         1.6866143 4.4467622  -7.0290399  10.402268
## Phi:time2:colony2  -1.1949708 4.7231094 -10.4522650   8.062324
## Phi:time3:colony2  -0.6958022 4.6076270  -9.7267513   8.335147
## Phi:time4:colony2  -0.0304250 4.5765440  -9.0004515   8.939602
## Phi:time5:colony2  -1.0212708 4.6004732 -10.0381990   7.995657
## Phi:time6:colony2 -17.4303200 0.0000000 -17.4303200 -17.430320
## Phi:time7:colony2  -0.9520139 4.5098500  -9.7913201   7.887292
## p:(Intercept)       0.3385430 0.5332328  -0.7065932   1.383679
## p:colony2           0.8957229 0.6063476  -0.2927184   2.084164
## 
## 
## Real Parameter Phi
## Group:colony1 
##           1         2         3         4         5 6         7
## 1 0.8619891 0.6178606 0.4990042 0.4645161 0.6094322 1 0.2978563
## 2           0.6178606 0.4990042 0.4645161 0.6094322 1 0.2978563
## 3                     0.4990042 0.4645161 0.6094322 1 0.2978563
## 4                               0.4645161 0.6094322 1 0.2978563
## 5                                         0.6094322 1 0.2978563
## 6                                                   1 0.2978563
## 7                                                     0.2978563
## 
## Group:colony2 
##           1        2         3         4         5         6        7
## 1 0.9712103 0.725542 0.7284611 0.8196554 0.7521794 0.7609105 0.469307
## 2           0.725542 0.7284611 0.8196554 0.7521794 0.7609105 0.469307
## 3                    0.7284611 0.8196554 0.7521794 0.7609105 0.469307
## 4                              0.8196554 0.7521794 0.7609105 0.469307
## 5                                        0.7521794 0.7609105 0.469307
## 6                                                  0.7609105 0.469307
## 7                                                            0.469307
## 
## 
## Real Parameter p
## Group:colony1 
##           2         3         4         5         6         7         8
## 1 0.5838366 0.5838366 0.5838366 0.5838366 0.5838366 0.5838366 0.5838366
## 2           0.5838366 0.5838366 0.5838366 0.5838366 0.5838366 0.5838366
## 3                     0.5838366 0.5838366 0.5838366 0.5838366 0.5838366
## 4                               0.5838366 0.5838366 0.5838366 0.5838366
## 5                                         0.5838366 0.5838366 0.5838366
## 6                                                   0.5838366 0.5838366
## 7                                                             0.5838366
## 
## Group:colony2 
##           2         3         4         5         6         7         8
## 1 0.7745643 0.7745643 0.7745643 0.7745643 0.7745643 0.7745643 0.7745643
## 2           0.7745643 0.7745643 0.7745643 0.7745643 0.7745643 0.7745643
## 3                     0.7745643 0.7745643 0.7745643 0.7745643 0.7745643
## 4                               0.7745643 0.7745643 0.7745643 0.7745643
## 5                                         0.7745643 0.7745643 0.7745643
## 6                                                   0.7745643 0.7745643
## 7                                                             0.7745643

####  ~~~~~~  Les AIC, nombres de paramètres par modèle  ~~~~~~  ####

#mod_phitc_pc$results # TOUS LES RESULTATS

cat("Le modèle calculé est :", mod_phitc_pcol$model.name, "\n")

## Le modèle calculé est : Phi(~time * colony)p(~colony)

cat("Le modèle a", mod_phitc_pcol$results[["npar.unadjusted"]][1], "paramètres non ajustés et", mod_phitc_pcol$results[["npar"]][1], "paramètres ajustés", "\n")

## Le modèle a 15 paramètres non ajustés et 16 paramètres ajustés

cat("-2lnL :", mod_phitc_pcol$results[["lnl"]][1], "\n")

## -2lnL : 351.9678

cat("L'AIC non ajusté du modèle est de", mod_phitc_pcol$results[["AICc.unadjusted"]][1], "et de", mod_phitc_pcol$results[["AICc"]][1], "pour l'AIC ajusté", "\n")

## L'AIC non ajusté du modèle est de 384.5485 et de 386.9084 pour l'AIC ajusté

Modèle 4

#modèle phi(t*colony)p(time+colony):
  
# specifier les formules
p.col.et.time <- list(formula=~colony+time)  

Phi.time.colony <- list(formula=~time*colony)

mod_phitc_pcolt <- mark(colonie_data.process,colonie_data.ddl,
                model.parameters=list(Phi = Phi.time.colony, p = p.col.et.time))

## 
## Note: only 21 parameters counted of 22 specified parameters

## AICc and parameter count have been adjusted upward

## 
## Output summary for CJS model
## Name : Phi(~time * colony)p(~colony + time) 
## 
## Npar :  22  (unadjusted=21)
## -2lnL:  344.1504
## AICc :  393.8041  (unadjusted=391.28378)
## 
## Beta
##                     estimate         se           lcl          ucl
## Phi:(Intercept)    1.1076174   1.262284    -1.3664600    3.5816948
## Phi:time2         -0.3236602   1.857408    -3.9641797    3.3168594
## Phi:time3         -0.3384571   2.367351    -4.9784661    4.3015519
## Phi:time4         -1.4344464   1.636627    -4.6422353    1.7733426
## Phi:time5         -0.9866023   1.651498    -4.2235380    2.2503334
## Phi:time6          1.1934129   4.772007    -8.1597207   10.5465460
## Phi:time7         -1.7582028 629.665840 -1235.9033000 1232.3869000
## Phi:colony2        1.3900111   1.838545    -2.2135380    4.9935603
## Phi:time2:colony2 -1.1341773   2.308995    -5.6598083    3.3914538
## Phi:time3:colony2 -0.8692506   2.741016    -6.2416427    4.5031414
## Phi:time4:colony2  0.2950286   2.203638    -4.0241022    4.6141594
## Phi:time5:colony2 -0.6291590   2.174614    -4.8914018    3.6330839
## Phi:time6:colony2 -2.7241000   4.836591   -12.2038190    6.7556194
## Phi:time7:colony2 -0.8004594 247.977610  -486.8365800  485.2356600
## p:(Intercept)      1.2812060   1.121532    -0.9169966    3.4794087
## p:colony2          1.1172080   0.671979    -0.1998708    2.4342869
## p:time3           -1.1337088   1.220195    -3.5252917    1.2578741
## p:time4           -2.1396268   1.188569    -4.4692221    0.1899684
## p:time5           -1.4302989   1.200339    -3.7829638    0.9223661
## p:time6           -0.2557990   1.310449    -2.8242783    2.3126804
## p:time7           -0.3092380   1.498368    -3.2460395    2.6275636
## p:time8           -1.1335313 893.406120 -1752.2096000 1749.9425000
## 
## 
## Real Parameter Phi
## Group:colony1 
##           1         2         3         4         5         6         7
## 1 0.7516847 0.6865324 0.6833392 0.4190124 0.5302169 0.9089623 0.3428576
## 2           0.6865324 0.6833392 0.4190124 0.5302169 0.9089623 0.3428576
## 3                     0.6833392 0.4190124 0.5302169 0.9089623 0.3428576
## 4                               0.4190124 0.5302169 0.9089623 0.3428576
## 5                                         0.5302169 0.9089623 0.3428576
## 6                                                   0.9089623 0.3428576
## 7                                                             0.3428576
## 
## Group:colony2 
##           1         2         3         4        5         6         7
## 1 0.9239754 0.7388097 0.7841338 0.7954687 0.707209 0.7245095 0.4847463
## 2           0.7388097 0.7841338 0.7954687 0.707209 0.7245095 0.4847463
## 3                     0.7841338 0.7954687 0.707209 0.7245095 0.4847463
## 4                               0.7954687 0.707209 0.7245095 0.4847463
## 5                                         0.707209 0.7245095 0.4847463
## 6                                                  0.7245095 0.4847463
## 7                                                            0.4847463
## 
## 
## Real Parameter p
## Group:colony1 
##          2         3         4         5         6         7         8
## 1 0.782655 0.5368076 0.2976694 0.4627957 0.7360245 0.7255116 0.5368517
## 2          0.5368076 0.2976694 0.4627957 0.7360245 0.7255116 0.5368517
## 3                    0.2976694 0.4627957 0.7360245 0.7255116 0.5368517
## 4                              0.4627957 0.7360245 0.7255116 0.5368517
## 5                                        0.7360245 0.7255116 0.5368517
## 6                                                  0.7255116 0.5368517
## 7                                                            0.5368517
## 
## Group:colony2 
##           2        3         4         5         6         7         8
## 1 0.9167063 0.779835 0.5643381 0.7247437 0.8949767 0.8898467 0.7798655
## 2           0.779835 0.5643381 0.7247437 0.8949767 0.8898467 0.7798655
## 3                    0.5643381 0.7247437 0.8949767 0.8898467 0.7798655
## 4                              0.7247437 0.8949767 0.8898467 0.7798655
## 5                                        0.8949767 0.8898467 0.7798655
## 6                                                  0.8898467 0.7798655
## 7                                                            0.7798655

####  ~~~~~~  Les AIC, nombres de paramètres par modèle  ~~~~~~  ####

#mod_phitc_pc$results # TOUS LES RESULTATS

cat("Le modèle calculé est :", mod_phitc_pcolt$model.name, "\n")

## Le modèle calculé est : Phi(~time * colony)p(~colony + time)

cat("Le modèle a", mod_phitc_pcolt$results[["npar.unadjusted"]][1], "paramètres non ajustés et", mod_phitc_pcolt$results[["npar"]][1], "paramètres ajustés", "\n")

## Le modèle a 21 paramètres non ajustés et 22 paramètres ajustés

cat("-2lnL :", mod_phitc_pcolt$results[["lnl"]][1], "\n")

## -2lnL : 344.1504

cat("L'AIC non ajusté du modèle est de", mod_phitc_pcolt$results[["AICc.unadjusted"]][1], "et de", mod_phitc_pcolt$results[["AICc"]][1], "pour l'AIC ajusté", "\n")

## L'AIC non ajusté du modèle est de 391.2838 et de 393.8041 pour l'AIC ajusté

Modèle 5

#modèle phi(t*colony)p(time*colony):
  
# specifier les formules
p.col.time <- list(formula=~colony*time)  

Phi.time.colony <- list(formula=~time*colony)

mod_phitc_pcol.t <- mark(colonie_data.process,colonie_data.ddl,
                model.parameters=list(Phi = Phi.time.colony, p = p.col.time))

## 
## Note: only 24 parameters counted of 28 specified parameters

## AICc and parameter count have been adjusted upward

## 
## Output summary for CJS model
## Name : Phi(~time * colony)p(~colony * time) 
## 
## Npar :  28  (unadjusted=24)
## -2lnL:  339.7054
## AICc :  405.0927  (unadjusted=394.48511)
## 
## Beta
##                        estimate          se           lcl          ucl
## Phi:(Intercept)    6.931812e-01   0.8660273    -1.0042322    2.3905947
## Phi:time2         -1.823735e-01   1.3478218    -2.8241043    2.4593573
## Phi:time3          1.460309e-04   2.3434064    -4.5929305    4.5932226
## Phi:time4          5.594892e-01   4.3031017    -7.8745903    8.9935686
## Phi:time5         -1.145186e+00   1.6289258    -4.3378802    2.0475089
## Phi:time6         -5.794038e-05   1.4999912    -2.9400408    2.9399249
## Phi:time7         -2.079449e+00   1.1730885    -4.3787022    0.2198048
## Phi:colony2        2.183192e+00   2.3652643    -2.4527265    6.8191096
## Phi:time2:colony2 -1.643750e+00   2.7387853    -7.0117690    3.7242694
## Phi:time3:colony2 -1.593916e+00   3.3135830    -8.0885387    4.9007070
## Phi:time4:colony2 -2.215577e+00   4.8797249   -11.7798380    7.3486844
## Phi:time5:colony2 -8.217636e-01   2.7814774    -6.2734595    4.6299322
## Phi:time6:colony2 -1.814881e+00   2.7374502    -7.1802837    3.5505214
## Phi:time7:colony2  3.880494e-01   0.0000000     0.3880494    0.3880494
## p:(Intercept)      1.597247e+01 284.7055200  -542.0503500  573.9953000
## p:colony2         -1.427599e+01 284.7061600  -572.3000700  543.7481000
## p:time3           -1.527931e+01 284.7083700  -573.3077200  542.7491100
## p:time4           -1.637802e+01 284.7053600  -574.4005400  541.6445000
## p:time5           -1.776425e+01 284.7107100  -575.7972500  540.2687500
## p:time6           -1.568479e+01 284.7093600  -573.7151600  542.3455700
## p:time7            8.375892e+00   0.0000000     8.3758921    8.3758921
## p:time8           -5.670662e+00 739.5516400 -1455.1919000 1443.8506000
## p:colony2:time3    1.466966e+01 284.7098000  -543.3615600  572.7008700
## p:colony2:time4    1.486693e+01 284.7063000  -543.1574200  572.8912900
## p:colony2:time5    1.737882e+01 284.7122000  -540.6571000  575.4147400
## p:colony2:time6    1.649299e+01 284.7122400  -541.5430200  574.5290000
## p:colony2:time7   -8.220016e+00   0.0000000    -8.2200164   -8.2200164
## p:colony2:time8    3.932805e+00 738.1708000 -1442.8820000 1450.7476000
## 
## 
## Real Parameter Phi
## Group:colony1 
##           1         2         3         4         5         6         7
## 1 0.6666742 0.6249958 0.6667067 0.7777618 0.3888843 0.6666614 0.2000043
## 2           0.6249958 0.6667067 0.7777618 0.3888843 0.6666614 0.2000043
## 3                     0.6667067 0.7777618 0.3888843 0.6666614 0.2000043
## 4                               0.7777618 0.3888843 0.6666614 0.2000043
## 5                                         0.3888843 0.6666614 0.2000043
## 6                                                   0.6666614 0.2000043
## 7                                                             0.2000043
## 
## Group:colony2 
##          1         2         3         4         5         6         7
## 1 0.946666 0.7408228 0.7828925 0.7721138 0.7128822 0.7429644 0.7658409
## 2          0.7408228 0.7828925 0.7721138 0.7128822 0.7429644 0.7658409
## 3                    0.7828925 0.7721138 0.7128822 0.7429644 0.7658409
## 4                              0.7721138 0.7128822 0.7429644 0.7658409
## 5                                        0.7128822 0.7429644 0.7658409
## 6                                                  0.7429644 0.7658409
## 7                                                            0.7658409
## 
## 
## Real Parameter p
## Group:colony1 
##           2         3         4         5         6 7         8
## 1 0.9999999 0.6666712 0.3999802 0.1428554 0.5714279 1 0.9999664
## 2           0.6666712 0.3999802 0.1428554 0.5714279 1 0.9999664
## 3                     0.3999802 0.1428554 0.5714279 1 0.9999664
## 4                               0.1428554 0.5714279 1 0.9999664
## 5                                         0.5714279 1 0.9999664
## 6                                                   1 0.9999664
## 7                                                     0.9999664
## 
## Group:colony2 
##           2         3        4         5         6         7         8
## 1 0.8450754 0.7477858 0.546218 0.7876906 0.9244698 0.8644043 0.4896589
## 2           0.7477858 0.546218 0.7876906 0.9244698 0.8644043 0.4896589
## 3                     0.546218 0.7876906 0.9244698 0.8644043 0.4896589
## 4                              0.7876906 0.9244698 0.8644043 0.4896589
## 5                                        0.9244698 0.8644043 0.4896589
## 6                                                  0.8644043 0.4896589
## 7                                                            0.4896589

####  ~~~~~~  Les AIC, nombres de paramètres par modèle  ~~~~~~  ####

#mod_phitc_pc$results # TOUS LES RESULTATS

cat("Le modèle calculé est :", mod_phitc_pcol.t$model.name, "\n")

## Le modèle calculé est : Phi(~time * colony)p(~colony * time)

cat("Le modèle a", mod_phitc_pcol.t$results[["npar.unadjusted"]][1], "paramètres non ajustés et", mod_phitc_pcol.t$results[["npar"]][1], "paramètres ajustés", "\n")

## Le modèle a 24 paramètres non ajustés et 28 paramètres ajustés

cat("-2lnL :", mod_phitc_pcol.t$results[["lnl"]][1], "\n")

## -2lnL : 339.7054

cat("Le modèle a", mod_phitc_pcol.t$results[["AICc.unadjusted"]][1], "pour AIC non ajustée et", mod_phitc_pcol.t$results[["AICc"]][1], "pour AIC ajusté", "\n")

## Le modèle a 394.4851 pour AIC non ajustée et 405.0927 pour AIC ajusté

Sélection du modèle 1 p(.) avec un p constant.

2. Maintenant que p() déterminé, continuer avec le modèle Phi() pour le sélectionner

Modèle 6

#modèle phi(.)p(.):
  
# specifier les formules
p.constant <- list(formula=~1)  

Phi.constant <- list(formula=~1)

mod_phic_pc <- mark(colonie_data.process,colonie_data.ddl,
                model.parameters=list(Phi = Phi.constant, p = p.constant))

## 
## Output summary for CJS model
## Name : Phi(~1)p(~1) 
## 
## Npar :  2
## -2lnL:  372.8533
## AICc :  376.9136
## 
## Beta
##                  estimate        se       lcl      ucl
## Phi:(Intercept) 0.8524383 0.1753794 0.5086948 1.196182
## p:(Intercept)   0.8881233 0.2391869 0.4193170 1.356930
## 
## 
## Real Parameter Phi
## Group:colony1 
##           1         2         3         4         5         6         7
## 1 0.7010784 0.7010784 0.7010784 0.7010784 0.7010784 0.7010784 0.7010784
## 2           0.7010784 0.7010784 0.7010784 0.7010784 0.7010784 0.7010784
## 3                     0.7010784 0.7010784 0.7010784 0.7010784 0.7010784
## 4                               0.7010784 0.7010784 0.7010784 0.7010784
## 5                                         0.7010784 0.7010784 0.7010784
## 6                                                   0.7010784 0.7010784
## 7                                                             0.7010784
## 
## Group:colony2 
##           1         2         3         4         5         6         7
## 1 0.7010784 0.7010784 0.7010784 0.7010784 0.7010784 0.7010784 0.7010784
## 2           0.7010784 0.7010784 0.7010784 0.7010784 0.7010784 0.7010784
## 3                     0.7010784 0.7010784 0.7010784 0.7010784 0.7010784
## 4                               0.7010784 0.7010784 0.7010784 0.7010784
## 5                                         0.7010784 0.7010784 0.7010784
## 6                                                   0.7010784 0.7010784
## 7                                                             0.7010784
## 
## 
## Real Parameter p
## Group:colony1 
##           2         3         4         5         6         7         8
## 1 0.7085027 0.7085027 0.7085027 0.7085027 0.7085027 0.7085027 0.7085027
## 2           0.7085027 0.7085027 0.7085027 0.7085027 0.7085027 0.7085027
## 3                     0.7085027 0.7085027 0.7085027 0.7085027 0.7085027
## 4                               0.7085027 0.7085027 0.7085027 0.7085027
## 5                                         0.7085027 0.7085027 0.7085027
## 6                                                   0.7085027 0.7085027
## 7                                                             0.7085027
## 
## Group:colony2 
##           2         3         4         5         6         7         8
## 1 0.7085027 0.7085027 0.7085027 0.7085027 0.7085027 0.7085027 0.7085027
## 2           0.7085027 0.7085027 0.7085027 0.7085027 0.7085027 0.7085027
## 3                     0.7085027 0.7085027 0.7085027 0.7085027 0.7085027
## 4                               0.7085027 0.7085027 0.7085027 0.7085027
## 5                                         0.7085027 0.7085027 0.7085027
## 6                                                   0.7085027 0.7085027
## 7                                                             0.7085027

####  ~~~~~~  Les AIC, nombres de paramètres par modèle  ~~~~~~  ####

#mod_phitc_pc$results # TOUS LES RESULTATS

cat("Le modèle calculé est :", mod_phic_pc$model.name, "\n")

## Le modèle calculé est : Phi(~1)p(~1)

cat("Le modèle a", mod_phic_pc$results[["npar"]][1], "paramètres", "\n")

## Le modèle a 2 paramètres

cat("-2lnL :", mod_phic_pc$results[["lnl"]][1], "\n")

## -2lnL : 372.8533

cat("Le modèle a", mod_phic_pc$results[["AICc"]][1], "pour AIC", "\n")

## Le modèle a 376.9136 pour AIC

Après un ajustement des paramètres, les nouveaux AIC et AIC non ajusté sont :

adjust.parameter.count(mod_phic_pc,1)

## 
## Number of parameters adjusted from 2 to 1

## Adjusted AICc = 374.87329
## Unadjusted AICc = 376.9136

Modèle 7

#modèle phi(t)p(.):
  
# specifier les formules
p.constant <- list(formula=~1)  

Phi.time <- list(formula=~time)

mod_phit_pc <- mark(colonie_data.process,colonie_data.ddl,
                model.parameters=list(Phi = Phi.time, p = p.constant))

## 
## Output summary for CJS model
## Name : Phi(~time)p(~1) 
## 
## Npar :  8
## -2lnL:  362.2662
## AICc :  379.0123
## 
## Beta
##                   estimate        se        lcl       ucl
## Phi:(Intercept)  2.2494587 1.3061138 -0.3105243 4.8094417
## Phi:time2       -1.5542454 1.4417278 -4.3800320 1.2715412
## Phi:time3       -1.4773121 1.3928766 -4.2073502 1.2527261
## Phi:time4       -1.2296975 1.3935760 -3.9611064 1.5017114
## Phi:time5       -1.2532921 1.3949732 -3.9874396 1.4808555
## Phi:time6       -0.9241488 1.4512735 -3.7686450 1.9203474
## Phi:time7       -2.5026018 1.3406331 -5.1302427 0.1250391
## p:(Intercept)    1.0638307 0.2537879  0.5664065 1.5612550
## 
## 
## Real Parameter Phi
## Group:colony1 
##           1         2         3         4         5         6       7
## 1 0.9046038 0.6671257 0.6839851 0.7349261 0.7303042 0.7900638 0.43705
## 2           0.6671257 0.6839851 0.7349261 0.7303042 0.7900638 0.43705
## 3                     0.6839851 0.7349261 0.7303042 0.7900638 0.43705
## 4                               0.7349261 0.7303042 0.7900638 0.43705
## 5                                         0.7303042 0.7900638 0.43705
## 6                                                   0.7900638 0.43705
## 7                                                             0.43705
## 
## Group:colony2 
##           1         2         3         4         5         6       7
## 1 0.9046038 0.6671257 0.6839851 0.7349261 0.7303042 0.7900638 0.43705
## 2           0.6671257 0.6839851 0.7349261 0.7303042 0.7900638 0.43705
## 3                     0.6839851 0.7349261 0.7303042 0.7900638 0.43705
## 4                               0.7349261 0.7303042 0.7900638 0.43705
## 5                                         0.7303042 0.7900638 0.43705
## 6                                                   0.7900638 0.43705
## 7                                                             0.43705
## 
## 
## Real Parameter p
## Group:colony1 
##           2         3         4         5         6         7         8
## 1 0.7434219 0.7434219 0.7434219 0.7434219 0.7434219 0.7434219 0.7434219
## 2           0.7434219 0.7434219 0.7434219 0.7434219 0.7434219 0.7434219
## 3                     0.7434219 0.7434219 0.7434219 0.7434219 0.7434219
## 4                               0.7434219 0.7434219 0.7434219 0.7434219
## 5                                         0.7434219 0.7434219 0.7434219
## 6                                                   0.7434219 0.7434219
## 7                                                             0.7434219
## 
## Group:colony2 
##           2         3         4         5         6         7         8
## 1 0.7434219 0.7434219 0.7434219 0.7434219 0.7434219 0.7434219 0.7434219
## 2           0.7434219 0.7434219 0.7434219 0.7434219 0.7434219 0.7434219
## 3                     0.7434219 0.7434219 0.7434219 0.7434219 0.7434219
## 4                               0.7434219 0.7434219 0.7434219 0.7434219
## 5                                         0.7434219 0.7434219 0.7434219
## 6                                                   0.7434219 0.7434219
## 7                                                             0.7434219

####  ~~~~~~  Les AIC, nombres de paramètres par modèle  ~~~~~~  ####

#mod_phitc_pc$results # TOUS LES RESULTATS

cat("Le modèle calculé est :", mod_phit_pc$model.name, "\n")

## Le modèle calculé est : Phi(~time)p(~1)

cat("Le modèle a", mod_phit_pc$results[["npar"]][1], "paramètres", "\n")

## Le modèle a 8 paramètres

cat("-2lnL :", mod_phit_pc$results[["lnl"]][1], "\n")

## -2lnL : 362.2662

cat("Le modèle a", mod_phit_pc$results[["AICc"]][1], "pour AIC", "\n")

## Le modèle a 379.0123 pour AIC

Modèle 8

#modèle phi(colony)p(.):
  
# specifier les formules
p.constant <- list(formula=~1)  

Phi.col <- list(formula=~colony)

mod_phicol_pc <- mark(colonie_data.process,colonie_data.ddl,
                model.parameters=list(Phi = Phi.col, p = p.constant))

## 
## Output summary for CJS model
## Name : Phi(~colony)p(~1) 
## 
## Npar :  3
## -2lnL:  367.4051
## AICc :  373.5263
## 
## Beta
##                  estimate        se        lcl       ucl
## Phi:(Intercept) 0.2221749 0.3109808 -0.3873474 0.8316973
## Phi:colony2     0.8582301 0.3646688  0.1434793 1.5729810
## p:(Intercept)   0.8815436 0.2388674  0.4133634 1.3497238
## 
## 
## Real Parameter Phi
## Group:colony1 
##           1         2         3         4         5         6         7
## 1 0.5553164 0.5553164 0.5553164 0.5553164 0.5553164 0.5553164 0.5553164
## 2           0.5553164 0.5553164 0.5553164 0.5553164 0.5553164 0.5553164
## 3                     0.5553164 0.5553164 0.5553164 0.5553164 0.5553164
## 4                               0.5553164 0.5553164 0.5553164 0.5553164
## 5                                         0.5553164 0.5553164 0.5553164
## 6                                                   0.5553164 0.5553164
## 7                                                             0.5553164
## 
## Group:colony2 
##           1         2         3         4         5         6         7
## 1 0.7465706 0.7465706 0.7465706 0.7465706 0.7465706 0.7465706 0.7465706
## 2           0.7465706 0.7465706 0.7465706 0.7465706 0.7465706 0.7465706
## 3                     0.7465706 0.7465706 0.7465706 0.7465706 0.7465706
## 4                               0.7465706 0.7465706 0.7465706 0.7465706
## 5                                         0.7465706 0.7465706 0.7465706
## 6                                                   0.7465706 0.7465706
## 7                                                             0.7465706
## 
## 
## Real Parameter p
## Group:colony1 
##          2        3        4        5        6        7        8
## 1 0.707142 0.707142 0.707142 0.707142 0.707142 0.707142 0.707142
## 2          0.707142 0.707142 0.707142 0.707142 0.707142 0.707142
## 3                   0.707142 0.707142 0.707142 0.707142 0.707142
## 4                            0.707142 0.707142 0.707142 0.707142
## 5                                     0.707142 0.707142 0.707142
## 6                                              0.707142 0.707142
## 7                                                       0.707142
## 
## Group:colony2 
##          2        3        4        5        6        7        8
## 1 0.707142 0.707142 0.707142 0.707142 0.707142 0.707142 0.707142
## 2          0.707142 0.707142 0.707142 0.707142 0.707142 0.707142
## 3                   0.707142 0.707142 0.707142 0.707142 0.707142
## 4                            0.707142 0.707142 0.707142 0.707142
## 5                                     0.707142 0.707142 0.707142
## 6                                              0.707142 0.707142
## 7                                                       0.707142

####  ~~~~~~  Les AIC, nombres de paramètres par modèle  ~~~~~~  ####

#mod_phitc_pc$results # TOUS LES RESULTATS

cat("Le modèle calculé est :", mod_phicol_pc$model.name, "\n")

## Le modèle calculé est : Phi(~colony)p(~1)

cat("Le modèle a", mod_phicol_pc$results[["npar"]][1], "paramètres", "\n")

## Le modèle a 3 paramètres

cat("-2lnL :", mod_phicol_pc$results[["lnl"]][1], "\n")

## -2lnL : 367.4051

cat("Le modèle a", mod_phicol_pc$results[["AICc"]][1], "pour AIC", "\n")

## Le modèle a 373.5263 pour AIC

Modèle 9

#modèle phi(t+colony)p(.):
  
# specifier les formules
p.constant <- list(formula=~1)  

Phi.time.et.colony <- list(formula=~time+colony)

mod_phitcol_pt <- mark(colonie_data.process,colonie_data.ddl,model.parameters=list(Phi=Phi.time.et.colony,p=p.constant))

## 
## Output summary for CJS model
## Name : Phi(~time + colony)p(~1) 
## 
## Npar :  9
## -2lnL:  355.613
## AICc :  374.5505
## 
## Beta
##                   estimate        se        lcl        ucl
## Phi:(Intercept)  1.6742752 1.2556969 -0.7868907  4.1354412
## Phi:time2       -1.5445203 1.3821782 -4.2535897  1.1645492
## Phi:time3       -1.6411512 1.3428176 -4.2730738  0.9907714
## Phi:time4       -1.3607398 1.3441206 -3.9952163  1.2737366
## Phi:time5       -1.4436287 1.3474757 -4.0846811  1.1974236
## Phi:time6       -1.1048127 1.4200991 -3.8882070  1.6785815
## Phi:time7       -2.7280767 1.2944459 -5.2651908 -0.1909627
## Phi:colony2      0.9591106 0.3729521  0.2281246  1.6900967
## p:(Intercept)    1.0624338 0.2539495  0.5646928  1.5601748
## 
## 
## Real Parameter Phi
## Group:colony1 
##          1         2         3        4         5         6         7
## 1 0.842145 0.5323933 0.5082803 0.577748 0.5574074 0.6386391 0.2584958
## 2          0.5323933 0.5082803 0.577748 0.5574074 0.6386391 0.2584958
## 3                    0.5082803 0.577748 0.5574074 0.6386391 0.2584958
## 4                              0.577748 0.5574074 0.6386391 0.2584958
## 5                                       0.5574074 0.6386391 0.2584958
## 6                                                 0.6386391 0.2584958
## 7                                                           0.2584958
## 
## Group:colony2 
##           1        2         3         4         5         6        7
## 1 0.9329796 0.748168 0.7295291 0.7811954 0.7666976 0.8217974 0.476345
## 2           0.748168 0.7295291 0.7811954 0.7666976 0.8217974 0.476345
## 3                    0.7295291 0.7811954 0.7666976 0.8217974 0.476345
## 4                              0.7811954 0.7666976 0.8217974 0.476345
## 5                                        0.7666976 0.8217974 0.476345
## 6                                                  0.8217974 0.476345
## 7                                                            0.476345
## 
## 
## Real Parameter p
## Group:colony1 
##           2         3         4         5         6         7         8
## 1 0.7431554 0.7431554 0.7431554 0.7431554 0.7431554 0.7431554 0.7431554
## 2           0.7431554 0.7431554 0.7431554 0.7431554 0.7431554 0.7431554
## 3                     0.7431554 0.7431554 0.7431554 0.7431554 0.7431554
## 4                               0.7431554 0.7431554 0.7431554 0.7431554
## 5                                         0.7431554 0.7431554 0.7431554
## 6                                                   0.7431554 0.7431554
## 7                                                             0.7431554
## 
## Group:colony2 
##           2         3         4         5         6         7         8
## 1 0.7431554 0.7431554 0.7431554 0.7431554 0.7431554 0.7431554 0.7431554
## 2           0.7431554 0.7431554 0.7431554 0.7431554 0.7431554 0.7431554
## 3                     0.7431554 0.7431554 0.7431554 0.7431554 0.7431554
## 4                               0.7431554 0.7431554 0.7431554 0.7431554
## 5                                         0.7431554 0.7431554 0.7431554
## 6                                                   0.7431554 0.7431554
## 7                                                             0.7431554

####  ~~~~~~  Les AIC, nombres de paramètres par modèle  ~~~~~~  ####

#mod_phitc_pc$results # TOUS LES RESULTATS

cat("Le modèle calculé est :", mod_phitcol_pt$model.name, "\n")

## Le modèle calculé est : Phi(~time + colony)p(~1)

cat("Le modèle a", mod_phitcol_pt$results[["npar"]][1], "paramètres", "\n")

## Le modèle a 9 paramètres

cat("-2lnL :", mod_phitcol_pt$results[["lnl"]][1], "\n")

## -2lnL : 355.613

cat("Le modèle a", mod_phitcol_pt$results[["AICc"]][1], "pour AIC", "\n")

## Le modèle a 374.5505 pour AIC

Modèle 10

#modèle phi(t*colony)p(.):
  
# specifier les formules
p.constant <- list(formula=~1)  

Phi.time.colony <- list(formula=~time*colony)

mod_phitc_pt <- mark(colonie_data.process,colonie_data.ddl,model.parameters=list(Phi=Phi.time.colony,p=p.constant))

## 
## Output summary for CJS model
## Name : Phi(~time * colony)p(~1) 
## 
## Npar :  15
## -2lnL:  353.9155
## AICc :  386.4962
## 
## Beta
##                     estimate        se         lcl        ucl
## Phi:(Intercept)    1.2070034 1.2744529  -1.2909243  3.7049311
## Phi:time2         -0.9779385 1.5339857  -3.9845505  2.0286735
## Phi:time3         -1.1893652 1.5902422  -4.3062400  1.9275096
## Phi:time4         -1.4147120 1.5273360  -4.4082905  1.5788666
## Phi:time5         -0.7913678 1.6399046  -4.0055809  2.4228453
## Phi:time6          0.9132993 3.4316443  -5.8127236  7.6393222
## Phi:time7         -2.3111286 1.5326346  -5.3150924  0.6928352
## Phi:colony2        2.8141120 6.3862767  -9.7029907 15.3312150
## Phi:time2:colony2 -2.0453372 6.6050831 -14.9913000 10.9006260
## Phi:time3:colony2 -1.8446664 6.4812431 -14.5479030 10.8585700
## Phi:time4:colony2 -1.0608478 6.4756873 -13.7531950 11.6314990
## Phi:time5:colony2 -2.1010278 6.4910165 -14.8234200 10.6213650
## Phi:time6:colony2 -3.7172660 7.2023979 -17.8339660 10.3994340
## Phi:time7:colony2 -1.7795010 6.4522797 -14.4259690 10.8669680
## p:(Intercept)      1.0702370 0.2539345   0.5725254  1.5679486
## 
## 
## Real Parameter Phi
## Group:colony1 
##           1         2         3         4         5         6         7
## 1 0.7697683 0.5570171 0.5044094 0.4482587 0.6024384 0.8928609 0.2489678
## 2           0.5570171 0.5044094 0.4482587 0.6024384 0.8928609 0.2489678
## 3                     0.5044094 0.4482587 0.6024384 0.8928609 0.2489678
## 4                               0.4482587 0.6024384 0.8928609 0.2489678
## 5                                         0.6024384 0.8928609 0.2489678
## 6                                                   0.8928609 0.2489678
## 7                                                             0.2489678
## 
## Group:colony2 
##          1         2         3         4         5         6         7
## 1 0.982383 0.7306336 0.7285115 0.8242709 0.7556026 0.7715614 0.4826284
## 2          0.7306336 0.7285115 0.8242709 0.7556026 0.7715614 0.4826284
## 3                    0.7285115 0.8242709 0.7556026 0.7715614 0.4826284
## 4                              0.8242709 0.7556026 0.7715614 0.4826284
## 5                                        0.7556026 0.7715614 0.4826284
## 6                                                  0.7715614 0.4826284
## 7                                                            0.4826284
## 
## 
## Real Parameter p
## Group:colony1 
##          2        3        4        5        6        7        8
## 1 0.744642 0.744642 0.744642 0.744642 0.744642 0.744642 0.744642
## 2          0.744642 0.744642 0.744642 0.744642 0.744642 0.744642
## 3                   0.744642 0.744642 0.744642 0.744642 0.744642
## 4                            0.744642 0.744642 0.744642 0.744642
## 5                                     0.744642 0.744642 0.744642
## 6                                              0.744642 0.744642
## 7                                                       0.744642
## 
## Group:colony2 
##          2        3        4        5        6        7        8
## 1 0.744642 0.744642 0.744642 0.744642 0.744642 0.744642 0.744642
## 2          0.744642 0.744642 0.744642 0.744642 0.744642 0.744642
## 3                   0.744642 0.744642 0.744642 0.744642 0.744642
## 4                            0.744642 0.744642 0.744642 0.744642
## 5                                     0.744642 0.744642 0.744642
## 6                                              0.744642 0.744642
## 7                                                       0.744642

####  ~~~~~~  Les AIC, nombres de paramètres par modèle  ~~~~~~  ####

#mod_phitc_pc$results # TOUS LES RESULTATS

cat("Le modèle calculé est :", mod_phitc_pt$model.name, "\n")

## Le modèle calculé est : Phi(~time * colony)p(~1)

cat("Le modèle a", mod_phitc_pt$results[["npar"]][1], "paramètres", "\n")

## Le modèle a 15 paramètres

cat("-2lnL :", mod_phitc_pt$results[["lnl"]][1], "\n")

## -2lnL : 353.9155

cat("Le modèle a", mod_phitc_pt$results[["AICc"]][1], "pour AIC", "\n")

## Le modèle a 386.4962 pour AIC

Goodness Of Fit

Impossible à faire sur MAC.

#~~~~~~~~~~~~~~~~~~~~~~~ Code des tableaux à la main ~~~~~~~~~~~~~~~~~~~~~~~#

Représentation R des données en tableaux

Tableau 1

# Créer vecteurs
Modeles <- c("Phi(temps * colonie)p(.)", "Phi(temps * colonie)p(temps)", "Phi(temps * colonie)p(colonie)", "Phi(temps * colonie)p(temps + colonie)", "Phi(temps * colonie)p(temps * colonie)")
Nb_de_parametres_estimables_non_ajustes <- c(15, 21, 16, 22, 28)
Nb_de_parametres_estimables_ajustes <- c(" ", 20, 15, 21, 24)
AICc <- c(386.4962, 393.9027, 386.9084, 393.8041, 405.0927)
AICc_ajuste <- c(" ", 391.41029, 384.54848, 391.28378, 394.48511)

# Créer un dataframe
df <- data.frame("Modèles" = Modeles, "Nombre de paramètres estimables" = Nb_de_parametres_estimables_non_ajustes, "Nombre de paramètres estimables ajustés" = Nb_de_parametres_estimables_ajustes, "AICc" = AICc, "AICc ajusté" = AICc_ajuste)

# Utiliser kable pour créer le tableau avec des options de formatage
df_format <- df %>%
  kable(col.names = c("Modèles", "Paramètres théoriques", "Paramètres estimés ajustés", "AIC", "AIC ajusté")) %>%
  kable_styling(bootstrap_options = "striped", latex_options = "scale_down", full_width = FALSE, position = "center", html_font = "arial")
df_format

Modèles	Paramètres théoriques	Paramètres estimés ajustés	AIC	AIC ajusté
Phi(temps * colonie)p(.)	15		386.4962
Phi(temps * colonie)p(temps)	21	20	393.9027	391.41029
Phi(temps * colonie)p(colonie)	16	15	386.9084	384.54848
Phi(temps * colonie)p(temps + colonie)	22	21	393.8041	391.28378
Phi(temps * colonie)p(temps * colonie)	28	24	405.0927	394.48511

Tableau 2

Modeles <- c("Phi(.)p(.)", "Phi(temps)p(.)", "Phi(colonie)p(.)", "Phi(temps + colonie)p(.)", "Phi(temps * colonie)p(.)")
Nb_de_parametres_estimables_non_ajustes <- c(2, 8, 3, 9, 15)
#Nb_de_parametres_estimables_ajustes <- c(2, 7, "Na", 9, 14)
AICc <- c(376.9136, 379.0123, 373.52628, 374.5505, 386.4962)
#AICc_ajuste <- c(374.87329, 379.0123, 371.465371, 372.3591, 384.1615)
Delta_AIC <- c(3.4078, 7.5469, 0, 0.8937, 12.6961)
#Poids_Akaike <- c(0.22, 0.027, 1.18, 0.76, 0.02063)


# Créer un dataframe
df <- data.frame("Modèles" = Modeles, "Nombre de paramètres estimables" = Nb_de_parametres_estimables_non_ajustes, "AIC" = AICc, "Delta" = Delta_AIC)

# Utiliser kable pour créer le tableau avec des options de formatage
df_format <- df %>%
  kable(col.names = c("Modèles", "Paramètres théoriques", "AIC", "Delta AIC")) %>%
  kable_styling(bootstrap_options = "striped", latex_options = "scale_down", full_width = FALSE, position = "center", html_font = "arial") ; df_format

Modèles	Paramètres théoriques	AIC	Delta AIC
Phi(.)p(.)	2	376.9136	3.4078
Phi(temps)p(.)	8	379.0123	7.5469
Phi(colonie)p(.)	3	373.5263	0.0000
Phi(temps + colonie)p(.)	9	374.5505	0.8937
Phi(temps * colonie)p(.)	15	386.4962	12.6961

Tableau 3

Tests <- c("TEST 2", "TEST 3", "TOTAL")
Chi <- c(3.3487, 5.8102, 9.1589)
ddl <- c(8, 16, 24)
p <- c(0.9106, 0.9900, 0.9972)


# Créer un dataframe
df <- data.frame(Tests, Chi, ddl, p)

# Utiliser kable pour créer le tableau avec des options de formatage
df_format <- df %>%
  kable(col.names = c("Tests", "Chi quarré", "Degrés de liberté", "P-value")) %>%
  kable_styling(bootstrap_options = "striped", latex_options = "scale_down", full_width = FALSE, position = "center", html_font = "arial") ; df_format

Tests	Chi quarré	Degrés de liberté	P-value
TEST 2	3.3487	8	0.9106
TEST 3	5.8102	16	0.9900
TOTAL	9.1589	24	0.9972