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README.md
In extBatchMarking: Extended Batch Marking Models
extBatchMarking: Implementation of Extended Batch Marking Model
The primary objective of extBatchMarking is to facilitate the fitting
of models developed by Cowen et al., 2017 for the ecologist. The marked
models can be seamlessly integrated with unmarked models to estimate
population size. The combined model harnesses the power of both the
N-mixture model and the Viterbi algorithm for hidden markov model to
provide accurate population size estimates.
The primary objective of extBatchMarking is to facilitate the fitting
of models developed by Cowen et al., 2017 for the ecologist. The marked
models can be seamlessly integrated with unmarked models to estimate
population size. The combined model harnesses the power of both the
N-mixture model and the Viterbi algorithm for hidden markov model to
provide accurate population size estimates.
In ecological research, it’s often challenging to directly count every
individual of a species due to various factors such as their elusive
nature or inaccessible habitats. As a result, Cowen et al., 2017 employ
two distinct modeling approaches: marked and unmarked models.
-
Marked Models: These models focus on individuals that have been
uniquely identified or ‘marked’ in some way, such as through
tagging, banding, or other identification methods. These marked
individuals are tracked over time, and their data is used to
estimate parameters related to the population, such as survival
rates, population growth, or movement patterns.
-
Unmarked Models: Unmarked models, on the other hand, are
designed to estimate population parameters without relying on
individual identification.
The beauty of combining these two modeling approaches lies in their
synergy. By leveraging both marked and unmarked data, ecologists can
achieve more accurate and robust estimates of population abundance.
Marked data provide insights into specific individuals, while unmarked
data give a broader perspective on the entire population.
In practice, this combination is achieved through sophisticated
statistical techniques, often utilizing concepts like the N-mixture
model and algorithms like the Viterbi algorithm. These methods allow
ecologists to integrate data from marked and unmarked individuals,
resulting in more comprehensive and reliable population abundance
estimates.
The models showcased in this example represent the foundational
instances drawn from a set of four complex models available within the
extBatchMarking package. These models serve as essential building
blocks for understanding the advanced functionalities and capabilities
offered by the package.
The extBatchMarking package is designed to empower researchers with a
powerful tool set for the analysis of batch-marked data in ecological
and population studies. It allows users to efficiently fit and assess
batch-marked models, aiding in the estimation of critical population
parameters such as survival and capture probabilities.
In particular, the models illustrated here provide a comprehensive
introduction to the core concepts and methodologies underpinning the
package’s functionality. They are intended to facilitate an initial
grasp of how to work with batch-marked data, offering insights into the
modeling techniques used in the field of population ecology.
It’s worth noting that the results obtained using the extBatchMarking
package align with the findings presented in Cowen et al. (2017). This
alignment demonstrates the package’s reliability and ability to
replicate established research outcomes. The Cowen et al. (2017) results
section serves as a benchmark against which the package’s performance
can be validated, providing users with confidence in the accuracy of
their analyses.
By starting with these basic examples, users can progressively delve
into more intricate and tailored analyses within the extBatchMarking
package, ultimately enabling them to make meaningful contributions to
the understanding of population dynamics and ecology. The package’s
versatility and fidelity to established research findings make it a
valuable resource for both novice and experienced researchers in the
field.
The example will guide you through the steps of how to employ this
approach effectively, demonstrating its relevance and importance in
ecological and wildlife studies. It showcases the power of merging
marked and unmarked models to gain a deeper understanding of species
populations and their dynamics within natural ecosystems.”
Installation
You can install the released version of extBatchMarking from
CRAN with:
devtools::load_all(".")
#> ℹ Loading extBatchMarking
devtools::document()
#> ℹ Updating extBatchMarking documentation
#> ℹ Loading extBatchMarking
devtools::load_all()
#> ℹ Loading extBatchMarking
Example 1
This is a basic example which shows how to fit a Batch marking model
with constant phi and p. Example 1 can also be found in the Cowen et
al., 2017 results using the WeatherLoach data used in the same paper:
Load the data WeatherLoach from the extBatchMarking package: Here is
the step-by-step guide on how to load data directly from
extBatchMarking package. The default data discussed in
Cowen et al. 2017.
data("WeatherLoach", package = "extBatchMarking")
First, we show with an example how to fit the batchMarkHmmLL and
batchMarkUnmarkHmmLL functions. batchMarkHmmLL and
batchMarkUnmarkHmmLL functions output the unoptimized log-likelihood
values of marked only model and the combined models. These allow users
know if the likelihood functions can be computed at the specified
initial values. Otherwise, NAN or Inf will be returned. If so, the
arguments of the functions should be revisited.
# Initial parameter
theta <- c(0, -1)
res1 <- batchMarkHmmLL(par = theta,
data = WeatherLoach,
choiceModel = "model4",
covariate_phi = NULL,
covariate_p = NULL)
res1
#> [1] 132.3349
[1] 132.3349
Example 2
thet <- c(0.1, 0.1, 7, -1.5)
res3 <- batchMarkUnmarkHmmLL(par = thet,
data = WeatherLoach,
choiceModel = "model4",
Umax = 1800,
nBins = 600,
covariate_phi = NULL,
covariate_p = NULL)
res3
#> [1] 870.0261
[1] 870.0261
Example 3
#> initial value 132.334856
#> final value 124.984186
#> converged
initial value 132.334856 final value 124.984186 converged
Print the results with the print.batchMarkOptim() function: This
prints to the console the log-likelihood, AIC, recapture probability and
survival probability with their corresponding standard errors.
print(res)
#> [[1]]
#>
#>
#> | log.likelihood| AIC|
#> |--------------:|--------:|
#> | 124.9842| 253.9684|
#>
#> [[2]]
#>
#>
#> | p| p_S.Error| phi| phi_S.Error|
#> |------:|---------:|------:|-----------:|
#> | 0.1964| 0.0206| 0.6042| 0.0261|
[[1]]
log.likelihood
AIC
124.9842
253.9684
[[2]]
p
p_S.Error
phi
phi_S.Error
0.1964
0.0206
0.6042
0.0261
Plot the results with the plot.batchMarkOptim() function: This plots
the goodness-of-fit plot to perform a goodness-of-fit test for the model
fit.
plot(res)
Example 4
This example serves as a fundamental illustration of the process of
combining both marked and unmarked models to estimate the population
abundance of a species. It demonstrates a key approach used in
ecological and wildlife studies to gain insights into the size of a
specific species population within a given habitat.
theta <- c(0.1, 0.1, 7, -1.5)
res2 <- batchMarkUnmarkOptim(par=theta,
data=WeatherLoach,
Umax=1800,
nBins=600,
choiceModel="model4",
popSize = "Horvitz_Thompson",
method="BFGS",
control=list(trace = 1),
covariate_phi = NULL,
covariate_p = NULL)
#> initial value 870.026082
#> iter 10 value 205.041347
#> final value 205.031738
#> converged
initial value 870.026082 iter 10 value 205.041347 final value 205.031738
converged
Print the results with the print.batchMarkUnmarkOptim() function: This
prints to the console the log-likelihood, AIC, recapture probability and
survival probability with their corresponding standard errors. The
species abundances are also provided which include number of unmarked
individuals, number of marked individuals, and Total abundance.
print(res2)
#> [[1]]
#>
#>
#> | log.likelihood| AIC|
#> |--------------:|--------:|
#> | 205.0317| 418.0635|
#>
#> [[2]]
#>
#>
#> | p| p_S.Error| phi| phi_S.Error|
#> |------:|---------:|-----:|-----------:|
#> | 0.1866| 0.0048| 0.614| 0.0169|
#>
#> [[3]]
#>
#>
#> | No.of.Unmarked.U.| No.of.Marked.M.| Abundance.N.|
#> |-----------------:|---------------:|------------:|
#> | 1500| 0| 1500|
#> | 900| 171| 1071|
#> | 900| 268| 1168|
#> | 900| 322| 1222|
#> | 300| 118| 418|
#> | 300| 107| 407|
#> | 300| 54| 354|
#> | 300| 86| 386|
#> | 300| 107| 407|
#> | 300| 139| 439|
#> | 300| 64| 364|
#>
#> [[4]]
#>
#>
#> | Lambda| Lambda_S.Error| Gam| Gam_S.Error|
#> |--------:|--------------:|------:|-----------:|
#> | 1346.844| 1903.361| 0.0599| 0.022|
[[1]]
log.likelihood
AIC
205.0317
418.0635
[[2]]
p
p_S.Error
phi
phi_S.Error
0.1866
0.0048
0.614
0.0169
[[3]]
No.of.Unmarked.U.
No.of.Marked.M.
Abundance.N.
1500
0
1500
900
171
1071
900
268
1168
900
322
1222
300
118
418
300
107
407
300
54
354
300
86
386
300
107
407
300
139
439
300
64
364
[[4]]
Lambda
Lambda_S.Error
Gam
Gam_S.Error
1346.844
1903.361
0.0599
0.022
Plot the results with the plot.batchMarkOptim() function: This plots
the googdness-of-fit plot to perform a goodness-of-fit test for the
model fit.
plot(res2)
Model 2 for marked model with covariate for phi
This provides some level of flexibility to the marked model by adding a
placeholder for time-dependent covariate to better estimate parameter
phi. For example, we might want to understand how temperature affects
the survival rate of a species.
#-------------------------------------------------
# Model 2: 10 phis and 1 prob
#-------------------------------------------------
theta <- c(-1, rep(0, 10))
cv <- matrix(seq(2, 10, length = 10), ncol = 1)
batchMarkHmmLL(theta, WeatherLoach, "model2", covariate_phi = cv, covariate_p = NULL)
#> [1] 132.3349
res <- batchMarkOptim(par=theta, data=WeatherLoach, covariate_phi = cv, covariate_p = NULL,
choiceModel = "model2", method="BFGS", control = list(trace = 1))
#> initial value 132.334856
#> iter 10 value 97.474508
#> iter 20 value 95.823647
#> iter 30 value 95.787362
#> iter 40 value 95.784462
#> iter 50 value 95.783391
#> iter 60 value 95.783072
#> final value 95.783042
#> converged
initial value 132.334856 iter 10 value 97.474508 iter 20 value 95.823647
iter 30 value 95.787362 iter 40 value 95.784462 iter 50 value 95.783391
iter 60 value 95.783072 final value 95.783042 converged
#-------------------------------------------------
# Model 2: 10 phis and 1 prob
#-------------------------------------------------
print(res)
#> [[1]]
#>
#>
#> | log.likelihood| AIC|
#> |--------------:|--------:|
#> | 95.783| 213.5661|
#>
#> [[2]]
#>
#>
#> | p| p_S.Error| phi| phi_S.Error|
#> |-----:|---------:|------:|-----------:|
#> | 0.181| 0.0316| 0.3268| 0.0000|
#> | 0.181| 0.0316| 0.0000| 0.0000|
#> | 0.181| 0.0316| 1.0000| 0.8321|
#> | 0.181| 0.0316| 0.1082| 0.1306|
#> | 0.181| 0.0316| 0.5680| 0.1388|
#> | 0.181| 0.0316| 0.4722| 0.0009|
#> | 0.181| 0.0316| 0.9973| 8.2224|
#> | 0.181| 0.0316| 0.6458| 0.0985|
#> | 0.181| 0.0316| 0.6619| 0.1316|
#> | 0.181| 0.0316| 0.4397| 0.0285|
[[1]]
log.likelihood
AIC
95.783
213.5661
[[2]]
p
p_S.Error
phi
phi_S.Error
0.181
0.0316
0.3268
0.0000
0.181
0.0316
0.0000
0.0000
0.181
0.0316
1.0000
0.8321
0.181
0.0316
0.1082
0.1306
0.181
0.0316
0.5680
0.1388
0.181
0.0316
0.4722
0.0009
0.181
0.0316
0.9973
8.2224
0.181
0.0316
0.6458
0.0985
0.181
0.0316
0.6619
0.1316
0.181
0.0316
0.4397
0.0285
plot(res)
Model 3 for marked model with covariate for p
This provides some level of flexibility to the marked model by adding a
placeholder for time-dependent covariate to better estimate parameter
p. For example, we might want to understand how temperature affects the
survival rate of a species.
#-------------------------------------------------
# Model 3: 1 phis and 10 prob
#-------------------------------------------------
theta <- c(-1, rep(0, 10))
cv <- matrix(seq(2, 10, length = 10), ncol = 1)
batchMarkHmmLL(theta, WeatherLoach, "model3", covariate_phi = NULL, covariate_p = cv)
#> [1] 200.0016
res <- batchMarkOptim(par=theta, data=WeatherLoach, covariate_phi = NULL, covariate_p = cv,
choiceModel = "model3", method="BFGS", control = list(trace = 1))
#> initial value 200.001592
#> iter 10 value 114.293180
#> final value 97.288967
#> converged
initial value 200.001592 iter 10 value 114.293180 final value 97.288967
converged
#-------------------------------------------------
# Model 2: 1 phis and 10 prob
#-------------------------------------------------
print(res)
#> [[1]]
#>
#>
#> | log.likelihood| AIC|
#> |--------------:|--------:|
#> | 97.289| 216.5779|
#>
#> [[2]]
#>
#>
#> | p| p_S.Error| phi| phi_S.Error|
#> |------:|---------:|-----:|-----------:|
#> | 0.9559| 0.0182| 0.627| 0.0297|
#> | 0.9991| 0.0011| 0.627| 0.0297|
#> | 0.0084| 0.0099| 0.627| 0.0297|
#> | 0.0156| 0.0078| 0.627| 0.0297|
#> | 0.0793| 0.0241| 0.627| 0.0297|
#> | 0.0933| 0.0260| 0.627| 0.0297|
#> | 0.2411| 0.0410| 0.627| 0.0297|
#> | 0.3234| 0.0388| 0.627| 0.0297|
#> | 0.3903| 0.0352| 0.627| 0.0297|
#> | 0.3164| 0.0311| 0.627| 0.0297|
plot(res)
[[1]]
log.likelihood
AIC
97.289
216.5779
[[2]]
p
p_S.Error
phi
phi_S.Error
0.9559
0.0182
0.627
0.0297
0.9991
0.0011
0.627
0.0297
0.0084
0.0099
0.627
0.0297
0.0156
0.0078
0.627
0.0297
0.0793
0.0241
0.627
0.0297
0.0933
0.0260
0.627
0.0297
0.2411
0.0410
0.627
0.0297
0.3234
0.0388
0.627
0.0297
0.3903
0.0352
0.627
0.0297
0.3164
0.0311
0.627
0.0297
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extBatchMarking: Implementation of Extended Batch Marking Model
The primary objective of extBatchMarking is to facilitate the fitting
of models developed by Cowen et al., 2017 for the ecologist. The marked
models can be seamlessly integrated with unmarked models to estimate
population size. The combined model harnesses the power of both the
N-mixture model and the Viterbi algorithm for hidden markov model to
provide accurate population size estimates.
The primary objective of extBatchMarking is to facilitate the fitting
of models developed by Cowen et al., 2017 for the ecologist. The marked
models can be seamlessly integrated with unmarked models to estimate
population size. The combined model harnesses the power of both the
N-mixture model and the Viterbi algorithm for hidden markov model to
provide accurate population size estimates.
In ecological research, it’s often challenging to directly count every individual of a species due to various factors such as their elusive nature or inaccessible habitats. As a result, Cowen et al., 2017 employ two distinct modeling approaches: marked and unmarked models.
-
Marked Models: These models focus on individuals that have been uniquely identified or ‘marked’ in some way, such as through tagging, banding, or other identification methods. These marked individuals are tracked over time, and their data is used to estimate parameters related to the population, such as survival rates, population growth, or movement patterns.
-
Unmarked Models: Unmarked models, on the other hand, are designed to estimate population parameters without relying on individual identification.
The beauty of combining these two modeling approaches lies in their synergy. By leveraging both marked and unmarked data, ecologists can achieve more accurate and robust estimates of population abundance. Marked data provide insights into specific individuals, while unmarked data give a broader perspective on the entire population.
In practice, this combination is achieved through sophisticated statistical techniques, often utilizing concepts like the N-mixture model and algorithms like the Viterbi algorithm. These methods allow ecologists to integrate data from marked and unmarked individuals, resulting in more comprehensive and reliable population abundance estimates.
The models showcased in this example represent the foundational
instances drawn from a set of four complex models available within the
extBatchMarking package. These models serve as essential building
blocks for understanding the advanced functionalities and capabilities
offered by the package.
The extBatchMarking package is designed to empower researchers with a
powerful tool set for the analysis of batch-marked data in ecological
and population studies. It allows users to efficiently fit and assess
batch-marked models, aiding in the estimation of critical population
parameters such as survival and capture probabilities.
In particular, the models illustrated here provide a comprehensive introduction to the core concepts and methodologies underpinning the package’s functionality. They are intended to facilitate an initial grasp of how to work with batch-marked data, offering insights into the modeling techniques used in the field of population ecology.
It’s worth noting that the results obtained using the extBatchMarking
package align with the findings presented in Cowen et al. (2017). This
alignment demonstrates the package’s reliability and ability to
replicate established research outcomes. The Cowen et al. (2017) results
section serves as a benchmark against which the package’s performance
can be validated, providing users with confidence in the accuracy of
their analyses.
By starting with these basic examples, users can progressively delve
into more intricate and tailored analyses within the extBatchMarking
package, ultimately enabling them to make meaningful contributions to
the understanding of population dynamics and ecology. The package’s
versatility and fidelity to established research findings make it a
valuable resource for both novice and experienced researchers in the
field.
The example will guide you through the steps of how to employ this approach effectively, demonstrating its relevance and importance in ecological and wildlife studies. It showcases the power of merging marked and unmarked models to gain a deeper understanding of species populations and their dynamics within natural ecosystems.”
Installation
You can install the released version of extBatchMarking from
CRAN with:
devtools::load_all(".")
#> ℹ Loading extBatchMarking
devtools::document()
#> ℹ Updating extBatchMarking documentation
#> ℹ Loading extBatchMarking
devtools::load_all()
#> ℹ Loading extBatchMarking
Example 1
This is a basic example which shows how to fit a Batch marking model
with constant phi and p. Example 1 can also be found in the Cowen et
al., 2017 results using the WeatherLoach data used in the same paper:
Load the data WeatherLoach from the extBatchMarking package: Here is
the step-by-step guide on how to load data directly from
extBatchMarking package. The default data discussed in
Cowen et al. 2017.
data("WeatherLoach", package = "extBatchMarking")
First, we show with an example how to fit the batchMarkHmmLL and
batchMarkUnmarkHmmLL functions. batchMarkHmmLL and
batchMarkUnmarkHmmLL functions output the unoptimized log-likelihood
values of marked only model and the combined models. These allow users
know if the likelihood functions can be computed at the specified
initial values. Otherwise, NAN or Inf will be returned. If so, the
arguments of the functions should be revisited.
# Initial parameter
theta <- c(0, -1)
res1 <- batchMarkHmmLL(par = theta,
data = WeatherLoach,
choiceModel = "model4",
covariate_phi = NULL,
covariate_p = NULL)
res1
#> [1] 132.3349
[1] 132.3349
Example 2
thet <- c(0.1, 0.1, 7, -1.5)
res3 <- batchMarkUnmarkHmmLL(par = thet,
data = WeatherLoach,
choiceModel = "model4",
Umax = 1800,
nBins = 600,
covariate_phi = NULL,
covariate_p = NULL)
res3
#> [1] 870.0261
[1] 870.0261
Example 3
#> initial value 132.334856
#> final value 124.984186
#> converged
initial value 132.334856 final value 124.984186 converged
Print the results with the print.batchMarkOptim() function: This
prints to the console the log-likelihood, AIC, recapture probability and
survival probability with their corresponding standard errors.
print(res)
#> [[1]]
#>
#>
#> | log.likelihood| AIC|
#> |--------------:|--------:|
#> | 124.9842| 253.9684|
#>
#> [[2]]
#>
#>
#> | p| p_S.Error| phi| phi_S.Error|
#> |------:|---------:|------:|-----------:|
#> | 0.1964| 0.0206| 0.6042| 0.0261|
[[1]]
log.likelihood AIC 124.9842 253.9684[[2]]
p p_S.Error phi phi_S.Error 0.1964 0.0206 0.6042 0.0261Plot the results with the plot.batchMarkOptim() function: This plots
the goodness-of-fit plot to perform a goodness-of-fit test for the model
fit.
plot(res)
Example 4
This example serves as a fundamental illustration of the process of combining both marked and unmarked models to estimate the population abundance of a species. It demonstrates a key approach used in ecological and wildlife studies to gain insights into the size of a specific species population within a given habitat.
theta <- c(0.1, 0.1, 7, -1.5)
res2 <- batchMarkUnmarkOptim(par=theta,
data=WeatherLoach,
Umax=1800,
nBins=600,
choiceModel="model4",
popSize = "Horvitz_Thompson",
method="BFGS",
control=list(trace = 1),
covariate_phi = NULL,
covariate_p = NULL)
#> initial value 870.026082
#> iter 10 value 205.041347
#> final value 205.031738
#> converged
initial value 870.026082 iter 10 value 205.041347 final value 205.031738 converged
Print the results with the print.batchMarkUnmarkOptim() function: This
prints to the console the log-likelihood, AIC, recapture probability and
survival probability with their corresponding standard errors. The
species abundances are also provided which include number of unmarked
individuals, number of marked individuals, and Total abundance.
print(res2)
#> [[1]]
#>
#>
#> | log.likelihood| AIC|
#> |--------------:|--------:|
#> | 205.0317| 418.0635|
#>
#> [[2]]
#>
#>
#> | p| p_S.Error| phi| phi_S.Error|
#> |------:|---------:|-----:|-----------:|
#> | 0.1866| 0.0048| 0.614| 0.0169|
#>
#> [[3]]
#>
#>
#> | No.of.Unmarked.U.| No.of.Marked.M.| Abundance.N.|
#> |-----------------:|---------------:|------------:|
#> | 1500| 0| 1500|
#> | 900| 171| 1071|
#> | 900| 268| 1168|
#> | 900| 322| 1222|
#> | 300| 118| 418|
#> | 300| 107| 407|
#> | 300| 54| 354|
#> | 300| 86| 386|
#> | 300| 107| 407|
#> | 300| 139| 439|
#> | 300| 64| 364|
#>
#> [[4]]
#>
#>
#> | Lambda| Lambda_S.Error| Gam| Gam_S.Error|
#> |--------:|--------------:|------:|-----------:|
#> | 1346.844| 1903.361| 0.0599| 0.022|
[[1]]
log.likelihood AIC 205.0317 418.0635[[2]]
p p_S.Error phi phi_S.Error 0.1866 0.0048 0.614 0.0169[[3]]
No.of.Unmarked.U. No.of.Marked.M. Abundance.N. 1500 0 1500 900 171 1071 900 268 1168 900 322 1222 300 118 418 300 107 407 300 54 354 300 86 386 300 107 407 300 139 439 300 64 364[[4]]
Lambda Lambda_S.Error Gam Gam_S.Error 1346.844 1903.361 0.0599 0.022Plot the results with the plot.batchMarkOptim() function: This plots
the googdness-of-fit plot to perform a goodness-of-fit test for the
model fit.
plot(res2)
Model 2 for marked model with covariate for phi
This provides some level of flexibility to the marked model by adding a placeholder for time-dependent covariate to better estimate parameter phi. For example, we might want to understand how temperature affects the survival rate of a species.
#-------------------------------------------------
# Model 2: 10 phis and 1 prob
#-------------------------------------------------
theta <- c(-1, rep(0, 10))
cv <- matrix(seq(2, 10, length = 10), ncol = 1)
batchMarkHmmLL(theta, WeatherLoach, "model2", covariate_phi = cv, covariate_p = NULL)
#> [1] 132.3349
res <- batchMarkOptim(par=theta, data=WeatherLoach, covariate_phi = cv, covariate_p = NULL,
choiceModel = "model2", method="BFGS", control = list(trace = 1))
#> initial value 132.334856
#> iter 10 value 97.474508
#> iter 20 value 95.823647
#> iter 30 value 95.787362
#> iter 40 value 95.784462
#> iter 50 value 95.783391
#> iter 60 value 95.783072
#> final value 95.783042
#> converged
initial value 132.334856 iter 10 value 97.474508 iter 20 value 95.823647 iter 30 value 95.787362 iter 40 value 95.784462 iter 50 value 95.783391 iter 60 value 95.783072 final value 95.783042 converged
#-------------------------------------------------
# Model 2: 10 phis and 1 prob
#-------------------------------------------------
print(res)
#> [[1]]
#>
#>
#> | log.likelihood| AIC|
#> |--------------:|--------:|
#> | 95.783| 213.5661|
#>
#> [[2]]
#>
#>
#> | p| p_S.Error| phi| phi_S.Error|
#> |-----:|---------:|------:|-----------:|
#> | 0.181| 0.0316| 0.3268| 0.0000|
#> | 0.181| 0.0316| 0.0000| 0.0000|
#> | 0.181| 0.0316| 1.0000| 0.8321|
#> | 0.181| 0.0316| 0.1082| 0.1306|
#> | 0.181| 0.0316| 0.5680| 0.1388|
#> | 0.181| 0.0316| 0.4722| 0.0009|
#> | 0.181| 0.0316| 0.9973| 8.2224|
#> | 0.181| 0.0316| 0.6458| 0.0985|
#> | 0.181| 0.0316| 0.6619| 0.1316|
#> | 0.181| 0.0316| 0.4397| 0.0285|
[[1]]
log.likelihood AIC 95.783 213.5661[[2]]
p p_S.Error phi phi_S.Error 0.181 0.0316 0.3268 0.0000 0.181 0.0316 0.0000 0.0000 0.181 0.0316 1.0000 0.8321 0.181 0.0316 0.1082 0.1306 0.181 0.0316 0.5680 0.1388 0.181 0.0316 0.4722 0.0009 0.181 0.0316 0.9973 8.2224 0.181 0.0316 0.6458 0.0985 0.181 0.0316 0.6619 0.1316 0.181 0.0316 0.4397 0.0285plot(res)
Model 3 for marked model with covariate for p
This provides some level of flexibility to the marked model by adding a placeholder for time-dependent covariate to better estimate parameter p. For example, we might want to understand how temperature affects the survival rate of a species.
#-------------------------------------------------
# Model 3: 1 phis and 10 prob
#-------------------------------------------------
theta <- c(-1, rep(0, 10))
cv <- matrix(seq(2, 10, length = 10), ncol = 1)
batchMarkHmmLL(theta, WeatherLoach, "model3", covariate_phi = NULL, covariate_p = cv)
#> [1] 200.0016
res <- batchMarkOptim(par=theta, data=WeatherLoach, covariate_phi = NULL, covariate_p = cv,
choiceModel = "model3", method="BFGS", control = list(trace = 1))
#> initial value 200.001592
#> iter 10 value 114.293180
#> final value 97.288967
#> converged
initial value 200.001592 iter 10 value 114.293180 final value 97.288967 converged
#-------------------------------------------------
# Model 2: 1 phis and 10 prob
#-------------------------------------------------
print(res)
#> [[1]]
#>
#>
#> | log.likelihood| AIC|
#> |--------------:|--------:|
#> | 97.289| 216.5779|
#>
#> [[2]]
#>
#>
#> | p| p_S.Error| phi| phi_S.Error|
#> |------:|---------:|-----:|-----------:|
#> | 0.9559| 0.0182| 0.627| 0.0297|
#> | 0.9991| 0.0011| 0.627| 0.0297|
#> | 0.0084| 0.0099| 0.627| 0.0297|
#> | 0.0156| 0.0078| 0.627| 0.0297|
#> | 0.0793| 0.0241| 0.627| 0.0297|
#> | 0.0933| 0.0260| 0.627| 0.0297|
#> | 0.2411| 0.0410| 0.627| 0.0297|
#> | 0.3234| 0.0388| 0.627| 0.0297|
#> | 0.3903| 0.0352| 0.627| 0.0297|
#> | 0.3164| 0.0311| 0.627| 0.0297|
plot(res)
[[1]]
log.likelihood AIC 97.289 216.5779[[2]]
p p_S.Error phi phi_S.Error 0.9559 0.0182 0.627 0.0297 0.9991 0.0011 0.627 0.0297 0.0084 0.0099 0.627 0.0297 0.0156 0.0078 0.627 0.0297 0.0793 0.0241 0.627 0.0297 0.0933 0.0260 0.627 0.0297 0.2411 0.0410 0.627 0.0297 0.3234 0.0388 0.627 0.0297 0.3903 0.0352 0.627 0.0297 0.3164 0.0311 0.627 0.0297Try the extBatchMarking package in your browser
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