The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.
tinyVAST includes features to fit a dynamic structural
equation model. We here show this using a bivariate vector
autoregressive model for wolf and moose abundance on Isle Royale.
data(isle_royale, package="dsem")
# Convert to long-form
data = expand.grid( "time"=isle_royale[,1], "var"=colnames(isle_royale[,2:3]) )
data$logn = unlist(log(isle_royale[2:3]))
# Define cross-lagged DSEM
dsem = "
# Link, lag, param_name
wolves -> wolves, 1, arW
moose -> wolves, 1, MtoW
wolves -> moose, 1, WtoM
moose -> moose, 1, arM
#wolves -> moose, 0, corr
wolves <-> moose, 0, corr
"
# fit model
mytiny = tinyVAST( spacetime_term = dsem,
data = data,
times = isle_royale[,1],
variables = colnames(isle_royale[,2:3]),
formula = logn ~ 0 + var )
mytiny
#> Call:
#> tinyVAST(formula = logn ~ 0 + var, data = data, spacetime_term = dsem,
#> times = isle_royale[, 1], variables = colnames(isle_royale[,
#> 2:3]))
#>
#> Run time:
#> Time difference of 0.3189759 secs
#>
#> Family:
#> $obs
#>
#> Family: gaussian
#> Link function: identity
#>
#>
#>
#>
#> sdreport(.) result
#> Estimate Std. Error
#> alpha_j 3.32526197 2.483494e-01
#> alpha_j 6.44165343 2.116035e-01
#> beta_z 0.89304266 8.420632e-02
#> beta_z 0.01420908 1.279150e-01
#> beta_z -0.13239996 3.454997e-02
#> beta_z 0.86147627 7.107386e-02
#> beta_z -0.01285890 5.063467e-02
#> beta_z 0.37727131 3.504314e-02
#> beta_z 0.17062266 1.584742e-02
#> log_sigma -12.62352160 2.012258e+04
#> Maximum gradient component: 3.60018e-05
#>
#> Proportion conditional deviance explained:
#> [1] 1
#>
#> spacetime_term:
#> heads to from parameter start lag Estimate Std_Error z_value
#> 1 1 wolves wolves 1 <NA> 1 0.89304266 0.08420632 10.6054118
#> 2 1 wolves moose 2 <NA> 1 0.01420908 0.12791496 0.1110823
#> 3 1 moose wolves 3 <NA> 1 -0.13239996 0.03454997 -3.8321293
#> 4 1 moose moose 4 <NA> 1 0.86147627 0.07107386 12.1208601
#> 5 2 moose wolves 5 <NA> 0 -0.01285890 0.05063467 -0.2539545
#> 6 2 wolves wolves 6 <NA> 0 0.37727131 0.03504314 10.7659099
#> 7 2 moose moose 7 <NA> 0 0.17062266 0.01584742 10.7665881
#> p_value
#> 1 2.812223e-26
#> 2 9.115511e-01
#> 3 1.270389e-04
#> 4 8.189516e-34
#> 5 7.995307e-01
#> 6 4.986648e-27
#> 7 4.950067e-27
#>
#> Fixed terms:
#> Estimate Std_Error z_value p_value
#> varwolves 3.325262 0.2483494 13.38945 6.969636e-41
#> varmoose 6.441653 0.2116035 30.44210 1.524034e-203
# Deviance explained relative to both intercepts
# Note that a process-error-only estimate with have devexpl -> 1
deviance_explained( mytiny,
null_formula = logn ~ 0 + var )
#> [1] 1
# See summary
knitr::kable( summary(mytiny,"spacetime_term"), digits=3 )| heads | to | from | parameter | start | lag | Estimate | Std_Error | z_value | p_value |
|---|---|---|---|---|---|---|---|---|---|
| 1 | wolves | wolves | 1 | NA | 1 | 0.893 | 0.084 | 10.605 | 0.000 |
| 1 | wolves | moose | 2 | NA | 1 | 0.014 | 0.128 | 0.111 | 0.912 |
| 1 | moose | wolves | 3 | NA | 1 | -0.132 | 0.035 | -3.832 | 0.000 |
| 1 | moose | moose | 4 | NA | 1 | 0.861 | 0.071 | 12.121 | 0.000 |
| 2 | moose | wolves | 5 | NA | 0 | -0.013 | 0.051 | -0.254 | 0.800 |
| 2 | wolves | wolves | 6 | NA | 0 | 0.377 | 0.035 | 10.766 | 0.000 |
| 2 | moose | moose | 7 | NA | 0 | 0.171 | 0.016 | 10.767 | 0.000 |
And we can specifically inspect the estimated interaction matrix:
| wolves | moose | |
|---|---|---|
| wolves | 0.893 | -0.132 |
| moose | 0.014 | 0.861 |
We can then compare this with package dsem
library(dsem)
# Keep in wide-form
dsem_data = ts( log(isle_royale[,2:3]), start=1959)
Family = c("normal", "normal")
# fit without delta0
# SEs aren't available because measurement errors goes to zero
mydsem = dsem::dsem( sem = dsem,
tsdata = dsem_data,
control = dsem_control(getsd=FALSE),
family = Family )
#> Coefficient_name Number_of_coefficients Type
#> 1 beta_z 7 Fixed
#> 2 lnsigma_j 2 Fixed
#> 3 mu_j 2 Random
#> 4 x_tj 122 Random
mydsem
#> $par
#> beta_z beta_z beta_z beta_z beta_z
#> 0.895834720 0.007358847 -0.124879928 0.874884847 -0.014394603
#> beta_z beta_z lnsigma_j lnsigma_j
#> 0.378522244 0.172997994 -17.248978101 -12.636038113
#>
#> $objective
#> [1] 7.739638
#> attr(,"logarithm")
#> [1] TRUE
#>
#> $convergence
#> [1] 0
#>
#> $iterations
#> [1] 74
#>
#> $evaluations
#> function gradient
#> 96 75
#>
#> $message
#> [1] "relative convergence (4)"
# See summary
knitr::kable( summary(mydsem), digits=3 )| path | lag | name | start | parameter | first | second | direction | Estimate |
|---|---|---|---|---|---|---|---|---|
| wolves -> wolves | 1 | arW | NA | 1 | wolves | wolves | 1 | 0.896 |
| moose -> wolves | 1 | MtoW | NA | 2 | moose | wolves | 1 | 0.007 |
| wolves -> moose | 1 | WtoM | NA | 3 | wolves | moose | 1 | -0.125 |
| moose -> moose | 1 | arM | NA | 4 | moose | moose | 1 | 0.875 |
| wolves <-> moose | 0 | corr | NA | 5 | wolves | moose | 2 | -0.014 |
| wolves <-> wolves | 0 | V[wolves] | NA | 6 | wolves | wolves | 2 | 0.379 |
| moose <-> moose | 0 | V[moose] | NA | 7 | moose | moose | 2 | 0.173 |
where we again inspect the estimated interaction matrix:
| wolves | moose | |
|---|---|---|
| wolves | 0.896 | -0.125 |
| moose | 0.007 | 0.875 |
Runtime for this vignette: 1.21 secs
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.