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Dynamic structural equation models

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## Dynamic structural equation models <a href='https://github.com/James-Thorson-NOAA/dsem'><img src='man/figures/logo.png' align="right" style="height:139px;"/></a>

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Package _dsem_ fits dynamic structural equation models, which includes as nested submodels:

1. structural equation models, including moderated variables
2. structural vector autoregressive models
3. dynamic factor analysis
4. state-space autoregressive integrated moving average (ARIMA) models
5. random-slope time-series models

The model has several advantages:

* It estimates direct, indirect, and total effects among system variables, including simultaneous and lagged effects, recursive (cyclic) dependencies, latent variables, moderated variables, and a variety of parametric families including variables without measurement error
* It can estimate the cumulative outcome from press or pulse experiments or initial conditions that differ from the stationary distribution of system dynamics
* It estimates structural linkages as regression slopes while jointly imputing missing values and/or measurement errors
* It is rapidly fitted as a Gaussian Markov random field (GMRF) in a Generalized Linear Mixed Model (GLMM), with speed and asymptotics associated with each, including (where identifiable) in models with any combination of cyclic dependencies, missing data, and variables without measurement error
* It allows granular control over the number of parameters (and restrictions on parameters) used to structure the covariance among variables and over time,

_dsem_ is specifically intended as a minimal implementation, and uses standard packages to simplify input/output formatting:

* Input: time-series defined using class _ts_, with `NA` for missing values
* Input: structural trade-offs specified using syntax defined by package _sem_
* Input: distributions for data specified using `family` arguments, e.g., as used in `glm(.)`
* Output: visualizing estimated trade-offs using _igraph_
* Output: access model output using standard S3-generic functions including `summary`, `predict`, `residuals`, `simulate`, and `AIC`

Please see package vignettes for more details regarding syntax and features.

### Citation

_For description of dynamic structural equation models and path-lag interface_

Thorson, J. T., Andrews, A. G., Essington, T., & Large, S. (2024). Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms. Methods in Ecology and Evolution 15(4): 744-755. https://doi.org/10.1111/2041-210X.14289

_For description of generalized graphical mixed models in general_

Thorson, J. T. (2026). Generalized graphical mixed models connect ecological theory with widely used statistical models. Methods in Ecology and Evolution, 17(4), 1290–1302. https://doi.org/10.1111/2041-210x.70272

_For description of moderated DSEM and varying path coefficients_

Thorson, J. T., & Kristensen, K. (In press). Ecological examples of nonstationarity, nonlinearity, and statistical interactions in dynamic structural equation models. Methods in Ecology and Evolution. https://ecoevorxiv.org/repository/view/11418/

# NOAA Enterprise GitHub disclaimer
This repository is a scientific product and is not official communication of the National Oceanic and Atmospheric Administration, or the United States Department of Commerce. All NOAA GitHub project code is provided on an ‘as is’ basis and the user assumes responsibility for its use. Any claims against the Department of Commerce or Department of Commerce bureaus stemming from the use of this GitHub project will be governed by all applicable Federal law. Any reference to specific commercial products, processes, or services by service mark, trademark, manufacturer, or otherwise, does not constitute or imply their endorsement, recommendation or favoring by the Department of Commerce. The Department of Commerce seal and logo, or the seal and logo of a DOC bureau, shall not be used in any manner to imply endorsement of any commercial product or activity by DOC or the United States Government.

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