dsem: Fit dynamic structural equation model

In dsem: Dynamic Structural Equation Models

Fit dynamic structural equation model

Description

Fits a dynamic structural equation model

Usage

dsem(
  sem,
  tsdata,
  family = rep("fixed", ncol(tsdata)),
  estimate_delta0 = FALSE,
  prior_negloglike = NULL,
  control = dsem_control(),
  covs = colnames(tsdata)
)

Arguments

sem	Specification for time-series structural equation model structure including lagged or simultaneous effects. See Details section in make_dsem_ram for more description
tsdata	time-series data, as outputted using ts, with NA for missing values.
family	Character-vector listing the distribution used for each column of tsdata, where each element must be fixed (for no measurement error), normal for normal measurement error using an identity link, gamma for a gamma measurement error using a fixed CV and log-link, bernoulli for a Bernoulli measurement error using a logit-link, or poisson for a Poisson measurement error using a log-link. family="fixed" is default behavior and assumes that a given variable is measured exactly. Other options correspond to different specifications of measurement error.
estimate_delta0	Boolean indicating whether to estimate deviations from equilibrium in initial year as fixed effects, or alternatively to assume that dynamics start at some stochastic draw away from the stationary distribution
prior_negloglike	A user-provided function that takes as input the vector of fixed effects out$obj$par returns the negative log-prior probability. For example prior_negloglike = function(obj) -1 * dnorm( obj$par[1], mean=0, sd=0.1, log=TRUE) specifies a normal prior probability for the for the first fixed effect with mean of zero and logsd of 0.1. NOTE: this implementation does not work well with tmbstan and is highly experimental. If using priors, considering using dsemRTMB instead. The option in dsem is mainly intended to validate its use in dsemRTMB. Note that the user must load RTMB using library(RTMB) prior to running the model.
control	Output from dsem_control, used to define user settings, and see documentation for that function for details.
covs	optional: a character vector of one or more elements, with each element giving a string of variable names, separated by commas. Variances and covariances among all variables in each such string are added to the model. Warning: covs="x1, x2" and covs=c("x1", "x2") are not equivalent: covs="x1, x2" specifies the variance of x1, the variance of x2, and their covariance, while covs=c("x1", "x2") specifies the variance of x1 and the variance of x2 but not their covariance. These same covariances can be added manually via argument sem, but using argument covs might save time for models with many variables.

Details

A DSEM involves (at a minimum):

Time series

a matrix \mathbf X where column \mathbf x_c for variable c is a time-series;

Path diagram

a user-supplied specification for the path coefficients, which define the precision (inverse covariance) \mathbf Q for a matrix of state-variables and see make_dsem_ram for more details on the math involved.

The model also estimates the time-series mean \mathbf{\mu}_c for each variable. The mean and precision matrix therefore define a Gaussian Markov random field for \mathbf X:

\mathrm{vec}(\mathbf X) \sim \mathrm{MVN}( \mathrm{vec}(\mathbf{I_T} \otimes \mathbf{\mu}), \mathbf{Q}^{-1})

Users can the specify a distribution for measurement errors (or assume that variables are measured without error) using argument family. This defines the link-function g_c(.) and distribution f_c(.) for each time-series c:

y_{t,c} \sim f_c( g_c^{-1}( x_{t,c} ), \theta_c )

dsem then estimates all specified coefficients, time-series means \mu_c, and distribution measurement errors \theta_c via maximizing a log-marginal likelihood, while also estimating state-variables x_{t,c}. summary.dsem then assembles estimates and standard errors in an easy-to-read format. Standard errors for fixed effects (path coefficients, exogenoux variance parameters, and measurement error parameters) are estimated from the matrix of second derivatives of the log-marginal likelihod, and standard errors for random effects (i.e., missing or state-space variables) are estimated from a generalization of this method (see sdreport for details).

Latent variables

Any column \mathbf x_c of tsdata that includes only NA values represents a latent variable, and all others are called manifest variables. The identifiability criteria for latent variables can be complicated. To explain, we ignore lagged effects (only simultaneous paths) and classify three types of latent variables:

factor latent variables:

any latent variable \mathbf F that includes paths out from it to manifest variables, but has no paths from manifest variables into \mathbf F is a factor variable. These are identifable by fixing their SD (i.e., at one), and using a trimmed Cholesky parameterization (i.e., each successive factor includes fewer paths to manifest variables). See the DFA vignette for an example. Factor latent variables can be used to represent residual covariance while also estimating the source of that covariance explicitly

intermediate latent variables:

Any latent variable \mathbf Y that includes paths in from some manifest variables \mathbf X and some paths out to manifest variables \mathbf Z is an intermediate latent variable. In general, the at least one path in or out must be fixed a priori (e.g., at one) to identify the scale of the intermediate LV. These intermediate latent variables can represent ecological concepts that serve as intermediate link between different manifest variables

composite latent variables:

Any latent variable \mathbf C that includes paths in from some manifest variables \mathbf X and no paths out to manifest variables is a composite latent variable. In general, you must fix all paths to composite variables a priori, and must also fix the SD a priori (e.g., at zero). These composite variables allow DSEM to estimate a response with standard errors that integrates across multiple manifest variables

As stated, these criteria do not involve paths from one to another latent variable. These are also possible, but involve more complicated identifiability criteria.

When to do (ot not do) model selection

In general, DSEM can be used for predictive modelling and/or structural causal modelling.

For predictive modelling, DSEM provides an expressive interface to specify any number of fixed effects and use these to represent the covariance among variables and over time. The predictive error is expected to decrease when using a parsimonious model, and model selection might be appropriate using either stepwise_selection or some manual rule for dropping coefficients that are not statistically significant using a likelihood ratio or Wald test.

However, structural causal modelling (SCM) is necessary for models to be transferable to new environments (patterns of colinearity), or for counterfactual analysis. In general, SCM does not involve using parsimony as a basis for model selection. Instead, SCM structure should be defined based on ecological knowledge, and models can be further elaborated using tests of directional separation (see test_dsep).

Value

An object (list) of class dsem. Elements include:

obj

TMB object from MakeADFun

ram

RAM parsed by make_dsem_ram

model

SEM structure parsed by make_dsem_ram as intermediate description of model linkages

tmb_inputs

The list of inputs passed to MakeADFun

opt

The output from nlminb

sdrep

The output from sdreport

interal

Objects useful for package function, i.e., all arguments passed during the call

run_time

Total time to run model

References

Introducing the package, its features, and comparison with other software (to cite when using dsem):

Thorson, J. T., Andrews, A., Essington, T., Large, S. (2024). Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms. Methods in Ecology and Evolution. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/2041-210X.14289")}

Examples

# Define model
sem = "
  # Link, lag, param_name
  cprofits -> consumption, 0, a1
  cprofits -> consumption, 1, a2
  pwage -> consumption, 0, a3
  gwage -> consumption, 0, a3
  cprofits -> invest, 0, b1
  cprofits -> invest, 1, b2
  capital -> invest, 0, b3
  gnp -> pwage, 0, c2
  gnp -> pwage, 1, c3
  time -> pwage, 0, c1
"

# Load data
data(KleinI, package="AER")
TS = ts(data.frame(KleinI, "time"=time(KleinI) - 1931))
tsdata = TS[,c("time","gnp","pwage","cprofits",'consumption',
               "gwage","invest","capital")]

# Fit model
fit = dsem( sem=sem,
            tsdata = tsdata,
            estimate_delta0 = TRUE,
            control = dsem_control(quiet=TRUE) )
summary( fit )
plot( fit )
plot( fit, edge_label="value" )

dsem documentation built on Sept. 16, 2025, 9:10 a.m.