The modelling problem

Let \(y_{itj}\) denote variable \(j\) for person \(i\) at occasion \(t\). The central target is the conditional relation among variables within a person’s ordered series. A temporal edge from -> to means from at \(t-1\) predicts to at \(t\), holding the other lagged variables constant. A contemporaneous edge is an undirected partial correlation: the within-occasion association left after lagged predictors and the remaining variables are conditioned out (Bringmann et al. 2013; Epskamp et al. 2018).

Single-subject VAR and graphical VAR estimate one parameter set for one person. Subject-network estimators repeat that single-person analysis for every person. Multilevel VAR and Bayesian DSEM estimate an average within-person dynamic system, optionally adding random effects or a between-person network. uSEM and GIMME treat the same lagged and contemporaneous relations as structural paths, with GIMME adding a group-search rule for paths shared by many people.

Method selection

Ordinary VAR is the transparent baseline when one person has many occasions relative to the number of variables. Graphical VAR is preferable when sparsity is substantively defensible or the number of candidate edges is large, because EBIC-regularized LASSO and graphical-lasso estimation shrink weak temporal and contemporaneous edges to zero.

Subject networks are appropriate when heterogeneity is itself the target. Multilevel VAR is appropriate when the target is an average within-person process across people and the analyst accepts partial pooling. Bayesian VAR and DSEM are appropriate when uncertainty intervals and dynamic SEM formulations are central. The native Bayesian examples are executed during vignette building; only the licensed external Mplus call is shown without execution.

Data and preprocessing

The package example is the srl data set: 36 students, 156 occasions per student, and nine self-regulated-learning indicators. The method vignettes use the same five-variable subset so that printed matrices remain readable.

vars <- c("efficacy", "value", "planning", "monitoring", "effort")

The preprocessing audit constructs the same lag-one design used by the estimators and reports stationarity risks, missingness, and retained pairs.

audit <- preprocess(srl, vars = vars, id = "name", min_obs = 100)
audit
#> Idiographic Preprocessing
#>   Variables:      5 (efficacy, value, planning, monitoring, effort)
#>   Ordered rows:   5616
#>   Retained pairs: 5548
#>   Trend flags:    10
#>   High AR flags:  0
#>   Drift flags:    1
#>   Unit-root risk: 0
#>   Zero variance:  0
#>   Tables:         x$pairs | x$counts | x$diagnostics
#> 
#> 10 of 180 subject-series show a trend or unit-root that can bias the temporal network. preprocess() only diagnosed this; to clean just the series that need it, re-run with:
#>   preprocess(data = srl, vars = vars, id = "name", min_obs = 100, detrend = "auto")

The audit retains 5548 lagged pairs from 5616 rows. It reports 10 trend flags, one drift flag, no high-autoregression flags, no unit-root risk, and no zero-variance variables. Those flags make stationarity an explicit modelling assumption rather than a hidden preprocessing step.

Worked selection example

A compact comparison of Grace’s ordinary and graphical VAR shows how the package exposes model choice as a table rather than a narrative judgement. Grace is used because the preceding five-variable stationarity audit gives her no trend, high-autoregression, drift, unit-root, or zero-variance flag.

cmp <- compare_idiographic(
  srl, vars = vars, id = "name",
  estimators = c("var", "graphical_var"),
  estimator_args = list(
    var = list(subject = "Grace", scale = TRUE),
    graphical_var = list(subject = "Grace", n_lambda = 8)
  )
)
as.data.frame(cmp)
#>          method         network n_nodes n_edges density mean_abs_weight
#> 1           var        temporal       5      20     1.0      0.07457677
#> 2           var contemporaneous       5      10     1.0      0.16039547
#> 3 graphical_var        temporal       5       0     0.0      0.00000000
#> 4 graphical_var contemporaneous       5       3     0.3      0.20679444
#>   n_positive n_negative n_self max_abs_weight
#> 1          9         11      5      0.1604470
#> 2          6          4      0      0.4667434
#> 3          0          0      0      0.0000000
#> 4          3          0      0      0.2514403

The OLS VAR has full temporal and contemporaneous density, with mean absolute temporal weight 0.075 and contemporaneous weight 0.160. The graphical VAR keeps no temporal edges and three contemporaneous edges, reducing the contemporaneous density to 0.30. The choice is therefore not about which model is more elaborate; it is whether Grace’s weak lagged coefficients should be retained as estimates or treated as regularization noise.

Caveats

All methods require an explicit alignment between the scientific estimand and the data-generating design. A single-person network is not a population network, a multilevel fixed effect is not an individual map, and a between-person edge is not a within-person mechanism. Stationarity, equal spacing, and missingness assumptions should be checked before model interpretation. Sparse estimators improve selection stability but bias surviving weights downward; unregularized estimators expose every coefficient but can overstate weak edges in small samples.