Dynamic Missingness Graphs and Sensitivity Analysis for EMA Data

Tools for diagnosing and correcting informative nonresponse in ecological momentary assessment (EMA) and other experience-sampling designs. Declares the assumed nonresponse mechanism as a dynamic missingness graph built from a taxonomy of seven motifs, following the graphical missing-data framework of Mohan and Pearl (2021) ; checks by d-separation which within-person and between-person estimands of a two-level vector autoregressive model remain recoverable and by which estimator; tests whether skipped prompts were informative (the silence test and the sensor-gap test, with cluster-robust inference after Cameron and Miller (2015) ); estimates the temporal and contemporaneous networks from answered adjacent prompts with the half-panel jackknife of Dhaene and Jochmans (2015) , by inverse-probability weighting on an observed context, and by full-information maximum likelihood with the state-space expectation-maximization (EM) algorithm of Shumway and Stoffer (1982) ; profiles the estimates over a self-censoring sensitivity parameter (inverse-probability weighting with a fixed probit selection model whose intercept is calibrated to the response rate); calibrates that parameter from passive sensors, randomized probes, or the post-skip contrast; computes worst-case bounds for person means in the spirit of Manski (2003) ; writes a preregistration-ready missingness declaration; and simulates experience-sampling data under every motif. The methods are described in Yu (2026, manuscript under review); the accompanying materials are archived at < https://osf.io/x6d2t/>.

silentema

Dynamic missingness graphs, recoverability checks, and sensitivity analysis for informative nonresponse in ecological momentary assessment (EMA) and other experience-sampling data.

Participants skip prompts, and the reasons are rarely unrelated to the states being measured. silentema lets an analyst

declare the assumed nonresponse mechanism as a dynamic missingness graph (dm_graph()), built from a taxonomy of seven motifs (completely random, lagged-state dependence, self-censoring, burden, person propensity, context confounding, and reactivity);
check by d-separation which estimands of a two-level VAR(1) (temporal network, contemporaneous network, person means, between-person law) remain structurally recoverable and by which estimator (recoverability());
test whether skipped prompts were informative, using the state after a skipped prompt (silence_test()) or an always-observed sensor (sensor_gap_test()), and describe response persistence (fatigue_check());
estimate from answered adjacent prompts with person-specific intercepts and a half-panel jackknife (fit_pairs()), by inverse-probability weighting on an observed context (fit_ipw()), or by full-information maximum likelihood under missing at random (MAR) (fit_fiml());
profile the estimates over a self-censoring sensitivity value by inverse-probability weighting with a fixed probit selection model whose intercept is calibrated to the response rate ("tilting") (fit_tilt(), tilt_profile(), break_even());
calibrate the sensitivity value from a passive sensor, randomized probes, or the post-skip contrast (calibrate_delta()), and compare with worst-case bounds (bounds_support());
report with a preregistration-ready missingness declaration (missingness_declaration()).

A simulator for the whole taxonomy (simulate_ema(), simulate_from_fit()) supports design planning and replication.

Installation

From CRAN (once the package is accepted):

install.packages("silentema")

The development version from GitHub:

# install.packages("remotes")
remotes::install_github("hsiutingyu/silentema")

The package contains C++ code (the state-space EM algorithm), so a compiler toolchain is needed to install from source: Rtools on Windows, Xcode command-line tools on macOS, r-base-dev or equivalent on Linux.

Minimal example

library(silentema)
sim <- simulate_ema(N = 100, n_prompts = 56, motifs = "M2", compliance = 0.7, delta = -1,
                    sensor_cor = 0.6, seed = 1)
g <- dm_graph("M2", sensor = TRUE)
recoverability(g)                       # what can be recovered under the declared mechanism?
silence_test(sim$data, sim$vars)        # was silence informative?
prof <- tilt_profile(sim$data, sim$vars, delta_grid = seq(-2, 0.5, by = 0.5))
cal <- calibrate_delta(prof, sim$data, method = "sensor")
break_even(prof, delta_max = 1.5)
cat(missingness_declaration(g, profile = prof, calibration = cal, plausible = c(-1.5, 0)), sep = "\n")

Documentation

vignette("silentema-workflow"): a complete analysis from declaration to report.
vignette("dm-graphs"): the motif taxonomy, d-separation and the recoverability report.
vignette("testing-informativeness"): the silence test, the sensor-gap test and the fatigue check.
vignette("sensitivity-analysis"): tilting, break-even values, calibration and reporting.
vignette("simulation-and-design"): the simulator and design planning.
Documentation site: https://hsiutingyu.github.io/silentema/

Citation

Yu, H.-T. (2026). What skipped prompts hide: Detecting, diagnosing, and correcting informative nonresponse in ecological momentary assessment. Manuscript under review. Materials: https://osf.io/x6d2t/

Yu, H.-T. (2026). silentema: Dynamic Missingness Graphs and Sensitivity Analysis for EMA Data. R package version 1.0.0. https://CRAN.R-project.org/package=silentema

Run citation("silentema") in R for BibTeX entries.