2. Declare a dynamic missingness graph and check recoverability
g <- dm_graph(motifs = "M2", sensor = TRUE, probe = TRUE)
g
#> Dynamic missingness graph (window of 5 prompts)
#> motifs: M2
#> context: none
#> sensor: TRUE probe: TRUE
#> nodes: 21 edges: 24
plot(g)
recoverability(g)
#> Recoverability report for motifs: M2
#>
#> * transition kernel (Phi, Psi, contemporaneous network)
#> [NOT recoverable] sensitivity analysis (tilt profile) or a calibration design is required
#> condition: R_t and X_t are d-connected given {X_{t-1},eta}
#> * transition kernel from probe prompts
#> [recoverable] complete pairs restricted to probe prompts (Z_t = 1); delta calibrated by the probe contrast
#> condition: Z_t _||_ X_t | {X_{t-1},eta}; R_t = 1 whenever Z_t = 1
#> * person mean via observed within-person mean
#> [NOT recoverable] biased
#> condition: R_t _||_ X_t | {eta}
#> * person mean via recovered dynamics
#> [NOT recoverable] not available
#> condition: transition kernel recoverable
#> * between-person law (mu, Sigma_mu), person-weighted
#> [NOT recoverable] not recoverable
#> condition: a person-mean estimator is available and P(R_t = 1 | eta) > 0
#> * between-person law, prompt-weighted (pooling answered prompts)
#> [NOT recoverable] biased: response rate depends on the person's states
#> condition: R_t _||_ X_t | {empty set}
#> * silence test (coefficient of R_t in X_{t+1} ~ X_{t-1} + R_t, within person)
#> non-null expected: silence is informative
#> condition: R_t _||_ X_{t+1} | {X_{t-1},eta,R_{t-1},R_{t+1}}
#> * sensor-gap test (coefficient of R_t in S_t ~ X_{t-1} + R_t, within person)
#> non-null expected: delta can be calibrated from the sensor gap
#> condition: R_t _||_ S_t | {X_{t-1},eta,R_{t-1}}The report says that the transition kernel (and therefore the temporal and contemporaneous networks) is not structurally recoverable under self-censoring, that the silence test and the sensor-gap test are expected to reject, and that the kernel can be recovered from probe prompts. Compare with a recoverable mechanism and with reactivity, under which the dynamics are recovered but the person mean must be read from the answered prompts rather than from the dynamics:
recoverability(dm_graph(c("M1", "M4")))
#> Recoverability report for motifs: M1 + M4
#>
#> * transition kernel (Phi, Psi, contemporaneous network)
#> [recoverable] complete adjacent pairs, within-person (person intercepts)
#> condition: R_t _||_ X_t | {X_{t-1},eta,zeta} and R_{t-1} _||_ X_t | {X_{t-1},eta,zeta, R_t}
#> * person mean via observed within-person mean
#> [NOT recoverable] biased
#> condition: R_t _||_ X_t | {eta,zeta}
#> * person mean via recovered dynamics
#> [recoverable] mu_i = (I - Phi)^{-1} c_i from the recovered kernel
#> condition: transition kernel recoverable
#> * between-person law (mu, Sigma_mu), person-weighted
#> [recoverable] one recovered mean per person (dynamics-recovered means), persons weighted equally; positivity assumed
#> condition: a person-mean estimator is available and P(R_t = 1 | eta) > 0
#> * between-person law, prompt-weighted (pooling answered prompts)
#> [NOT recoverable] biased: response rate depends on the person's states
#> condition: R_t _||_ X_t | {empty set}
#> * silence test (coefficient of R_t in X_{t+1} ~ X_{t-1} + R_t, within person)
#> null expected (test valid as a test of the recoverable class)
#> condition: R_t _||_ X_{t+1} | {X_{t-1},eta,zeta,R_{t-1},R_{t+1}}
recoverability(dm_graph("M6"))
#> Recoverability report for motifs: M6
#>
#> * transition kernel (Phi, Psi, contemporaneous network)
#> [recoverable] complete adjacent pairs recover the assessment-conditioned kernel p(X_t | X_{t-1}, eta, R_{t-1} = 1): Phi and Psi are unaffected when reactivity shifts the level (additive), but the person intercept absorbs the shift
#> condition: reactivity edge R_{t-1} -> X_t declared; all complete pairs have R_{t-1} = 1
#> * person mean via observed within-person mean
#> [recoverable] mean of answered prompts, per person
#> condition: R_t _||_ X_t | {eta}
#> * person mean via recovered dynamics
#> [NOT recoverable] biased: the answered-pair intercept is the intercept of the assessed process (it absorbs the reactivity shift)
#> condition: transition kernel recoverable and no reactivity
#> * between-person law (mu, Sigma_mu), person-weighted
#> [recoverable] one recovered mean per person (observed means), persons weighted equally; positivity assumed
#> condition: a person-mean estimator is available and P(R_t = 1 | eta) > 0
#> * between-person law, prompt-weighted (pooling answered prompts)
#> [recoverable] pooled answered prompts
#> condition: R_t _||_ X_t | {empty set}
#> * silence test (coefficient of R_t in X_{t+1} ~ X_{t-1} + R_t, within person)
#> non-null expected: silence is informative
#> condition: R_t _||_ X_{t+1} | {X_{t-1},eta,R_{t-1},R_{t+1}}
