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The sensor-gap test: does an always-observed sensor differ at skipped prompts?

Source: R/tests_informative.R
sensor_gap_test.Rd

Regresses a passive-sensor channel at prompt \(t\) on the state at \(t-1\) and the response indicator at \(t\), within person, over all prompts whose predecessor was answered. Under the recoverable motifs the coefficient of \(R_t\) is zero, including under M1 + M3 (no collider is conditioned on, because the sensor is always observed). Under self-censoring the gap identifies the direction of the tilt and, through calibrate_delta, its magnitude.

Usage

sensor_gap_test(
  data,
  vars,
  sensor = "S",
  id = "id",
  time = "time",
  day = NULL,
  R = "R",
  se = NULL,
  B = 500,
  seed = NULL
)

Arguments

data

Long data frame with one row per scheduled prompt.

vars

Names of the state columns.

sensor

Name of the sensor column.

id, time

Names of the person and prompt-index columns.

day

Optional name of a day column; pairs are formed only within a day (the overnight gap is not a lag-1 transition).

R

Name of the response-indicator column (0/1, no NA). If the default name is not among the columns of data, a prompt counts as answered when all vars are non-missing; any other name must exist.

se

"cluster" (cluster-robust by person with \(t(G-1)\) and \(F(q, G-1)\) reference distributions; the default when there are at least 10 persons) or "dayblock" (block bootstrap that resamples person-day blocks with replacement; the default with fewer than 10 persons; requires day).

B

Number of bootstrap resamples for se = "dayblock".

seed

Optional seed for the bootstrap (the caller's random-number state is restored).

Value

A one-row data frame of class c("sensor_gap_test", "data.frame") with the columns coef_R (coefficient of

\(R_t\)), se, z and p, and the attributes

loading (the regression coefficients of the sensor on the state variables, estimated within person from answered prompts), n (the number of prompts used) and se (the method used). It has a

print method.

Examples

sim <- simulate_ema(N = 40, n_prompts = 30, motifs = "M2", delta = -1, sensor_cor = 0.6, seed = 1)
sg <- sensor_gap_test(sim$data, sim$vars, sensor = "S")
sg
#> Sensor-gap test: S_t ~ X_{t-1} + R_t (within person), 870 prompts with answered predecessor
#>   coefficient of R_t: -0.830 (SE 0.093), z = -8.91, p = 6.08e-11   [SE: cluster]
#>   sensor loading on states (answered prompts): 0.635 0.007 -0.008 -0.017 
attr(sg, "loading")
#>         NegA         PosA       Stress      Fatigue 
#>  0.635273000  0.007027500 -0.008433486 -0.017089419 
# under a recoverable mechanism the gap is null
sim1 <- simulate_ema(N = 40, n_prompts = 30, motifs = "M1", sensor_cor = 0.6, seed = 1)
sensor_gap_test(sim1$data, sim1$vars, sensor = "S")
#> Sensor-gap test: S_t ~ X_{t-1} + R_t (within person), 870 prompts with answered predecessor
#>   coefficient of R_t: -0.230 (SE 0.090), z = -2.55, p = 0.0147   [SE: cluster]
#>   sensor loading on states (answered prompts): 0.651 0.039 0 0.003