Build piecewise regression coding for single-case design phases
Source:R/utils-data.R
process_scd_phases.RdAdds level, trend, and slope-change columns suitable for a piecewise
multilevel model with time-series intervention coding inside a three-level
meta-analytic structure. Every change point is coded within each tier (the
combination of the columns returned by tier_vars()) at that tier's own
onset, using the actual time values, so unequally spaced sessions and
staggered onsets are honored.
Details
AB, multiple baseline, multiple probe. time_A = t - T_A on
every row, where T_A is the first baseline time of the tier, so the
intercept is the expected level at the start of baseline and
time_A carries the baseline trend through all phases.
level_AB is 1 from the first intervention time T_B on and
trend_AB = (t - T_B) * level_AB, so level_AB is the
immediate change at T_B relative to the projected baseline line and
trend_AB the change in slope. Maintenance and
generalization phases add level_BM/trend_BM and
level_BG/trend_BG coded the same way from their own onsets:
the first maintenance-role time and the first generalization-role time,
so an A-B-G tier carries no maintenance step and level_BG is the
change at the generalization onset.
time_B, time_M, time_G hold t minus the
corresponding onset on every row. Phases absent from a tier are coded 0.
Reversal (ABAB, BAB, ABA, ABABAB). Labels with a known role (see
phase_role(), including numeric codes 0/1/2/3 and numbered labels such
as "Baseline 1" or "A_2") are renamed to the role letters
A, B, M, G; other labels keep their letters. Runs are then numbered by
occurrence within the tier (A1, B1, A2, B2, M1). The first-run time
(time_<first run>) is t - T_1 on every row of the tier. Each
transition into run k adds a cumulative step
level_<prev><next> = 1[t >= T_k] (step coding) and a continuing
slope change trend_<prev><next> = (t - T_k) * 1[t >= T_k]. This is
the centered ABAB model: each level coefficient
is the change between adjacent phases at the first observation of the
later phase, and each trend coefficient the change in slope between
adjacent phases. When tiers start in different phases (an ABAB tier next
to a BAB tier), every first-run time column is kept (0 on the other
tiers) and a warning notes that the onset steps differ across tiers and
are estimated separately.
Changing criterion. time_A = t - T_A on every row. Each
criterion subphase j (split on a numeric criterion,
crit, criterion_level, or criterion_value column when
present, otherwise on phase-label runs) adds a cumulative step
level_crit<j> = 1[t >= T_cj] and a continuing
trend_crit<j> = (t - T_cj) * level_crit<j>, so each step compares
adjacent subphases. A return to an earlier criterion opens a new
subphase. A return to baseline after a criterion subphase adds the step
level_ret<k> = 1[t >= T_rk]. Without any baseline phase,
time_A runs from the first session of the tier and
level_crit1/trend_crit1 are dropped with a warning, since
they would equal the intercept and time_A. The collapsed
treatment (intervention vs baseline) column
is an intervention indicator; time_treatment = (t - T_c1) *
treatment is a centered variant of an uncentered session-number time
variable.
Alternating treatments. The first baseline-role condition (else
the first condition) is the reference; every other condition, including a
second baseline-role label such as "Control", gets a dummy
atd_<condition>. The atd_ prefix keeps data columns such as
treatment_fidelity out of the condition terms. A general session
trend time_session = t - T_1, the session
time centered at the first session of the tier; centering at the first
session only shifts the intercept. Without it, a general trend loads on the
condition dummies whenever conditions are unevenly spread over time.
Alternation blocks are counted within each tier.
The time column is structure$time_vars[1] when supplied, otherwise
find_time_var() (case-insensitive); with neither, sessions are numbered
in row order within each tier, with a warning that concurrence across
tiers cannot be assessed.
Examples
d <- simulate_scd_data(n_cases = 2, n_phase_a = 5, n_phase_b = 5)
process_scd_phases(d, structure = list(), scd_type = "AB")
#> case time phase phase_num time_center time_since_change outcome
#> 1 C1 1 A 0 0 0 39.43664
#> 2 C1 2 A 0 1 0 51.98777
#> 3 C1 3 A 0 2 0 56.50534
#> 4 C1 4 A 0 3 0 53.43913
#> 5 C1 5 A 0 4 0 64.77532
#> 6 C1 6 B 1 5 0 50.72026
#> 7 C1 7 B 1 6 1 71.26445
#> 8 C1 8 B 1 7 2 35.23803
#> 9 C1 9 B 1 8 3 54.07888
#> 10 C1 10 B 1 9 4 63.93978
#> 11 C2 1 A 0 0 0 53.60278
#> 12 C2 2 A 0 1 0 56.54550
#> 13 C2 3 A 0 2 0 60.52155
#> 14 C2 4 A 0 3 0 30.20445
#> 15 C2 5 A 0 4 0 62.08386
#> 16 C2 6 B 1 5 0 48.30720
#> 17 C2 7 B 1 6 1 52.95030
#> 18 C2 8 B 1 7 2 62.66341
#> 19 C2 9 B 1 8 3 38.64657
#> 20 C2 10 B 1 9 4 38.68946
#> phase_numeric time_A time_B level_AB trend_AB intervention_start
#> 1 0 0 -5 0 0 6
#> 2 0 1 -4 0 0 6
#> 3 0 2 -3 0 0 6
#> 4 0 3 -2 0 0 6
#> 5 0 4 -1 0 0 6
#> 6 1 5 0 1 0 6
#> 7 1 6 1 1 1 6
#> 8 1 7 2 1 2 6
#> 9 1 8 3 1 3 6
#> 10 1 9 4 1 4 6
#> 11 0 0 -5 0 0 6
#> 12 0 1 -4 0 0 6
#> 13 0 2 -3 0 0 6
#> 14 0 3 -2 0 0 6
#> 15 0 4 -1 0 0 6
#> 16 1 5 0 1 0 6
#> 17 1 6 1 1 1 6
#> 18 1 7 2 1 2 6
#> 19 1 8 3 1 3 6
#> 20 1 9 4 1 4 6