Fit the marginal mean model for generalize outcomes.
Source:R/fit_SensIAT_marginal_mean_model_generalized.R
fit_SensIAT_marginal_mean_model_generalized.RdThis function supports multiple integration methods for term2 computation, including adaptive and fixed-grid approaches. The implementation includes numerical stability improvements (exp(-μ) multiplication vs division) and extensive caching optimizations for repeated expected value computations.
Usage
fit_SensIAT_marginal_mean_model_generalized(
data,
time,
id,
alpha,
knots,
outcome.model,
intensity.model,
impute_data,
loss = c("lp_mse", "quasi-likelihood"),
link = c("identity", "log", "logit"),
spline.degree = 3L,
...,
BBsolve.control = list(maxit = 1000, tol = 1e-06),
term2_method = c("fast", "original", "fixed_grid", "seeded_adaptive", "gauss_legendre"),
term2_grid_n = 100,
use_expected_cache = TRUE
)Arguments
- data
Data for evaluation of the model. Should match the data used to fit the intensity and outcome models.
- time
The time variable in the data. Can be provided as a column name or vector.
- id
The subject identifier variable in the data. Lazy evaluation is used, so it can be a symbol or a string.
- alpha
Sensitivity parameter, a vector of values.
- knots
Location of spline knots. If a
SplineBasisobject is provided, it is used directly.- outcome.model
The observed effects model.
- intensity.model
The assessment time intensity model.
- impute_data
A function that takes (t, df) and returns the imputed data at time t. Should handle extrapolation from the last observed time point.
- loss
The loss function to use. Options are "lp_mse", "mean_mse", and "quasi-likelihood".
- link
The link function to use. Options are "identity", "log", and "logit".
- spline.degree
The degree of the spline basis, default is 3 (cubic splines).
- ...
Additional arguments passed to
compute_influence_terms.- BBsolve.control
Control parameters for the BB::sane optimizer, including
maxitandtol.- term2_method
Method for computing term2 influence components. Options are:
"fast": Optimized closure-based integrand with adaptive Simpson's (default)"original": Standard implementation with adaptive Simpson's"fixed_grid": Pre-computed expected values on fixed grid with composite Simpson's rule"seeded_adaptive": Adaptive Simpson's seeded with pre-computed grid points"gauss_legendre": Gauss-Legendre quadrature (requires \pkgstatmod package)
- term2_grid_n
Number of grid points/nodes for
fixed_grid,seeded_adaptive, andgauss_legendremethods (default 100)- use_expected_cache
Logical; whether to cache expected values for performance (default TRUE)
Details
Integration Methods for Term2
The function offers four integration methods with different performance/accuracy tradeoffs:
Adaptive Methods (fast, original):
Use adaptive Simpson's quadrature with automatic subdivision
Best accuracy for irregular integrands
fastmethod uses optimized closure-based integrand construction
Fixed-Grid Method (fixed_grid):
Pre-computes expected values at fixed grid points (once per alpha)
Uses composite Simpson's rule for integration
2-5x faster when optimizing over beta (multiple iterations)
Best for smooth integrands with sufficient grid density
Seeded Adaptive Method (seeded_adaptive):
Combines pre-computation with adaptive refinement
Starts with pre-computed grid, subdivides where needed
Good balance of speed and accuracy
Gauss-Legendre Method (gauss_legendre):
Uses Gauss-Legendre quadrature via
statmod::gauss.quad()Highly accurate for smooth integrands with fewer evaluation points
Exact for polynomials up to degree 2n-1 using n points
Requires the statmod package
Outcome Model Compatibility
Unlike simulation code that assumes specific single-index model formulas, this
function supports any outcome model with a compute_SensIAT_expected_values
method, including:
Single-index models (
fit_SensIAT_single_index_*_model)Generalized linear models (GLM)
Linear models (LM)
Negative binomial models
Performance Optimizations
Term1 Optimizations (alpha-independent):
Y-scaled observations pre-computed once
Patient index mappings cached for O(1) lookups
Identity link: weights pre-computed (don't depend on beta or alpha)
Single-index models: global PMF constants extracted once
Term2 Optimizations:
Integration grids pre-computed (alpha-independent)
Basis evaluations at grid points pre-computed
Expected values computed once per alpha (for grid methods)
Per-patient caching of expected values
Weight functions use numerically stable exp(-μ) multiplication
Weight functions use numerically stable exp(-μ) multiplication
Fast method uses closure-based integration with reduced allocations
Examples
library(survival)
library(splines)
data_with_lags <- SensIAT_example_data |>
dplyr::group_by(Subject_ID) |>
dplyr::mutate(
..prev_outcome.. = dplyr::lag(Outcome, default = NA_real_, order_by = Time),
..prev_time.. = dplyr::lag(Time, default = 0, order_by = Time),
..delta_time.. = Time - dplyr::lag(.data$Time, default = NA_real_, order_by = Time)
)
# Create the observation time intensity model
intensity.model <-
coxph(Surv(..prev_time.., Time, !is.na(Outcome)) ~ ..prev_outcome.. + strata(Visit),
data = data_with_lags |> dplyr::filter(.data$Time > 0)
)
# Create the observed outcome model
outcome.model <-
fit_SensIAT_single_index_fixed_coef_model(
Outcome ~ ns(..prev_outcome.., df = 3) + ..delta_time.. - 1,
id = Subject_ID,
data = data_with_lags |> dplyr::filter(.data$Time > 0)
)
fit_SensIAT_marginal_mean_model_generalized(
data = data_with_lags,
time = data_with_lags$Time,
id = data_with_lags$Subject_ID,
alpha = 0,
knots = c(60, 260, 460),
outcome.model = outcome.model,
intensity.model = intensity.model,
loss = "lp_mse",
link = "log",
impute_data = \(t, df){
data_wl <- df |>
mutate(
..prev_time.. = Time,
..prev_outcome.. = Outcome,
..delta_time.. = 0
)
extrapolate_from_last_observation(t, data_wl, "Time", slopes = c("..delta_time.." = 1))
}
)
#> Iteration: 0 ||F(x0)||: 227.2529
#> $models
#> $models$intensity
#> Call:
#> coxph(formula = Surv(..prev_time.., Time, !is.na(Outcome)) ~
#> ..prev_outcome.. + strata(Visit), data = dplyr::filter(data_with_lags,
#> .data$Time > 0))
#>
#> coef exp(coef) se(coef) z p
#> ..prev_outcome.. 0.003586 1.003592 0.033948 0.106 0.916
#>
#> Likelihood ratio test=0.01 on 1 df, p=0.9159
#> n= 579, number of events= 579
#>
#> $models$outcome
#> $coef
#> [1] 1.0000000000 -2.7221528895 0.8950004459 0.0004330739
#>
#> $bandwidth
#> [1] 0.712211
#>
#> $details
#> $details$par
#> [1] -2.7221528895 0.8950004459 0.0004330739 -0.3393811138
#>
#> $details$value
#> [1] 0.1584609
#>
#> $details$feval
#> [1] 89
#>
#> $details$restarts
#> [1] 0
#>
#> $details$convergence
#> [1] 0
#>
#> $details$message
#> [1] "Successful convergence"
#>
#>
#> $frame
#> Outcome ns(..prev_outcome.., df = 3).1 ns(..prev_outcome.., df = 3).2
#> 1 4.5000000 0.434163861 0.434714928
#> 2 4.1666667 0.361640165 0.344520612
#> 3 1.3333333 0.432597299 0.349257972
#> 4 0.8333333 -0.147255800 0.578149895
#> 5 0.5000000 0.434163861 0.434714928
#> 6 2.0000000 -0.108530441 0.267286120
#> 7 1.5000000 0.061389411 0.594623773
#> 8 1.8333333 -0.116230314 0.603609988
#> 9 0.1666667 -0.135660792 0.347815206
#> 10 0.3333333 -0.038761518 0.091542884
#> 11 1.1666667 0.135611590 0.571902398
#> 12 0.8333333 -0.162773063 0.538004737
#> 13 1.1666667 -0.155037031 0.421001760
#> 14 0.3333333 -0.162773063 0.538004737
#> 15 4.1666667 0.458179790 0.354388605
#> 16 4.5000000 0.432597299 0.349257972
#> 17 3.6666667 0.361640165 0.344520612
#> 18 4.0000000 0.480104130 0.397352002
#> 19 4.0000000 0.458179790 0.354388605
#> 20 2.1666667 -0.135660792 0.347815206
#> 21 1.8333333 0.135611590 0.571902398
#> 22 1.0000000 -0.155037031 0.421001760
#> 23 0.6666667 -0.164720630 0.485010148
#> 24 1.3333333 -0.135660792 0.347815206
#> 25 2.1666667 0.480104130 0.397352002
#> 26 1.0000000 0.135611590 0.571902398
#> 27 3.8333333 0.486460094 0.371036886
#> 28 0.8333333 0.476340223 0.361590702
#> 29 4.0000000 0.317502531 0.344568641
#> 30 5.5000000 0.458179790 0.354388605
#> 31 3.8333333 0.034963882 0.362070987
#> 32 2.5000000 0.215001653 0.348635005
#> 33 1.1666667 0.281022057 0.513990526
#> 34 1.3333333 -0.162773063 0.538004737
#> 35 1.0000000 -0.147255800 0.578149895
#> 36 1.5000000 0.480104130 0.397352002
#> 37 1.8333333 -0.116230314 0.603609988
#> 38 0.8333333 -0.008164666 0.609384367
#> 39 2.3333333 -0.155037031 0.421001760
#> 40 4.1666667 -0.008164666 0.609384367
#> 41 3.8333333 0.432597299 0.349257972
#> 42 3.1666667 0.317502531 0.344568641
#> 43 3.6666667 0.462391286 0.414566177
#> 44 2.5000000 0.343691246 0.484506641
#> 45 1.8333333 0.281022057 0.513990526
#> 46 2.1666667 0.210242322 0.544073547
#> 47 1.3333333 0.135611590 0.571902398
#> 48 2.5000000 0.394803349 0.457970875
#> 49 2.5000000 0.281022057 0.513990526
#> 50 2.1666667 0.281022057 0.513990526
#> 51 4.3333333 0.135611590 0.571902398
#> 52 3.3333333 0.486460094 0.371036886
#> 53 5.8333333 0.480104130 0.397352002
#> 54 3.3333333 0.317502531 0.344568641
#> 55 1.0000000 0.480104130 0.397352002
#> 56 0.8333333 -0.135660792 0.347815206
#> 57 0.5000000 -0.155037031 0.421001760
#> 58 1.1666667 -0.108530441 0.267286120
#> 59 0.6666667 0.281022057 0.513990526
#> 60 0.6666667 -0.135660792 0.347815206
#> 61 1.6666667 -0.135660792 0.347815206
#> 62 0.6666667 -0.068791091 0.613330874
#> 63 1.5000000 -0.155037031 0.421001760
#> 64 3.6666667 -0.116230314 0.603609988
#> 65 1.5000000 0.486460094 0.371036886
#> 66 1.1666667 -0.116230314 0.603609988
#> 67 4.0000000 0.434163861 0.434714928
#> 68 3.0000000 0.458179790 0.354388605
#> 69 0.8333333 0.434163861 0.434714928
#> 70 1.1666667 -0.155037031 0.421001760
#> 71 1.5000000 0.434163861 0.434714928
#> 72 1.5000000 -0.116230314 0.603609988
#> 73 1.1666667 -0.116230314 0.603609988
#> 74 2.0000000 0.210242322 0.544073547
#> 75 3.5000000 0.061389411 0.594623773
#> 76 3.6666667 0.487920898 0.382899779
#> 77 0.8333333 0.486460094 0.371036886
#> 78 1.8333333 0.135611590 0.571902398
#> 79 3.0000000 -0.008164666 0.609384367
#> 80 2.0000000 0.434163861 0.434714928
#> 81 3.6666667 0.434163861 0.434714928
#> 82 2.1666667 0.486460094 0.371036886
#> 83 1.5000000 0.135611590 0.571902398
#> 84 0.5000000 -0.116230314 0.603609988
#> 85 2.8333333 -0.147255800 0.578149895
#> 86 2.6666667 0.394803349 0.457970875
#> 87 2.1666667 0.343691246 0.484506641
#> 88 0.1666667 0.434163861 0.434714928
#> 89 3.1666667 -0.038761518 0.091542884
#> 90 3.5000000 0.462391286 0.414566177
#> 91 2.6666667 0.487920898 0.382899779
#> 92 1.0000000 -0.162773063 0.538004737
#> 93 2.8333333 -0.164720630 0.485010148
#> 94 1.6666667 0.281022057 0.513990526
#> 95 2.6666667 -0.068791091 0.613330874
#> 96 5.1666667 0.343691246 0.484506641
#> 97 0.8333333 0.487920898 0.382899779
#> 98 1.8333333 -0.155037031 0.421001760
#> 99 0.5000000 -0.008164666 0.609384367
#> 100 0.5000000 -0.108530441 0.267286120
#> 101 1.5000000 -0.155037031 0.421001760
#> 102 1.3333333 -0.116230314 0.603609988
#> 103 4.3333333 0.476340223 0.361590702
#> 104 6.0000000 0.400211256 0.346026182
#> 105 4.0000000 -0.161773517 0.380167765
#> 106 6.0000000 0.458179790 0.354388605
#> 107 1.3333333 0.210242322 0.544073547
#> 108 1.3333333 -0.147255800 0.578149895
#> 109 0.1666667 -0.147255800 0.578149895
#> 110 2.8333333 0.434163861 0.434714928
#> 111 1.5000000 0.394803349 0.457970875
#> 112 3.0000000 -0.116230314 0.603609988
#> 113 2.0000000 0.210242322 0.544073547
#> 114 0.8333333 -0.162773063 0.538004737
#> 115 2.1666667 -0.155037031 0.421001760
#> 116 2.8333333 0.135611590 0.571902398
#> 117 1.5000000 0.394803349 0.457970875
#> 118 2.8333333 0.210242322 0.544073547
#> 119 3.5000000 0.394803349 0.457970875
#> 120 1.8333333 -0.008164666 0.609384367
#> 121 2.5000000 -0.008164666 0.609384367
#> 122 3.5000000 0.281022057 0.513990526
#> 123 2.1666667 0.487920898 0.382899779
#> 124 3.1666667 -0.116230314 0.603609988
#> 125 1.5000000 0.462391286 0.414566177
#> 126 2.6666667 0.061389411 0.594623773
#> 127 3.0000000 0.343691246 0.484506641
#> 128 3.0000000 0.434163861 0.434714928
#> 129 2.8333333 0.434163861 0.434714928
#> 130 4.1666667 -0.147255800 0.578149895
#> 131 2.3333333 0.432597299 0.349257972
#> 132 2.0000000 0.210242322 0.544073547
#> 133 2.1666667 0.061389411 0.594623773
#> 134 2.6666667 -0.008164666 0.609384367
#> 135 1.8333333 0.343691246 0.484506641
#> 136 2.0000000 -0.008164666 0.609384367
#> 137 2.0000000 0.462391286 0.414566177
#> 138 2.0000000 0.061389411 0.594623773
#> 139 3.1666667 0.487920898 0.382899779
#> 140 3.5000000 0.487920898 0.382899779
#> 141 3.0000000 0.487920898 0.382899779
#> 142 1.3333333 0.434163861 0.434714928
#> 143 1.1666667 -0.147255800 0.578149895
#> 144 1.6666667 -0.008164666 0.609384367
#> 145 2.1666667 -0.068791091 0.613330874
#> 146 1.8333333 0.135611590 0.571902398
#> 147 1.3333333 -0.008164666 0.609384367
#> 148 2.0000000 0.343691246 0.484506641
#> 149 2.1666667 0.061389411 0.594623773
#> 150 3.0000000 0.135611590 0.571902398
#> 151 2.1666667 0.215001653 0.348635005
#> 152 0.6666667 0.135611590 0.571902398
#> 153 0.5000000 -0.135660792 0.347815206
#> 154 0.3333333 -0.108530441 0.267286120
#> 155 1.6666667 -0.038761518 0.091542884
#> 156 2.3333333 -0.068791091 0.613330874
#> 157 1.3333333 0.210242322 0.544073547
#> 158 0.6666667 -0.147255800 0.578149895
#> 159 3.1666667 0.486460094 0.371036886
#> 160 2.1666667 0.462391286 0.414566177
#> 161 1.3333333 0.135611590 0.571902398
#> 162 1.8333333 -0.147255800 0.578149895
#> 163 2.0000000 0.434163861 0.434714928
#> 164 0.0000000 0.061389411 0.594623773
#> 165 2.3333333 0.000000000 0.000000000
#> 166 0.3333333 0.210242322 0.544073547
#> 167 0.6666667 -0.162773063 0.538004737
#> 168 2.6666667 -0.135660792 0.347815206
#> 169 1.0000000 0.343691246 0.484506641
#> 170 2.0000000 -0.008164666 0.609384367
#> 171 2.0000000 0.061389411 0.594623773
#> 172 2.0000000 0.061389411 0.594623773
#> 173 2.0000000 0.061389411 0.594623773
#> 174 2.5000000 -0.038761518 0.091542884
#> 175 0.1666667 0.281022057 0.513990526
#> 176 2.5000000 -0.038761518 0.091542884
#> 177 3.1666667 0.434163861 0.434714928
#> 178 2.5000000 0.462391286 0.414566177
#> 179 3.1666667 0.281022057 0.513990526
#> 180 1.3333333 0.462391286 0.414566177
#> 181 1.5000000 0.135611590 0.571902398
#> 182 2.6666667 -0.116230314 0.603609988
#> 183 3.6666667 0.343691246 0.484506641
#> 184 1.6666667 0.486460094 0.371036886
#> 185 1.3333333 0.061389411 0.594623773
#> 186 3.0000000 -0.147255800 0.578149895
#> 187 2.3333333 0.434163861 0.434714928
#> 188 2.5000000 0.210242322 0.544073547
#> 189 3.3333333 0.462391286 0.414566177
#> 190 2.0000000 0.210242322 0.544073547
#> 191 3.3333333 0.061389411 0.594623773
#> 192 1.6666667 0.281022057 0.513990526
#> 193 2.5000000 -0.068791091 0.613330874
#> 194 2.3333333 -0.147255800 0.578149895
#> 195 3.1666667 0.210242322 0.544073547
#> 196 2.3333333 0.462391286 0.414566177
#> 197 1.1666667 0.210242322 0.544073547
#> 198 0.6666667 -0.155037031 0.421001760
#> 199 0.5000000 -0.135660792 0.347815206
#> 200 0.8333333 -0.108530441 0.267286120
#> 201 3.5000000 -0.162773063 0.538004737
#> 202 3.0000000 0.487920898 0.382899779
#> 203 4.5000000 0.317502531 0.344568641
#> 204 3.3333333 0.361640165 0.344520612
#> 205 4.1666667 0.480104130 0.397352002
#> 206 2.3333333 0.432597299 0.349257972
#> 207 0.8333333 0.432597299 0.349257972
#> 208 2.5000000 -0.155037031 0.421001760
#> 209 0.6666667 0.281022057 0.513990526
#> 210 3.5000000 -0.116230314 0.603609988
#> 211 3.6666667 0.487920898 0.382899779
#> 212 5.1666667 0.486460094 0.371036886
#> 213 2.5000000 -0.038761518 0.091542884
#> 214 3.3333333 0.281022057 0.513990526
#> 215 3.8333333 0.434163861 0.434714928
#> 216 3.5000000 0.476340223 0.361590702
#> 217 1.8333333 0.487920898 0.382899779
#> 218 1.0000000 -0.008164666 0.609384367
#> 219 2.6666667 -0.162773063 0.538004737
#> 220 1.0000000 0.343691246 0.484506641
#> 221 2.3333333 -0.164720630 0.485010148
#> 222 1.6666667 0.210242322 0.544073547
#> 223 0.8333333 0.432597299 0.349257972
#> 224 3.5000000 -0.155037031 0.421001760
#> 225 1.8333333 0.487920898 0.382899779
#> 226 2.6666667 -0.008164666 0.609384367
#> 227 5.0000000 0.215001653 0.348635005
#> 228 1.1666667 0.394803349 0.457970875
#> 229 1.8333333 -0.162773063 0.538004737
#> 230 1.6666667 -0.008164666 0.609384367
#> 231 2.0000000 0.135611590 0.571902398
#> 232 4.0000000 0.061389411 0.594623773
#> 233 3.6666667 0.458179790 0.354388605
#> 234 2.8333333 0.486460094 0.371036886
#> 235 3.0000000 0.462391286 0.414566177
#> 236 2.6666667 0.434163861 0.434714928
#> 237 3.6666667 -0.147255800 0.578149895
#> 238 2.8333333 0.486460094 0.371036886
#> 239 1.6666667 0.394803349 0.457970875
#> 240 1.5000000 -0.068791091 0.613330874
#> 241 1.6666667 0.210242322 0.544073547
#> 242 4.0000000 -0.068791091 0.613330874
#> 243 3.1666667 0.458179790 0.354388605
#> 244 1.8333333 0.462391286 0.414566177
#> 245 2.3333333 0.434163861 0.434714928
#> 246 1.6666667 0.210242322 0.544073547
#> 247 6.0000000 0.317502531 0.344568641
#> 248 3.5000000 -0.161773517 0.380167765
#> 249 3.3333333 0.487920898 0.382899779
#> 250 0.3333333 0.480104130 0.397352002
#> 251 2.1666667 0.394803349 0.457970875
#> 252 1.6666667 0.135611590 0.571902398
#> 253 1.5000000 -0.068791091 0.613330874
#> 254 3.8333333 -0.116230314 0.603609988
#> 255 1.3333333 -0.116230314 0.603609988
#> 256 1.3333333 -0.147255800 0.578149895
#> 257 5.5000000 0.486460094 0.371036886
#> 258 0.3333333 -0.008164666 0.609384367
#> 259 0.8333333 -0.075584507 0.181250135
#> 260 0.6666667 -0.155037031 0.421001760
#> 261 3.0000000 -0.162773063 0.538004737
#> 262 1.6666667 0.434163861 0.434714928
#> 263 2.5000000 -0.068791091 0.613330874
#> 264 1.8333333 0.281022057 0.513990526
#> 265 1.3333333 -0.116230314 0.603609988
#> 266 1.1666667 -0.147255800 0.578149895
#> 267 1.6666667 -0.135660792 0.347815206
#> 268 1.3333333 -0.162773063 0.538004737
#> 269 0.8333333 -0.147255800 0.578149895
#> 270 2.1666667 -0.155037031 0.421001760
#> 271 1.0000000 0.135611590 0.571902398
#> 272 1.6666667 0.281022057 0.513990526
#> 273 1.1666667 -0.068791091 0.613330874
#> 274 1.0000000 -0.162773063 0.538004737
#> 275 1.3333333 -0.164720630 0.485010148
#> 276 1.6666667 0.480104130 0.397352002
#> 277 1.6666667 -0.068791091 0.613330874
#> 278 1.5000000 -0.068791091 0.613330874
#> 279 0.6666667 -0.116230314 0.603609988
#> 280 4.1666667 0.432597299 0.349257972
#> 281 1.3333333 0.432597299 0.349257972
#> 282 5.0000000 -0.095369711 0.373905343
#> 283 2.6666667 0.215001653 0.348635005
#> 284 5.8333333 0.343691246 0.484506641
#> 285 5.6666667 -0.095369711 0.373905343
#> 286 2.0000000 -0.008164666 0.609384367
#> 287 1.1666667 0.061389411 0.594623773
#> 288 0.3333333 -0.162773063 0.538004737
#> 289 1.3333333 0.135611590 0.571902398
#> 290 1.5000000 -0.147255800 0.578149895
#> 291 2.5000000 -0.116230314 0.603609988
#> 292 1.8333333 0.281022057 0.513990526
#> 293 3.6666667 -0.008164666 0.609384367
#> 294 2.5000000 0.486460094 0.371036886
#> 295 4.8333333 0.215001653 0.348635005
#> 296 1.8333333 0.268416859 0.345997646
#> 297 2.0000000 0.487920898 0.382899779
#> 298 1.5000000 0.061389411 0.594623773
#> 299 1.5000000 -0.116230314 0.603609988
#> 300 0.6666667 0.462391286 0.414566177
#> 301 1.6666667 -0.135660792 0.347815206
#> 302 1.8333333 -0.068791091 0.613330874
#> 303 0.5000000 -0.155037031 0.421001760
#> 304 1.0000000 -0.108530441 0.267286120
#> 305 2.8333333 -0.164720630 0.485010148
#> 306 1.1666667 0.434163861 0.434714928
#> 307 1.6666667 -0.162773063 0.538004737
#> 308 1.5000000 -0.068791091 0.613330874
#> 309 0.6666667 -0.116230314 0.603609988
#> 310 3.3333333 0.486460094 0.371036886
#> 311 3.3333333 0.480104130 0.397352002
#> 312 3.6666667 0.480104130 0.397352002
#> 313 0.3333333 0.434163861 0.434714928
#> 314 0.5000000 -0.075584507 0.181250135
#> 315 1.1666667 -0.108530441 0.267286120
#> 316 1.0000000 -0.162773063 0.538004737
#> 317 2.0000000 0.434163861 0.434714928
#> 318 3.6666667 0.061389411 0.594623773
#> 319 5.3333333 0.486460094 0.371036886
#> 320 0.8333333 -0.155037031 0.421001760
#> 321 0.5000000 -0.155037031 0.421001760
#> 322 1.5000000 -0.147255800 0.578149895
#> 323 1.5000000 -0.147255800 0.578149895
#> 324 2.8333333 -0.116230314 0.603609988
#> 325 0.8333333 -0.147255800 0.578149895
#> 326 1.0000000 -0.155037031 0.421001760
#> 327 2.0000000 0.343691246 0.484506641
#> 328 1.5000000 0.061389411 0.594623773
#> 329 2.0000000 -0.116230314 0.603609988
#> 330 1.5000000 0.432597299 0.349257972
#> 331 2.0000000 -0.116230314 0.603609988
#> 332 2.1666667 0.061389411 0.594623773
#> 333 0.1666667 -0.108530441 0.267286120
#> 334 1.0000000 -0.038761518 0.091542884
#> 335 1.1666667 -0.164720630 0.485010148
#> 336 1.3333333 -0.162773063 0.538004737
#> 337 1.6666667 -0.135660792 0.347815206
#> 338 3.5000000 -0.068791091 0.613330874
#> 339 3.6666667 0.487920898 0.382899779
#> 340 5.0000000 0.486460094 0.371036886
#> 341 1.0000000 -0.155037031 0.421001760
#> 342 1.5000000 -0.164720630 0.485010148
#> 343 1.8333333 -0.116230314 0.603609988
#> 344 1.6666667 -0.008164666 0.609384367
#> 345 1.0000000 -0.116230314 0.603609988
#> 346 0.8333333 -0.164720630 0.485010148
#> 347 3.1666667 0.480104130 0.397352002
#> 348 1.8333333 0.462391286 0.414566177
#> 349 2.6666667 -0.008164666 0.609384367
#> 350 1.3333333 0.343691246 0.484506641
#> 351 2.6666667 0.480104130 0.397352002
#> 352 2.1666667 0.343691246 0.484506641
#> 353 2.6666667 0.135611590 0.571902398
#> 354 1.1666667 -0.116230314 0.603609988
#> 355 0.6666667 -0.162773063 0.538004737
#> 356 2.1666667 0.486460094 0.371036886
#> 357 0.5000000 0.135611590 0.571902398
#> 358 1.1666667 -0.108530441 0.267286120
#> 359 1.1666667 -0.162773063 0.538004737
#> 360 2.0000000 -0.008164666 0.609384367
#> 361 1.3333333 0.061389411 0.594623773
#> 362 2.8333333 0.135611590 0.571902398
#> 363 1.0000000 0.394803349 0.457970875
#> 364 1.6666667 -0.164720630 0.485010148
#> 365 0.8333333 -0.068791091 0.613330874
#> 366 0.5000000 0.000000000 0.000000000
#> 367 0.6666667 0.434163861 0.434714928
#> 368 2.1666667 -0.135660792 0.347815206
#> 369 3.6666667 0.135611590 0.571902398
#> 370 2.8333333 0.486460094 0.371036886
#> 371 0.8333333 -0.008164666 0.609384367
#> 372 1.0000000 -0.155037031 0.421001760
#> 373 0.6666667 -0.164720630 0.485010148
#> 374 2.1666667 0.458179790 0.354388605
#> 375 3.0000000 0.135611590 0.571902398
#> 376 3.0000000 0.434163861 0.434714928
#> 377 2.6666667 0.434163861 0.434714928
#> 378 3.1666667 0.434163861 0.434714928
#> 379 3.1666667 0.462391286 0.414566177
#> 380 1.8333333 0.462391286 0.414566177
#> 381 1.8333333 -0.008164666 0.609384367
#> 382 2.0000000 -0.068791091 0.613330874
#> 383 1.6666667 0.061389411 0.594623773
#> 384 1.5000000 0.281022057 0.513990526
#> 385 1.0000000 -0.116230314 0.603609988
#> 386 1.0000000 -0.164720630 0.485010148
#> 387 2.3333333 0.434163861 0.434714928
#> 388 1.8333333 0.210242322 0.544073547
#> 389 1.1666667 -0.008164666 0.609384367
#> 390 1.6666667 -0.162773063 0.538004737
#> 391 1.5000000 -0.155037031 0.421001760
#> 392 0.6666667 -0.116230314 0.603609988
#> 393 0.6666667 -0.135660792 0.347815206
#> 394 0.8333333 -0.135660792 0.347815206
#> 395 4.0000000 -0.116230314 0.603609988
#> 396 2.6666667 0.458179790 0.354388605
#> 397 2.6666667 0.343691246 0.484506641
#> 398 5.5000000 -0.095369711 0.373905343
#> 399 4.0000000 0.034963882 0.362070987
#> 400 2.0000000 0.458179790 0.354388605
#> 401 1.8333333 0.061389411 0.594623773
#> 402 2.0000000 -0.008164666 0.609384367
#> 403 0.6666667 0.061389411 0.594623773
#> 404 2.8333333 0.434163861 0.434714928
#> 405 0.8333333 0.394803349 0.457970875
#> 406 0.8333333 -0.155037031 0.421001760
#> 407 1.3333333 -0.155037031 0.421001760
#> 408 1.0000000 -0.116230314 0.603609988
#> 409 0.8333333 -0.164720630 0.485010148
#> 410 0.1666667 -0.155037031 0.421001760
#> 411 1.1666667 -0.147255800 0.578149895
#> 412 2.8333333 -0.162773063 0.538004737
#> 413 1.3333333 0.394803349 0.457970875
#> 414 2.6666667 -0.147255800 0.578149895
#> 415 2.0000000 0.000000000 0.000000000
#> 416 1.8333333 0.061389411 0.594623773
#> 417 2.3333333 -0.008164666 0.609384367
#> 418 1.6666667 0.281022057 0.513990526
#> 419 4.1666667 -0.068791091 0.613330874
#> 420 3.0000000 0.432597299 0.349257972
#> 421 1.6666667 0.061389411 0.594623773
#> 422 0.8333333 -0.068791091 0.613330874
#> 423 1.1666667 -0.155037031 0.421001760
#> 424 1.3333333 -0.162773063 0.538004737
#> 425 5.3333333 0.343691246 0.484506641
#> 426 2.1666667 0.097656660 0.356844298
#> 427 3.8333333 0.462391286 0.414566177
#> 428 4.6666667 0.476340223 0.361590702
#> 429 3.3333333 0.317502531 0.344568641
#> 430 1.1666667 0.458179790 0.354388605
#> 431 2.1666667 -0.162773063 0.538004737
#> 432 1.8333333 0.135611590 0.571902398
#> 433 1.3333333 -0.008164666 0.609384367
#> 434 1.6666667 -0.116230314 0.603609988
#> 435 2.1666667 -0.068791091 0.613330874
#> 436 2.1666667 0.135611590 0.571902398
#> 437 5.3333333 0.394803349 0.457970875
#> 438 3.6666667 0.097656660 0.356844298
#> 439 2.6666667 0.434163861 0.434714928
#> 440 1.1666667 0.343691246 0.484506641
#> 441 0.6666667 -0.162773063 0.538004737
#> 442 1.5000000 -0.135660792 0.347815206
#> 443 2.0000000 0.343691246 0.484506641
#> 444 1.3333333 0.061389411 0.594623773
#> 445 1.6666667 -0.147255800 0.578149895
#> 446 1.0000000 -0.068791091 0.613330874
#> 447 1.1666667 0.061389411 0.594623773
#> 448 1.6666667 -0.162773063 0.538004737
#> 449 0.5000000 -0.068791091 0.613330874
#> 450 1.6666667 -0.108530441 0.267286120
#> 451 2.0000000 0.281022057 0.513990526
#> 452 0.6666667 0.061389411 0.594623773
#> 453 1.0000000 -0.155037031 0.421001760
#> 454 2.0000000 -0.164720630 0.485010148
#> 455 3.3333333 0.061389411 0.594623773
#> 456 3.1666667 0.480104130 0.397352002
#> 457 1.1666667 -0.135660792 0.347815206
#> 458 3.0000000 -0.162773063 0.538004737
#> 459 3.5000000 0.135611590 0.571902398
#> 460 1.8333333 0.487920898 0.382899779
#> 461 0.5000000 -0.008164666 0.609384367
#> 462 0.3333333 -0.108530441 0.267286120
#> 463 1.1666667 -0.008164666 0.609384367
#> 464 0.5000000 -0.162773063 0.538004737
#> 465 0.8333333 -0.116230314 0.603609988
#> 466 0.8333333 -0.155037031 0.421001760
#> 467 1.8333333 -0.155037031 0.421001760
#> 468 0.8333333 -0.008164666 0.609384367
#> 469 2.8333333 -0.108530441 0.267286120
#> 470 2.8333333 0.476340223 0.361590702
#> 471 3.0000000 0.394803349 0.457970875
#> 472 3.8333333 -0.155037031 0.421001760
#> 473 2.5000000 0.476340223 0.361590702
#> 474 1.6666667 0.210242322 0.544073547
#> 475 2.3333333 -0.068791091 0.613330874
#> 476 2.6666667 0.210242322 0.544073547
#> 477 1.5000000 0.343691246 0.484506641
#> 478 1.0000000 -0.155037031 0.421001760
#> 479 2.5000000 -0.164720630 0.485010148
#> 480 4.5000000 0.281022057 0.513990526
#> 481 2.8333333 0.361640165 0.344520612
#> 482 1.6666667 0.343691246 0.484506641
#> 483 1.5000000 -0.068791091 0.613330874
#> 484 1.3333333 -0.116230314 0.603609988
#> 485 1.1666667 -0.147255800 0.578149895
#> 486 2.6666667 -0.116230314 0.603609988
#> 487 2.1666667 0.343691246 0.484506641
#> 488 3.3333333 -0.116230314 0.603609988
#> 489 2.8333333 0.480104130 0.397352002
#> 490 0.8333333 0.394803349 0.457970875
#> 491 0.5000000 0.210242322 0.544073547
#> 492 2.8333333 -0.108530441 0.267286120
#> 493 3.8333333 0.394803349 0.457970875
#> 494 1.0000000 -0.038761518 0.091542884
#> 495 1.6666667 -0.164720630 0.485010148
#> 496 1.0000000 -0.008164666 0.609384367
#> 497 1.1666667 -0.164720630 0.485010148
#> 498 3.0000000 -0.162773063 0.538004737
#> 499 2.1666667 0.210242322 0.544073547
#> 500 2.6666667 0.135611590 0.571902398
#> 501 2.5000000 0.480104130 0.397352002
#> 502 1.5000000 0.281022057 0.513990526
#> 503 3.8333333 -0.116230314 0.603609988
#> 504 1.0000000 -0.147255800 0.578149895
#> 505 0.0000000 -0.164720630 0.485010148
#> 506 0.3333333 0.000000000 0.000000000
#> 507 3.0000000 -0.075584507 0.181250135
#> 508 2.3333333 0.462391286 0.414566177
#> 509 0.3333333 0.210242322 0.544073547
#> 510 1.8333333 -0.075584507 0.181250135
#> 511 1.6666667 -0.008164666 0.609384367
#> 512 1.8333333 0.317502531 0.344568641
#> 513 1.0000000 0.462391286 0.414566177
#> 514 1.3333333 -0.164720630 0.485010148
#> 515 3.0000000 0.434163861 0.434714928
#> 516 1.0000000 0.434163861 0.434714928
#> 517 0.8333333 -0.164720630 0.485010148
#> 518 1.6666667 -0.155037031 0.421001760
#> 519 1.0000000 -0.147255800 0.578149895
#> 520 2.0000000 -0.164720630 0.485010148
#> 521 1.6666667 0.061389411 0.594623773
#> 522 1.8333333 -0.068791091 0.613330874
#> 523 3.0000000 0.317502531 0.344568641
#> 524 1.8333333 0.434163861 0.434714928
#> 525 2.5000000 0.210242322 0.544073547
#> 526 2.6666667 0.281022057 0.513990526
#> 527 2.3333333 0.343691246 0.484506641
#> 528 2.1666667 0.210242322 0.544073547
#> 529 2.1666667 0.135611590 0.571902398
#> 530 0.3333333 0.135611590 0.571902398
#> 531 1.1666667 -0.164720630 0.485010148
#> 532 2.0000000 -0.162773063 0.538004737
#> 533 3.0000000 0.061389411 0.594623773
#> 534 1.8333333 0.434163861 0.434714928
#> 535 0.6666667 -0.038761518 0.091542884
#> 536 0.5000000 -0.135660792 0.347815206
#> 537 0.5000000 -0.108530441 0.267286120
#> 538 1.3333333 -0.108530441 0.267286120
#> 539 2.6666667 0.343691246 0.484506641
#> 540 1.1666667 0.343691246 0.484506641
#> 541 0.3333333 -0.162773063 0.538004737
#> 542 1.1666667 -0.108530441 0.267286120
#> 543 1.1666667 -0.162773063 0.538004737
#> 544 2.0000000 -0.162773063 0.538004737
#> 545 0.6666667 0.061389411 0.594623773
#> 546 1.3333333 0.210242322 0.544073547
#> 547 0.3333333 -0.147255800 0.578149895
#> 548 0.8333333 -0.075584507 0.181250135
#> 549 2.8333333 -0.155037031 0.421001760
#> 550 1.0000000 -0.135660792 0.347815206
#> 551 0.6666667 -0.164720630 0.485010148
#> 552 2.0000000 -0.135660792 0.347815206
#> 553 0.8333333 -0.135660792 0.347815206
#> 554 0.6666667 -0.155037031 0.421001760
#> 555 2.0000000 0.434163861 0.434714928
#> 556 3.1666667 0.061389411 0.594623773
#> 557 1.6666667 0.462391286 0.414566177
#> 558 0.6666667 -0.068791091 0.613330874
#> 559 0.8333333 -0.135660792 0.347815206
#> 560 1.5000000 -0.155037031 0.421001760
#> 561 2.3333333 0.434163861 0.434714928
#> 562 3.3333333 0.210242322 0.544073547
#> 563 2.5000000 0.480104130 0.397352002
#> 564 3.3333333 0.281022057 0.513990526
#> 565 3.1666667 -0.162773063 0.538004737
#> 566 3.6666667 0.462391286 0.414566177
#> 567 0.1666667 0.486460094 0.371036886
#> 568 0.8333333 -0.038761518 0.091542884
#> 569 2.3333333 0.281022057 0.513990526
#> 570 2.0000000 0.210242322 0.544073547
#> 571 1.0000000 0.061389411 0.594623773
#> 572 0.6666667 -0.164720630 0.485010148
#> 573 1.8333333 -0.162773063 0.538004737
#> 574 3.0000000 -0.008164666 0.609384367
#> 575 1.8333333 0.434163861 0.434714928
#> 576 1.5000000 0.215001653 0.348635005
#> 577 3.0000000 -0.116230314 0.603609988
#> 578 0.5000000 0.434163861 0.434714928
#> 579 1.6666667 -0.108530441 0.267286120
#> ns(..prev_outcome.., df = 3).3 ..delta_time.. (id)
#> 1 -0.168878788 214 1
#> 2 0.256339223 78 1
#> 3 0.149677650 78 1
#> 4 -0.332128663 71 1
#> 5 -0.168878788 72 2
#> 6 -0.153547346 109 2
#> 7 -0.338552866 116 2
#> 8 -0.346754674 69 2
#> 9 -0.199808736 214 3
#> 10 -0.052588465 282 3
#> 11 -0.321334902 105 4
#> 12 -0.309066551 49 4
#> 13 -0.241852075 205 4
#> 14 -0.309066551 41 4
#> 15 0.098542716 132 5
#> 16 0.149677650 238 5
#> 17 0.256339223 308 5
#> 18 -0.088155720 92 6
#> 19 0.098542716 417 6
#> 20 -0.199808736 81 7
#> 21 -0.321334902 84 7
#> 22 -0.241852075 86 8
#> 23 -0.278622851 236 8
#> 24 -0.199808736 381 8
#> 25 -0.088155720 89 9
#> 26 -0.321334902 126 9
#> 27 0.001350756 322 10
#> 28 0.049054671 71 10
#> 29 0.311591380 352 11
#> 30 0.098542716 86 11
#> 31 0.601576241 18 11
#> 32 0.425252231 77 12
#> 33 -0.270955044 135 12
#> 34 -0.309066551 60 12
#> 35 -0.332128663 67 12
#> 36 -0.088155720 143 13
#> 37 -0.346754674 28 13
#> 38 -0.349171274 81 13
#> 39 -0.241852075 150 13
#> 40 -0.349171274 119 14
#> 41 0.149677650 456 14
#> 42 0.311591380 108 15
#> 43 -0.129683801 265 15
#> 44 -0.239720521 53 16
#> 45 -0.270955044 375 16
#> 46 -0.298481066 233 17
#> 47 -0.321334902 11 17
#> 48 -0.205603442 79 18
#> 49 -0.270955044 102 18
#> 50 -0.270955044 110 18
#> 51 -0.321334902 67 18
#> 52 0.001350756 108 19
#> 53 -0.088155720 248 19
#> 54 0.311591380 62 20
#> 55 -0.088155720 193 20
#> 56 -0.199808736 519 21
#> 57 -0.241852075 257 21
#> 58 -0.153547346 28 21
#> 59 -0.270955044 75 22
#> 60 -0.199808736 238 22
#> 61 -0.199808736 100 22
#> 62 -0.352226438 17 22
#> 63 -0.241852075 95 23
#> 64 -0.346754674 230 23
#> 65 0.001350756 2 23
#> 66 -0.346754674 48 23
#> 67 -0.168878788 140 24
#> 68 0.098542716 76 24
#> 69 -0.168878788 84 24
#> 70 -0.241852075 82 24
#> 71 -0.168878788 96 26
#> 72 -0.346754674 90 26
#> 73 -0.346754674 130 26
#> 74 -0.298481066 118 27
#> 75 -0.338552866 51 27
#> 76 -0.044431788 172 27
#> 77 0.001350756 28 27
#> 78 -0.321334902 72 28
#> 79 -0.349171274 205 28
#> 80 -0.168878788 59 28
#> 81 -0.168878788 214 29
#> 82 0.001350756 361 29
#> 83 -0.321334902 19 29
#> 84 -0.346754674 88 29
#> 85 -0.332128663 261 30
#> 86 -0.205603442 18 30
#> 87 -0.239720521 128 30
#> 88 -0.168878788 167 32
#> 89 -0.052588465 156 32
#> 90 -0.129683801 44 32
#> 91 -0.044431788 19 32
#> 92 -0.309066551 322 33
#> 93 -0.278622851 304 33
#> 94 -0.270955044 64 34
#> 95 -0.352226438 299 34
#> 96 -0.239720521 315 34
#> 97 -0.044431788 101 35
#> 98 -0.241852075 305 35
#> 99 -0.349171274 241 36
#> 100 -0.153547346 344 36
#> 101 -0.241852075 115 37
#> 102 -0.346754674 371 37
#> 103 0.049054671 107 38
#> 104 0.202322233 87 38
#> 105 0.781605752 126 38
#> 106 0.098542716 65 38
#> 107 -0.298481066 119 39
#> 108 -0.332128663 140 39
#> 109 -0.332128663 230 39
#> 110 -0.168878788 94 40
#> 111 -0.205603442 72 40
#> 112 -0.346754674 140 40
#> 113 -0.298481066 183 42
#> 114 -0.309066551 82 43
#> 115 -0.241852075 126 43
#> 116 -0.321334902 65 43
#> 117 -0.205603442 69 43
#> 118 -0.298481066 510 44
#> 119 -0.205603442 90 44
#> 120 -0.349171274 178 45
#> 121 -0.349171274 18 45
#> 122 -0.270955044 108 45
#> 123 -0.044431788 101 45
#> 124 -0.346754674 448 46
#> 125 -0.129683801 80 46
#> 126 -0.338552866 86 47
#> 127 -0.239720521 62 47
#> 128 -0.168878788 101 47
#> 129 -0.168878788 127 47
#> 130 -0.332128663 73 48
#> 131 0.149677650 133 48
#> 132 -0.298481066 29 48
#> 133 -0.338552866 158 48
#> 134 -0.349171274 168 49
#> 135 -0.239720521 35 49
#> 136 -0.349171274 67 49
#> 137 -0.129683801 358 50
#> 138 -0.338552866 222 50
#> 139 -0.044431788 421 51
#> 140 -0.044431788 90 52
#> 141 -0.044431788 85 52
#> 142 -0.168878788 115 52
#> 143 -0.332128663 144 52
#> 144 -0.349171274 231 53
#> 145 -0.352226438 83 53
#> 146 -0.321334902 39 53
#> 147 -0.349171274 48 53
#> 148 -0.239720521 127 54
#> 149 -0.338552866 112 54
#> 150 -0.321334902 73 54
#> 151 0.425252231 95 55
#> 152 -0.321334902 94 55
#> 153 -0.199808736 67 55
#> 154 -0.153547346 104 55
#> 155 -0.052588465 111 56
#> 156 -0.352226438 269 56
#> 157 -0.298481066 7 56
#> 158 -0.332128663 3 56
#> 159 0.001350756 168 57
#> 160 -0.129683801 16 57
#> 161 -0.321334902 193 57
#> 162 -0.332128663 5 57
#> 163 -0.168878788 91 58
#> 164 -0.338552866 70 58
#> 165 0.000000000 101 58
#> 166 -0.298481066 73 58
#> 167 -0.309066551 122 59
#> 168 -0.199808736 112 59
#> 169 -0.239720521 55 59
#> 170 -0.349171274 257 60
#> 171 -0.338552866 69 60
#> 172 -0.338552866 143 60
#> 173 -0.338552866 198 60
#> 174 -0.052588465 379 61
#> 175 -0.270955044 128 61
#> 176 -0.052588465 32 61
#> 177 -0.168878788 194 62
#> 178 -0.129683801 30 62
#> 179 -0.270955044 64 62
#> 180 -0.129683801 62 62
#> 181 -0.321334902 142 64
#> 182 -0.346754674 30 64
#> 183 -0.239720521 91 64
#> 184 0.001350756 90 64
#> 185 -0.338552866 95 65
#> 186 -0.332128663 226 65
#> 187 -0.168878788 6 65
#> 188 -0.298481066 19 65
#> 189 -0.129683801 218 66
#> 190 -0.298481066 69 67
#> 191 -0.338552866 562 67
#> 192 -0.270955044 439 68
#> 193 -0.352226438 35 68
#> 194 -0.332128663 120 69
#> 195 -0.298481066 33 69
#> 196 -0.129683801 111 69
#> 197 -0.298481066 101 69
#> 198 -0.241852075 89 71
#> 199 -0.199808736 147 71
#> 200 -0.153547346 177 71
#> 201 -0.309066551 98 72
#> 202 -0.044431788 186 72
#> 203 0.311591380 86 73
#> 204 0.256339223 97 73
#> 205 -0.088155720 87 73
#> 206 0.149677650 278 73
#> 207 0.149677650 85 74
#> 208 -0.241852075 198 74
#> 209 -0.270955044 424 74
#> 210 -0.346754674 80 75
#> 211 -0.044431788 84 75
#> 212 0.001350756 160 75
#> 213 -0.052588465 211 77
#> 214 -0.270955044 41 77
#> 215 -0.168878788 112 78
#> 216 0.049054671 82 78
#> 217 -0.044431788 182 78
#> 218 -0.349171274 14 78
#> 219 -0.309066551 99 79
#> 220 -0.239720521 60 79
#> 221 -0.278622851 121 79
#> 222 -0.298481066 64 79
#> 223 0.149677650 97 80
#> 224 -0.241852075 120 80
#> 225 -0.044431788 88 80
#> 226 -0.349171274 13 80
#> 227 0.425252231 203 81
#> 228 -0.205603442 77 82
#> 229 -0.309066551 104 82
#> 230 -0.349171274 185 82
#> 231 -0.321334902 69 83
#> 232 -0.338552866 162 83
#> 233 0.098542716 74 83
#> 234 0.001350756 15 83
#> 235 -0.129683801 267 84
#> 236 -0.168878788 194 84
#> 237 -0.332128663 128 85
#> 238 0.001350756 197 85
#> 239 -0.205603442 38 85
#> 240 -0.352226438 258 85
#> 241 -0.298481066 90 86
#> 242 -0.352226438 68 86
#> 243 0.098542716 180 86
#> 244 -0.129683801 43 86
#> 245 -0.168878788 101 87
#> 246 -0.298481066 64 87
#> 247 0.311591380 320 88
#> 248 0.781605752 53 88
#> 249 -0.044431788 16 88
#> 250 -0.088155720 17 88
#> 251 -0.205603442 138 89
#> 252 -0.321334902 142 89
#> 253 -0.352226438 18 89
#> 254 -0.346754674 139 89
#> 255 -0.346754674 111 90
#> 256 -0.332128663 133 90
#> 257 0.001350756 501 91
#> 258 -0.349171274 138 92
#> 259 -0.104122418 106 92
#> 260 -0.241852075 85 92
#> 261 -0.309066551 188 93
#> 262 -0.168878788 21 93
#> 263 -0.352226438 120 93
#> 264 -0.270955044 26 93
#> 265 -0.346754674 98 94
#> 266 -0.332128663 428 94
#> 267 -0.199808736 477 95
#> 268 -0.309066551 66 96
#> 269 -0.332128663 160 96
#> 270 -0.241852075 248 96
#> 271 -0.321334902 51 96
#> 272 -0.270955044 202 98
#> 273 -0.352226438 112 98
#> 274 -0.309066551 8 98
#> 275 -0.278622851 47 98
#> 276 -0.088155720 90 99
#> 277 -0.352226438 114 99
#> 278 -0.352226438 53 99
#> 279 -0.346754674 101 99
#> 280 0.149677650 330 100
#> 281 0.149677650 50 100
#> 282 0.721412927 83 101
#> 283 0.425252231 300 101
#> 284 -0.239720521 9 101
#> 285 0.721412927 20 101
#> 286 -0.349171274 59 102
#> 287 -0.338552866 136 102
#> 288 -0.309066551 175 102
#> 289 -0.321334902 172 103
#> 290 -0.332128663 118 103
#> 291 -0.346754674 93 103
#> 292 -0.270955044 64 103
#> 293 -0.349171274 73 104
#> 294 0.001350756 259 104
#> 295 0.425252231 275 105
#> 296 0.367941463 32 105
#> 297 -0.044431788 109 106
#> 298 -0.338552866 255 106
#> 299 -0.346754674 7 106
#> 300 -0.129683801 70 107
#> 301 -0.199808736 269 107
#> 302 -0.352226438 117 107
#> 303 -0.241852075 181 108
#> 304 -0.153547346 61 108
#> 305 -0.278622851 525 108
#> 306 -0.168878788 98 109
#> 307 -0.309066551 128 109
#> 308 -0.352226438 20 109
#> 309 -0.346754674 152 109
#> 310 0.001350756 110 110
#> 311 -0.088155720 210 110
#> 312 -0.088155720 125 110
#> 313 -0.168878788 106 111
#> 314 -0.104122418 152 111
#> 315 -0.153547346 89 111
#> 316 -0.309066551 452 111
#> 317 -0.168878788 227 112
#> 318 -0.338552866 97 112
#> 319 0.001350756 141 112
#> 320 -0.241852075 78 113
#> 321 -0.241852075 68 113
#> 322 -0.332128663 379 114
#> 323 -0.332128663 73 115
#> 324 -0.346754674 156 115
#> 325 -0.332128663 83 116
#> 326 -0.241852075 260 116
#> 327 -0.239720521 76 117
#> 328 -0.338552866 96 117
#> 329 -0.346754674 247 117
#> 330 0.149677650 109 118
#> 331 -0.346754674 49 118
#> 332 -0.338552866 111 118
#> 333 -0.153547346 93 119
#> 334 -0.052588465 178 119
#> 335 -0.278622851 14 119
#> 336 -0.309066551 99 119
#> 337 -0.199808736 175 120
#> 338 -0.352226438 20 120
#> 339 -0.044431788 111 120
#> 340 0.001350756 315 120
#> 341 -0.241852075 90 121
#> 342 -0.278622851 85 121
#> 343 -0.346754674 134 121
#> 344 -0.349171274 80 121
#> 345 -0.346754674 79 122
#> 346 -0.278622851 198 122
#> 347 -0.088155720 120 123
#> 348 -0.129683801 151 123
#> 349 -0.349171274 27 123
#> 350 -0.239720521 238 123
#> 351 -0.088155720 121 124
#> 352 -0.239720521 79 124
#> 353 -0.321334902 101 124
#> 354 -0.346754674 66 125
#> 355 -0.309066551 118 125
#> 356 0.001350756 78 126
#> 357 -0.321334902 135 126
#> 358 -0.153547346 92 126
#> 359 -0.309066551 15 126
#> 360 -0.349171274 106 127
#> 361 -0.338552866 118 127
#> 362 -0.321334902 142 128
#> 363 -0.205603442 47 128
#> 364 -0.278622851 168 128
#> 365 -0.352226438 6 128
#> 366 0.000000000 116 129
#> 367 -0.168878788 217 130
#> 368 -0.199808736 18 130
#> 369 -0.321334902 38 130
#> 370 0.001350756 206 130
#> 371 -0.349171274 357 132
#> 372 -0.241852075 38 132
#> 373 -0.278622851 270 132
#> 374 0.098542716 173 133
#> 375 -0.321334902 45 133
#> 376 -0.168878788 67 133
#> 377 -0.168878788 111 133
#> 378 -0.168878788 108 134
#> 379 -0.129683801 276 134
#> 380 -0.129683801 304 134
#> 381 -0.349171274 115 134
#> 382 -0.352226438 288 135
#> 383 -0.338552866 46 135
#> 384 -0.270955044 173 136
#> 385 -0.346754674 265 136
#> 386 -0.278622851 273 136
#> 387 -0.168878788 95 137
#> 388 -0.298481066 61 137
#> 389 -0.349171274 228 137
#> 390 -0.309066551 4 137
#> 391 -0.241852075 85 138
#> 392 -0.346754674 153 138
#> 393 -0.199808736 42 138
#> 394 -0.199808736 81 138
#> 395 -0.346754674 183 139
#> 396 0.098542716 57 139
#> 397 -0.239720521 224 139
#> 398 0.721412927 72 140
#> 399 0.601576241 159 140
#> 400 0.098542716 49 140
#> 401 -0.338552866 60 140
#> 402 -0.349171274 187 141
#> 403 -0.338552866 311 141
#> 404 -0.168878788 114 142
#> 405 -0.205603442 90 142
#> 406 -0.241852075 138 142
#> 407 -0.241852075 66 142
#> 408 -0.346754674 100 143
#> 409 -0.278622851 445 143
#> 410 -0.241852075 168 143
#> 411 -0.332128663 94 144
#> 412 -0.309066551 299 144
#> 413 -0.205603442 8 144
#> 414 -0.332128663 420 144
#> 415 0.000000000 104 145
#> 416 -0.338552866 409 145
#> 417 -0.349171274 193 145
#> 418 -0.270955044 147 146
#> 419 -0.352226438 16 146
#> 420 0.149677650 171 146
#> 421 -0.338552866 106 147
#> 422 -0.352226438 64 147
#> 423 -0.241852075 130 147
#> 424 -0.309066551 51 147
#> 425 -0.239720521 346 148
#> 426 0.542206861 147 148
#> 427 -0.129683801 79 149
#> 428 0.049054671 129 149
#> 429 0.311591380 326 149
#> 430 0.098542716 63 150
#> 431 -0.309066551 142 150
#> 432 -0.321334902 60 150
#> 433 -0.349171274 92 150
#> 434 -0.346754674 98 151
#> 435 -0.352226438 262 151
#> 436 -0.321334902 166 151
#> 437 -0.205603442 210 152
#> 438 0.542206861 303 152
#> 439 -0.168878788 101 153
#> 440 -0.239720521 48 153
#> 441 -0.309066551 116 153
#> 442 -0.199808736 91 153
#> 443 -0.239720521 193 154
#> 444 -0.338552866 175 154
#> 445 -0.332128663 4 154
#> 446 -0.352226438 14 154
#> 447 -0.338552866 164 155
#> 448 -0.309066551 38 155
#> 449 -0.352226438 107 155
#> 450 -0.153547346 19 155
#> 451 -0.270955044 204 156
#> 452 -0.338552866 26 156
#> 453 -0.241852075 94 157
#> 454 -0.278622851 136 157
#> 455 -0.338552866 41 157
#> 456 -0.088155720 97 157
#> 457 -0.199808736 315 158
#> 458 -0.309066551 154 158
#> 459 -0.321334902 297 159
#> 460 -0.044431788 67 159
#> 461 -0.349171274 23 159
#> 462 -0.153547346 53 159
#> 463 -0.349171274 527 160
#> 464 -0.309066551 248 160
#> 465 -0.346754674 185 161
#> 466 -0.241852075 24 161
#> 467 -0.241852075 73 161
#> 468 -0.349171274 65 161
#> 469 -0.153547346 118 162
#> 470 0.049054671 104 163
#> 471 -0.205603442 103 163
#> 472 -0.241852075 89 164
#> 473 0.049054671 395 164
#> 474 -0.298481066 164 165
#> 475 -0.352226438 57 165
#> 476 -0.298481066 96 165
#> 477 -0.239720521 88 165
#> 478 -0.241852075 407 166
#> 479 -0.278622851 15 166
#> 480 -0.270955044 44 166
#> 481 0.256339223 174 166
#> 482 -0.239720521 95 167
#> 483 -0.352226438 70 167
#> 484 -0.346754674 234 167
#> 485 -0.332128663 15 167
#> 486 -0.346754674 93 168
#> 487 -0.239720521 126 168
#> 488 -0.346754674 229 169
#> 489 -0.088155720 144 169
#> 490 -0.205603442 53 169
#> 491 -0.298481066 92 171
#> 492 -0.153547346 76 171
#> 493 -0.205603442 66 171
#> 494 -0.052588465 330 172
#> 495 -0.278622851 231 172
#> 496 -0.349171274 94 173
#> 497 -0.278622851 94 173
#> 498 -0.309066551 213 173
#> 499 -0.298481066 63 174
#> 500 -0.321334902 240 174
#> 501 -0.088155720 240 175
#> 502 -0.270955044 63 175
#> 503 -0.346754674 97 175
#> 504 -0.332128663 109 176
#> 505 -0.278622851 103 176
#> 506 0.000000000 100 176
#> 507 -0.104122418 46 176
#> 508 -0.129683801 161 177
#> 509 -0.298481066 110 177
#> 510 -0.104122418 23 177
#> 511 -0.349171274 45 177
#> 512 0.311591380 516 178
#> 513 -0.129683801 409 179
#> 514 -0.278622851 42 179
#> 515 -0.168878788 98 180
#> 516 -0.168878788 110 180
#> 517 -0.278622851 92 180
#> 518 -0.241852075 34 180
#> 519 -0.332128663 108 181
#> 520 -0.278622851 76 181
#> 521 -0.338552866 171 181
#> 522 -0.352226438 22 181
#> 523 0.311591380 381 183
#> 524 -0.168878788 185 183
#> 525 -0.298481066 244 184
#> 526 -0.270955044 136 184
#> 527 -0.239720521 73 185
#> 528 -0.298481066 185 185
#> 529 -0.321334902 30 185
#> 530 -0.321334902 67 185
#> 531 -0.278622851 107 186
#> 532 -0.309066551 53 186
#> 533 -0.338552866 201 186
#> 534 -0.168878788 79 186
#> 535 -0.052588465 109 187
#> 536 -0.199808736 88 187
#> 537 -0.153547346 80 187
#> 538 -0.153547346 185 187
#> 539 -0.239720521 108 188
#> 540 -0.239720521 74 188
#> 541 -0.309066551 147 188
#> 542 -0.153547346 95 189
#> 543 -0.309066551 110 189
#> 544 -0.309066551 56 189
#> 545 -0.338552866 79 189
#> 546 -0.298481066 122 191
#> 547 -0.332128663 48 191
#> 548 -0.104122418 127 191
#> 549 -0.241852075 183 191
#> 550 -0.199808736 159 192
#> 551 -0.278622851 10 192
#> 552 -0.199808736 152 192
#> 553 -0.199808736 92 193
#> 554 -0.241852075 56 193
#> 555 -0.168878788 113 194
#> 556 -0.338552866 99 194
#> 557 -0.129683801 81 194
#> 558 -0.352226438 76 194
#> 559 -0.199808736 182 195
#> 560 -0.241852075 61 195
#> 561 -0.168878788 87 196
#> 562 -0.298481066 69 196
#> 563 -0.088155720 106 196
#> 564 -0.270955044 114 196
#> 565 -0.309066551 83 197
#> 566 -0.129683801 201 197
#> 567 0.001350756 80 197
#> 568 -0.052588465 12 197
#> 569 -0.270955044 253 198
#> 570 -0.298481066 120 198
#> 571 -0.338552866 9 198
#> 572 -0.278622851 47 198
#> 573 -0.309066551 310 199
#> 574 -0.349171274 84 199
#> 575 -0.168878788 102 199
#> 576 0.425252231 47 200
#> 577 -0.346754674 163 200
#> 578 -0.168878788 47 200
#> 579 -0.153547346 139 200
#>
#> $data
#> # A tibble: 579 × 7
#> # Groups: Subject_ID [189]
#> Subject_ID Visit Time Outcome ..prev_outcome.. ..prev_time.. ..delta_time..
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1 214 4.5 3 0 214
#> 2 1 2 292 4.17 4.5 214 78
#> 3 1 3 370 1.33 4.17 292 78
#> 4 1 4 441 0.833 1.33 370 71
#> 5 2 1 72 0.5 3 0 72
#> 6 2 2 181 2 0.5 72 109
#> 7 2 3 297 1.5 2 181 116
#> 8 2 4 366 1.83 1.5 297 69
#> 9 3 1 214 0.167 0.667 0 214
#> 10 3 2 496 0.333 0.167 214 282
#> # ℹ 569 more rows
#>
#> attr(,"class")
#> [1] "SensIAT::outcome-model" "SensIAT::Single-index-outcome-model"
#> attr(,"kernel")
#> [1] "K2_Biweight"
#> attr(,"terms")
#> Outcome ~ ns(..prev_outcome.., df = 3) + ..delta_time.. - 1
#> attr(,"variables")
#> list(Outcome, ns(..prev_outcome.., df = 3), ..delta_time..)
#> attr(,"factors")
#> ns(..prev_outcome.., df = 3) ..delta_time..
#> Outcome 0 0
#> ns(..prev_outcome.., df = 3) 1 0
#> ..delta_time.. 0 1
#> attr(,"term.labels")
#> [1] "ns(..prev_outcome.., df = 3)" "..delta_time.."
#> attr(,"order")
#> [1] 1 1
#> attr(,"intercept")
#> [1] 0
#> attr(,"response")
#> [1] 1
#> attr(,".Environment")
#> <environment: 0x55e865f9ba88>
#> attr(,"predvars")
#> list(Outcome, ns(..prev_outcome.., knots = c(1.5, 2.66666666666667
#> ), Boundary.knots = c(0, 6), intercept = FALSE), ..delta_time..)
#> attr(,"dataClasses")
#> Outcome ns(..prev_outcome.., df = 3)
#> "numeric" "nmatrix.3"
#> ..delta_time.. (id)
#> "numeric" "numeric"
#> attr(,"id")
#> Subject_ID
#> attr(,"initial")
#> dir1
#> ns(..prev_outcome.., df = 3)1 3.447011e-01
#> ns(..prev_outcome.., df = 3)2 -9.046159e-01
#> ns(..prev_outcome.., df = 3)3 2.507013e-01
#> ..delta_time.. 6.023219e-06
#>
#>
#> $data
#> # A tibble: 779 × 7
#> # Groups: Subject_ID [200]
#> Subject_ID Visit Time Outcome ..prev_outcome.. ..prev_time.. ..delta_time..
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 0 0 3 NA 0 NA
#> 2 1 1 214 4.5 3 0 214
#> 3 1 2 292 4.17 4.5 214 78
#> 4 1 3 370 1.33 4.17 292 78
#> 5 1 4 441 0.833 1.33 370 71
#> 6 2 0 0 3 NA 0 NA
#> 7 2 1 72 0.5 3 0 72
#> 8 2 2 181 2 0.5 72 109
#> 9 2 3 297 1.5 2 181 116
#> 10 2 4 366 1.83 1.5 297 69
#> # ℹ 769 more rows
#>
#> $influence
#> $influence[[1]]
#> # A tibble: 200 × 4
#> id term1 term2 total
#> <int> <list> <list> <list>
#> 1 1 <dbl [5]> <dbl [5]> <dbl [5]>
#> 2 2 <dbl [5]> <dbl [5]> <dbl [5]>
#> 3 3 <dbl [5]> <dbl [5]> <dbl [5]>
#> 4 4 <dbl [5]> <dbl [5]> <dbl [5]>
#> 5 5 <dbl [5]> <dbl [5]> <dbl [5]>
#> 6 6 <dbl [5]> <dbl [5]> <dbl [5]>
#> 7 7 <dbl [5]> <dbl [5]> <dbl [5]>
#> 8 8 <dbl [5]> <dbl [5]> <dbl [5]>
#> 9 9 <dbl [5]> <dbl [5]> <dbl [5]>
#> 10 10 <dbl [5]> <dbl [5]> <dbl [5]>
#> # ℹ 190 more rows
#>
#>
#> $alpha
#> [1] 0
#>
#> $coefficients
#> $coefficients[[1]]
#> [1] 0.7374201 0.6245074 0.9857981 0.5872858 0.7683575
#>
#>
#> $coefficient.variance
#> $coefficient.variance[[1]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0002319694 -0.0004404666 0.0006461592 -0.0004030434 0.0001834052
#> [2,] -0.0004404666 0.0008702148 -0.0012983560 0.0008187804 -0.0003748022
#> [3,] 0.0006461592 -0.0012983560 0.0019585362 -0.0012448757 0.0005741166
#> [4,] -0.0004030434 0.0008187804 -0.0012448757 0.0007976140 -0.0003716807
#> [5,] 0.0001834052 -0.0003748022 0.0005741166 -0.0003716807 0.0001779540
#>
#>
#> $influence.args
#> list()
#>
#> $base
#> Spline Basis
#> Order: 4
#> Degree: 3
#> Knots: 60 60 60 60 260 460 460 460 460
#>
#> $V.inverse
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0575 -0.04500000 0.0425 -0.02000000 0.0075
#> [2,] -0.0450 0.09333333 -0.1025 0.05166667 -0.0200
#> [3,] 0.0425 -0.10250000 0.1725 -0.10250000 0.0425
#> [4,] -0.0200 0.05166667 -0.1025 0.09333333 -0.0450
#> [5,] 0.0075 -0.02000000 0.0425 -0.04500000 0.0575
#>
#> attr(,"class")
#> [1] "SensIAT_marginal_mean_model_generalized"
#> attr(,"call")
#> fit_SensIAT_marginal_mean_model_generalized(data = data_with_lags,
#> time = data_with_lags$Time, id = data_with_lags$Subject_ID,
#> alpha = 0, knots = c(60, 260, 460), outcome.model = outcome.model,
#> intensity.model = intensity.model, impute_data = function(t,
#> df) {
#> data_wl <- mutate(df, ..prev_time.. = Time, ..prev_outcome.. = Outcome,
#> ..delta_time.. = 0)
#> extrapolate_from_last_observation(t, data_wl, "Time",
#> slopes = c(..delta_time.. = 1))
#> }, loss = "lp_mse", link = "log")
time <- data_with_lags$Time
id <- data_with_lags$Subject_ID