Bootstrap a modsem Model

A generic interface for parametric and non‑parametric bootstrap procedures for structural equation models estimated with the modsem ecosystem. The function dispatches on the class of model; currently dedicated methods exist for modsem_pi (product‑indicator approach) and modsem_da (distributional‑analytic approach).

Usage

bootstrap_modsem(model, FUN, ...)

# S3 method for class 'modsem_pi'
bootstrap_modsem(model, FUN, ...)

# S3 method for class 'modsem_da'
bootstrap_modsem(
  model,
  FUN = "coef",
  R = 1000L,
  P.max = 1e+05,
  type = c("nonparametric", "parameteric"),
  verbose = interactive(),
  calc.se = FALSE,
  optimize = FALSE,
  ...
)

Arguments

model: A fitted modsem object.
FUN: A function that returns the statistic of interest when applied to a fitted model. The function must accept a single argument, the model object, and should ideally return a numeric vector; see Value.
...: Additional arguments forwarded to lavaan::bootstrapLavaan for modsem_pi objects, or modsem_da for modsem_da objects.
R: number of bootstrap replicates.
P.max: ceiling for the simulated population size.
type: Bootstrap flavour, see Details.
verbose: Should progress information be printed to the console?
calc.se: Should standard errors for each replicate. Defaults to FALSE.
optimize: Should starting values be re-optimized for each replicate. Defaults to FALSE.

Value

Depending on the return type of FUN either

numeric: A matrix with R rows (bootstrap replicates) and as many columns as length(FUN(model)).
other: A list of length R; each element is the raw output of FUN. NOTE: Only applies for modsem_da objects

Details

A thin wrapper around lavaan::bootstrapLavaan() that performs the necessary book‑keeping so that FUN receives a fully‑featured modsem_pi object—rather than a bare lavaan fit—at every iteration.

The function internally resamples the observed data (non‑parametric case) or simulates from the estimated parameter table (parametric case), feeds the sample to modsem_da, evaluates FUN on the refitted object and finally collates the results.

Methods (by class)

bootstrap_modsem(modsem_pi): Bootstrap a modsem_pi model by delegating to bootstrapLavaan.
bootstrap_modsem(modsem_da): Parametric or non‑parametric bootstrap for modsem_da models.

Examples


m1 <- '
  X =~ x1 + x2
  Z =~ z1 + z2
  Y =~ y1 + y2

  Y ~ X + Z + X:Z
'

fit_pi <- modsem(m1, oneInt)
bootstrap_modsem(fit_pi, FUN = coef, R = 10L)
#>           X=~x2     Z=~z2     Y=~y2       Y~X       Y~Z      Y~XZ  XZ=~x2z1
#>  [1,] 0.8884237 0.8262879 0.7797705 0.7407114 0.5918870 0.6707317 0.8246330
#>  [2,] 0.8347994 0.8233353 0.8025760 0.6824978 0.6016801 0.6865373 0.8116811
#>  [3,] 0.8206546 0.8518766 0.8007877 0.6971329 0.5362172 0.6820370 0.8238181
#>  [4,] 0.8189006 0.8113157 0.8325491 0.6869278 0.5782950 0.7256083 0.7789803
#>  [5,] 0.7947128 0.8558326 0.7924540 0.7333650 0.6106507 0.7282757 0.8221329
#>  [6,] 0.8254009 0.8749817 0.7929519 0.6579637 0.6131392 0.7361599 0.8396432
#>  [7,] 0.8332576 0.7692559 0.8131625 0.7067837 0.5708261 0.7091723 0.8355242
#>  [8,] 0.8619048 0.8171167 0.7882294 0.7320317 0.6299300 0.7734579 0.8497304
#>  [9,] 0.8272198 0.8581544 0.8065377 0.7420436 0.5475846 0.7715898 0.7902094
#> [10,] 0.8325728 0.8515355 0.8051629 0.6431409 0.6255022 0.7367125 0.8150739
#>        XZ=~x1z2  XZ=~x2z2 x1z1~~x1z2 x1z1~~x2z1 x1z2~~x2z2 x2z1~~x2z2    x1~~x1
#>  [1,] 0.7706057 0.6378158  0.1321030 0.12470048 0.13859185  0.1236854 0.2695500
#>  [2,] 0.7620211 0.6213905  0.1510716 0.08864615 0.15350198  0.1165963 0.2064331
#>  [3,] 0.8140617 0.6704431  0.1392288 0.12953526 0.12479679  0.1391153 0.2037414
#>  [4,] 0.7923717 0.6249382  0.1028956 0.14624920 0.13305408  0.1534371 0.2024947
#>  [5,] 0.8138680 0.6766186  0.1016855 0.17156133 0.13094839  0.1542808 0.1466010
#>  [6,] 0.7600386 0.6436328  0.1071415 0.07537641 0.17072580  0.1236519 0.1713316
#>  [7,] 0.7848949 0.6607577  0.1366991 0.11834861 0.13430508  0.1109281 0.2181188
#>  [8,] 0.8331755 0.7173464  0.1227065 0.15731268 0.08557116  0.1282096 0.2078369
#>  [9,] 0.8248556 0.6578495  0.1125763 0.16228584 0.10511858  0.1216584 0.2034808
#> [10,] 0.8145436 0.6751385  0.1228619 0.15560824 0.12230915  0.1129503 0.1708143
#>          x2~~x2    z1~~z1    z2~~z2    y1~~y1    y2~~y2 x1z1~~x1z1 x2z1~~x2z1
#>  [1,] 0.1068363 0.2120969 0.1364207 0.1522135 0.1715433  0.3467576  0.2808781
#>  [2,] 0.1326718 0.1849395 0.1475439 0.1745294 0.1382708  0.3035680  0.2380796
#>  [3,] 0.1548883 0.1971554 0.1424606 0.1466531 0.1517053  0.3601218  0.2922566
#>  [4,] 0.1458213 0.1939336 0.1492024 0.1856174 0.1279031  0.3284856  0.3442310
#>  [5,] 0.1768187 0.2159352 0.1325914 0.1723244 0.1427089  0.3648349  0.3440650
#>  [6,] 0.1504944 0.2341332 0.1190925 0.1613587 0.1484900  0.2417272  0.2421190
#>  [7,] 0.1401831 0.1358201 0.1775705 0.1744732 0.1359542  0.3335131  0.2663161
#>  [8,] 0.1369614 0.2094457 0.1333073 0.1566526 0.1512443  0.3620863  0.3218547
#>  [9,] 0.1455015 0.2406770 0.1118286 0.2188779 0.1184675  0.3601850  0.3186712
#> [10,] 0.1532201 0.2130209 0.1350956 0.1946312 0.1367605  0.3495799  0.2831961
#>       x1z2~~x1z2 x2z2~~x2z2      X~~X      Z~~Z      Y~~Y    XZ~~XZ      X~~Z
#>  [1,]  0.3058370  0.2433937 0.9250376 0.9509946 1.0404153 0.9839416 0.1510574
#>  [2,]  0.3521438  0.2414933 0.9325914 1.0209942 0.9759887 1.1139648 0.1684377
#>  [3,]  0.3048880  0.2515079 0.9511693 0.9631768 0.9344947 1.1739524 0.1752234
#>  [4,]  0.2790108  0.2581793 0.9726406 1.0246144 0.9579877 1.1140874 0.1988152
#>  [5,]  0.2749447  0.2623786 1.0739408 0.9043633 0.9671002 0.9805299 0.1828608
#>  [6,]  0.3181851  0.2738636 0.9577705 0.9431554 0.9825834 1.0354563 0.1617813
#>  [7,]  0.3089064  0.2212350 0.8914256 1.0704986 0.9203757 0.9886425 0.1810837
#>  [8,]  0.2373762  0.1982495 0.8862861 1.0080460 0.9482141 0.8543592 0.2248769
#>  [9,]  0.2559218  0.2049166 0.9444809 0.9177360 0.9206756 0.9224049 0.1949300
#> [10,]  0.2906092  0.2260151 0.9269864 0.9611296 0.9645808 0.8736839 0.1970902
#>               X~~XZ      Z~~XZ
#>  [1,]  0.0045452923 0.06431493
#>  [2,] -0.0094172460 0.08608002
#>  [3,]  0.0412521613 0.13538289
#>  [4,] -0.0004327796 0.06455298
#>  [5,] -0.0391503620 0.04776190
#>  [6,]  0.0258802984 0.03401701
#>  [7,]  0.0028456548 0.05461465
#>  [8,]  0.0450855234 0.02570986
#>  [9,] -0.0242799280 0.04269811
#> [10,]  0.0395353338 0.04479171
#> attr(,"error.idx")
#> integer(0)
#> attr(,"nonadmissible")
#> integer(0)
#> attr(,"seed")
#> [1] 80750137


m1 <- '
  X =~ x1 + x2
  Z =~ z1 + z2
  Y =~ y1 + y2

  Y ~ X + Z + X:Z
'

# \dontrun{
fit_lms <- modsem(m1, oneInt, method = "lms")
bootstrap_modsem(fit_lms, FUN = coef, R = 10L)
#>           X=~x2     Z=~z2     Y=~y2     x1~1     x2~1      z1~1     z2~1
#>  [1,] 0.8144003 0.7994969 0.8106792 1.005678 1.208908 0.9603175 1.168526
#>  [2,] 0.8305667 0.8108889 0.8212616 1.076854 1.277735 1.0245837 1.200803
#>  [3,] 0.8408636 0.7971195 0.8096376 1.013152 1.206650 1.0068273 1.196258
#>  [4,] 0.8191455 0.8223470 0.8043703 1.014141 1.216866 1.0273827 1.221252
#>  [5,] 0.8008017 0.8275087 0.8096398 1.025941 1.219654 0.9858933 1.175210
#>  [6,] 0.8363479 0.8233188 0.8009718 1.004424 1.206887 1.0223509 1.218075
#>  [7,] 0.8125059 0.8008573 0.8140952 1.036395 1.229375 1.0026206 1.198682
#>  [8,] 0.8045093 0.7978530 0.8107005 1.046770 1.210967 0.9939469 1.212620
#>  [9,] 0.8055632 0.8456173 0.8016989 1.028315 1.226056 1.0126419 1.214307
#> [10,] 0.8064619 0.7876747 0.8108583 1.023187 1.217798 1.0113295 1.216341
#>            y1~1     y2~1    x1~~x1    x2~~x2    z1~~z1    z2~~z2    y1~~y1
#>  [1,] 0.9665918 1.159976 0.1789661 0.1396912 0.1693366 0.1540438 0.1973418
#>  [2,] 1.0666389 1.261958 0.1727841 0.1387836 0.1808257 0.1426023 0.2013036
#>  [3,] 1.0488971 1.227408 0.1939891 0.1303049 0.1561264 0.1580959 0.1854701
#>  [4,] 1.0681430 1.247761 0.1668152 0.1415997 0.1663170 0.1502107 0.1882028
#>  [5,] 1.0197591 1.208849 0.1591775 0.1524078 0.1819070 0.1524821 0.1896973
#>  [6,] 0.9934481 1.188831 0.1975663 0.1472956 0.1708857 0.1433798 0.1893417
#>  [7,] 1.0246796 1.201612 0.1658557 0.1521500 0.1584666 0.1626799 0.1793366
#>  [8,] 1.0630799 1.237754 0.1937012 0.1342085 0.1665521 0.1675723 0.2023360
#>  [9,] 1.0513124 1.234489 0.1761450 0.1558055 0.1800036 0.1431390 0.1806828
#> [10,] 1.0198644 1.200668 0.1568596 0.1628377 0.1550352 0.1532384 0.2126190
#>          y2~~y2      X~~X      X~~Z      Z~~Z      Y~~Y       Y~X       Y~Z
#>  [1,] 0.1451493 0.9902767 0.2198218 1.0515644 0.9866315 0.6443917 0.5409160
#>  [2,] 0.1331143 0.9295143 0.1841595 1.0742640 0.9083721 0.7405474 0.5659758
#>  [3,] 0.1310227 0.9245535 0.1959096 1.0876359 0.9546722 0.6641445 0.5606902
#>  [4,] 0.1337160 0.9683446 0.1975083 0.9778979 0.9539470 0.6622323 0.6199707
#>  [5,] 0.1345668 0.9636634 0.2145205 1.0405604 0.9411491 0.6203583 0.5886062
#>  [6,] 0.1424908 0.9230809 0.1642395 0.9896369 0.9251874 0.6755627 0.5761540
#>  [7,] 0.1348998 0.9797343 0.2209607 1.0334759 0.9256103 0.6400104 0.5748232
#>  [8,] 0.1233925 0.9785712 0.2420869 1.0436009 0.9968020 0.6749390 0.5781515
#>  [9,] 0.1445184 0.9671654 0.2444591 1.0410265 0.9125756 0.6249548 0.6094542
#> [10,] 0.1175989 1.0169742 0.2238477 1.0504369 0.9804817 0.6439944 0.5900795
#>           Y~X:Z
#>  [1,] 0.7502220
#>  [2,] 0.7320932
#>  [3,] 0.7468363
#>  [4,] 0.7604845
#>  [5,] 0.7705250
#>  [6,] 0.7076948
#>  [7,] 0.7296513
#>  [8,] 0.7172962
#>  [9,] 0.7245370
#> [10,] 0.6588935
# }