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 = modsem, 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,
  ...
)

# S3 method for class '`function`'
bootstrap_modsem(
  model = modsem,
  FUN = "coef",
  data,
  R = 1000L,
  verbose = interactive(),
  FUN.args = list(),
  ...
)

Arguments

model: A fitted modsem object, or a function to be bootstrapped (e.g., modsem, modsem_da and modsem_pi)
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.
data: Dataset to be resampled.
FUN.args: Arguments passed to FUN

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.

This is a more general version of boostrap_modsem for bootstrapping modsem functions, not modsem objects. model is now a function to be boostrapped, and ... are now passed to the function (model), not FUN. To pass arguments to FUN use FUN.args.

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.
bootstrap_modsem(`function`): Non-parametric bootstrap of modsem functions

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,] 0.8144249 0.7994558 0.8106055 1.005050 1.208416 0.9601928 1.168434
#>  [2,] 0.8306618 0.8110611 0.8213023 1.077158 1.277789 1.0247542 1.200896
#>  [3,] 0.8411607 0.7972488 0.8095984 1.013350 1.206820 1.0068561 1.196302
#>  [4,] 0.8191819 0.8223422 0.8043713 1.014464 1.217126 1.0274982 1.221347
#>  [5,] 0.8011285 0.8277382 0.8095597 1.025258 1.219122 0.9861196 1.175388
#>  [6,] 0.8372476 0.8234276 0.8009580 1.004623 1.207068 1.0231868 1.218734
#>  [7,] 0.8122819 0.8009942 0.8140702 1.035939 1.228986 1.0025992 1.198659
#>  [8,] 0.8045314 0.7979068 0.8106893 1.046972 1.211095 0.9939626 1.212647
#>  [9,] 0.8055473 0.8456199 0.8017031 1.028694 1.226362 1.0127911 1.214436
#> [10,] 0.8061172 0.7877519 0.8109209 1.023713 1.218222 1.0122960 1.217087
#>            y1~1     y2~1    x1~~x1    x2~~x2    z1~~z1    z2~~z2    y1~~y1
#>  [1,] 0.9662349 1.159700 0.1789629 0.1396592 0.1693207 0.1540739 0.1973072
#>  [2,] 1.0668095 1.262117 0.1729039 0.1387757 0.1809208 0.1425726 0.2013929
#>  [3,] 1.0491994 1.227669 0.1944130 0.1300357 0.1562650 0.1580442 0.1853396
#>  [4,] 1.0685017 1.248043 0.1668592 0.1415672 0.1662921 0.1502297 0.1882442
#>  [5,] 1.0197621 1.208855 0.1595008 0.1521806 0.1821325 0.1523385 0.1896113
#>  [6,] 0.9945248 1.189701 0.1984813 0.1467717 0.1709734 0.1434117 0.1892290
#>  [7,] 1.0245044 1.201537 0.1655852 0.1523672 0.1585768 0.1625813 0.1793059
#>  [8,] 1.0631284 1.237800 0.1936810 0.1342058 0.1665919 0.1675431 0.2023190
#>  [9,] 1.0516512 1.234766 0.1761351 0.1558178 0.1800263 0.1431118 0.1806793
#> [10,] 1.0207796 1.201399 0.1564162 0.1631285 0.1551158 0.1531997 0.2128208
#>          y2~~y2      X~~X      X~~Z      Z~~Z      Y~~Y       Y~X       Y~Z
#>  [1,] 0.1451890 0.9903107 0.2199216 1.0517475 0.9875343 0.6443155 0.5405837
#>  [2,] 0.1330980 0.9294362 0.1841670 1.0740669 0.9077634 0.7407449 0.5662418
#>  [3,] 0.1310587 0.9244601 0.1959024 1.0873494 0.9554678 0.6641158 0.5610568
#>  [4,] 0.1336907 0.9683357 0.1974863 0.9777329 0.9537110 0.6623360 0.6202128
#>  [5,] 0.1346769 0.9632715 0.2142341 1.0401253 0.9412764 0.6207919 0.5884689
#>  [6,] 0.1425606 0.9218639 0.1639074 0.9894723 0.9250406 0.6770013 0.5763097
#>  [7,] 0.1349305 0.9799755 0.2209489 1.0331289 0.9255412 0.6396911 0.5747478
#>  [8,] 0.1234008 0.9786263 0.2422323 1.0435471 0.9970825 0.6748976 0.5782958
#>  [9,] 0.1445198 0.9671834 0.2444986 1.0410502 0.9124814 0.6250333 0.6097863
#> [10,] 0.1174835 1.0174541 0.2237963 1.0503501 0.9801075 0.6446188 0.5908044
#>           Y~X:Z
#>  [1,] 0.7504803
#>  [2,] 0.7323244
#>  [3,] 0.7465220
#>  [4,] 0.7605423
#>  [5,] 0.7708292
#>  [6,] 0.7081364
#>  [7,] 0.7297743
#>  [8,] 0.7173830
#>  [9,] 0.7245055
#> [10,] 0.6588931
# }

tpb <- "
# Outer Model (Based on Hagger et al., 2007)
  ATT =~ att1 + att2 + att3 + att4 + att5
  SN =~ sn1 + sn2
  PBC =~ pbc1 + pbc2 + pbc3
  INT =~ int1 + int2 + int3
  BEH =~ b1 + b2

# Inner Model (Based on Steinmetz et al., 2011)
  INT ~ ATT + SN + PBC
  BEH ~ INT + PBC + INT:PBC
"

# \dontrun{
boot <- bootstrap_modsem(model = modsem,
                         model.syntax = tpb, data = TPB,
                         method = "dblcent", rcs = TRUE,
                         rcs.scale.corrected = TRUE,
                         FUN = "coef", R = 50L)
coef <- apply(boot, MARGIN = 2, FUN = mean, na.rm = TRUE)
se   <- apply(boot, MARGIN = 2, FUN = sd, na.rm = TRUE)

cat("Parameter Estimates:\n")
#> Parameter Estimates:
print(coef)
#>        INT~ATT         INT~SN        INT~PBC        BEH~INT        BEH~PBC 
#>     0.21064177     0.17371320     0.21826009     0.19047476     0.22884408 
#>     BEH~INTPBC       ATT~~ATT         SN~~SN       PBC~~PBC       INT~~INT 
#>     0.20029927     1.00077490     0.98767221     0.95575485     0.48684160 
#>       BEH~~BEH INTPBC~~INTPBC        ATT~~SN       ATT~~PBC    ATT~~INTPBC 
#>     0.45493022     0.98187014     0.62834518     0.67576214     0.08174600 
#>        SN~~PBC     SN~~INTPBC    PBC~~INTPBC 
#>     0.67174267     0.05357099     0.08065211 

cat("Standard Errors: \n")
#> Standard Errors: 
print(se)
#>        INT~ATT         INT~SN        INT~PBC        BEH~INT        BEH~PBC 
#>     0.02179516     0.02874696     0.03060897     0.02590732     0.01933352 
#>     BEH~INTPBC       ATT~~ATT         SN~~SN       PBC~~PBC       INT~~INT 
#>     0.02245272     0.03847476     0.04044220     0.03699584     0.01935323 
#>       BEH~~BEH INTPBC~~INTPBC        ATT~~SN       ATT~~PBC    ATT~~INTPBC 
#>     0.02626266     0.07504883     0.02947911     0.02879307     0.03194062 
#>        SN~~PBC     SN~~INTPBC    PBC~~INTPBC 
#>     0.03039619     0.03055908     0.03852186 

# }