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", "parametric"),
  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(),
  cluster.boot = NULL,
  ...
)

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
cluster.boot: Variable to cluster bootstrapping by

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,] 0.8136484 0.8500430 0.8110152 0.6358254 0.5905760 0.7472894 0.8215820
#>  [2,] 0.8369350 0.8154262 0.8004077 0.6899507 0.5333423 0.7045921 0.8009471
#>  [3,] 0.8193689 0.8243714 0.8258594 0.6800059 0.6003536 0.7129113 0.7903911
#>  [4,] 0.8297118 0.8362229 0.8166558 0.6677046 0.5576306 0.6903168 0.8284198
#>  [5,] 0.8307095 0.8887698 0.7976096 0.7219239 0.5996120 0.7278261 0.8264926
#>  [6,] 0.8121286 0.8724687 0.7876008 0.7034304 0.6188457 0.7483131 0.8518372
#>  [7,] 0.7788113 0.8702692 0.8246190 0.6400031 0.5836320 0.6607929 0.7787292
#>  [8,] 0.8032927 0.7888484 0.8038280 0.6765742 0.5504360 0.6863738 0.8032864
#>  [9,] 0.8208329 0.8641453 0.7939066 0.6686026 0.6048411 0.7246705 0.8285727
#> [10,] 0.8296936 0.8573718 0.8125555 0.7296370 0.6051996 0.7124973 0.7832825
#>        XZ=~x1z2  XZ=~x2z2 x1z1~~x1z2 x1z1~~x2z1 x1z2~~x2z2 x2z1~~x2z2    x1~~x1
#>  [1,] 0.7918972 0.6596057 0.12370297 0.13889128  0.1172727  0.1342505 0.1665013
#>  [2,] 0.7576199 0.6101557 0.10466718 0.11801127  0.1130634  0.1349378 0.1877195
#>  [3,] 0.8214692 0.6505752 0.12175153 0.13952473  0.1119078  0.1348786 0.1836008
#>  [4,] 0.8083159 0.6773176 0.08699855 0.12647627  0.1171038  0.1441987 0.1789220
#>  [5,] 0.7866702 0.6561173 0.12263182 0.12617532  0.1437002  0.1337387 0.1704570
#>  [6,] 0.7968685 0.6790424 0.13455646 0.12643290  0.1441988  0.1141236 0.1658553
#>  [7,] 0.7633713 0.6018760 0.10623231 0.07292419  0.1505601  0.1193927 0.1536954
#>  [8,] 0.7721933 0.6235792 0.12880970 0.14632912  0.1489538  0.1264121 0.1521982
#>  [9,] 0.7856241 0.6609857 0.13753382 0.09753028  0.1272841  0.1354970 0.1798341
#> [10,] 0.8020772 0.6331495 0.12284117 0.12556676  0.1250333  0.1222860 0.1874125
#>          x2~~x2    z1~~z1    z2~~z2    y1~~y1    y2~~y2 x1z1~~x1z1 x2z1~~x2z1
#>  [1,] 0.1582221 0.2018391 0.1242125 0.1646320 0.1461259  0.3447423  0.2920502
#>  [2,] 0.1383405 0.2099865 0.1357289 0.1738040 0.1454113  0.2833608  0.2954195
#>  [3,] 0.1580124 0.1796666 0.1605001 0.2074109 0.1183935  0.3327544  0.3049153
#>  [4,] 0.1436572 0.2235916 0.1185838 0.1790459 0.1383758  0.2849227  0.2992222
#>  [5,] 0.1567684 0.2606311 0.1025253 0.1785238 0.1423744  0.3074855  0.2918664
#>  [6,] 0.1494631 0.2317927 0.1245398 0.1308891 0.1803976  0.3542515  0.2592201
#>  [7,] 0.1573897 0.2151401 0.1212760 0.2221052 0.1084483  0.2394239  0.2269702
#>  [8,] 0.1701046 0.1849171 0.1635234 0.1865713 0.1311614  0.3750065  0.3016734
#>  [9,] 0.1543777 0.2472318 0.1129482 0.1486773 0.1473279  0.2904846  0.2826039
#> [10,] 0.1378897 0.1965681 0.1346538 0.2137346 0.1177881  0.3068628  0.2726606
#>       x1z2~~x1z2 x2z2~~x2z2      X~~X      Z~~Z      Y~~Y    XZ~~XZ      X~~Z
#>  [1,]  0.2701594  0.2413436 0.9612714 0.9566120 0.8673828 0.9617711 0.1989054
#>  [2,]  0.2611397  0.2263317 0.8979856 1.0565069 0.9394979 1.0639000 0.1617591
#>  [3,]  0.2762069  0.2342220 0.9136864 0.9982688 0.8968371 1.0105718 0.1532475
#>  [4,]  0.2409287  0.2413748 0.9392982 0.9768119 0.9282766 0.9512990 0.1957230
#>  [5,]  0.3207610  0.2517865 0.9311308 0.9511813 0.9446710 0.9580283 0.1829304
#>  [6,]  0.3166977  0.2369791 0.9692179 0.9057911 1.0169956 0.9009328 0.2067670
#>  [7,]  0.3090138  0.2443715 0.9741209 0.9223777 1.0219705 1.0842307 0.1717285
#>  [8,]  0.3177139  0.2466006 0.9950408 1.0815355 0.9854947 1.1713601 0.1924369
#>  [9,]  0.3103478  0.2361521 0.8838294 0.9775601 0.9525338 0.9327275 0.1762067
#> [10,]  0.3023479  0.2211091 0.9456390 0.9598558 0.9827999 1.1117709 0.2242517
#>              X~~XZ        Z~~XZ
#>  [1,]  0.044921413  0.056898032
#>  [2,] -0.006111644 -0.031508318
#>  [3,] -0.028332321  0.053120218
#>  [4,]  0.034576119  0.062798313
#>  [5,] -0.010095331  0.033752225
#>  [6,] -0.012587866  0.017041183
#>  [7,] -0.060305244 -0.020297514
#>  [8,] -0.016367164  0.020789443
#>  [9,]  0.016583979  0.004200049
#> [10,] -0.065478686 -0.004399217
#> attr(,"error.idx")
#> integer(0)
#> attr(,"nonadmissible")
#> integer(0)
#> attr(,"seed")
#> [1] 874600660


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,] 0.8437269 0.8307269 0.8281022 1.0376443 1.239684 0.9692303 1.158909
#>  [2,] 0.8092461 0.7850037 0.7977322 1.0105589 1.191039 1.0249024 1.227655
#>  [3,] 0.7863686 0.8047917 0.8143782 0.9997175 1.207396 0.9873804 1.185932
#>  [4,] 0.8280870 0.8185702 0.7969667 1.0144560 1.213569 1.0379122 1.203201
#>  [5,] 0.7962489 0.8421955 0.8151035 1.0141417 1.185240 1.0182663 1.210591
#>  [6,] 0.8276120 0.8134586 0.8035415 1.0304363 1.227630 1.0112397 1.209996
#>  [7,] 0.7992115 0.8283630 0.8080566 1.0261032 1.186344 0.9694229 1.182991
#>  [8,] 0.8430520 0.8011515 0.8030153 1.0615445 1.256642 1.0567498 1.240979
#>  [9,] 0.8229801 0.7824344 0.8121265 1.0413766 1.223534 1.0410223 1.216023
#> [10,] 0.8247024 0.7967354 0.8061774 1.0129461 1.202239 0.9995481 1.203658
#>            y1~1     y2~1    x1~~x1    x2~~x2    z1~~z1    z2~~z2    y1~~y1
#>  [1,] 1.0737298 1.245064 0.2256917 0.1272870 0.1686491 0.1626732 0.2039789
#>  [2,] 0.9776911 1.167156 0.1792006 0.1483568 0.1645192 0.1590036 0.1454201
#>  [3,] 1.0134770 1.224280 0.1471497 0.1834376 0.1632104 0.1591790 0.1761449
#>  [4,] 1.0069714 1.195304 0.1672354 0.1518147 0.1786971 0.1588920 0.1738811
#>  [5,] 1.0250271 1.206731 0.1642201 0.1504121 0.1909535 0.1493238 0.1863755
#>  [6,] 0.9896400 1.199485 0.1642867 0.1649139 0.1761926 0.1466266 0.1897818
#>  [7,] 1.0318394 1.199603 0.1632716 0.1548219 0.1958846 0.1376460 0.1616034
#>  [8,] 1.0613314 1.243645 0.1938119 0.1425991 0.1625572 0.1693882 0.1439872
#>  [9,] 1.0385475 1.224171 0.1703982 0.1627438 0.1314194 0.1726512 0.1624785
#> [10,] 1.0697933 1.248079 0.1921548 0.1440672 0.1554198 0.1652573 0.1952393
#>          y2~~y2      X~~X      X~~Z      Z~~Z      Y~~Y       Y~X       Y~Z
#>  [1,] 0.1315218 0.9026554 0.2113799 1.0025561 0.9154441 0.6603187 0.5405408
#>  [2,] 0.1546290 0.9695671 0.2202224 1.0408157 0.9750196 0.7533053 0.5723498
#>  [3,] 0.1395586 1.0129084 0.1634353 1.0320925 0.9709077 0.6200670 0.5584930
#>  [4,] 0.1370424 0.9006536 0.2179743 1.0649683 0.9706859 0.7820276 0.5864314
#>  [5,] 0.1354589 0.9631058 0.2115380 0.9947168 0.9901809 0.6803392 0.5865532
#>  [6,] 0.1225861 0.9459654 0.2195528 1.0465243 0.9382915 0.6838813 0.5632198
#>  [7,] 0.1549709 1.0118320 0.1865688 0.9817782 0.9572839 0.6689487 0.5643617
#>  [8,] 0.1579117 0.9671704 0.2025762 1.0512785 1.0091321 0.7199200 0.6311793
#>  [9,] 0.1439877 0.9721045 0.2251818 1.0906231 0.9318039 0.7112641 0.5368693
#> [10,] 0.1284379 0.9682524 0.1885586 1.0618492 0.8822520 0.7462400 0.5379499
#>           Y~X:Z
#>  [1,] 0.7324089
#>  [2,] 0.7181520
#>  [3,] 0.6866947
#>  [4,] 0.6798579
#>  [5,] 0.7591866
#>  [6,] 0.6991846
#>  [7,] 0.7460267
#>  [8,] 0.7162097
#>  [9,] 0.7065186
#> [10,] 0.7386004
# }

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 
#>     0.21613756     0.17447574     0.21754632     0.19157083     0.22797399 
#>     BEH~INTPBC       ATT~~ATT         SN~~SN       PBC~~PBC       INT~~INT 
#>     0.20376362     1.00193405     0.98106985     0.96499948     0.48918955 
#>       BEH~~BEH INTPBC~~INTPBC        ATT~~SN       ATT~~PBC    ATT~~INTPBC 
#>     0.44943800     1.01771341     0.62704719     0.67983189     0.08404097 
#>        SN~~PBC     SN~~INTPBC    PBC~~INTPBC 
#>     0.67814613     0.05777815     0.08944000 

cat("Standard Errors: \n")
#> Standard Errors: 
print(se)
#>        INT~ATT         INT~SN        INT~PBC        BEH~INT        BEH~PBC 
#>     0.02471326     0.02505800     0.02761024     0.02340060     0.02034168 
#>     BEH~INTPBC       ATT~~ATT         SN~~SN       PBC~~PBC       INT~~INT 
#>     0.01842627     0.03621253     0.03741315     0.03489927     0.02291011 
#>       BEH~~BEH INTPBC~~INTPBC        ATT~~SN       ATT~~PBC    ATT~~INTPBC 
#>     0.02483194     0.08937553     0.02929924     0.02795997     0.03848342 
#>        SN~~PBC     SN~~INTPBC    PBC~~INTPBC 
#>     0.03046179     0.03568838     0.04466642 

# }