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,] 0.8439914 0.8306664 0.8280576 1.0368173 1.238975 0.9685517 1.158335
#>  [2,] 0.8091064 0.7849298 0.7976872 1.0104667 1.190907 1.0246590 1.227494
#>  [3,] 0.7862627 0.8048153 0.8142898 0.9993567 1.207108 0.9874045 1.185939
#>  [4,] 0.8280318 0.8185326 0.7969994 1.0138076 1.212999 1.0373556 1.202727
#>  [5,] 0.7960258 0.8422551 0.8151019 1.0134844 1.184783 1.0180378 1.210387
#>  [6,] 0.8273825 0.8133551 0.8035218 1.0302584 1.227456 1.0112090 1.209964
#>  [7,] 0.7991845 0.8285807 0.8080086 1.0255405 1.185888 0.9689374 1.182577
#>  [8,] 0.8430450 0.8009657 0.8029533 1.0607866 1.255990 1.0560955 1.240445
#>  [9,] 0.8229511 0.7825258 0.8120604 1.0407533 1.223069 1.0404157 1.215530
#> [10,] 0.8247294 0.7966398 0.8061111 1.0124835 1.201855 0.9991429 1.203303
#>            y1~1     y2~1    x1~~x1    x2~~x2    z1~~z1    z2~~z2    y1~~y1
#>  [1,] 1.0725567 1.244097 0.2259017 0.1269995 0.1685929 0.1626381 0.2039092
#>  [2,] 0.9775742 1.167126 0.1790474 0.1484282 0.1644433 0.1589852 0.1453440
#>  [3,] 1.0132930 1.224122 0.1468947 0.1834565 0.1632646 0.1591024 0.1760099
#>  [4,] 1.0059908 1.194518 0.1671207 0.1518639 0.1786966 0.1589233 0.1738612
#>  [5,] 1.0244786 1.206281 0.1638713 0.1505128 0.1910553 0.1491868 0.1864432
#>  [6,] 0.9896160 1.199491 0.1640741 0.1649867 0.1760568 0.1466788 0.1897061
#>  [7,] 1.0308388 1.198788 0.1630729 0.1547994 0.1960561 0.1374712 0.1616821
#>  [8,] 1.0600403 1.242605 0.1937487 0.1424855 0.1623829 0.1694605 0.1439453
#>  [9,] 1.0376854 1.223458 0.1702579 0.1627613 0.1315105 0.1726509 0.1624597
#> [10,] 1.0692477 1.247629 0.1921070 0.1439855 0.1553083 0.1652408 0.1952157
#>          y2~~y2      X~~X      X~~Z      Z~~Z      Y~~Y       Y~X       Y~Z
#>  [1,] 0.1315184 0.9018577 0.2112101 1.0024653 0.9154232 0.6599517 0.5399378
#>  [2,] 0.1546451 0.9690960 0.2201002 1.0406903 0.9750058 0.7528829 0.5725847
#>  [3,] 0.1396114 1.0122897 0.1632057 1.0319942 0.9707447 0.6203496 0.5583714
#>  [4,] 0.1370952 0.9001471 0.2178026 1.0648874 0.9706347 0.7816199 0.5860735
#>  [5,] 0.1354281 0.9628799 0.2113690 0.9943785 0.9898472 0.6800490 0.5862176
#>  [6,] 0.1225859 0.9456681 0.2194834 1.0466016 0.9386279 0.6839265 0.5631715
#>  [7,] 0.1549185 1.0112645 0.1865090 0.9813222 0.9575413 0.6684284 0.5644568
#>  [8,] 0.1579272 0.9666427 0.2025390 1.0514988 1.0089014 0.7194884 0.6306179
#>  [9,] 0.1439958 0.9715419 0.2249601 1.0902798 0.9320522 0.7107070 0.5366545
#> [10,] 0.1284270 0.9676143 0.1883906 1.0618651 0.8823236 0.7460848 0.5375465
#>           Y~X:Z
#>  [1,] 0.7326105
#>  [2,] 0.7180157
#>  [3,] 0.6869211
#>  [4,] 0.6798119
#>  [5,] 0.7590759
#>  [6,] 0.6988168
#>  [7,] 0.7462527
#>  [8,] 0.7160884
#>  [9,] 0.7065497
#> [10,] 0.7385862
# }

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 

# }