Type:	Package
Title:	Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)
Version:	1.0.11
Maintainer:	Kjell Solem Slupphaug <slupphaugkjell@gmail.com>
Description:	Estimation of interaction (i.e., moderation) effects between latent variables in structural equation models (SEM). The supported methods are: The constrained approach (Algina & Moulder, 2001). The unconstrained approach (Marsh et al., 2004). The residual centering approach (Little et al., 2006). The double centering approach (Lin et al., 2010). The latent moderated structural equations (LMS) approach (Klein & Moosbrugger, 2000). The quasi-maximum likelihood (QML) approach (Klein & Muthén, 2007) The constrained- unconstrained, residual- and double centering- approaches are estimated via 'lavaan' (Rosseel, 2012), whilst the LMS- and QML- approaches are estimated via 'modsem' it self. Alternatively model can be estimated via 'Mplus' (Muthén & Muthén, 1998-2017). References: Algina, J., & Moulder, B. C. (2001). <doi:10.1207/S15328007SEM0801_3>. "A note on estimating the Jöreskog-Yang model for latent variable interaction using 'LISREL' 8.3." Klein, A., & Moosbrugger, H. (2000). <doi:10.1007/BF02296338>. "Maximum likelihood estimation of latent interaction effects with the LMS method." Klein, A. G., & Muthén, B. O. (2007). <doi:10.1080/00273170701710205>. "Quasi-maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects." Lin, G. C., Wen, Z., Marsh, H. W., & Lin, H. S. (2010). <doi:10.1080/10705511.2010.488999>. "Structural equation models of latent interactions: Clarification of orthogonalizing and double-mean-centering strategies." Little, T. D., Bovaird, J. A., & Widaman, K. F. (2006). <doi:10.1207/s15328007sem1304_1>. "On the merits of orthogonalizing powered and product terms: Implications for modeling interactions among latent variables." Marsh, H. W., Wen, Z., & Hau, K. T. (2004). <doi:10.1037/1082-989X.9.3.275>. "Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction." Muthén, L.K. and Muthén, B.O. (1998-2017). "'Mplus' User’s Guide. Eighth Edition." https://www.statmodel.com/. Rosseel Y (2012). <doi:10.18637/jss.v048.i02>. "'lavaan': An R Package for Structural Equation Modeling."
License:	MIT + file LICENSE
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.2
LinkingTo:	Rcpp, RcppArmadillo
Imports:	Rcpp, purrr, stringr, lavaan, rlang, MplusAutomation, nlme, dplyr, mvnfast, stats, fastGHQuad, mvtnorm, ggplot2, parallel, plotly, Deriv, MASS, Amelia, grDevices, cli
Depends:	R (≥ 4.1.0)
URL:	https://modsem.org
Suggests:	knitr, rmarkdown
VignetteBuilder:	knitr
NeedsCompilation:	yes
Packaged:	2025-07-22 15:50:06 UTC; kss
Author:	Kjell Solem Slupphaug [aut, cre], Mehmet Mehmetoglu [ctb], Matthias Mittner [ctb]
Repository:	CRAN
Date/Publication:	2025-07-22 16:31:01 UTC

modsem: Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)

Description

Estimation of interaction (i.e., moderation) effects between latent variables in structural equation models (SEM). The supported methods are: The constrained approach (Algina & Moulder, 2001). The unconstrained approach (Marsh et al., 2004). The residual centering approach (Little et al., 2006). The double centering approach (Lin et al., 2010). The latent moderated structural equations (LMS) approach (Klein & Moosbrugger, 2000). The quasi-maximum likelihood (QML) approach (Klein & Muthén, 2007) The constrained- unconstrained, residual- and double centering- approaches are estimated via 'lavaan' (Rosseel, 2012), whilst the LMS- and QML- approaches are estimated via 'modsem' it self. Alternatively model can be estimated via 'Mplus' (Muthén & Muthén, 1998-2017). References: Algina, J., & Moulder, B. C. (2001). doi:10.1207/S15328007SEM0801_3. "A note on estimating the Jöreskog-Yang model for latent variable interaction using 'LISREL' 8.3." Klein, A., & Moosbrugger, H. (2000). doi:10.1007/BF02296338. "Maximum likelihood estimation of latent interaction effects with the LMS method." Klein, A. G., & Muthén, B. O. (2007). doi:10.1080/00273170701710205. "Quasi-maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects." Lin, G. C., Wen, Z., Marsh, H. W., & Lin, H. S. (2010). doi:10.1080/10705511.2010.488999. "Structural equation models of latent interactions: Clarification of orthogonalizing and double-mean-centering strategies." Little, T. D., Bovaird, J. A., & Widaman, K. F. (2006). doi:10.1207/s15328007sem1304_1. "On the merits of orthogonalizing powered and product terms: Implications for modeling interactions among latent variables." Marsh, H. W., Wen, Z., & Hau, K. T. (2004). doi:10.1037/1082-989X.9.3.275. "Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction." Muthén, L.K. and Muthén, B.O. (1998-2017). "'Mplus' User’s Guide. Eighth Edition." https://www.statmodel.com/. Rosseel Y (2012). doi:10.18637/jss.v048.i02. "'lavaan': An R Package for Structural Equation Modeling."

Author(s)

Maintainer: Kjell Solem Slupphaug slupphaugkjell@gmail.com (ORCID)

Other contributors:

• Mehmet Mehmetoglu mehmetm@ntnu.no (ORCID) [contributor]

• Matthias Mittner matthias.mittner@uit.no (ORCID) [contributor]

See Also

Useful links:

• https://modsem.org

TPB

Description

A simulated dataset based on the Theory of Planned Behaviour

Examples

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
"

est <- modsem(tpb, data = TPB)
summary(est)

TPB_1SO

Description

A simulated dataset based on the Theory of Planned Behaviour, where INT is a higher order construct of ATT, SN, and PBC.

Examples

tpb <- '
  # First order constructs
  ATT =~ att1 + att2 + att3
  SN  =~ sn1 + sn2 + sn3
  PBC =~ pbc1 + pbc2 + pbc3
  BEH =~ b1 + b2

  # Higher order constructs
  INT =~ ATT + PBC + SN

  # Higher order interaction
  INTxPBC =~ ATT:PBC + SN:PBC + PBC:PBC
  
  # Structural model
  BEH ~ PBC + INT + INTxPBC
'

## Not run: 
est_ca <- modsem(tpb, data = TPB_1SO, method = "ca")
summary(est_ca)

est_dblcent  <- modsem(tpb, data = TPB_1SO, method = "dblcent")
summary(est_dblcent)

## End(Not run)

TPB_2SO

Description

A simulated dataset based on the Theory of Planned Behaviour, where INT is a higher order construct of ATT and SN, and PBC is a higher order construct of PC and PB.

Examples

tpb <- '
  # First order constructs
  ATT =~ att1 + att2 + att3
  SN  =~ sn1 + sn2 + sn3
  PB =~ pb1 + pb2 + pb3
  PC =~ pc1 + pc2 + pc3
  BEH =~ b1 + b2

  # Higher order constructs
  INT =~ ATT + SN
  PBC =~ PC + PB

  # Higher order interaction
  INTxPBC =~ ATT:PC + ATT:PB + SN:PC + SN:PB
  
  # Structural model
  BEH ~ PBC + INT + INTxPBC
'

## Not run: 
est <- modsem(tpb, data = TPB_2SO, method = "ca")
summary(est)

## End(Not run)

TPB_UK

Description

A dataset based on the Theory of Planned Behaviour from a UK sample. 4 variables with high communality were selected for each latent variable (ATT, SN, PBC, INT, BEH), from two time points (t1 and t2).

Source

Gathered from a replication study by Hagger et al. (2023).

Obtained from doi:10.23668/psycharchives.12187

Examples

tpb_uk <- "
# Outer Model (Based on Hagger et al., 2007)
 ATT =~ att3 + att2 + att1 + att4
 SN =~ sn4 + sn2 + sn3 + sn1
 PBC =~ pbc2 + pbc1 + pbc3 + pbc4
 INT =~ int2 + int1 + int3 + int4
 BEH =~ beh3 + beh2 + beh1 + beh4

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

est <- modsem(tpb_uk, data = TPB_UK)
summary(est)

Bootstrap a modsem Model

Description

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

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.

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

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

See Also

bootstrapLavaan, modsem_pi, modsem_da

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)


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

  Y ~ X + Z + X:Z
'

## Not run: 
fit_lms <- modsem(m1, oneInt, method = "lms")
bootstrap_modsem(fit_lms, FUN = coef, R = 10L)

## End(Not run)

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
"

## Not run: 
boot <- bootstrap_modsem(model = modsem, 
                         model.syntax = tpb, data = TPB,
                         method = "dblcent", rcs = TRUE, 
                         rcs.scale.corrected = TRUE,
                         FUN = "coef")
coef <- apply(boot, MARGIN = 2, FUN = mean, na.rm = TRUE)
se   <- apply(boot, MARGIN = 2, FUN = sd, na.rm = TRUE)

cat("Parameter Estimates:\n")
print(coef)

cat("Standard Errors: \n")
print(se)


## End(Not run)

Get Centered Interaction Term Estimates

Description

Computes centered estimates of model parameters. This is relevant when there is an interaction term in the model, as the simple main effects depend upon the mean structure of the structural model. Currenlty only available for modsem_da and lavaan object. It is not relevant for the PI approaches (excluding the "pind" method, which is not recommended), since the indicators are centered before computing the product terms. The centering can be applied to observed variable interactions in lavaan models and latent interactions estimated using the sam function.

Usage

centered_estimates(object, ...)

## S3 method for class 'lavaan'
centered_estimates(
  object,
  monte.carlo = FALSE,
  mc.reps = 10000,
  tolerance.zero = 1e-10,
  ...
)

## S3 method for class 'modsem_da'
centered_estimates(
  object,
  monte.carlo = FALSE,
  mc.reps = 10000,
  tolerance.zero = 1e-10,
  ...
)

Arguments

Value

A data.frame with centered estimates in the est column.

Methods (by class)

• centered_estimates(lavaan): Method for lavaan objects

• centered_estimates(modsem_da): Method for modsem_da objects

Examples

m1 <- '
  # Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

  # Inner Model
  Y ~ X + Z + X:Z
'
## Not run: 
est_lms <- modsem(m1, oneInt, method = "lms")
centered_estimates(est_lms)

## End(Not run)

Capture, colorise, and emit console text

Description

Capture, colorise, and emit console text

Usage

colorize_output(
  expr,
  positive = MODSEM_COLORS$positive,
  negative = MODSEM_COLORS$negative,
  true = MODSEM_COLORS$true,
  false = MODSEM_COLORS$false,
  nan = MODSEM_COLORS$nan,
  na = MODSEM_COLORS$na,
  inf = MODSEM_COLORS$inf,
  string = MODSEM_COLORS$string,
  split = FALSE,
  append = "\n"
)

Arguments

Value

Invisibly returns the *plain* captured text.

Examples

set_modsem_colors(positive = "red3", 
                  negative = "red3",
                  true = "darkgreen", 
                  false = "red3", 
                  na = "purple",
                  string = "darkgreen")

m1 <- "
# Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3
# Inner Model
  Y ~ X + Z + X:Z
"

est <- modsem(m1, data = oneInt)
colorize_output(summary(est))
colorize_output(est) # same as colorize_output(print(est))
colorize_output(modsem_inspect(est, what = "coef"))

## Not run: 
colorize_output(split = TRUE, {
  # Get live (uncolored) output
  # And print colored output at the end of execution

  est_lms <- modsem(m1, data = oneInt, method = "lms")
  summary(est_lms)
}) 
                
colorize_output(modsem_inspect(est_lms))

## End(Not run)

compare model fit for modsem models

Description

Compare the fit of two models using the likelihood ratio test (LRT). est_h0 is the null hypothesis model, and est_h1 the alternative hypothesis model. Importantly, the function assumes that est_h0 does not have more free parameters (i.e., degrees of freedom) than est_h1 (the alternative hypothesis model).

Usage

compare_fit(est_h1, est_h0, ...)

Arguments

Examples

## Not run: 
m1 <- "
 # Outer Model
 X =~ x1 + x2 + x3
 Y =~ y1 + y2 + y3
 Z =~ z1 + z2 + z3

 # Inner model
 Y ~ X + Z + X:Z
"

# LMS approach
est_h1 <- modsem(m1, oneInt, "lms")
est_h0 <- estimate_h0(est_h1, calc.se=FALSE) # std.errors are not needed
compare_fit(est_h1 = est_h1, est_h0 = est_h0)

# Double centering approach
est_h1 <- modsem(m1, oneInt, method = "dblcent")
est_h0 <- estimate_h0(est_h1, oneInt)

compare_fit(est_h1 = est_h1, est_h0 = est_h0)

# Constrained approach
est_h1 <- modsem(m1, oneInt, method = "ca")
est_h0 <- estimate_h0(est_h1, oneInt)

compare_fit(est_h1 = est_h1, est_h0 = est_h0)

## End(Not run)

default arguments fro LMS and QML approach

Description

This function returns the default settings for the LMS and QML approach.

Usage

default_settings_da(method = c("lms", "qml"))

Arguments

Value

list

Examples

library(modsem)
default_settings_da()

default arguments for product indicator approaches

Description

This function returns the default settings for the product indicator approaches

Usage

default_settings_pi(method = c("rca", "uca", "pind", "dblcent", "ca"))

Arguments

Value

list

Examples

library(modsem)
default_settings_pi()

Estimate baseline model for modsem models

Description

Estimates a baseline model (H0) from a given model (H1). The baseline model is estimated by removing all interaction terms from the model.

Usage

estimate_h0(object, warn_no_interaction = TRUE, ...)

## S3 method for class 'modsem_da'
estimate_h0(object, warn_no_interaction = TRUE, ...)

## S3 method for class 'modsem_pi'
estimate_h0(object, warn_no_interaction = TRUE, reduced = TRUE, ...)

Arguments

Methods (by class)

• estimate_h0(modsem_da): Estimate baseline model for modsem_da objects

• estimate_h0(modsem_pi): Estimate baseline model for modsem_pi objects

Examples

## Not run: 
m1 <- "
 # Outer Model
 X =~ x1 + x2 + x3
 Y =~ y1 + y2 + y3
 Z =~ z1 + z2 + z3

 # Inner model
 Y ~ X + Z + X:Z
"

# LMS approach
est_h1 <- modsem(m1, oneInt, "lms")
est_h0 <- estimate_h0(est_h1, calc.se=FALSE) # std.errors are not needed
compare_fit(est_h1 = est_h1, est_h0 = est_h0)

# Double centering approach
est_h1 <- modsem(m1, oneInt, method = "dblcent")
est_h0 <- estimate_h0(est_h1, oneInt)

compare_fit(est_h1 = est_h1, est_h0 = est_h0)

# Constrained approach
est_h1 <- modsem(m1, oneInt, method = "ca")
est_h0 <- estimate_h0(est_h1, oneInt)

compare_fit(est_h1 = est_h1, est_h0 = est_h0)

## End(Not run)

extract lavaan object from modsem object estimated using product indicators

Description

extract lavaan object from modsem object estimated using product indicators

Usage

extract_lavaan(object)

Arguments

Value

lavaan object

Examples

library(modsem)
m1 <- '
  # Outer Model
  X =~ x1 + x2 + x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3

  # Inner model
  Y ~ X + Z + X:Z
'
est <- modsem_pi(m1, oneInt)
lav_est <- extract_lavaan(est)

Fit measures for QML and LMS models

Description

Calculates chi-sq test and p-value, as well as RMSEA for the LMS and QML models. Note that the Chi-Square based fit measures should be calculated for the baseline model, i.e., the model without the interaction effect

Usage

fit_modsem_da(model, chisq = TRUE)

Arguments

Get data with product indicators for different approaches

Description

get_pi_data() is a function for creating a dataset with product indiactors used for estimating latent interaction models using one of the product indicator approaches.

Usage

get_pi_data(model.syntax, data, method = "dblcent", match = FALSE, ...)

Arguments

Value

data.frame

Examples

library(modsem)
library(lavaan)
m1 <- '
  # Outer Model
  X =~ x1 + x2 +x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3

  # Inner model
  Y ~ X + Z + X:Z
'
syntax <- get_pi_syntax(m1)
data <- get_pi_data(m1, oneInt)
est <- sem(syntax, data)
summary(est)

Get lavaan syntax for product indicator approaches

Description

get_pi_syntax() is a function for creating the lavaan syntax used for estimating latent interaction models using one of the product indicator approaches.

Usage

get_pi_syntax(
  model.syntax,
  method = "dblcent",
  match = FALSE,
  data = NULL,
  ...
)

Arguments

Value

character vector

Examples

library(modsem)
library(lavaan)
m1 <- '
  # Outer Model
  X =~ x1 + x2 + x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3

  # Inner model
  Y ~ X + Z + X:Z
'
syntax <- get_pi_syntax(m1)
data <- get_pi_data(m1, oneInt)
est <- sem(syntax, data)
summary(est)

Jordan subset of PISA 2006 data

Description

The data stem from the large-scale assessment study PISA 2006 (Organisation for Economic Co-Operation and Development, 2009) where competencies of 15-year-old students in reading, mathematics, and science are assessed using nationally representative samples in 3-year cycles. In this example, data from the student background questionnaire from the Jordan sample of PISA 2006 were used. Only data of students with complete responses to all 15 items (N = 6,038) were considered.

Format

A data frame of fifteen variables and 6,038 observations:

enjoy1

indicator for enjoyment of science, item ST16Q01: I generally have fun when I am learning <broad science> topics.

enjoy2

indicator for enjoyment of science, item ST16Q02: I like reading about <broad science>.

enjoy3

indicator for enjoyment of science, item ST16Q03: I am happy doing <broad science> problems.

enjoy4

indicator for enjoyment of science, item ST16Q04: I enjoy acquiring new knowledge in <broad science>.

enjoy5

indicator for enjoyment of science, item ST16Q05: I am interested in learning about <broad science>.

academic1

indicator for academic self-concept in science, item ST37Q01: I can easily understand new ideas in <school science>.

academic2

indicator for academic self-concept in science, item ST37Q02: Learning advanced <school science> topics would be easy for me.

academic3

indicator for academic self-concept in science, item ST37Q03: I can usually give good answers to <test questions> on <school science> topics.

academic4

indicator for academic self-concept in science, item ST37Q04: I learn <school science> topics quickly.

academic5

indicator for academic self-concept in science, item ST37Q05: <School science> topics are easy for me.

academic6

indicator for academic self-concept in science, item ST37Q06: When I am being taught <school science>, I can understand the concepts very well.

career1

indicator for career aspirations in science, item ST29Q01: I would like to work in a career involving <broad science>.

career2

indicator for career aspirations in science, item ST29Q02: I would like to study <broad science> after <secondary school>.

career3

indicator for career aspirations in science, item ST29Q03: I would like to spend my life doing advanced <broad science>.

career4

indicator for career aspirations in science, item ST29Q04: I would like to work on <broad science> projects as an adult.

Source

This version of the dataset, as well as the description was gathered from the documentation of the 'nlsem' package (https://cran.r-project.org/package=nlsem), where the only difference is that the names of the variables were changed

Originally the dataset was gathered by the Organisation for Economic Co-Operation and Development (2009). Pisa 2006: Science competencies for tomorrow's world (Tech. Rep.). Paris, France. Obtained from: https://www.oecd.org/pisa/pisaproducts/database-pisa2006.htm

Examples

## Not run: 
m1 <- "
  ENJ =~ enjoy1 + enjoy2 + enjoy3 + enjoy4 + enjoy5
  CAREER =~ career1 + career2 + career3 + career4
  SC =~ academic1 + academic2 + academic3 + academic4 + academic5 + academic6
  CAREER ~ ENJ + SC + ENJ:ENJ + SC:SC + ENJ:SC
"

est <- modsem(m1, data = jordan, method = "qml")
summary(est)

## End(Not run)

Estimate interaction effects in structural equation models (SEMs)

Description

modsem() is a function for estimating interaction effects between latent variables in structural equation models (SEMs). Methods for estimating interaction effects in SEMs can basically be split into two frameworks:

1. Product Indicator (PI) based approaches ("dblcent", "rca", "uca", "ca", "pind")

2. Distributionally (DA) based approaches ("lms", "qml").

For the product indicator-based approaches, modsem() is essentially a fancy wrapper for lavaan::sem() which generates the necessary syntax and variables for the estimation of models with latent product indicators.

The distributionally based approaches are implemented separately and are not estimated using lavaan::sem(), but rather using custom functions (largely written in C++ for performance reasons). For greater control, it is advised that you use one of the sub-functions (modsem_pi, modsem_da, modsem_mplus) directly, as passing additional arguments to them via modsem() can lead to unexpected behavior.

Usage

modsem(model.syntax = NULL, data = NULL, method = "dblcent", ...)

Arguments

Value

modsem object with class modsem_pi, modsem_da, or modsem_mplus

Examples

library(modsem)
# For more examples, check README and/or GitHub.
# One interaction
m1 <- '
  # Outer Model
  X =~ x1 + x2 +x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3

  # Inner model
  Y ~ X + Z + X:Z
'

# Double centering approach
est1 <- modsem(m1, oneInt)
summary(est1)

## Not run: 
# The Constrained Approach
est1_ca <- modsem(m1, oneInt, method = "ca")
summary(est1_ca)

# LMS approach
est1_lms <- modsem(m1, oneInt, method = "lms")
summary(est1_lms)

# QML approach
est1_qml <- modsem(m1, oneInt, method = "qml")
summary(est1_qml)

## End(Not run)

# Theory Of Planned Behavior
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
  BEH ~ INT:PBC
'

# Double centering approach
est_tpb <- modsem(tpb, data = TPB)
summary(est_tpb)

## Not run: 
# The Constrained Approach
est_tpb_ca <- modsem(tpb, data = TPB, method = "ca")
summary(est_tpb_ca)

# LMS approach
est_tpb_lms <- modsem(tpb, data = TPB, method = "lms", nodes = 32)
summary(est_tpb_lms)

# QML approach
est_tpb_qml <- modsem(tpb, data = TPB, method = "qml")
summary(est_tpb_qml)

## End(Not run)

Wrapper for coef

Description

wrapper for coef, to be used with modsem::modsem_coef, since coef is not in the namespace of modsem, but stats.

Usage

modsem_coef(object, ...)

Arguments

Interaction between latent variables using LMS and QML approaches

Description

modsem_da() is a function for estimating interaction effects between latent variables in structural equation models (SEMs) using distributional analytic (DA) approaches. Methods for estimating interaction effects in SEMs can basically be split into two frameworks: 1. Product Indicator-based approaches ("dblcent", "rca", "uca", "ca", "pind") 2. Distributionally based approaches ("lms", "qml").

modsem_da() handles the latter and can estimate models using both QML and LMS, necessary syntax, and variables for the estimation of models with latent product indicators.

NOTE: Run default_settings_da to see default arguments.

Usage

modsem_da(
  model.syntax = NULL,
  data = NULL,
  method = "lms",
  verbose = NULL,
  optimize = NULL,
  nodes = NULL,
  impute.na = NULL,
  convergence.abs = NULL,
  convergence.rel = NULL,
  optimizer = NULL,
  center.data = NULL,
  standardize.data = NULL,
  standardize.out = NULL,
  standardize = NULL,
  mean.observed = NULL,
  cov.syntax = NULL,
  double = NULL,
  calc.se = NULL,
  FIM = NULL,
  EFIM.S = NULL,
  OFIM.hessian = NULL,
  EFIM.parametric = NULL,
  robust.se = NULL,
  R.max = NULL,
  max.iter = NULL,
  max.step = NULL,
  start = NULL,
  epsilon = NULL,
  quad.range = NULL,
  adaptive.quad = NULL,
  adaptive.frequency = NULL,
  adaptive.quad.tol = NULL,
  n.threads = NULL,
  algorithm = NULL,
  em.control = NULL,
  rcs = FALSE,
  rcs.choose = NULL,
  rcs.scale.corrected = TRUE,
  orthogonal.x = NULL,
  orthogonal.y = NULL,
  auto.fix.first = NULL,
  auto.fix.single = NULL,
  auto.split.syntax = NULL,
  ...
)

Arguments

Value

modsem_da object

Examples

library(modsem)
# For more examples, check README and/or GitHub.
# One interaction
m1 <- "
  # Outer Model
  X =~ x1 + x2 +x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3

  # Inner model
  Y ~ X + Z + X:Z
"

## Not run: 
# QML Approach
est_qml <- modsem_da(m1, oneInt, method = "qml")
summary(est_qml)

# Theory Of Planned Behavior
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
  BEH ~ INT:PBC
"

# LMS Approach
est_lms <- modsem_da(tpb, data = TPB, method = "lms")
summary(est_lms)

## End(Not run)

Inspect model information

Description

function used to inspect fitted object. Similar to lavaan::lavInspect argument what decides what to inspect

modsem_inspect.modsem_da Lets you pull matrices, optimiser diagnostics, expected moments, or fit measures from a modsem_da object.

Usage

modsem_inspect(object, what = NULL, ...)

## S3 method for class 'lavaan'
modsem_inspect(object, what = "free", ...)

## S3 method for class 'modsem_da'
modsem_inspect(object, what = NULL, ...)

## S3 method for class 'modsem_pi'
modsem_inspect(object, what = "free", ...)

Arguments

Details

For modsem_pi objects, it is just a wrapper for lavaan::lavInspect. For modsem_da objects an internal function is called, which takes different keywords for the what argument.

Below is a list of possible values for the what argument, organised in several sections. Keywords are case-sensitive.

Presets

"default"

Everything in Sample information, Optimiser diagnostics Parameter tables, Model matrices, and Expected-moment matrices except the raw data slot

"coef"

Coefficients and variance-covariance matrix of both free and constrained parameters (same as "coef.all").

"coef.all"

Coefficients and variance-covariance matrix of both free and constrained parameters (same as "coef").

"coef.free"

Coefficients and variance-covariance matrix of the free parameters.

"all"

All items listed below, including data.

"matrices"

The model matrices.

"optim"

Only the items under Optimiser diagnostics

.

"fit"

A list with fit.h0, fit.h1, comparative.fit

Sample information:

"N"

Number of analysed rows (integer).

Parameter estimates and standard errors:

"coefficients.free"

Free parameter values.

"coefficients.all"

Both free and constrained parameter values.

"vcov.free"

Variance–covariance of free coefficients only.

"vcov.all"

Variance–covariance of both free and constrained coefficients.

Optimiser diagnostics:

"coefficients.free"

Free parameter values.

"vcov.free"

Variance–covariance of free coefficients only.

"information"

Fisher information matrix.

"loglik"

Log-likelihood.

"iterations"

Optimiser iteration count.

"convergence"

TRUE/FALSE indicating whether the model converged.

Parameter tables:

"partable"

Parameter table with estimated parameters.

"partable.input"

Parsed model syntax.

Model matrices:

"lambda"

\Lambda – Factor loadings.

"tau"

\tau – Intercepts for indicators.

"theta"

\Theta – Residual (Co-)Variances for indicators.

"gamma.xi"

\Gamma_{\xi} – Structural coefficients between exogenous and endogenous variables.

"gamma.eta"

\Gamma_{\eta} – Structural coefficients between endogenous variables.

"omega.xi.xi"

\Omega_{\xi\xi} – Interaction effects between exogenous variables

"omega.eta.xi"

\Omega_{\eta\xi} – Interaction effects between exogenous and endogenous variables

"phi"

\Phi – (Co-)Variances among exogenous variables.

"psi"

\Psi – Residual (co-)variances among engoenous variables.

"alpha"

\alpha – Intercepts for endogenous variables

"beta0"

\beta_0 – Intercepts for exogenous variables

Model-implied matrices:

"cov.ov"

Model-implied covariance of observed variables.

"cov.lv"

Model-implied covariance of latent variables.

"cov.all"

Joint covariance of observed + latent variables.

"cor.ov"

Correlation counterpart of "cov.ov".

"cor.lv"

Correlation counterpart of "cov.lv".

"cor.all"

Correlation counterpart of "cov.all".

"mean.ov"

Expected means of observed variables.

"mean.lv"

Expected means of latent variables.

"mean.all"

Joint mean vector.

R-squared and standardized residual variances:

"r2.all"

R-squared values for both observed (i.e., indicators) and latent endogenous variables.

"r2.lv"

R-squared values for latent endogenous variables.

"r2.ov"

R-squared values for observed (i.e., indicators) variables.

"res.all"

Standardized residuals (i.e., 1 - R^2) for both observed (i.e., indicators) and latent endogenous variables.

"res.lv"

Standardized residuals (i.e., 1 - R^2) for latent endogenous variables.

"res.ov"

Standardized residuals (i.e., 1 - R^2) for observed variables (i.e., indicators).

Interaction-specific caveats:

• If the model contains an uncentred latent interaction term it is centred internally before any cov.*, cor.*, or mean.* matrices are calculated.

• These matrices should not be used to compute fit-statistics (e.g., chi-square and RMSEA) if there is an interaction term in the model.

Value

A named list with the extracted information. If a single piece of information is returned, it is returned as is; not as a named element in a list.

Methods (by class)

• modsem_inspect(lavaan): Inspect a lavaan object

• modsem_inspect(modsem_da): Inspect a modsem_da object

• modsem_inspect(modsem_pi): Inspect a modsem_pi object

Examples

## Not run: 
m1 <- "
 # Outer Model
 X =~ x1 + x2 + x3
 Y =~ y1 + y2 + y3
 Z =~ z1 + z2 + z3

 # Inner model
 Y ~ X + Z + X:Z
"

est <- modsem(m1, oneInt, "lms")

modsem_inspect(est) # everything except "data"
modsem_inspect(est, what = "optim")
modsem_inspect(est, what = "phi")

## End(Not run)

Estimate a modsem model using multiple imputation

Description

Estimate a modsem model using multiple imputation

Usage

modsem_mimpute(
  model.syntax,
  data,
  method = "lms",
  m = 25,
  verbose = interactive(),
  se = c("simple", "full"),
  ...
)

Arguments

Details

modsem_impute is currently only available for the DA approaches (LMS and QML). It performs multiple imputation using Amelia::amelia and returns aggregated coefficients from the multiple imputations, along with corrected standard errors.

Examples

m1 <- '
  # Outer Model
  X =~ x1 + x2 +x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3

  # Inner model
  Y ~ X + Z + X:Z
'

oneInt2 <- oneInt

set.seed(123)
k <- 200
I <- sample(nrow(oneInt2), k, replace = TRUE)
J <- sample(ncol(oneInt2), k, replace = TRUE)
for (k_i in seq_along(I)) oneInt2[I[k_i], J[k_i]] <- NA

## Not run: 
est <- modsem_mimpute(m1, oneInt2, m = 25)
summary(est)

## End(Not run)

Estimation latent interactions through Mplus

Description

Estimation latent interactions through Mplus

Usage

modsem_mplus(
  model.syntax,
  data,
  estimator = "ml",
  type = "random",
  algorithm = "integration",
  processors = 2,
  integration = 15,
  rcs = FALSE,
  rcs.choose = NULL,
  rcs.scale.corrected = TRUE,
  ...
)

Arguments

Value

modsem_mplus object

Examples

# Theory Of Planned Behavior
m1 <- '
# Outer Model
  X =~ x1 + x2
  Z =~ z1 + z2
  Y =~ y1 + y2 

# Inner model
  Y ~ X + Z + X:Z
'

## Not run: 
# Check if Mplus is installed
run <- tryCatch({MplusAutomation::detectMplus(); TRUE},
                error = \(e) FALSE)

if (run) {
  est_mplus <- modsem_mplus(m1, data = oneInt)
  summary(est_mplus)
}

## End(Not run)

Wrapper for nobs

Description

wrapper for nobs, to be used with modsem::modsem_nobs, since nobs is not in the namespace of modsem, but stats.

Usage

modsem_nobs(object, ...)

Arguments

Interaction between latent variables using product indicators

Description

modsem_pi() is a function for estimating interaction effects between latent variables, in structural equation models (SEMs), using product indicators. Methods for estimating interaction effects in SEMs can basically be split into two frameworks: 1. Product Indicator based approaches ("dblcent", "rca", "uca", "ca", "pind"), and 2. Distributionally based approaches ("lms", "qml"). modsem_pi() is essentially a fancy wrapper for lavaan::sem() which generates the necessary syntax and variables for the estimation of models with latent product indicators. Use default_settings_pi() to get the default settings for the different methods.

Usage

modsem_pi(
  model.syntax = NULL,
  data = NULL,
  method = "dblcent",
  match = NULL,
  match.recycle = NULL,
  standardize.data = FALSE,
  center.data = FALSE,
  first.loading.fixed = FALSE,
  center.before = NULL,
  center.after = NULL,
  residuals.prods = NULL,
  residual.cov.syntax = NULL,
  constrained.prod.mean = NULL,
  constrained.loadings = NULL,
  constrained.var = NULL,
  res.cov.method = NULL,
  res.cov.across = NULL,
  auto.scale = "none",
  auto.center = "none",
  estimator = "ML",
  group = NULL,
  cluster = NULL,
  run = TRUE,
  na.rm = FALSE,
  suppress.warnings.lavaan = FALSE,
  suppress.warnings.match = FALSE,
  rcs = FALSE,
  rcs.choose = NULL,
  rcs.res.cov.xz = rcs,
  rcs.mc.reps = 1e+05,
  rcs.scale.corrected = TRUE,
  LAVFUN = lavaan::sem,
  ...
)

Arguments

Value

modsem object

Examples

library(modsem)
# For more examples, check README and/or GitHub.
# One interaction
m1 <- '
  # Outer Model
  X =~ x1 + x2 +x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3

  # Inner model
  Y ~ X + Z + X:Z
'

# Double centering approach
est <- modsem_pi(m1, oneInt)
summary(est)

## Not run: 
# The Constrained Approach
est_ca <- modsem_pi(m1, oneInt, method = "ca")
summary(est_ca)

## End(Not run)

# Theory Of Planned Behavior
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)
  # Covariances
  ATT ~~ SN + PBC
  PBC ~~ SN
  # Causal Relationships
  INT ~ ATT + SN + PBC
  BEH ~ INT + PBC
  BEH ~ INT:PBC
'

# Double centering approach
est_tpb <- modsem_pi(tpb, data = TPB)
summary(est_tpb)

## Not run: 
# The Constrained Approach
est_tpb_ca <- modsem_pi(tpb, data = TPB, method = "ca")
summary(est_tpb_ca)

## End(Not run)

Predict From modsem Models

Description

A generic function (and corresponding methods) that produces predicted values or factor scores from modsem models.

Usage

modsem_predict(object, ...)

## S3 method for class 'modsem_da'
modsem_predict(
  object,
  standardized = FALSE,
  H0 = TRUE,
  newdata = NULL,
  center.data = TRUE,
  ...
)

## S3 method for class 'modsem_pi'
modsem_predict(object, ...)

Arguments

Value

* For modsem_pi: whatever lavaan::predict(), which usually returns a matrix of factor scores. * For modsem_da: a numeric matrix n \times p, where n is the number of (complete) observations in the dataset, and p the number of latent variables. Each column contains either raw or standardised factor scores, depending on the standardized argument.

Methods (by class)

• modsem_predict(modsem_da): Computes (optionally standardised) factor scores via the regression method using the baseline model unless H0 = FALSE.

• modsem_predict(modsem_pi):

Examples

m1 <- '
# Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

# Inner Model
  Y ~ X + Z + X:Z
'

est_dca <- modsem(m1, oneInt, method = "dblcent")
head(modsem_predict(est_dca))

## Not run: 
est_lms <- modsem(m1, oneInt, method = "lms")
head(modsem_predict(est_lms))

## End(Not run)

Wrapper for vcov

Description

wrapper for vcov, to be used with modsem::modsem_vcov, since vcov is not in the namespace of modsem, but stats.

Usage

modsem_vcov(object, ...)

Arguments

Generate parameter table for lavaan syntax

Description

Generate parameter table for lavaan syntax

Usage

modsemify(syntax)

Arguments

Value

data.frame with columns lhs, op, rhs, mod

Examples

library(modsem)
m1 <- '
  # Outer Model
  X =~ x1 + x2 +x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3

  # Inner model
  Y ~ X + Z + X:Z
'
modsemify(m1)

oneInt

Description

A simulated dataset based on the elementary interaction model.

Examples

m1 <- "
# Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3
# Inner Model
  Y ~ X + Z + X:Z
"

est <- modsem(m1, data = oneInt)
summary(est)

Extract parameterEstimates from an estimated model

Description

Extract parameterEstimates from an estimated model

Usage

parameter_estimates(object, ...)

## S3 method for class 'lavaan'
parameter_estimates(object, colon.pi = TRUE, ...)

## S3 method for class 'modsem_da'
parameter_estimates(object, ...)

## S3 method for class 'modsem_mplus'
parameter_estimates(object, ...)

## S3 method for class 'modsem_pi'
parameter_estimates(object, colon.pi = FALSE, ...)

Arguments

Methods (by class)

• parameter_estimates(lavaan): Get parameter estimates of a lavaan object

• parameter_estimates(modsem_da): Get parameter estimates of a modsem_da object

• parameter_estimates(modsem_mplus): Get parameter estimates of a modsem_mplus object

• parameter_estimates(modsem_pi): Get parameter estimates of a modsem_pi object

Examples

m1 <- '
  # Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

  # Inner Model
  Y ~ X + Z + X:Z
'
# Double centering approach
est_dca <- modsem(m1, oneInt)

pars <- parameter_estimates(est_dca) # no correction

# Pretty summary
summarize_partable(pars)

# Only print the data.frame
pars

Plot Interaction Effects in a SEM Model

Description

This function creates an interaction plot of the outcome variable (y) as a function of a focal predictor (x) at multiple values of a moderator (z). It is designed for use with structural equation modeling (SEM) objects (e.g., those from modsem). Predicted means (or predicted individual values) are calculated via simple_slopes, and then plotted with ggplot2 to display multiple regression lines and confidence/prediction bands.

Usage

plot_interaction(
  x,
  z,
  y,
  xz = NULL,
  vals_x = seq(-3, 3, 0.001),
  vals_z,
  model,
  alpha_se = 0.15,
  digits = 2,
  ci_width = 0.95,
  ci_type = "confidence",
  rescale = TRUE,
  standardized = FALSE,
  ...
)

Arguments

Details

Computation Steps:

1. Calls simple_slopes to compute the predicted values of y at the specified grid of x and z values.

2. Groups the resulting predictions by unique z-values (rounded to digits) to create colored lines.

3. Plots these lines using ggplot2, adding ribbons for confidence (or prediction) intervals, with transparency controlled by alpha_se.

Interpretation: Each line in the plot corresponds to the regression of y on x at a given level of z. The shaded region around each line (ribbon) shows either the confidence interval for the predicted mean (if ci_type = "confidence") or the prediction interval for individual observations (if ci_type = "prediction"). Where the ribbons do not overlap, there is evidence that the lines differ significantly over that range of x.

Value

A ggplot object that can be further customized (e.g., with additional + theme(...) layers). By default, it shows lines for each moderator value and a shaded region corresponding to the interval type (confidence or prediction).

Examples

## Not run: 
library(modsem)

# Example 1: Interaction of X and Z in a simple SEM
m1 <- "
# Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

# Inner Model
  Y ~ X + Z + X:Z
"
est1 <- modsem(m1, data = oneInt)

# Plot interaction using a moderate range of X and two values of Z
plot_interaction(x = "X", z = "Z", y = "Y", xz = "X:Z",
                 vals_x = -3:3, vals_z = c(-0.2, 0), model = est1)

# Example 2: Interaction in a theory-of-planned-behavior-style model
tpb <- "
# Outer Model
  ATT =~ att1 + att2 + att3 + att4 + att5
  SN  =~ sn1 + sn2
  PBC =~ pbc1 + pbc2 + pbc3
  INT =~ int1 + int2 + int3
  BEH =~ b1 + b2

# Inner Model
  INT ~ ATT + SN + PBC
  BEH ~ INT + PBC
  BEH ~ PBC:INT
"
est2 <- modsem(tpb, data = TPB, method = "lms", nodes = 32)

# Plot with custom Z values and a denser X grid
plot_interaction(x = "INT", z = "PBC", y = "BEH",
                 xz = "PBC:INT",
                 vals_x = seq(-3, 3, 0.01),
                 vals_z = c(-0.5, 0.5),
                 model = est2)

## End(Not run)

Plot Interaction Effect Using the Johnson-Neyman Technique

Description

This function plots the simple slopes of an interaction effect across different values of a moderator variable using the Johnson-Neyman technique. It identifies regions where the effect of the predictor on the outcome is statistically significant.

Usage

plot_jn(
  x,
  z,
  y,
  xz = NULL,
  model,
  min_z = -3,
  max_z = 3,
  sig.level = 0.05,
  alpha = 0.2,
  detail = 1000,
  sd.line = 2,
  standardized = FALSE,
  ...
)

Arguments

Details

The function calculates the simple slopes of the predictor variable x on the outcome variable y at different levels of the moderator variable z. It uses the Johnson-Neyman technique to identify the regions of z where the effect of x on y is statistically significant.

It extracts the necessary coefficients and variance-covariance information from the fitted model object. The function then computes the critical t-value and solves the quadratic equation derived from the t-statistic equation to find the Johnson-Neyman points.

The plot displays:

• The estimated simple slopes across the range of z.

• Confidence intervals around the slopes.

• Regions where the effect is significant (shaded areas).

• Vertical dashed lines indicating the Johnson-Neyman points.

• Text annotations providing the exact values of the Johnson-Neyman points.

Value

A ggplot object showing the interaction plot with regions of significance.

Examples

## Not run: 
library(modsem)

m1 <-  ' 
  visual  =~ x1 + x2 + x3 
  textual =~ x4 + x5 + x6
  speed   =~ x7 + x8 + x9

  visual ~ speed + textual + speed:textual
'

est <- modsem(m1, data = lavaan::HolzingerSwineford1939, method = "ca")
plot_jn(x = "speed", z = "textual", y = "visual", model = est, max_z = 6)

## End(Not run)

Plot Surface for Interaction Effects

Description

Generates a 3D surface plot to visualize the interaction effect of two variables (x and z) on an outcome (y) using parameter estimates from a supported model object (e.g., lavaan or modsem). The function allows specifying ranges for x and z in standardized z-scores, which are then transformed back to the original scale based on their means and standard deviations.

Usage

plot_surface(
  x,
  z,
  y,
  xz = NULL,
  model,
  min_x = -3,
  max_x = 3,
  min_z = -3,
  max_z = 3,
  standardized = FALSE,
  detail = 0.01,
  ...
)

Arguments

Details

The input min_x, max_x, min_z, and max_z define the range of x and z values in z-scores. These are scaled by the standard deviations and shifted by the means of the respective variables, obtained from the model parameter table. The resulting surface shows the predicted values of y over the grid of x and z.

The function supports models of class modsem (with subclasses modsem_pi, modsem_da, modsem_mplus) and lavaan. For lavaan models, it is not designed for multigroup models, and a warning will be issued if multiple groups are detected.

Value

A plotly surface plot object displaying the predicted values of y across the grid of x and z values. The color bar shows the values of y.

Note

The interaction term (xz) may need to be manually specified for some models. For non-lavaan models, interaction terms may have their separator (:) removed based on circumstances.

Examples

m1 <- "
# Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

# Inner model
  Y ~ X + Z + X:Z
"
est1 <- modsem(m1, data = oneInt)
plot_surface("X", "Z", "Y", model = est1)

## Not run: 
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
  BEH ~ PBC:INT
"

est2 <- modsem(tpb, TPB, method = "lms", nodes = 32)
plot_surface(x = "INT", z = "PBC", y = "BEH", model = est2)

## End(Not run)

Reliability‑Corrected Single‑Item SEM

Description

Replace (some of) the first‑order latent variables in a lavaan measurement model by single composite indicators whose error variances are fixed from Cronbach's \alpha. The function returns a modified lavaan model syntax together with an augmented data set that contains the newly created composite variables, so that you can fit the full SEM in a single step.

Usage

relcorr_single_item(
  syntax,
  data,
  choose = NULL,
  scale.corrected = TRUE,
  warn.lav = TRUE
)

Arguments

Details

The resulting object can be fed directly into modsem or lavaan::sem by supplying syntax = $syntax and data = $data.

Value

An object of S3 class modsem_relcorr (a named list) with elements:

syntax

Modified lavaan syntax string.

data

Data frame with additional composite indicator columns.

parTable

Parameter table corresponding to 'syntax'.

reliability

Named numeric vector of reliabilities (one per latent variable).

AVE

Named numeric vector with Average Variance Extracted values.

lVs

Character vector of latent variables that were corrected.

single.items

Character vector with names for the generated reliability corrected items

Examples

## Not run: 
tpb_uk <- "
# Outer Model (Based on Hagger et al., 2007)
 ATT =~ att3 + att2 + att1 + att4
 SN =~ sn4 + sn2 + sn3 + sn1
 PBC =~ pbc2 + pbc1 + pbc3 + pbc4
 INT =~ int2 + int1 + int3 + int4
 BEH =~ beh3 + beh2 + beh1 + beh4

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

corrected <- relcorr_single_item(syntax = tpb_uk, data = TPB_UK)
print(corrected)

syntax <- corrected$syntax
data   <- corrected$data

est_dca <- modsem(syntax, data = data, method = "dblcent")
est_lms <- modsem(syntax, data = data, method="lms", nodes=32)
summary(est_lms)

## End(Not run)

Define or disable the color theme used by modsem

Description

All arguments are optional; omitted ones fall back to the defaults below. Pass active = FALSE to turn highlighting off (and reset the palette).

Usage

set_modsem_colors(
  positive = "green3",
  negative = positive,
  true = "green3",
  false = "red",
  nan = "purple",
  na = "purple",
  inf = "purple",
  string = "cyan",
  active = TRUE
)

Arguments

Value

TRUE if colors are active afterwards, otherwise FALSE.

Examples

set_modsem_colors(positive = "red3", 
                  negative = "red3",
                  true = "darkgreen", 
                  false = "red3", 
                  na = "purple",
                  string = "darkgreen")

m1 <- "
# Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3
# Inner Model
  Y ~ X + Z + X:Z
"

est <- modsem(m1, data = oneInt)
colorize_output(summary(est))
colorize_output(est) # same as colorize_output(print(est))
colorize_output(modsem_inspect(est, what = "coef"))

## Not run: 
colorize_output(split = TRUE, {
  # Get live (uncolored) output
  # And print colored output at the end of execution

  est_lms <- modsem(m1, data = oneInt, method = "lms")
  summary(est_lms)
}) 
                
colorize_output(modsem_inspect(est_lms))

## End(Not run)

Get the simple slopes of a SEM model

Description

This function calculates simple slopes (predicted values of the outcome variable) at user-specified values of the focal predictor (x) and moderator (z) in a structural equation modeling (SEM) framework. It supports interaction terms (xz), computes standard errors (SE), and optionally returns confidence or prediction intervals for these predicted values. It also provides p-values for hypothesis testing. This is useful for visualizing and interpreting moderation effects or to see how the slope changes at different values of the moderator.

Usage

simple_slopes(
  x,
  z,
  y,
  xz = NULL,
  model,
  vals_x = -3:3,
  vals_z = -1:1,
  rescale = TRUE,
  ci_width = 0.95,
  ci_type = "confidence",
  relative_h0 = TRUE,
  standardized = FALSE,
  ...
)

Arguments

Details

Computation Steps

1. The function extracts parameter estimates (and, if necessary, their covariance matrix) from the fitted SEM model (model).

2. It identifies the coefficients for x, z, and x:z in the model's parameter table, as well as the variance of x, z and the residual variance of y.

3. If xz is not provided, it will be constructed by combining x and z with a colon (":"). Depending on the approach used to estimate the model, the colon may be removed or replaced internally; the function attempts to reconcile that.

4. A grid of x and z values is created from vals_x and vals_z. If rescale = TRUE, these values are transformed back into raw metric units for display in the output.

5. For each point in the grid, a predicted value of y is computed via (beta0 + beta_x * x + beta_z * z + beta_xz * x * z) and, if included, a mean offset.

6. The standard error (std.error) is derived from the covariance matrix of the relevant parameters, and if ci_type = "prediction", adds the residual variance.

7. Confidence (or prediction) intervals are formed using ci_width (defaulting to 95%). The result is a table-like data frame with predicted values, CIs, standard errors, z-values, and p-values.

Value

A data.frame (invisibly inheriting class "simple_slopes") with columns:

• vals_x, vals_z: The requested grid values of x and z.

• predicted: The predicted value of y at that combination of x and z.

• std.error: The standard error of the predicted value.

• z.value, p.value: The z-statistic and corresponding p-value for testing the null hypothesis that predicted == h0.

• ci.lower, ci.upper: Lower and upper bounds of the confidence (or prediction) interval.

An attribute "variable_names" (list of x, z, y) is attached for convenience.

Examples

## Not run: 
library(modsem)

m1 <- "
# Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

# Inner model
  Y ~ X + Z + X:Z
"
est1 <- modsem(m1, data = oneInt)

# Simple slopes at X in [-3, 3] and Z in [-1, 1], rescaled to the raw metric.
simple_slopes(x = "X", z = "Z", y = "Y", model = est1)

# If the data or user wants unscaled values, set rescale = FALSE, etc.
simple_slopes(x = "X", z = "Z", y = "Y", model = est1, rescale = FALSE)

## End(Not run)

Standardize a fitted modsem_da model

Description

standardize_model() post-processes the output of modsem_da() (or of modsem()) when method = "lms" / method = "qml"), replacing the unstandardized coefficient vector ($coefs) and its variance–covariance matrix ($vcov) with fully standardized counterparts (including the measurement model).The procedure is purely algebraic— no re-estimation is carried out —and is therefore fast and deterministic.

Usage

standardize_model(model, monte.carlo = FALSE, mc.reps = 10000, ...)

Arguments

Value

The same object (returned invisibly) with three slots overwritten

$parTable

Parameter table whose columns est and std.error now hold standardized estimates and their (delta-method) standard errors, as produced by standardized_estimates().

$coefs

Named numeric vector of standardized coefficients. Intercepts (operator ~1) are removed, because a standardized variable has mean 0 by definition.

$vcov

Variance–covariance matrix corresponding to the updated coefficient vector. Rows/columns for intercepts are dropped, and the sub-matrix associated with rescaled parameters is adjusted so that its diagonal equals the squared standardized standard errors.

The object keeps its class attributes, allowing seamless use by downstream S3 methods such as summary(), coef(), or vcov().

Because the function merely transforms existing estimates, parameter constraints imposed through shared labels remain satisfied.

See Also

standardized_estimates()

Obtains the fully standardized parameter table used here.

modsem()

Fit model using LMS or QML approaches.

modsem_da()

Fit model using LMS or QML approaches.

Examples

## Not run: 
# Latent interaction estimated with LMS and standardized afterwards
syntax <- "
  X =~ x1 + x2 + x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3
  Y ~ X + Z + X:Z
"
fit  <- modsem_da(syntax, data = oneInt, method = "lms")
sfit <- standardize_model(fit, monte.carlo = TRUE)

# Compare unstandardized vs. standardized summaries
summary(fit)  # unstandardized
summary(sfit) # standardized 

## End(Not run)

Get Standardized Estimates

Description

Computes standardized estimates of model parameters for various types of modsem objects.

Usage

standardized_estimates(object, ...)

## S3 method for class 'lavaan'
standardized_estimates(
  object,
  monte.carlo = FALSE,
  mc.reps = 10000,
  tolerance.zero = 1e-10,
  ...
)

## S3 method for class 'modsem_da'
standardized_estimates(
  object,
  monte.carlo = FALSE,
  mc.reps = 10000,
  tolerance.zero = 1e-10,
  ...
)

## S3 method for class 'modsem_pi'
standardized_estimates(
  object,
  correction = FALSE,
  std.errors = c("rescale", "delta", "monte.carlo"),
  mc.reps = 10000,
  colon.pi = FALSE,
  ...
)

Arguments

Details

Standard errors can either be calculated using the delta method, or a monte.carlo simulation (monte.carlo is not available for modsem_pi objects if correction == FALSE.). NOTE that the standard errors of the standardized paramters change the assumptions of the model, and will in most cases yield different z and p-values, compared to the unstandardized solution. In almost all cases, significance testing should be based on the unstandardized solution. Since, the standardization process changes the model assumptions, it also changes what the p-statistics measure. I.e., the test statistics for the standardized and unstandardized solutions belong to different sets of hypothesis, which are not exactly equivalent to each other.

For modsem_da and modsem_mplus objects, the interaction term is not a formal variable in the model and therefore lacks a defined variance. Under assumptions of normality and zero-mean variables, the interaction variance is estimated as:

var(xz) = var(x) * var(z) + cov(x, z)^2

This means the standardized estimate for the interaction differs from approaches like lavaan, which treats the interaction as a latent variable with unit variance.

For modsem_pi objects, the interaction term is standardized by default assuming var(xz) = 1, but this can be overridden using the correction argument.

NOTE: Standardized estimates are always placed in the est column, not est.std, regardless of model type.

Value

A data.frame with standardized estimates in the est column.

Methods (by class)

• standardized_estimates(lavaan): Method for lavaan objects

• standardized_estimates(modsem_da): Method for modsem_da objects

• standardized_estimates(modsem_pi): Method for modsem_pi objects

Examples

m1 <- '
  # Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

  # Inner Model
  Y ~ X + Z + X:Z
'
# Double centering approach
est_dca <- modsem(m1, oneInt)

std1 <- standardized_estimates(est_dca) # no correction
summarize_partable(std1)

std2 <- standardized_estimates(est_dca, correction = TRUE) # apply correction
summarize_partable(std2)

## Not run: 
est_lms <- modsem(m1, oneInt, method = "lms")
standardized_estimates(est_lms) # correction not relevant for lms

## End(Not run)

Summarize a parameter table from a modsem model.

Description

Summarize a parameter table from a modsem model.

Usage

summarize_partable(
  parTable,
  scientific = FALSE,
  ci = FALSE,
  digits = 3,
  loadings = TRUE,
  regressions = TRUE,
  covariances = TRUE,
  intercepts = TRUE,
  variances = TRUE
)

Arguments

Value

A summary object containing the parameter table and additional information.

Examples

m1 <- '
  # Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

  # Inner Model
  Y ~ X + Z + X:Z
'
# Double centering approach
est_dca <- modsem(m1, oneInt)

std <- standardized_estimates(est_dca, correction = TRUE)
summarize_partable(std)

summary for modsem objects

Description

summary for modsem objects

summary for modsem objects

summary for modsem objects

Usage

## S3 method for class 'modsem_da'
summary(
  object,
  H0 = TRUE,
  verbose = interactive(),
  r.squared = TRUE,
  adjusted.stat = FALSE,
  digits = 3,
  scientific = FALSE,
  ci = FALSE,
  standardized = FALSE,
  centered = FALSE,
  monte.carlo = FALSE,
  mc.reps = 10000,
  loadings = TRUE,
  regressions = TRUE,
  covariances = TRUE,
  intercepts = TRUE,
  variances = TRUE,
  var.interaction = FALSE,
  ...
)

## S3 method for class 'modsem_mplus'
summary(
  object,
  scientific = FALSE,
  standardize = FALSE,
  ci = FALSE,
  digits = 3,
  loadings = TRUE,
  regressions = TRUE,
  covariances = TRUE,
  intercepts = TRUE,
  variances = TRUE,
  ...
)

## S3 method for class 'modsem_pi'
summary(
  object,
  H0 = TRUE,
  r.squared = TRUE,
  adjusted.stat = FALSE,
  digits = 3,
  scientific = FALSE,
  verbose = TRUE,
  ...
)

Arguments

Examples

## Not run: 
m1 <- "
 # Outer Model
 X =~ x1 + x2 + x3
 Y =~ y1 + y2 + y3
 Z =~ z1 + z2 + z3

 # Inner model
 Y ~ X + Z + X:Z
"

est1 <- modsem(m1, oneInt, "qml")
summary(est1, ci = TRUE, scientific = TRUE)

## End(Not run)

Estimate formulas for (co-)variance paths using Wright's path tracing rules

Description

This function estimates the path from x to y using the path tracing rules. Note that it only works with structural parameters, so "=~" are ignored, unless measurement.model = TRUE. If you want to use the measurement model, "~" should be in the mod column of pt.

Usage

trace_path(
  pt,
  x,
  y,
  parenthesis = TRUE,
  missing.cov = FALSE,
  measurement.model = TRUE,
  maxlen = 100,
  paramCol = "mod",
  ...
)

Arguments

Value

A string with the estimated path (simplified if possible)

Examples

library(modsem)
m1 <- '
  # Outer Model
  X =~ x1 + x2 +x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3

  # Inner model
  Y ~ X + Z + X:Z
'
pt <- modsemify(m1)
trace_path(pt, x = "Y", y = "Y", missing.cov = TRUE) # variance of Y

Estimate interaction effects in structural equation models (SEMs) using a twostep procedure

Description

Estimate an interaction model using a twostep procedure. For the PI approaches, the lavaan::sam function is used to optimize the models, instead of lavaan::sem. Note that the product indicators are still used, and not the newly developed SAM approach to estimate latent interactions. For the DA approaches (LMS and QML) the measurement model is estimated using a CFA (lavaan::cfa). The structural model is estimated using modsem_da, where the estimates in the measurement model are fixed, based on the CFA estimates. Note that standard errors are uncorrected (i.e., naive), and do not account for the uncertainty in the CFA estimates. NOTE, this is an experimental feature!

Usage

twostep(model.syntax, data, method = "lms", ...)

Arguments

Value

modsem object with class modsem_pi or modsem_da.

Examples

library(modsem)
m1 <- '
  # Outer Model
  X =~ x1 + x2 +x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3

  # Inner model
  Y ~ X + Z + X:Z
'

est_dblcent <- twostep(m1, oneInt, method = "dblcent")
summary(est_dblcent)

## Not run: 
est_lms <- twostep(m1, oneInt, method = "lms")
summary(est_lms)

est_qml <- twostep(m1, oneInt, method = "qml")
summary(est_qml)

## End(Not run)

tpb_uk <- "
# Outer Model (Based on Hagger et al., 2007)
 ATT =~ att3 + att2 + att1 + att4
 SN =~ sn4 + sn2 + sn3 + sn1
 PBC =~ pbc2 + pbc1 + pbc3 + pbc4
 INT =~ int2 + int1 + int3 + int4
 BEH =~ beh3 + beh2 + beh1 + beh4

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

uk_dblcent <- twostep(tpb_uk, TPB_UK, method = "dblcent")
summary(uk_dblcent)

## Not run: 
  uk_qml <- twostep(tpb_uk, TPB_UK, method = "qml")

  uk_lms <- twostep(tpb_uk, TPB_UK, method = "lms", nodes = 32, adaptive.quad = TRUE)
  summary(uk_lms)

## End(Not run)

Extract or modify parTable from an estimated model with estimated variances of interaction terms

Description

Extract or modify parTable from an estimated model with estimated variances of interaction terms

Usage

var_interactions(object, ...)

Arguments