modsem (version 1.0.11)

modsem_pi: 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,
  ...
)

Value

modsem object

Arguments

model.syntax

lavaan syntax

data

dataframe

method

method to use:

"dblcent"

double centering approach (passed to lavaan).

"ca"

constrained approach (passed to lavaan).

"rca"

residual centering approach (passed to lavaan).

"uca"

unconstrained approach (passed to lavaan).

"pind"

prod ind approach, with no constraints or centering (passed to lavaan).

match

should the product indicators be created by using the match-strategy

match.recycle

should the indicators be recycled when using the match-strategy? I.e., if one of the latent variables have fewer indicators than the other, some indicators are recycled to match the latent variable with the most indicators.

standardize.data

should data be scaled before fitting model

center.data

should data be centered before fitting model

first.loading.fixed

Should the first factor loading in the latent product be fixed to one? Defaults to FALSE, as this already happens in lavaan by default. If TRUE, the first factor loading in the latent product is fixed to one. Manually in the generated syntax (e.g., XZ =~ 1*x1z1).'

center.before

should indicators in products be centered before computing products.

center.after

should indicator products be centered after they have been computed?

residuals.prods

should indicator products be centered using residuals.

residual.cov.syntax

should syntax for residual covariances be produced.

constrained.prod.mean

should syntax for product mean be produced.

constrained.loadings

should syntax for constrained loadings be produced.

constrained.var

should syntax for constrained variances be produced.

res.cov.method

method for constraining residual covariances. Options are

"simple"

Residuals of product indicators with variables in common are allowed to covary freely. Defualt for most approches.

"ca"

Residual covariances of product indicators are constrained according to the constrained approach.

"equality"

Residuals of product indicators with variables in common are constrained to have equal covariances". Can be useful for models where the model is unidentifiable using res.cov.method == "simple", (e.g., when there is an interaction between an observed and a latent variable).

"none"

Residual covariances between product indicators are not specificed (i.e., constrained to zero). Produces the same results as constrained.cov.syntax = FALSE. Can be useful for models where the model is unidentifiable using res.cov.method == "simple", (e.g., when there is an interaction between an observed and a latent variable).

res.cov.across

Should residual covariances be specified/freed across different interaction terms. For example if you have two interaction terms X:Z and X:W the residuals of the generated product indicators x1:z1 and x1:w1 may be correlated. If TRUE residual covariances are allowed across different latent interaction terms. If FALSE residual covariances are only allowed between product indicators which belong to the same latent interaction term.

auto.scale

methods which should be scaled automatically (usually not useful)

auto.center

methods which should be centered automatically (usually not useful)

estimator

estimator to use in lavaan

group

group variable for multigroup analysis

cluster

cluster variable for multilevel models

run

should the model be run via lavaan, if FALSE only modified syntax and data is returned

na.rm

should missing values be removed (case-wise)? Defaults to FALSE. If TRUE, missing values are removed case-wise. If FALSE they are not removed.

suppress.warnings.lavaan

should warnings from lavaan be suppressed?

suppress.warnings.match

should warnings from match be suppressed?

rcs

Should latent variable indicators be replaced with reliability-corrected single item indicators instead? See relcorr_single_item.

rcs.choose

Which latent variables should get their indicators replaced with reliability-corrected single items? It is passed to relcorr_single_item as the choose argument.

rcs.res.cov.xz

Should the residual (co-)variances of the product indicators created from the reliability-corrected single items (created if rcs = TRUE) be specified and constrained before estimating the model? If TRUE the estimates for the constraints are approximated using a monte carlo simulation (see the rcs.mc.reps argument). If FALSE the residual variances are not specified, which usually mean that all are constrained to zero.

rcs.mc.reps

Sample size used in monte-carlo simulation, when approximating the the estimates of the residual (co-)variances between the product indicators formed by reliabiliyt-corrected single items (see the rcs.res.cov.xz argument).

rcs.scale.corrected

Should reliability corrected items be scale-corrected? If TRUE reliability-corrected single items are corrected for differences in factor loadings between the items. Default is TRUE.

LAVFUN

Function used to estimate the model. Defaults to lavaan::sem.

...

arguments passed to LAVFUN

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)

if (FALSE) {
# The Constrained Approach
est_ca <- modsem_pi(m1, oneInt, method = "ca")
summary(est_ca)
}

# 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)

if (FALSE) {
# The Constrained Approach
est_tpb_ca <- modsem_pi(tpb, data = TPB, method = "ca")
summary(est_tpb_ca)
}