modsem_da: Interaction between latent variables using lms and qml...

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

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,
  convergence = 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,
  fix.estep = NULL,
  start = NULL,
  epsilon = NULL,
  quad.range = NULL,
  n.threads = NULL,
  ...
)

Arguments

model.syntax	lavaan syntax
data	dataframe
method	method to use: "lms" = latent model structural equations (not passed to lavaan). "qml" = quasi maximum likelihood estimation of latent model structural equations (not passed to lavaan).
verbose	should estimation progress be shown
optimize	should starting parameters be optimized
nodes	number of quadrature nodes (points of integration) used in lms, increased number gives better estimates but slower computation. How many are needed depends on the complexity of the model. For simple models, somewhere between 16-24 nodes should be enough; for more complex models, higher numbers may be needed. For models where there is an interaction effect between an endogenous and exogenous variable, the number of nodes should be at least 32, but practically (e.g., ordinal/skewed data), more than 32 is recommended. In cases where data is non-normal, it might be better to use the qml approach instead. For large numbers of nodes, you might want to change the 'quad.range' argument.
convergence	convergence criterion. Lower values give better estimates but slower computation.
optimizer	optimizer to use, can be either "nlminb" or "L-BFGS-B". For LMS, "nlminb" is recommended. For QML, "L-BFGS-B" may be faster if there is a large number of iterations, but slower if there are few iterations.
center.data	should data be centered before fitting model
standardize.data	should data be scaled before fitting model, will be overridden by standardize if standardize is set to TRUE. NOTE: It is recommended that you estimate the model normally and then standardize the output using standardized_estimates.
standardize.out	should output be standardized (note will alter the relationships of parameter constraints since parameters are scaled unevenly, even if they have the same label). This does not alter the estimation of the model, only the output. NOTE: It is recommended that you estimate the model normally and then standardize the output using standardized_estimates.
standardize	will standardize the data before fitting the model, remove the mean structure of the observed variables, and standardize the output. Note that standardize.data, mean.observed, and standardize.out will be overridden by standardize if standardize is set to TRUE. NOTE: It is recommended that you estimate the model normally and then standardize the output using standardized_estimates.
mean.observed	should the mean structure of the observed variables be estimated? This will be overridden by standardize if standardize is set to TRUE. NOTE: Not recommended unless you know what you are doing.
cov.syntax	model syntax for implied covariance matrix (see vignette("interaction_two_etas", "modsem"))
double	try to double the number of dimensions of integration used in LMS, this will be extremely slow but should be more similar to mplus.
calc.se	should standard errors be computed? NOTE: If FALSE, the information matrix will not be computed either.
FIM	should the Fisher information matrix be calculated using the observed or expected values? Must be either "observed" or "expected".
EFIM.S	if the expected Fisher information matrix is computed, EFIM.S selects the number of Monte Carlo samples. Defaults to 100. NOTE: This number should likely be increased for better estimates (e.g., 1000-10000), but it might drasticly increase computation time.
OFIM.hessian	should the observed Fisher information be computed using the Hessian? If FALSE, it is computed using the gradient.
EFIM.parametric	should data for calculating the expected Fisher information matrix be simulated parametrically (simulated based on the assumptions and implied parameters from the model), or non-parametrically (stochastically sampled)? If you believe that normality assumptions are violated, EFIM.parametric = FALSE might be the better option.
robust.se	should robust standard errors be computed? Meant to be used for QML, can be unreliable with the LMS approach.
R.max	Maximum population size (not sample size) used in the calculated of the expected fischer information matrix.
max.iter	maximum number of iterations.
max.step	maximum steps for the M-step in the EM algorithm (LMS).
fix.estep	if TRUE, the E-step will be fixed, and the prior probabilities will be set to the best prior probabilities, if the log-likelihood decreases for more than 30 iterations.
start	starting parameters.
epsilon	finite difference for numerical derivatives.
quad.range	range in z-scores to perform numerical integration in LMS using Gaussian-Hermite Quadratures. By default Inf, such that f(t) is integrated from -Inf to Inf, but this will likely be inefficient and pointless at a large number of nodes. Nodes outside +/- quad.range will be ignored.
n.threads	number of cores to use for parallel processing. If NULL, it will use <= 2 threads. If an integer is specified, it will use that number of threads (e.g., n.threads = 4 will use 4 threads). If "default", it will use the default number of threads (2). If "max", it will use all available threads, "min" will use 1 thread.
...	additional arguments to be passed to the estimation function.

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
est1 <- modsem_da(m1, oneInt, method = "qml")
summary(est1)

# 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
"

# LMS Approach
estTpb <- modsem_da(tpb, data = TPB, method = lms, EFIM.S = 1000)
summary(estTpb)

## End(Not run)

modsem documentation built on April 3, 2025, 7:51 p.m.