em: Maximum likelihood estimation of structural equation mixture...

In nlsem: Fitting Structural Equation Mixture Models

Maximum likelihood estimation of structural equation mixture models

Description

Fits a structural equation model with latent interaction effects using mixture approaches (LMS, SEMM, NSEMM).

Usage

  em(model, data, start, qml = FALSE, verbose = FALSE, convergence = 1e-02,
     max.iter = 100, m = 16, optimizer = c("nlminb", "optim"),
     max.mstep = 1, max.singleClass = 1, neg.hessian = TRUE, ...) 

Arguments

model	a specified structural equation model of class singleClass, semm, or nsemm.
data	the data the model should be fitted to. Data needs to be a matrix and variables need to be in the order x1, x2, ..., y1, y2, ... as specified in specify_sem. Data matrix needs no column names (will be ignored anyways).
start	starting values for parameters.
qml	logical. Indicating if QML estimation should be used instead of LMS for estimation of nonlinear effects. Defaults to FALSE. QML is much faster, though.
verbose	if output of EM algorithm should be shown during fitting.
convergence	convergence threshold.
max.iter	maximum number of iterations before EM algorithm stops.
m	number of nodes for Hermite-Gaussian quadrature. Defaults to 16. See Datails.
optimizer	which optimizer should be used in maximization step of EM algorithm: nlminb or optim.
max.mstep	maximum iteration steps the optimizer should use in its mstep during one EM iteration. Defaults to 1.
max.singleClass	maximum iteration steps for singleClass model inside of NSEMM model. Defaults to 1 (and should only be changed for valid reasons).
neg.hessian	should negative Hessian be calculated in last step of iteration.
...	additional arguments. See Details.

Details

em can be used to estimate parameters for structural equation mixture models with latent interaction effects with an EM algorithm. The maximization step of the EM algorithm can use two different optimizers: optim or nlminb. Default is nlminb.

Additional arguments can be passed to ... for these optimizers. See documentation for optim and nlminb.

The LMS approach (Klein & Moosbrugger, 2000) uses Hermite-Gauss quadrature for numerical approximation. The nodes used in this approximation need to be prespecified by the user. The more nodes are used the better the numerical approximation but also the slower the calculations.

Value

An object of class emEst that consists of the following components:

model.class	class of model that was fitted, can be singleClass, semm, or nsemm.
coefficients	estimated parameters.
objective	final loglikelihood obtained with EM algorithm.
em_convergence	yes or no. Did EM algorithm converge?
Hessian	Hessian matrix for final parameter estimation.
loglikelihoods	loglikelihoods obtained during each iteration of EM algorithm.
info	list of number of exogenous (num.xi) and endogenous (num.eta) variables and of indicators (num.x and num.y). Corresponds to specifications given to specify_sem when specifiying structural equation model.

References

Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997). STEMM: A General Finite Mixture Structural Equation Model, Journal of Classification, 14, 23–50. doi:http://dx.doi.org/10.1007/s003579900002

Kelava, A., Nagengast, B., & Brandt, H. (2014). A nonlinear structural equation mixture modeling approach for non-normally distributed latent predictor variables. Structural Equation Modeling, 21, 468-481. doi:http://dx.doi.org/10.1080/10705511.2014.915379

Klein, A. &, Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. Psychometrika, 65, 457–474. doi:http://dx.doi.org/10.1007/bf02296338

See Also

specify_sem

Examples

###### Example for SEMM ######
# load data
data("PoliticalDemocracy", package = "lavaan")
dat <- as.matrix(PoliticalDemocracy[ ,c(9:11,1:8)])

# specify model of class SEMM
model <- specify_sem(num.x = 3, num.y = 8, num.xi = 1, num.eta = 2, 
  xi = "x1-x3", eta = "y1-y4,y5-y8", rel.lat = "eta1~xi1,eta2~xi1,eta2~eta1",
  num.classes = 2, constraints = "direct1")

# fit model
set.seed(911)
start <- runif(count_free_parameters(model))
## Not run: 
res <- em(model, dat, start, convergence = 0.1, max.iter = 200)
summary(res)
plot(res)

## End(Not run)

###### Example for LMS ######
model <- specify_sem(num.x = 11, num.y = 4, num.xi = 2, num.eta = 1,
  xi = "x1-x5,x6-x11", eta = "y1-y4", interaction = "eta1~xi1:xi2")

data("jordan")

set.seed(110)
start <- runif(count_free_parameters(model))
## Not run: 
res <- em(model, jordan, start, convergence=1, verbose=TRUE)
summary(res)
plot(res)

## End(Not run)

###### Example using lavaan syntax ######
lav.model <- '
  eta =~ y1 + y2 + y3 + y4
  xi1 =~ x1 + x2 + x3 + x4 + x5
  xi2 =~ x6 + x7 + x8 + x9 + x10 + x11

  eta ~ xi1 + xi2 + xi1:xi2 + xi1:xi1'

model <- lav2nlsem(lav.model)

data("jordan")

set.seed(1118)
start <- runif(count_free_parameters(model))
## Not run: 
res <- em(model, jordan, start, convergence=1, verbose=TRUE)

## End(Not run)

nlsem documentation built on Aug. 31, 2023, 5:14 p.m.