sirt (version 1.6-0)

lsem.estimate: Local Structural Equation Models (LSEM)

Description

Local structural equation models (LSEM) are structural equation models (SEM) which are evaluated for each value of a pre-defined moderator variable (Hildenbrandt, Wilhelm, & Robitzsch, 2009). Like in nonparametric regression models, observations near a focal point - at which the model is evaluated - obtain higher weights, far distant obervations obtain lower weight. The LSEM can be specified by making use of lavaan syntax. It is also possible to specify a discretized version of LSEM which means that values of the moderator are grouped into a small number of groups. The LSEM can be tested by employing a permutation test, see lsem.permutationTest. The function lsem.MGM.stepfunctions outputs stepwise functions for a multiple group model evaluated at a grid of focal points of the moderator, specified in moderator.grid.

Usage

lsem.estimate(data, moderator, moderator.grid, lavmodel, type="LSEM", h = 1.1, 
    residualize=TRUE, fit_measures = c("rmsea", "tli", "gfi", "srmr"), eps = 1e-08,
    verbose = TRUE, ...)
    
## S3 method for class 'lsem':
summary(object, file=NULL, digits=3, ...)

## S3 method for class 'lsem':
plot(x , parindex=NULL , ask=TRUE , ci = TRUE , lintrend = TRUE , 
       parsummary = TRUE , ylim=NULL , xlab=NULL,  ylab=NULL , main=NULL , 
       digits=3, ...)
       
lsem.MGM.stepfunctions( object , moderator.grid )

Arguments

data

Data frame

moderator

Variable name of the moderator

moderator.grid

Focal points at which the LSEM should be evaluated. If type="MGM", breaks are defined in this vector.

lavmodel

Specified SEM in lavaan. The function sem (lavaan) is used.

type

Type of estimated model. The default is type="LSEM" which means that a local structural equation model is estimated. A multiple group model with a discretized moderator as the grouping variable can be estimated with type="MGM"

h

Bandwidth factor

residualize

Logical indicating whether a residualization should be applied.

fit_measures

Vector with names of fit measures following the labels in lavaan

eps

Minimum number for weights

verbose

Optional logical printing information about computation progress.

object

Object of class lsem

file

A file name in which the summary output will be written.

digits

Number of digits.

x

Object of class lsem.

parindex

Vector of indices for parameters in plot function.

ask

A logical which asks for changing the graphic for each parameter.

ci

Logical indicating whether confidence intervals should be plotted.

lintrend

Logical indicating whether a linear trend should be plotted.

parsummary

Logical indicating whether a parameter summary should be displayed.

ylim

Plot parameter ylim. Can be a list, see Examples.

xlab

Plot parameter xlab. Can be a vector.

ylab

Plot parameter ylab. Can be a vector.

main

Plot parameter main. Can be a vector.

...

Further arguments to be passed to sem (lavaan).

Value

• List with following entries
• parameters
  Data frame with all parameters estimated at focal points of moderator
• weights
  Data frame with weights at each focal point
• bw
  Used bandwidth
• h
  Used bandwidth factor
• N
  Sample size
• moderator.density
  Estimated frequencies and effective sample size for moderator at focal points
• moderator.stat
  Descriptive statistics for moderator
• moderator
  Variable name of moderator
• moderator.grid
  Used grid of focal points for moderator
• moderator.grouped
  Data frame with informations about grouping of moderator if type="MGM".
• residualized.intercepts
  Estmated intercept functions used for residualization.
• lavmodel
  Used lavaan model
• data
  Used data frame, possibly residualized if residualize=TRUE

References

Hildebrandt, A., Wilhelm, O., & Robitzsch, A. (2009). Complementary and competing factor analytic approaches for the investigation of measurement invariance. Review of Psychology, 16, 87-102.

See Also

lsem.permutationTest

Examples

#############################################################################
# EXAMPLE 1: data.lsem01 | Age differentiation
#############################################################################	
	
data(data.lsem01)
dat <- data.lsem01

# specify lavaan model
lavmodel <- "
        F =~ v1+v2+v3+v4+v5
        F ~~ 1*F"
        
# define grid of moderator variable age
moderator.grid <- seq(4,23,1)

#********************************
#*** Model 1: estimate LSEM with bandwidth 2
mod1 <- lsem.estimate( dat , moderator="age" , moderator.grid=moderator.grid , 
               lavmodel=lavmodel , h=2 , std.lv=TRUE)
summary(mod1)
plot(mod1 , parindex=1:5)

# perform permutation test for Model 1
pmod1 <- lsem.permutationTest( mod1 , B=10 )    
          # only for illustrative purposes the number of permutations B is set 
          # to a low number of 10
summary(pmod1)
plot(pmod1, type="global")

#********************************
#*** Model 2: estimate multiple group model with 4 age groups

# define breaks for age groups
moderator.grid <- seq( 3.5 , 23.5 , len=5) # 4 groups 
# estimate model
mod2 <- lsem.estimate( dat , moderator="age" , moderator.grid=moderator.grid , 
           lavmodel=lavmodel , type="MGM" , std.lv=TRUE)
summary(mod2)

# output step functions
smod2 <- lsem.MGM.stepfunctions( lsem.object=mod2 , moderator.grid=seq(4,23,1) )
str(smod2)