Fit Structural Equation Models using the SAM approach

Fit a Structural Equation Model (SEM) using the Structural After Measurement (SAM) approach.

Usage

sam(model = NULL, data = NULL, cmd = "sem", se = "twostep", 
    mm.list = NULL, mm.args = list(bounds = "wide.zerovar"), 
    struc.args = list(estimator = "ML"), 
    sam.method = "local", ..., 
    local.options = list(M.method = "ML", lambda.correction = TRUE, 
                         alpha.correction = 0L, twolevel.method = "h1"), 
    global.options = list(), 
    bootstrap.args = list(R = 1000L, type = "ordinary", show.progress = FALSE),
    output = "lavaan")

Arguments

model: A description of the user-specified model. Typically, the model is described using the lavaan model syntax. See model.syntax for more information. Alternatively, a parameter table (eg. the output of the lavParTable() function) is also accepted.
data: A data frame containing the observed variables used in the model.
cmd: Character. Which command is used to run the sem models. The possible choices are "sem", "cfa" or "lavaan", determining how we deal with default options.
se: Character. The type of standard errors that are used in the final (structural) model. If "twostep" (the default), the standard errors take the estimation uncertainty of the first (measurement) stage into account. If "standard", this uncertainty is ignored, and we treat the measurement information as known. If "none", no standard errors are computed.
mm.list: List. Define the measurement blocks. Each element of the list should be either a single name of a latent variable, or a vector of latent variable names. If omitted, a separate measurement block is used for each latent variable.
mm.args: List. Optional arguments for the fitting function(s) of the measurement block(s) only. See lavOptions for a complete list.
struc.args: List. Optional arguments for the fitting function of the structural part only. See lavOptions for a complete list.
sam.method: Character. Can be set to "local", "global" or "fsr". In the latter case, the results are the same as if Bartlett factor scores were used, without any bias correction.
...: Many more additional options can be defined, using 'name = value'. See lavOptions for a complete list. These options affect both the measurement blocks and the structural part.
local.options: List. Options specific for local SAM method (these options may change over time). If lambda.correction = TRUE, we ensure that the variance matrix of the latent variables (VETA) is positive definite. The alpha.correction options must be an integer. Acceptable values are in the range 0 till N-1. If zero (the default), no small sample correction is performed, and the bias-correction is the same as with local SAM. When equal to N-1, the bias-correction is eliminated, and the results are the same as naive FSR. Typical values are 0, P+1 (where P is the number of predictors in the structural model), P+5, and (N-1)/2.
global.options: List. Options specific for global SAM method (not used for now).
bootstrap.args: List. Only used when se = "bootstrap". Typical elements of this list are R: the number of bootstrap samples, and type, which can be set to "ordinary" (the default) or "parametric".
output: Character. If "lavaan", a lavaan object returned. If "list", a list is returned with all the ingredients from the different stages.

Details

The sam function tries to automate the SAM approach, by first estimating the measurement part of the model, and then the structural part of the model. See reference for more details.

Note that in the current implementation, all indicators of latent variables have to be observed. This implies: no support for second-order factor structures (for now).

Value

If output = "lavaan", an object of class lavaan, for which several methods are available, including a summary method. If output = "list", a list.

References

Rosseel and Loh (2021). A structural-after-measurement approach to Structural Equation Modeling. Psychological Methods. Advance online publication. https://dx.doi.org/10.1037/met0000503

Examples

## The industrialization and Political Democracy Example 
## Bollen (1989), page 332
model <- ' 
  # latent variable definitions
     ind60 =~ x1 + x2 + x3
     dem60 =~ y1 + a*y2 + b*y3 + c*y4
     dem65 =~ y5 + a*y6 + b*y7 + c*y8

  # regressions
    dem60 ~ ind60
    dem65 ~ ind60 + dem60

  # residual correlations
    y1 ~~ y5
    y2 ~~ y4 + y6
    y3 ~~ y7
    y4 ~~ y8
    y6 ~~ y8
'

fit.sam <- sam(model, data = PoliticalDemocracy,
               mm.list = list(ind = "ind60", dem = c("dem60", "dem65")))
summary(fit.sam)
#> This is lavaan 0.6-21 -- using the SAM approach to SEM
#> 
#>   SAM method                                     LOCAL
#>   Mapping matrix M method                           ML
#>   Number of measurement blocks                       2
#>   Estimator measurement part                        ML
#>   Estimator  structural part                        ML
#> 
#>   Number of observations                            75
#> 
#> Summary Information Measurement + Structural:
#> 
#>   Block      Latent Nind Chisq Df
#>       1       ind60    3  0.00  0
#>       2 dem60,dem65    8 15.32 16
#> 
#>   Model-based reliability latent variables:
#> 
#>   ind60 dem60 dem65
#>   0.966 0.868  0.87
#> 
#>   Summary Information Structural part:
#> 
#>   chisq df cfi rmsea srmr
#>       0  0   1     0    0
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                              Twostep
#>   Information                                 Expected
#>   Information saturated (h1) model          Structured
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   dem60 ~                                             
#>     ind60             1.454    0.389    3.741    0.000
#>   dem65 ~                                             
#>     ind60             0.558    0.225    2.480    0.013
#>     dem60             0.871    0.076   11.497    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>     ind60             0.446    0.087    5.135    0.000
#>    .dem60             3.766    0.848    4.439    0.000
#>    .dem65             0.189    0.224    0.843    0.399
#>