Grand Standardized Solution

Grand standardized solution of a two-stage path analysis model.

Usage

grand_standardized_solution(
  object,
  model_list = NULL,
  se = TRUE,
  acov_par = NULL,
  free_list = NULL,
  level = 0.95
)

grandStandardizedSolution(
  object,
  model_list = NULL,
  se = TRUE,
  acov_par = NULL,
  free_list = NULL,
  level = 0.95
)

Arguments

object: An object of class lavaan.
model_list: A list of string variable describing the structural path model, in lavaan syntax.
se: A Boolean variable. If TRUE, standard errors for the grand standardized parameters will be computed.
acov_par: An asymptotic variance-covariance matrix for a fitted model object; defaults to vcov(object). Supplying the covariance of an SE-corrected tspa() fit (produced with tspa(corrected_se = TRUE)) carries the first-order correction through to the grand-standardized standard errors reported by this function.
free_list: A list of model matrices that indicate the position of the free parameters in the parameter vector.
level: The confidence level required.

Value

A data frame (class lavaan.data.frame) with one row per structural (~) parameter in partable order: lhs, op, rhs, exo, group, block, label, the grand standardized estimate est.std, and, when se = TRUE, se, z, pvalue, ci.lower, and ci.upper.

Details

For a multigroup fit the grand standardized solution is computed from the grand (pooled) means and variance-covariances and is not equivalent to lavaan::standardizedSolution(), which matches it only in the single-group case (the function emits that message when it applies). When the input fit is an SE-corrected tspa() fit (produced with tspa(corrected_se = TRUE), attribute tspa_corrected = TRUE) — or when acov_par = vcov(corrected_fit) is supplied — the reported standard errors are the first-order corrected grand-standardized standard errors, while the point estimates (est.std) are unchanged.

Structural slopes may be free or user-fixed. A user-fixed slope is reported alongside the free ones: its est.std is the user value rescaled by the (grand) SD ratio, and its se is the first-order delta approximation, both matching lavaan::standardizedSolution() (which also reports a delta SE for fixed slopes). A structural regression whose outcome or predictor is not part of the beta matrix (e.g. observed-on-observed) is still rejected with an error. The delta-method SEs are propagated over the free beta/psi (and alpha, single group) elements as marked by the lavaan free-position matrices; a free parameter whose block matrix carries no mark contributes no first-order term (in lavaan 0.7-x the free-position matrices do not mark, e.g., some observed-variable intercept blocks, whose omission only matters when their sampling uncertainty affects the group means pooled into the grand covariance).

Examples

library(lavaan)

## A single-group, two-factor example
mod1 <- '
   # latent variables
     ind60 =~ x1 + x2 + x3
     dem60 =~ y1 + y2 + y3 + y4
   # regressions
     dem60 ~ ind60
'
fit1 <- sem(model = mod1,
          data  = PoliticalDemocracy)
grand_standardized_solution(fit1)
#> The grand standardized solution is equivalent to lavaan::standardizedSolution() for a model with a single group.
#>     lhs op   rhs exo group block label est.std  se     z pvalue ci.lower
#> 8 dem60  ~ ind60   0     1     1          0.46 0.1 4.593      0    0.264
#>   ci.upper
#> 8    0.657

## A single-group, three-factor example
mod2 <- '
    # latent variables
      ind60 =~ x1 + x2 + x3
      dem60 =~ y1 + y2 + y3 + y4
      dem65 =~ y5 + y6 + y7 + y8
    # regressions
      dem60 ~ ind60
      dem65 ~ ind60 + dem60
'
fit2 <- sem(model = mod2,
            data  = PoliticalDemocracy)
grand_standardized_solution(fit2)
#> The grand standardized solution is equivalent to lavaan::standardizedSolution() for a model with a single group.
#>      lhs op   rhs exo group block label est.std    se      z pvalue ci.lower
#> 12 dem60  ~ ind60   0     1     1         0.448 0.102  4.393  0.000    0.248
#> 13 dem65  ~ ind60   0     1     1         0.146 0.070  2.071  0.038    0.008
#> 14 dem65  ~ dem60   0     1     1         0.913 0.048 19.120  0.000    0.819
#>    ci.upper
#> 12    0.648
#> 13    0.283
#> 14    1.006

## A multigroup, two-factor example
mod3 <- '
  # latent variable definitions
    visual =~ x1 + x2 + x3
    speed =~ x7 + x8 + x9
  # regressions
    visual ~ c(b1, b1) * speed
'
fit3 <- sem(mod3, data = HolzingerSwineford1939,
            group = "school",
            group.equal = c("loadings", "intercepts"))
grand_standardized_solution(fit3)
#>       lhs op   rhs exo group block label est.std    se     z pvalue ci.lower
#> 7  visual  ~ speed   0     1     1    b1   0.431 0.073 5.867      0    0.287
#> 30 visual  ~ speed   0     2     2    b1   0.431 0.073 5.867      0    0.287
#>    ci.upper
#> 7     0.575
#> 30    0.575

## A multigroup, three-factor example
mod4 <- '
  # latent variable definitions
    visual =~ x1 + x2 + x3
    textual =~ x4 + x5 + x6
    speed =~ x7 + x8 + x9

  # regressions
    visual ~ c(b1, b1) * textual + c(b2, b2) * speed
'
fit4 <- sem(mod4, data = HolzingerSwineford1939,
            group = "school",
            group.equal = c("loadings", "intercepts"))
grand_standardized_solution(fit4)
#>       lhs op     rhs exo group block label est.std    se     z pvalue ci.lower
#> 10 visual  ~ textual   0     1     1    b1   0.419 0.073 5.704      0    0.275
#> 11 visual  ~   speed   0     1     1    b2   0.324 0.078 4.145      0    0.171
#> 46 visual  ~ textual   0     2     2    b1   0.419 0.073 5.704      0    0.275
#> 47 visual  ~   speed   0     2     2    b2   0.324 0.078 4.145      0    0.171
#>    ci.upper
#> 10    0.563
#> 11    0.477
#> 46    0.563
#> 47    0.477

Usage

Arguments

Value

Details

See also

Examples