Gets a lavaan_rerun() output and computes the
standardized changes in selected parameters for each case
if included.
Arguments
- rerun_out
The output from
lavaan_rerun().- parameters
A character vector to specify the selected parameters. Each parameter is named as in
lavaansyntax, e.g.,x ~ yorx ~~ y, as appeared in the columnslhs,op, andrhsin the output oflavaan::parameterEstimates(). Supports specifying an operator to select all parameters with this operators:~,~~,=~, and~1. This vector can contain both parameter names and operators. More details can be found in the help ofpars_id(). If omitted orNULL, the default, changes on all free parameters will be computed.
Value
An est_change-class object, which is
matrix with the number of columns equals to the number of
requested parameters plus one, the last column being the
generalized Cook's
distance. The number of rows equal to the number
of cases. The row names are the case identification values used in
lavaan_rerun(). The elements are the standardized difference.
Please see Pek and MacCallum (2011), Equation 7.
A print method is available for user-friendly output.
Details
For each case, est_change() computes the differences in
the estimates of selected parameters with and without this case:
(Estimate with all case) - (Estimate without this case).
The differences are standardized by dividing the raw differences by their standard errors (Pek & MacCallum, 2011). This is a measure of the standardized influence of a case on the parameter estimates if it is included.
If the value of a case is positive, including the case increases an estimate.
If the value of a case is negative, including the case decreases an estimate.
If the analysis is not admissible or does not converge when a case
is deleted, NAs will be turned for this case on the differences.
Unlike est_change_raw(), est_change() does not support
computing the standardized changes of standardized estimates.
It will also compute generalized Cook's distance (gCD), proposed by Pek and MacCallum (2011) for structural equation modeling. Only the parameters selected (all free parameters, by default) will be used in computing gCD.
Since version 0.1.4.8, if (a) a model has one or more equality constraints, and (b) some selected parameters are linearly dependent or constrained to be equal due to the constraint(s), gCD will be computed by removing parameters such that the remaining parameters are not linearly dependent nor constrained to be equal. (Support for equality constraints and linearly dependent parameters available in 0.1.4.8 and later version).
Supports both single-group and multiple-group models. (Support for multiple-group models available in 0.1.4.8 and later version).
References
Pek, J., & MacCallum, R. (2011). Sensitivity analysis in structural equation models: Cases and their influence. Multivariate Behavioral Research, 46(2), 202-228. doi:10.1080/00273171.2011.561068
Author
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448.
Examples
library(lavaan)
# A path model
dat <- pa_dat
mod <-
"
m1 ~ a1 * iv1 + a2 * iv2
dv ~ b * m1
a1b := a1 * b
a2b := a2 * b
"
# Fit the model
fit <- lavaan::sem(mod, dat)
summary(fit)
#> lavaan 0.6.17 ended normally after 1 iteration
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 5
#>
#> Number of observations 100
#>
#> Model Test User Model:
#>
#> Test statistic 6.711
#> Degrees of freedom 2
#> P-value (Chi-square) 0.035
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Regressions:
#> Estimate Std.Err z-value P(>|z|)
#> m1 ~
#> iv1 (a1) 0.215 0.106 2.036 0.042
#> iv2 (a2) 0.522 0.099 5.253 0.000
#> dv ~
#> m1 (b) 0.517 0.106 4.895 0.000
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .m1 0.903 0.128 7.071 0.000
#> .dv 1.321 0.187 7.071 0.000
#>
#> Defined Parameters:
#> Estimate Std.Err z-value P(>|z|)
#> a1b 0.111 0.059 1.880 0.060
#> a2b 0.270 0.075 3.581 0.000
#>
# Fit the model several times. Each time with one case removed.
# For illustration, do this only for four selected cases
fit_rerun <- lavaan_rerun(fit, parallel = FALSE,
to_rerun = c(2, 4, 7, 9))
#> The expected CPU time is 0.16 second(s).
#> Could be faster if run in parallel.
# Compute the standardized changes in parameter estimates
# if a case is included vs. if this case is excluded.
# That is, case influence on parameter estimates, standardized.
out <- est_change(fit_rerun)
# Case influence:
out
#>
#> -- Standardized Case Influence on Parameter Estimates --
#>
#> a1 a2 b m1~~m1 dv~~dv gcd
#> 9 -0.048 -0.025 -0.083 -0.033 0.283 0.091
#> 7 -0.119 0.073 0.065 -0.002 -0.040 0.026
#> 2 0.007 0.003 -0.013 -0.067 -0.058 0.008
#> 4 -0.024 -0.003 0.022 -0.051 -0.044 0.006
#>
#> Note:
#> - Changes are standardized raw changes if a case is included.
#> - All stored cases are displayed.
#> - Cases sorted by generalized Cook's distance.
# Note that these are the differences divided by the standard errors
# The rightmost column, `gcd`, contains the
# generalized Cook's distances (Pek & MacCallum, 2011).
out[, "gcd", drop = FALSE]
#> gcd
#> 2 0.008147128
#> 4 0.005610493
#> 7 0.025740465
#> 9 0.090844702
# Compute the changes for the paths from iv1 and iv2 to m1
out2 <- est_change(fit_rerun, c("m1 ~ iv1", "m1 ~ iv2"))
# Case influence:
out2
#>
#> -- Standardized Case Influence on Parameter Estimates --
#>
#> a1 a2 gcd
#> 7 -0.119 0.073 0.020
#> 9 -0.048 -0.025 0.003
#> 4 -0.024 -0.003 0.001
#> 2 0.007 0.003 0.000
#>
#> Note:
#> - Changes are standardized raw changes if a case is included.
#> - All stored cases are displayed.
#> - Cases sorted by generalized Cook's distance.
# Note that only the changes in the selected parameters are included.
# The generalized Cook's distance is computed only from the selected
# parameter estimates.
# A CFA model
dat <- cfa_dat
mod <-
"
f1 =~ x1 + x2 + x3
f2 =~ x4 + x5 + x6
f1 ~~ f2
"
# Fit the model
fit <- lavaan::cfa(mod, dat)
# Examine four selected cases
fit_rerun <- lavaan_rerun(fit, parallel = FALSE,
to_rerun = c(2, 3, 5, 7))
#> The expected CPU time is 0.25 second(s).
#> Could be faster if run in parallel.
# Compute the standardized changes in parameter estimates
# if a case is included vs. if a case is excluded.
# That is, case influence on parameter estimates, standardized.
# For free loadings only
out <- est_change(fit_rerun, parameters = "=~")
out
#>
#> -- Standardized Case Influence on Parameter Estimates --
#>
#> f1=~x2 f1=~x3 f2=~x5 f2=~x6 gcd
#> 3 -0.916 -0.444 -0.514 -0.043 1.132
#> 2 0.463 0.446 0.155 -0.087 0.338
#> 5 -0.019 -0.106 0.006 -0.026 0.014
#> 7 -0.021 -0.011 -0.029 -0.011 0.001
#>
#> Note:
#> - Changes are standardized raw changes if a case is included.
#> - All stored cases are displayed.
#> - Cases sorted by generalized Cook's distance.
# A latent variable model
dat <- sem_dat
mod <-
"
f1 =~ x1 + x2 + x3
f2 =~ x4 + x5 + x6
f3 =~ x7 + x8 + x9
f2 ~ a * f1
f3 ~ b * f2
ab := a * b
"
# Fit the model
fit <- lavaan::sem(mod, dat)
# Examine four selected cases
fit_rerun <- lavaan_rerun(fit, parallel = FALSE,
to_rerun = c(2, 3, 5, 7))
#> The expected CPU time is 0.28 second(s).
#> Could be faster if run in parallel.
# Compute the changes in parameter estimates if a case is included
# vs. if a case is excluded.
# That is, standardized case influence on parameter estimates.
# For structural paths only
out <- est_change(fit_rerun, parameters = "~")
out
#>
#> -- Standardized Case Influence on Parameter Estimates --
#>
#> a b gcd
#> 3 -0.123 -0.096 0.027
#> 7 -0.048 0.110 0.014
#> 2 0.044 -0.092 0.010
#> 5 -0.065 -0.018 0.005
#>
#> Note:
#> - Changes are standardized raw changes if a case is included.
#> - All stored cases are displayed.
#> - Cases sorted by generalized Cook's distance.