est_change {semfindr}

Standardized Case Influence on Parameter Estimates

Description

Gets a lavaan_rerun() output and computes the standardized changes in selected parameters for each case if included.

Usage

est_change(rerun_out, parameters = NULL)

Arguments

rerun_out

The output from lavaan_rerun().

parameters

A character vector to specify the selected parameters. Each parameter is named as in lavaan syntax, e.g., x ~ y or x ~~ y, as appeared in the columns lhs, op, and rhs in the output of lavaan::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 of pars_id(). If omitted or NULL, the default, changes on all free parameters will be computed.

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).

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.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448.

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

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)
# 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))
# 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
# 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]

# 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
# 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))
# 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

# 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))
# 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