est_change_approx {semfindr}

Standardized Case Influence on Parameter Estimates (Approximate)

Description

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

Usage

est_change_approx(
  fit,
  parameters = NULL,
  case_id = NULL,
  allow_inadmissible = FALSE,
  skip_all_checks = FALSE
)

Arguments

fit

The output from lavaan::lavaan() or its wrappers (e.g., lavaan::cfa() and lavaan::sem()).

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 these 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.

case_id

If it is a character vector of length equals to the number of cases (the number of rows in the data in fit), then it is the vector of case identification values. If it is NULL, the default, then case.idx used by lavaan functions will be used as case identification values.

allow_inadmissible

If TRUE, accepts a fit object with inadmissible results (i.e., post.check from lavaan::lavInspect() is FALSE). Default is FALSE.

skip_all_checks

If TRUE, skips all checks and allows users to run this function on any object of the lavaan class. For users to experiment this and other functions on models not officially supported. Default is FALSE.

Details

For each case, est_change_approx() computes the approximate 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 approximate raw differences by their standard errors. 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.

The model is not refitted. Therefore, the result is only an approximation of that of est_change(). However, this approximation is useful for identifying potentially influential cases when the sample size is very large or the model takes a long time to fit. This function can be used to identify potentially influential cases quickly and then select them to conduct the leave-one-out sensitivity analysis using lavaan_rerun() and est_change().

This function also computes the approximate generalized Cook's distance (gCD). To avoid confusion, it is labelled gcd_approx.

For the technical details, please refer to the vignette on this approach: vignette("casewise_scores", package = "semfindr")

The approximate approach supports a model with equality constraints (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 approximate 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 approximate standardized differences. A print method is available for user-friendly output.

Author(s)

Idea by Mark Hok Chio Lai https://orcid.org/0000-0002-9196-7406, implemented by 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)

# Approximate standardized changes and gCD
out_approx <- est_change_approx(fit)
head(out_approx)

# Fit the model several times. Each time with one case removed.
# For illustration, do this only for the first 10 cases.
fit_rerun <- lavaan_rerun(fit, parallel = FALSE,
                          to_rerun = 1:10)
# Compute the changes in chisq if a case is removed
out <- est_change(fit_rerun)
head(out)

# Compare the results
plot(out_approx[1:10, 1], out[, 1])
abline(a = 0, b = 1)
plot(out_approx[1:10, 2], out[, 2])
abline(a = 0, b = 1)
plot(out_approx[1:10, 3], out[, 3])
abline(a = 0, b = 1)
plot(out_approx[1:10, "gcd_approx"], out[, "gcd"])
abline(a = 0, b = 1)

# 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)
summary(fit)

# Approximate standardized changes and gCD
# Compute gCD only for free loadings
out_approx <- est_change_approx(fit,
                                parameters = "=~")
head(out_approx)

# 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)
summary(fit)

# Approximate standardized changes and gCD
# Compute gCD only for structural paths
out_approx <- est_change_approx(fit,
                                parameters = "~")
head(out_approx)