Case Influence on Fit Measures (Approximate) — fit_measures_change

Gets a lavaan::lavaan() output and computes the approximate change in selected fit measures if a case is included.

Usage

fit_measures_change_approx(
  fit,
  fit_measures = c("chisq", "cfi", "rmsea", "tli"),
  baseline_model = 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()).
fit_measures: The argument fit.measures used in lavaan::fitMeasures. Default is c("chisq", "cfi", "rmsea", "tli"). Currently, the approximate method supports only these four measures.
baseline_model: The argument baseline.model used in lavaan::fitMeasures. Default is NULL.
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 lavaan class. For users to experiment this and other functions on models not officially supported. Default is FALSE.

Value

An fit_measures_change-class object, which is matrix with the number of columns equals to the number of requested fit measures, and the number of rows equals to the number of cases. The row names are case identification values. A print method is available for user-friendly output.

Details

For each case, fit_measures_change_approx() computes the approximate differences in selected fit measures with and without this case:

(Fit measure with all case) - (Fit measure without this case).

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.

Note that an increase is an improvement in fit for goodness of fit measures such as CFI and TLI, but a decrease is an improvement in fit for badness of fit measures such as RMSEA and model chi-square. This is a measure of the influence of a case on a fit measure if it is included.

The model is not refitted. Therefore, the result is only an approximation of that of fit_measures_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 fit_measures_change().

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

Supports both single-group and multiple-group models. (Support for multiple-group models available in 0.1.4.8 and later version).

Author

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)
#> 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
#> 

# Approximate changes
out_approx <- fit_measures_change_approx(fit, fit_measures = "chisq")
head(out_approx)
#>         chisq
#> 1  0.15956516
#> 2 -0.01892880
#> 3 -0.38907022
#> 4 -0.15078126
#> 5  0.09685352
#> 6  0.11602751
# 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 = 1:5)
#> The expected CPU time is 0.18 second(s).
#> Could be faster if run in parallel.
# Compute the changes in chisq if a case is included
# vs. if this case is excluded.
# That is, case influence on model chi-squared.
out <- fit_measures_change(fit_rerun, fit_measures = "chisq")
# Case influence, for the first few cases
head(out)
#>         chisq
#> 1  0.15407944
#> 2 -0.01944571
#> 3 -0.41673808
#> 4 -0.15430823
#> 5  0.09730667
# Compare the results
plot(out_approx[1:5, "chisq"], out)
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)

out_approx <- fit_measures_change_approx(fit, fit_measures = "chisq")
head(out_approx)
#>         chisq
#> 1 -0.76276453
#> 2  0.99160651
#> 3 -0.13684245
#> 4 -0.02940289
#> 5 -0.54686780
#> 6  0.60740826

fit_rerun <- lavaan_rerun(fit, parallel = FALSE,
                          to_rerun = 1:5)
#> The expected CPU time is 0.82 second(s).
#> Could be faster if run in parallel.
# Compute the changes in chisq if a case is included
# vs. if this case is excluded.
# That is, case influence on fit measures.
out <- fit_measures_change(fit_rerun, fit_measures = "chisq")
# Results excluding a case, for the first few cases
head(out)
#>         chisq
#> 1 -0.99210274
#> 2  0.90763725
#> 3 -0.25394609
#> 4 -0.03468346
#> 5 -0.63365168
# Compare the results
plot(out_approx[1:5, "chisq"], out)
abline(a = 0, b = 1)


# 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)

out_approx <- fit_measures_change_approx(fit, fit_measures = "chisq")
head(out_approx)
#>        chisq
#> 1 -0.1283103
#> 2 -0.5320442
#> 3  0.6467449
#> 4  1.3578723
#> 5 -0.4206413
#> 6  0.2202259

fit_rerun <- lavaan_rerun(fit, parallel = FALSE,
                          to_rerun = 1:5)
#> The expected CPU time is 0.32 second(s).
#> Could be faster if run in parallel.
# Compute the changes in chisq if a case is excluded
# vs. if this case is included.
# That is, case influence on model chi-squared.
out <- fit_measures_change(fit_rerun, fit_measures = "chisq")
# Case influence, for the first few cases
head(out)
#>        chisq
#> 1 -0.3385932
#> 2 -0.6367473
#> 3  0.5199304
#> 4  1.2366084
#> 5 -0.5428558
# Compare the results
plot(out_approx[1:5, "chisq"], out)
abline(a = 0, b = 1)