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Plots of Influence Measures

Source: R/influence_plot.R
influence_plot.Rd

Gets an influence_stat() output and plots selected statistics.

Usage

gcd_plot(
  influence_out,
  cutoff_gcd = NULL,
  largest_gcd = 1,
  point_aes = list(),
  vline_aes = list(),
  cutoff_line_aes = list(),
  case_label_aes = list()
)

md_plot(
  influence_out,
  cutoff_md = FALSE,
  cutoff_md_qchisq = 0.975,
  largest_md = 1,
  point_aes = list(),
  vline_aes = list(),
  cutoff_line_aes = list(),
  case_label_aes = list()
)

gcd_gof_plot(
  influence_out,
  fit_measure,
  cutoff_gcd = NULL,
  cutoff_fit_measure = NULL,
  largest_gcd = 1,
  largest_fit_measure = 1,
  point_aes = list(),
  hline_aes = list(),
  cutoff_line_gcd_aes = list(),
  cutoff_line_fit_measures_aes = list(),
  case_label_aes = list()
)

gcd_gof_md_plot(
  influence_out,
  fit_measure,
  cutoff_md = FALSE,
  cutoff_fit_measure = NULL,
  circle_size = 2,
  cutoff_md_qchisq = 0.975,
  cutoff_gcd = NULL,
  largest_gcd = 1,
  largest_md = 1,
  largest_fit_measure = 1,
  point_aes = list(),
  hline_aes = list(),
  cutoff_line_md_aes = list(),
  cutoff_line_gcd_aes = list(),
  cutoff_line_fit_measures_aes = list(),
  case_label_aes = list()
)

Arguments

influence_out

The output from influence_stat().

cutoff_gcd

Cases with generalized Cook's distance or approximate generalized Cook's distance larger than this value will be labeled. Default is NULL. If NULL, no cutoff line will be drawn.

largest_gcd

The number of cases with the largest generalized Cook's distance or approximate generalized Cook's distance to be labelled. Default is 1. If not an integer, it will be rounded to the nearest integer.

point_aes

A named list of arguments to be passed to ggplot2::geom_point() to modify how to draw the points. Default is list() and internal default settings will be used.

vline_aes

A named list of arguments to be passed to ggplot2::geom_segment() to modify how to draw the line for each case in the index plot. Default is list() and internal default settings will be used.

cutoff_line_aes

A named list of arguments to be passed to ggplot2::geom_vline() or ggplot2::geom_hline() to modify how to draw the line for user cutoff value. Default is list() and internal default settings will be used.

case_label_aes

A named list of arguments to be passed to ggrepel::geom_label_repel() to modify how to draw the labels for cases marked (based on arguments such as cutoff_gcd or largest_gcd). Default is list() and internal default settings will be used.

cutoff_md

Cases with Mahalanobis distance larger than this value will be labeled. If it is TRUE, the (cutoff_md_qchisq x 100)th percentile of the chi-square distribution with the degrees of freedom equal to the number of variables will be used. Default is FALSE, no cutoff value.

cutoff_md_qchisq

This value multiplied by 100 is the percentile to be used for labeling case based on Mahalanobis distance. Default is .975.

largest_md

The number of cases with the largest Mahalanobis distance to be labelled. Default is 1. If not an integer, it will be rounded to the nearest integer.

fit_measure

The fit measure to be used in a plot. Use the name in the lavaan::fitMeasures() function. No default value.

cutoff_fit_measure

Cases with fit_measure larger than this cutoff in magnitude will be labeled. No default value and must be specified.

largest_fit_measure

The number of cases with the largest selected fit measure change in magnitude to be labelled. Default is

  1. If not an integer, it will be rounded to the nearest integer.

hline_aes

A named list of arguments to be passed to ggplot2::geom_hline() to modify how to draw the horizontal line for zero case influence. Default is list() and internal default settings will be used.

cutoff_line_gcd_aes

Similar to cutoff_line_aes but control the line for the cutoff value of gCD.

cutoff_line_fit_measures_aes

Similar to cutoff_line_aes but control the line for the cutoff value of the selected fit measure.

circle_size

The size of the largest circle when the size of a circle is controlled by a statistic.

cutoff_line_md_aes

Similar to cutoff_line_aes but control the line for the cutoff value of the Mahalanobis distance.

Value

A ggplot2 plot. Plotted by default. If assigned to a variable or called inside a function, it will not be plotted. Use plot() to plot it.

Details

The output of influence_stat() is simply a matrix. Therefore, these functions will work for any matrix provided. Row number will be used on the x-axis if applicable. However, case identification values in the output from influence_stat() will be used for labeling individual cases.

The default settings for the plots should be good enough for diagnostic purpose. If so desired, users can use the *_aes arguments to nearly fully customize all the major elements of the plots, as they would do for building a ggplot2 plot.

Functions

  • gcd_plot(): Index plot of generalized Cook's distance.

  • md_plot(): Index plot of Mahalanobis distance.

  • gcd_gof_plot(): Plot the case influence of the selected fit measure against generalized Cook's distance.

  • gcd_gof_md_plot(): Bubble plot of the case influence of the selected fit measure against Mahalanobis distance, with the size of a bubble determined by generalized Cook's distance.

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

See also

influence_stat().

Author

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

Examples

library(lavaan)
dat <- pa_dat
# The model
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 n times. Each time with one case removed.
# For illustration, do this only for selected cases.
fit_rerun <- lavaan_rerun(fit, parallel = FALSE,
                          to_rerun = 1:10)
#> The expected CPU time is 0.38 second(s).
#> Could be faster if run in parallel.
# Get all default influence stats
out <- influence_stat(fit_rerun)
head(out)
#>         chisq           cfi         rmsea           tli           a1
#> 1  0.15407944 -0.0019968390  0.0017700811 -0.0049920976  0.024466586
#> 2 -0.01944571  0.0011486763 -0.0010912308  0.0028716908  0.007153846
#> 3 -0.41673808  0.0082048797 -0.0074508538  0.0205121991 -0.038282397
#> 4 -0.15430823  0.0036670450 -0.0032789585  0.0091676124 -0.024048244
#> 5  0.09730667  0.0002954311  0.0008280336  0.0007385778  0.066686613
#> 6  0.11601736 -0.0010911517  0.0011378622 -0.0027278793  0.004007056
#>              a2            b      m1~~m1      dv~~dv         gcd        md
#> 1 -0.0300705396  0.051965997 -0.03663071  0.01717427 0.005891665 1.9107778
#> 2  0.0034230301 -0.013043400 -0.06744802 -0.05802199 0.008147128 0.4442464
#> 3 -0.0401051535 -0.029790144 -0.06335355 -0.04479763 0.009834826 3.7867385
#> 4 -0.0031358865  0.021674577 -0.05137193 -0.04379632 0.005610493 1.0653437
#> 5  0.0278462201  0.032782898  0.04979077 -0.06598323 0.013001467 1.9803351
#> 6  0.0009699846  0.009509592 -0.06910195 -0.05422999 0.007823146 0.2875484

# Plot generalized Cook's distance. Label the 3 cases with the largest distances.
gcd_plot(out, largest_gcd = 3)


# Plot Mahalanobis distance. Label the 3 cases with the largest distances.
md_plot(out, largest_md = 3)


# Plot case influence on model chi-square against generalized Cook's distance.
# Label the 3 cases with the largest absolute influence.
# Label the 3 cases with the largest generalized Cook's distance.
gcd_gof_plot(out, fit_measure = "chisq", largest_gcd = 3,
             largest_fit_measure = 3)


# Plot case influence on model chi-square against Mahalanobis distance.
# Size of bubble determined by generalized Cook's distance.
# Label the 3 cases with the largest absolute influence.
# Label the 3 cases with the largest Mahalanobis distance.
# Label the 3 cases with the largest generalized Cook's distance.

gcd_gof_md_plot(out, fit_measure = "chisq",
                     largest_gcd = 3,
                     largest_fit_measure = 3,
                     largest_md = 3,
                     circle_size = 10)


# Use the approximate method that does not require refitting the model.

# 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
#> 
out <- influence_stat(fit)
head(out)
#>         chisq           cfi         rmsea          tli       m1~iv1
#> 1  0.15956516 -0.0020929857  0.0018614175 -0.005232464  0.024713396
#> 2 -0.01892880  0.0011399150 -0.0010827859  0.002849787  0.007254736
#> 3 -0.38907022  0.0077186573 -0.0070161267  0.019296643 -0.037982774
#> 4 -0.15078126  0.0036048257 -0.0032221332  0.009012064 -0.024353717
#> 5  0.09685352  0.0003104848  0.0008205378  0.000776212  0.067010210
#> 6  0.11602751 -0.0010913266  0.0011380304 -0.002728316  0.004065567
#>         m1~iv2        dv~m1      m1~~m1      dv~~dv  gcd_approx        md
#> 1 -0.030383580  0.052370026 -0.03784100  0.01630488 0.005850455 1.9107778
#> 2  0.003469647 -0.013223396 -0.06916983 -0.05953293 0.008312026 0.4442464
#> 3 -0.039820283 -0.030150418 -0.06518369 -0.04609708 0.009904544 3.7867385
#> 4 -0.003172373  0.021948305 -0.05277394 -0.04504791 0.005719499 1.0653437
#> 5  0.027951233  0.032981527  0.04860722 -0.06774242 0.012793226 1.9803351
#> 6  0.000983731  0.009640981 -0.07086163 -0.05565453 0.007984573 0.2875484

# Plot approximate generalized Cook's distance.
# Label the 3 cases with the largest values.
gcd_plot(out, largest_gcd = 3)


# Plot Mahalanobis distance.
# Label the 3 cases with the largest values.
md_plot(out, largest_md = 3)


# Plot approximate case influence on model chi-square against
# approximate generalized Cook's distance.
# Label the 3 cases with the largest absolute approximate case influence.
# Label the 3 cases with the largest approximate generalized Cook's distance.
gcd_gof_plot(out, fit_measure = "chisq", largest_gcd = 3,
             largest_fit_measure = 3)


# Plot approximate case influence on model chi-square against Mahalanobis distance.
# The size of a bubble determined by approximate generalized Cook's distance.
# Label the 3 cases with the largest absolute approximate case influence.
# Label the 3 cases with the largest Mahalanobis distance.
# Label the 3 cases with the largest approximate generalized Cook's distance.

gcd_gof_md_plot(out, fit_measure = "chisq",
                     largest_gcd = 3,
                     largest_fit_measure = 3,
                     largest_md = 3,
                     circle_size = 10)


# Customize elements in the plot.
# For example, change the color and shape of the points.

gcd_gof_plot(out, fit_measure = "chisq", largest_gcd = 3,
             largest_fit_measure = 3,
             point_aes = list(shape = 3, color = "red"))