Case Influence on Parameter Estimates (Approximate)
Source:R/est_change_raw_approx.R
est_change_raw_approx.RdGets a lavaan::lavaan() output and computes the
approximate changes in selected parameters for each case
if included.
Usage
est_change_raw_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()andlavaan::sem()).- 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 these 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.- 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 isNULL, the default, thencase.idxused bylavaanfunctions will be used as case identification values.- allow_inadmissible
If
TRUE, accepts a fit object with inadmissible results (i.e.,post.checkfromlavaan::lavInspect()isFALSE). Default isFALSE.- skip_all_checks
If
TRUE, skips all checks and allows users to run this function on any object oflavaanclass. For users to experiment this and other functions on models not officially supported. Default isFALSE.
Value
An est_change-class object, which is
matrix with the number of columns equals to the number of
requested parameters, and the number of rows equals to the number
of cases. The row names are case identification values. The
elements are the raw differences.
A print method is available for user-friendly output.
Details
For each case, est_change_raw_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 change is the approximate raw change. The change is not divided by the standard error of an estimate (hence "raw" in the function name). This is a measure of the 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_raw(). 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_raw().
Unlike est_change_raw(), it does not yet support computing the
changes for the standardized solution.
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).
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
#>
# Compute the approximate changes in parameter estimates if a case is included
# vs. if this case is excluded.
# That is, the approximate case influence on parameter estimates.
out_approx <- est_change_raw_approx(fit)
head(out_approx)
#> m1~iv1 m1~iv2 dv~m1 m1~~m1 dv~~dv
#> 1 0.0025826195 -2.987160e-03 0.005478785 -0.004783799 0.003015677
#> 2 0.0007581403 3.411181e-04 -0.001383390 -0.008744342 -0.011010937
#> 3 -0.0039693069 -3.914928e-03 -0.003154241 -0.008240420 -0.008525904
#> 4 -0.0025450320 -3.118916e-04 0.002296162 -0.006671599 -0.008331854
#> 5 0.0070027557 2.748024e-03 0.003450422 0.006144848 -0.012529327
#> 6 0.0004248632 9.671545e-05 0.001008609 -0.008958217 -0.010293608
# Fit the model several times. Each time with one case removed.
# For illustration, do this only for 10 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.
# Compute the changes in parameter estimates if a case is included
# vs. if this case is excluded.
# That is, the case influence on the parameter estimates.
out <- est_change_raw(fit_rerun)
out
#>
#> -- Case Influence on Parameter Estimates --
#>
#> id m1~iv1 id m1~iv2 id dv~m1 id m1~~m1 id dv~~dv id a1b id a2b
#> 1 7 -0.013 7 0.007 9 -0.009 6 -0.009 9 0.051 7 -0.005 7 0.007
#> 2 5 0.007 8 0.007 10 -0.008 2 -0.009 8 -0.013 10 -0.005 9 -0.006
#> 3 8 0.006 10 0.004 7 0.007 3 -0.008 5 -0.013 9 -0.005 8 0.005
#> 4 10 -0.006 3 -0.004 1 0.005 10 -0.007 2 -0.011 5 0.004 3 -0.004
#> 5 9 -0.005 1 -0.003 5 0.004 8 -0.007 6 -0.010 8 0.004 5 0.003
#> 6 3 -0.004 5 0.003 3 -0.003 4 -0.007 3 -0.008 3 -0.003 10 -0.002
#> 7 1 0.003 9 -0.003 8 0.003 5 0.006 4 -0.008 1 0.003 1 0.001
#> 8 4 -0.003 2 0.000 4 0.002 1 -0.005 7 -0.008 4 -0.001 4 0.001
#> 9 2 0.001 4 0.000 2 -0.001 9 -0.004 10 0.007 6 0.000 6 0.001
#> 10 6 0.000 6 0.000 6 0.001 7 0.000 1 0.003 2 0.000 2 -0.001
#>
#> Note:
#> - Changes are raw changes if a case is included.
#> - All stored cases are displayed.
#> - Cases sorted by the absolute changes for each variable.
# Compare the results
plot(out_approx[1:10, 1], out[, 1])
abline(a = 0, b = 1)
plot(out_approx[1:10, 5], out[, 5])
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)
#> lavaan 0.6.17 ended normally after 37 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 13
#>
#> Number of observations 100
#>
#> Model Test User Model:
#>
#> Test statistic 12.027
#> Degrees of freedom 8
#> P-value (Chi-square) 0.150
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Latent Variables:
#> Estimate Std.Err z-value P(>|z|)
#> f1 =~
#> x1 1.000
#> x2 0.767 0.225 3.405 0.001
#> x3 1.047 0.296 3.542 0.000
#> f2 =~
#> x4 1.000
#> x5 2.114 0.869 2.431 0.015
#> x6 0.992 0.377 2.635 0.008
#>
#> Covariances:
#> Estimate Std.Err z-value P(>|z|)
#> f1 ~~
#> f2 0.171 0.091 1.884 0.060
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .x1 0.841 0.221 3.802 0.000
#> .x2 1.214 0.208 5.823 0.000
#> .x3 1.018 0.251 4.064 0.000
#> .x4 1.103 0.186 5.918 0.000
#> .x5 0.993 0.437 2.270 0.023
#> .x6 0.882 0.158 5.575 0.000
#> f1 0.708 0.262 2.703 0.007
#> f2 0.250 0.151 1.659 0.097
#>
# Compute the approximate changes in parameter estimates if a case is included
# vs. if this case is excluded.
# That is, approximate case influence on parameter estimates.
# Compute changes for free loadings only.
out_approx <- est_change_raw_approx(fit,
parameters = "=~")
head(out_approx)
#> f1=~x2 f1=~x3 f2=~x5 f2=~x6
#> 1 0.001920110 0.010740746 0.004541900 -0.0144098708
#> 2 0.058933568 0.073874875 0.057340739 -0.0434930940
#> 3 -0.144211320 -0.004047592 -0.436403769 -0.0108782714
#> 4 -0.009547216 -0.011335796 -0.000486256 0.0022414847
#> 5 0.004914233 -0.021463799 0.006004056 -0.0086035844
#> 6 0.002934830 0.018952764 -0.016648522 0.0001674064
# 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)
#> lavaan 0.6.17 ended normally after 37 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 20
#>
#> Number of observations 200
#>
#> Model Test User Model:
#>
#> Test statistic 41.768
#> Degrees of freedom 25
#> P-value (Chi-square) 0.019
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Latent Variables:
#> Estimate Std.Err z-value P(>|z|)
#> f1 =~
#> x1 1.000
#> x2 0.590 0.145 4.054 0.000
#> x3 0.808 0.168 4.812 0.000
#> f2 =~
#> x4 1.000
#> x5 0.730 0.099 7.400 0.000
#> x6 0.429 0.083 5.166 0.000
#> f3 =~
#> x7 1.000
#> x8 2.019 0.589 3.426 0.001
#> x9 2.747 0.788 3.486 0.000
#>
#> Regressions:
#> Estimate Std.Err z-value P(>|z|)
#> f2 ~
#> f1 (a) 1.115 0.233 4.788 0.000
#> f3 ~
#> f2 (b) 0.206 0.061 3.394 0.001
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .x1 1.183 0.173 6.831 0.000
#> .x2 1.129 0.127 8.909 0.000
#> .x3 1.027 0.134 7.667 0.000
#> .x4 0.833 0.173 4.812 0.000
#> .x5 1.078 0.140 7.714 0.000
#> .x6 1.234 0.132 9.367 0.000
#> .x7 1.056 0.112 9.428 0.000
#> .x8 1.042 0.139 7.478 0.000
#> .x9 1.077 0.197 5.470 0.000
#> f1 0.658 0.190 3.474 0.001
#> .f2 0.647 0.215 3.010 0.003
#> .f3 0.062 0.035 1.771 0.077
#>
#> Defined Parameters:
#> Estimate Std.Err z-value P(>|z|)
#> ab 0.230 0.079 2.895 0.004
#>
# Compute the approximate changes in parameter estimates if a case is included
# vs. if this case is excluded.
# That is, the approximate case influence on parameter estimates.
# Compute changes for structural paths only
out_approx <- est_change_raw_approx(fit,
parameters = c("~"))
head(out_approx)
#> f2~f1 f3~f2
#> 1 -0.001088313 -0.0078430905
#> 2 0.010965561 -0.0055003320
#> 3 -0.031284855 -0.0054784700
#> 4 0.060426691 0.0002338238
#> 5 -0.014994222 -0.0009711227
#> 6 -0.002126077 -0.0009193544