Standardized coefficient estimation using do_mc

[weberhw]

library(lavaan)
library(manymome)

path_ex = "

• #path of main model
• homejob1 ~ loading1
• emo1 ~ displin1
• engage1 ~ homejob1
• engage1 ~ emo1
• engage1 ~ loading1
• engage1 ~ displin1
• effica1 ~ engage1
• effica1 ~ sex + edu
• homejob1 ~~ emo1
• "

path.fit = lavaan::sem(model = path_ex,

•                  data = path_da, 
  

•                  estimator = "WLSMV", 
  

•                  missing = "listwise",
  

•                  baseline.conditional.x.free.slopes = FALSE,
  

•                  fixed.x = TRUE,
  

•                  parameterization = "theta",
  

•                  ordered = c("homejob1", "emo1", "engage1",
  

•                              "effica1",  "loading1", "displin1", 
  

•                              "sex", "edu" ))
  

path.sum = summary(path.fit, fit.measures = TRUE,

•              standardized = TRUE, rsquare = TRUE)
  

mc_med <- do_mc(path.m, R = 1000, seed = 98171)
Stage 1: Simulate estimates
|++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=02s
Stage 2: Compute implied statistics
|++++++++++++++++++++++++++++++++++++++++++++++++++| 100% elapsed=02s
all_paths <- all_indirect_paths(path.fit)
ind_out <- many_indirect_effects(paths = all_paths,

•                            fit = path.m,
  

•                            mc_out = mc_med,
  

•                            boot_ci = F,
  

•                            mc_ci = TRUE,
  

•                            standardized_x = TRUE,
  

•                            standardized_y = TRUE)
  

An error occurred at if (const(t, min(1e-08, mean(t, na.rm = TRUE)/1e+06))) {: missing value where TRUE/FALSE needed.

ind_out <- many_indirect_effects(paths = all_paths,

•                              fit = path.m,
  

•                              mc_out = mc_med,
  

•                              boot_ci = F,
  

•                              mc_ci = TRUE,
  

•                              standardized_x = FALSE,
  

•                              standardized_y = FALSE)
  

This issue occurred when running mc for my model. I was trying to obtain Monte Carlo estimates of standardized coefficients, but the model returned an error message. I suspect that this happens when, in some simulated datasets, the standard deviation becomes 0 or another error occurs, resulting in NA values. When this happens, do_mc() does not automatically exclude the failed simulations, which causes the process to stop with an error. This is different from do_boot(), which can exclude failed bootstrap samples and continue.

As a result, my model fails to obtain standardized indirect effects. However, when I use monteCarloCI() from the semTools package for the same task, it successfully provides standardized coefficients and MC confidence intervals.

Similarly, if I use a non-standardized approach with other models, will they also fail to produce results if any simulated dataset fails? Is there any argument or option in this function to handle such cases by excluding failed simulations and continuing the estimation?

[sfcheung]

Thanks for reporting this issue. I did a quick check, and it is not because of inadmissible solutions or failed replications, but because of something else.

To compute standardized effects, we rely on the model-implied variances reported by lavaan using this function call:

lavInspect(path.fit, "cov.all")

The square roots of the diagonal elements are the implied SDs of the variables.

Normally, lavaan reports them even with fixed.x = FALSE. For example (ignore the values)

> lavInspect(path.fit, "implied")
$cov
         homjb1   emo1 engag1 effic1 lodng1 dspln1    sex    edu
homejob1  0.247
emo1      0.003  0.242
engage1   0.014  0.063  0.243
effica1   0.001  0.008  0.035  0.245
loading1 -0.037 -0.004  0.041  0.009  0.248
displin1  0.006  0.025 -0.005 -0.014 -0.040  0.250
sex      -0.003 -0.001  0.003  0.029  0.021 -0.010  0.250       
edu      -0.001 -0.008  0.001  0.039  0.008 -0.075  0.004  0.245

However, in the model you specified, somehow lavaan does not include them when requested:

> lavInspect(path.fit, "cov.all")
         homjb1   emo1 engag1 effic1
homejob1  1.000
emo1     -0.004  1.000
engage1   0.099  0.408  1.000
effica1   0.019  0.078  0.191  1.000

Unfortunately, this problem may not have a quick fix. Therefore, you may need to use other tools for this model, such as monteCarloCI() form semTools.

By the way, for standardized effects, monteCarloCI() can form the CI because it adopts a different approach.

do_mc() simulates model parameter estimates directly and then computes the implied standardized solution. It uses the standard error method that researchers decided to use when fitting a model.

monteCarloCI(), on the other hand, computes the sampling variance-covariance matrix of the standardized solution first, using the delta-method (given by lavInspect(object, "vcov.std.all")), and then does Monte Carlo using this variance-covariance matrix. It avoids the "division by 0 or a very small SDs" problem because standardization is done not during, but before, the Monte Carlo simulation.

I am not aware of any empirical comparisons of these two approaches. Like all Monte Carlo CI methods that use the variance-covariance (VCOV) matrix of the parameter estimates, they are only "as good as" the VCOV matrix and the distributional assumptions made (nearly always a multivariate normal distribution). For the "raw" model parameter estimates, the multivariate normal distribution assumption is usually fine. However, for the standardized solution, this may not be the case. For example, a covariance in the standardized solution is a correlation, and it is well-known that its sampling distribution is not normal unless the sample size is large. Therefore, I have reservations about forming Monte Carlo CI this way (just like forming Monte Carlo CI for a Pearson's r).

Nevertheless, in your scenario, the approach by monteCarloCI() seems to be a feasible solution. Therefore, despite my comment above, I would also recommend you use monteCarloCI(), given that do_mc() does not work due to the issue mentioned above.

By the way, I noticed that you declare all variables as ordered. For the non-x variables, their SDs are already equal to one (because of the way to handle the ordinal variables), and so there is no need to standardize them. If you do want to treat the x-variables as ordered, is it necessary or meaningful to standardize them?

A side-note: all_indirect_paths() also does not work correctly in your model because somehow lavaan does not include the paths from the x variables in the beta matrix that stores the regression path:

> lavaan::lavInspect(path.fit)$beta
         homjb1 emo1 engag1 effic1
homejob1      0    0      0      0
emo1          0    0      0      0
engage1       3    4      0      0
effica1       0    0      7      0

[weberhw]

Thank you. Your explanation has helped me better understand the core of this issue. I need standardized coefficients because journal articles typically report standardized coefficients. Since my data can only be estimated using WLSMV, I require the Monte Carlo (MC) method to estimate the indirect effects. Shu Fai Cheung ***@***.***> 於 2025年7月6日 週日 上午11:20寫道：

…

*sfcheung* left a comment (sfcheung/manymome#231) <#231 (comment)> Thanks for reporting this issue. I did a quick check, and it is not because of inadmissible solutions or failed replications, but because of something else. To compute standardized effects, we rely on the model-implied variances reported by lavaan using this function call: lavInspect(path.fit, "cov.all") The square roots of the diagonal elements are the implied SDs of the variables. Normally, lavaan reports them even with fixed.x = FALSE. For example (ignore the values) > lavInspect(path.fit, "implied")$cov homjb1 emo1 engag1 effic1 lodng1 dspln1 sex eduhomejob1 0.247emo1 0.003 0.242engage1 0.014 0.063 0.243effica1 0.001 0.008 0.035 0.245loading1 -0.037 -0.004 0.041 0.009 0.248displin1 0.006 0.025 -0.005 -0.014 -0.040 0.250sex -0.003 -0.001 0.003 0.029 0.021 -0.010 0.250 edu -0.001 -0.008 0.001 0.039 0.008 -0.075 0.004 0.245 However, in the model you specified, somehow lavaan does not include them when requested: > lavInspect(path.fit, "cov.all") homjb1 emo1 engag1 effic1homejob1 1.000emo1 -0.004 1.000engage1 0.099 0.408 1.000effica1 0.019 0.078 0.191 1.000 Unfortunately, this problem may not have a quick fix. Therefore, you may need to use other tools for this model, such as monteCarloCI() form semTools. By the way, for standardized effects, monteCarloCI() can form the CI because it adopts a different approach. do_mc() simulates model parameter estimates directly and then computes the implied standardized solution. It uses the standard error method that researchers decided to use when fitting a model. monteCarloCI(), on the other hand, computes the sampling variance-covariance matrix of the standardized solution first, using the delta-method (given by lavInspect(object, "vcov.std.all")), and then does Monte Carlo using this variance-covariance matrix. It avoids the "division by 0 or a very small SDs" problem because standardization is done not during, but before, the Monte Carlo simulation. I am not aware of any empirical comparisons of these two approaches. Like all Monte Carlo CI methods that use the variance-covariance (VCOV) matrix of the parameter estimates, they are only "as good as" the VCOV matrix and the distributional assumptions made (nearly always a multivariate normal distribution). For the "raw" model parameter estimates, the multivariate normal distribution assumption is usually fine. However, for the standardized solution, this may not be the case. For example, a covariance in the standardized solution is a correlation, and it is well-known that its sampling distribution is not normal unless the sample size is large. Therefore, I have reservations about forming Monte Carlo CI this way (just like forming Monte Carlo CI for a Pearson's r). Nevertheless, in your scenario, the approach by monteCarloCI() seems to be a feasible solution. Therefore, despite my comment above, I would also recommend you use monteCarloCI(), given that do_mc() does not work due to the issue mentioned above. By the way, I noticed that you declare all variables as ordered. For the non-x variables, their SDs are already equal to one (because of the way to handle the ordinal variables), and so there is no need to standardize them. If you do want to treat the x-variables as ordered, is it necessary or meaningful to standardize them? A side-note: all_indirect_paths() also does not work correctly in your model because somehow lavaan does not include the paths from the x variables in the beta matrix that stores the regression path: > lavaan::lavInspect(path.fit)$beta homjb1 emo1 engag1 effic1homejob1 0 0 0 0emo1 0 0 0 0engage1 3 4 0 0effica1 0 0 7 0 — Reply to this email directly, view it on GitHub <#231 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/BOEHEJ2ELBG62QN3ZT7MQ7T3HCIWHAVCNFSM6AAAAACA3SQXHKVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZTANBQGY3DCOJSHA> . You are receiving this because you authored the thread.Message ID: ***@***.***>