Hi,

if your data violates the assumption of multinormality (not just normality)--what it always does, then you have to use robust ML. Bootstrapping won't do it and rather serves a different reason (to empirically gain standard errors in situtations where no analytical solution exists).

Perhaps a reason to switch to R / lavaan packge where this can be done in a very way (just by adding "estimator = MLR" to the sem() function. Take a look onto the lavaan webpage where you can find tutorials.

Good luck

Holger

It is possible to use Bootstrap Bias-corrected confidence intervals (CI) when performing the CB-SEM (Confirmatory Bias-Corrected Structural Equation Modeling) model for hypothesis testing. Bootstrap is a commonly used resampling technique in CB-SEM to estimate the standard errors, confidence intervals, and p-values of the model parameters.

The Bootstrap Bias-corrected CI is a type of confidence interval that adjusts for any bias in the estimates due to the limited sample size. This adjustment can improve the accuracy of the confidence intervals, particularly when the sample size is small.

To use the Bootstrap Bias-corrected CI in CB-SEM, you would first fit the CB-SEM model to the observed data and obtain the parameter estimates. Then, you would generate multiple Bootstrap samples by random sampling with replacements from the original dataset. For each Bootstrap sample, you would fit the CB-SEM model and obtain the parameter estimates. This process is repeated many times to obtain a distribution of parameter estimates for each parameter of interest.

Next, you would use these distributions to estimate the parameters' standard errors, p-values, and confidence intervals. The Bootstrap Bias-corrected CI adjusts for any bias in the estimates by using a correction factor based on the distribution of the Bootstrap estimates. This correction factor can be calculated using specialized software or formulas.

In summary, Bootstrap Bias-corrected confidence intervals can be used in CB-SEM to improve the accuracy of the standard errors, p-values, and confidence intervals of the model parameters, particularly when the sample size is small.

Hi Ma'Mon Abu Hammad ,

as you said by yourself, bootstrapping serves to get standard errors (and thus, CIs and p value). When the assumption about multinormality fails, then each of the parameter estimates across the bootstrapped sample is biased. Hence, boostrappping over repeatedly biased estimates will (in my opinion) not magically correct the bias but I admit that I am no an expert regarding the statistical depths of parameter estimation in SEM.

So, if you are right: Do you have a reference that shows that bootstrapping helps? Would be helpful.

All the best

Holger

Hey Holger Steinmetz,

normality is not required for the ML estimator to produce consist estimate in the SEM context.

Thư Nguyễn, see for example Fox (2006).

Best regards,

Florian

J. Fox, “Teacher’s corner: structural equation modeling with the sem package in R,” Structural Equation Modeling: A Multidisciplinary Journal, vol. 13, no. 3, pp. 465–486, 2006.

Hello Holger Steinmetz ,

Thank you so much for your answer and further discussion. Although I am also not an expert in SEM and I don't have any statistic foundation, but I want to share that I discovered the use of Bootstrapping in SEM through the third edition of "Structural Equation Modeling with Amos" written by Barbara M. Byrne (2016) and "Handbook of Structural Equation Modeling" written by Rick H. Hoyle (2012). In those books, the authors provided some empirical studies related to applying Bootstrapping in SEM to correct the bias. One of them is "Performance of bootstrapping approaches to model test statistics and parameter standard error estimation in structural equation modeling" by Nevitt, J., & Hancock, G. R. (2001).

Hope it might help.

Hi Florian,

yes you are right! Completely forgot that ML estimates is robust against violation but if I remember correctly, the chisquare value and SEs are not.

Thư Nguyễn: Thank you for the addon. I learnt something new :) I never thought about this as robust ML is so easily available ;)

All the best,

Holger