The answer to your specific question about SEM is here: Article Structural equation modeling with ordinal variables: A large...

Now the question is do you want convenient or best?

This question has appeared literally millions of times here. To cut to the chase, Likert data CANNOT be modeled as continuous but should be treated by ORDINAL LOGISTIC REGRESSION. That is the kind of data it was meant to handle. A Set of Reference Notes(with computer examples) is attached For more you should

Further see:

My tome on Likert DV’s and ordinal logistic regression can be found here:

https://www.researchgate.net/post/Can_you_help_with_statistical_analysis_advice

https://statisticalanalysisconsulting.com/how-to-analyze-likert-type-dependent-variables/

https://www.researchgate.net/post/Possibility_of_using_point-scale_data_in_a_mixed-model_ANOVA

https://www.researchgate.net/post/Possibility_of_using_point-scale_data_in_a_mixed-model_ANOVA

https://www.researchgate.net/post/What_quantitative_research_analysis_would_best_suit

Further discussion:

https://www.researchgate.net/post/Which_statistical_test_to_use15

Even more:

https://www.researchgate.net/post/Deal_with_Outliers_for_5_point_Likert_Scale_Data

Further:

Ordinal lasso regression:

https://www.researchgate.net/post/What_would_be_the_best_linear_regression_strategy

https://www.researchgate.net/post/Can_anyone_help_me_figure_out_the_right_statistical_analysis_for_my_dissertation

https://www.researchgate.net/post/In_the_ordinal_regression_model_should_estimates_coefficient_slopes_and_thresholds_modified_to_accommodate_significant_explanatory_variables_only

Take home: Use ORDINAL LOGISTIC REGRESSION FOR LIKERT

PLEASE SEARCH the RG question section for the remaining 10^k entries.

Best wishes, David Booth

David Eugene Booth thoughts on using a slider anchored to 7-intervals instead of 7-points scale?

• Dario Bonaretti 7points , 20 points, 10^23 points LIKERT SCALES ARE ORDINAL NOT CONTINUOUS. Please read the relevant literature. David Booth PS Abraham Lincoln is said to have asked a man: How many legs does a horse have? The man said 4. Lincoln then said suppose you call the tail a leg, how many?. The man said 5. Lincoln said No it has 4, calling a tail a leg does not make it so. Now to your specific question Consider the set R of real numbers and it's subset,N*=[1,7]. It is true that N* is a continuous set and R is a continuous set Now the domain of the Normal distribution is R and N* is only a proper subset of R Thus any distribution defined only on N* cannot be normal because the domains are different. Hence Normal theory methods cannot apply to your example. Thus OLS regression does not apply. Best, David Booth

Thank you for your response, David Eugene Booth. I appreciate your passion for statistical methods to handle categorical data. I should rephrase my question - When comparing ML with bootstrapping and MLR, what are the pros and cons of one over the other?

Lendi Joy You didn't click on the first reference. It is a study about that. I don't have a passion for categorical data. I have a passion for correct answers. BTW my dissertation was on Robust methods. If I thought that was best, I would say so.

David Eugene Booth This is one example of relevant literature that doesn't conclude you "cannot" use estimation methods for continuous variables with 5+ categories:

Kline, Rex B. Principles and practice of structural equation modeling. Guilford publications, 2016. (page 323)

Also, wouldn't time related variables Age, Seniority N*=(0,∞], or physical proporties weight , height N*=[0,∞] also be subsets of R?

David Eugene Booth, I did look through the resources your provided. The article from the first link is not available through that link. Would you happen to have a direct link to the article?

Edit: I was able to find the article elsewhere and unfortunately, it does not answer my question. My question was not on whether to use ML estimation vs ADF estimation, but rather which robust correction for ML would be better. In the article, the researchers concluded that ADF > MLR > ML in terms of fit statistics with categorical indicators with 5 categories. I understand that assessing model fit is obviously the first step in interpreting an SEM model; however, it is not the only consideration. I also respect your position that a cat is a cat is a cat and to treat it as anything else would be incorrect. Perhaps this article based on a simulation study could provide additional information in that regard: Article When Can Categorical Variables Be Treated as Continuous? A C...

At some point I realize the argument of which estimator and/or which correction to use is simple a citation game and in many ways is just a matter of who you decide to cite. Nonetheless, I am interested in better understanding the differences and advantages/disadvantages between using MLR and ML with bootstrapping.

Dario Bonaretti Certainly those sets would be but that is not what you asked. If you had of asked that, I would say they are but the domains are still wrong. The only way to make a silk purse out a sow's ear is to start with a silk sow. BTW I can't speak about Rex Kline I don't know him or his book. I do know Frank Harrell and his book is as tight as they come. As you saw in the references I gave a number of people think you can use OLS methods with Likert data including my first cite. I agree OLS is more convenient but I am interested in best available.