Assessing and managing nonnormality in SEM using AMOS

[@rustumsalvana4368]

Thanks greatly help, particularly the sources with specific pages

[@DeepakSharma-pr9nd]

It's a very helpful video. Thank you!

[@seongyonglee5747]

Wow. This lecture is awesomely helpful!!

[@mikecrowson2462]

Thanks, Seongyong. I appreciate you watching!

[@aliamini4698]

That was so helpful Mike. The issue of a "correct model" is seemed to me kind of weird! there seems to be a lot of conteroversies around much of the criteria and indeces in SEM. Most well-known of them which is argued by meny of authors is the chi-sqaure with its p-value as an exact fit hyphothesis. I hope I could find more about the Bollen-Stine bootstrap p-value and its ctiticism. Thanks so much.

[@zachariamhmed]

Thank you. I have multivariate outliers,when I deleted the out liers every time the quality of model fit indices become low each time,and there is no fault with enter data....etc. For that reasons I make a decision to keep the outliers. and dont lose sample size (220) Is that correct? Note:I use amos (cb-sem) with bootstrap

[@karthe345ggffhgcg]

The more the sample size becomes ,the less the normality concerns.

[@nargisali7298]

Hi Mike, Thanks for sharing knowledge through youtube. Can you please tell me how to check the intention to choose product varies by ethnic group in Amos?

[@kepo364]

Hi. If the sample is approx 20000, do we have to meet multivariate normality? (provided we use the bootstrapping method)

[@tsegayewedajo949]

Not only the facts you are dealing with but most importantly the generosity you display attracts me to follow your sessions. In data analysis which is based on primary data, AMOS is a vital instrument. However, some features like Reflective-Reflective, Formative-Reflective models analysis, which are simply preformed with SmartPLS, are not visible for me with AMOS SEM. Is there an option for such analysis with AMOS? How can I run otherwise with AMOS to perform those model analysis?

[@mikecrowson2462]

Hi there. Thank you for your kind words. To your question: Unfortunately AMOS is seriously limited in the things it can do. I am not a huge fan of it, but make the videos for folks who are learning AMOS in classes or still using it for their research. There is no way to perform analyses using a PLS algorithm in AMOS. When you refer to Reflective-Reflective and Formative-Reflective analysis, I'm not exactly sure what you are meaning. If you are asking about including formative and reflective indicators in the same model it is possible to do this using MIMIC modeling. I have not spent a lot of time on this. However, Kline (2016) has a very nice treatment of formative measurement models in SEM on pages 352-360. I hope this helps!

[@MrDouglasrussell]

Hi Mike, thanks for the great video. Does this video also apply to confirmatory factor analysis? (As I am not even looking at chi-square statistics). Not sure wif I need to bootstrap or not. (my data is not normally distributed - its skewed and kurtoic)

[@mikecrowson2462]

Hi Douglas. Thanks for your message. Yes, the video also applies to CFA, as the assumption is that your indicator variables are normally distributed. If you are testing the factor loadings for significance (which you probably are), then you would want to perform the bootstrap. The Bollen-Stine bootstrap is useful when making decisions about the overall fit of the model. I'll be honest. It's not my favorite approach with non-normal data when evaluating overall model fit. The options that seems more often utilized is to use the Satorra-Bentler chi-square (and derivatives thereof), which are available through other programs, such as R/Lavaan package & Lisrel). Hope this helps!

[@MrDouglasrussell]

@@mikecrowson2462 Thanks Mike. I'm using AMOS so can only do the Bollen-Stine (however the chi-square is coming up significant anyway but the model is a good fit otherwise - so not sure where to from here). Also, another quick question again. I have 73 items in my CFA. Too many (I think) to make a publishable path diagram (struggling to fit things in). My co-author has suggested a table with all 73 items and the 3 key results (Squared Mult Correlations, intercepts and std residuals) however I'm wondering if 5 separate diagrams showing the four factors and each of those and then a fifth showing the correlations between latent factors. Your thoughts are greatly appreciated.

[@mikecrowson2462]

Hi Douglas, one possibility is to run the model with and without bootstrapping and report on the overall fit using your standard CFI, RMSEA, etc. (from the original model) and the Bollen-Stine test (using bootstrapping) and treat them as as set of indicators of overall fit. Of course, with 73 indicators, I can see how overall fit can be a problem, as there is ample opportunity for misspecifications to "add up" in the model. Another possibility is to assess the individual indicators for non-normality (you get skewnness and kurtosis statistics when you ask for "tests of normality" under the options menu - provided you have complete data and haven't clicked "estimate means and intercepts"). From there you could try non-linear data transformations (particularly of the worst offenders) in SPSS to try to see if increase the likelihood of your data exhibiting greater multivariate normality - and then run the model in the standard way (if you achieve normality) to obtain the other fit statistics. Or you could do a combination of this and what I noted above. Short of using a different program that would allow for the Satarra-Bentler chi-square to be estimated (along with bias corrected standard errors & other possible fit indices derived from the scaled-chi-square) that's about all I can suggest on that front. But, one other thing to consider - which is ultimately the most important thing - is the issue of how the model itself is specified: If you are accounting for non-normality using the Bollen-Stine and finding evidence of model misspecification, then you might need to reconsider how you have specified your model. It could be 4 factors - or maybe more. On the other hand, it could be that there is a need to add correlated errors or need some other specifications. If you are adopting kind of an exploratory approach, you could use modification indices option - again, you can only do this with complete data - to explore the possible benefits that adding additional parameters might give to your model. I can't recall if you can request these if you have bootstrapping selected. But if you can't, you could always turn it off and run the model in the standard way - examining the model fit indices for suggestions about possible parameters to add. Just make sure the additions are defensible. I know this is a lot of info, but there are a variety of possible ways to go!

[@widadbenzine4832]

When testing the data distribution of the original model using bootstrapping it appears to be non-normal, but when performing confirmatory factor analysis, the distribution becomes normal. Is my work in this way correct?

[@Pleinpotentiel]

I am not sure how to interpet and report these results... do you have something to help me with that ? What should i report in my article when using Bootstrapping ?

[@darkdistinctplaces]

Dear Mr. Crowson, thank you very much for the video! So, how to decide which bootstrapping method to use? When I do ML, I have significant effects. But when I do Bollen-Stine, the model doesn`t fit at all...

[@mikecrowson2462]

Hi there, Kostiantyn. You can use the Bollen-Stine to evaluate the overall fit of the model in cases where you have evidence of a violation of the assumption of multivariate normality for the endogenous variables in your model. If you have evidence of a violation, you could theoretically report on both the standard fit indices, and then supplement with a statement of the results from the Bollen-Stine given the violation. The reason Bollen-Stine might be used is that one of the main effects of the violation of normality is that it inflates your chi-square (computed using ML estimation). Since chi-square is used in the computation of many of the additional fit statistics, the violation can lead to the impression that the model is a poorer fit to the data than it really is. So, you could theoretically reference the Bollen-Stine as an additional source of information concerning model fit, if the normality assumption is not met. By the way, if the Bollen-Stine p-value is not indicating significance, then that's actually considered an indication that your model is a reasonable fit to your data. If it is significant then that would signify lack of fit. Another effect of a violation of normality is that the standard errors for your regression parameters can become too small, thereby increasing the risk of type 1 error. So you can use bootstrapping of the parameters in your model to generate bootstrap standard errors to test those parameters for significance. I'll be honest. I personally prefer programs such as Stata or Lavaan to deal with the problem of non-normality, as robust measures of model fit and robust standard errors can be easily generated. In AMOS, the above is your best bet. I hope this helps!

[@darkdistinctplaces]

​@@mikecrowson2462 Dear Mike! Thank you very much for such a comprehensive answer, I really appreciate it. But is it still valid to report significant effect estimates and squared multiple correlations if the general model is a bad fit?

[@mikecrowson2462]

@@darkdistinctplaces Typically, if the fit of a proposed model is poor, then one proceeds to respecifying that model by adding or removing parameters to improve the fit. Sometimes folks rely solely on modification indices or other empirical considerations alone when making decisions about what to modify in the model. However, it is extremely important that any modifications you make to your original model comports with theory and logic. It is also important to report on your original model and any modifications you make during the course of re-specification. You shouldn't present your final re-specified model as though that was what you originally proposed. cheers!

[@hibald9458]

Thanks, it's a great video Please, I want to ask about the assesment of normality in path analysis with observed variables, if we should put the variables in amos like CFA to analyse multivariate normality ( in path analysis with observed variables) ?

[@ghadalaajili9755]

Thank you this was helpful ! I tried doing the normality test on a covariance matrix but no result showed, is it because it needs to be an initial matrix (raw) ?

[@mikecrowson2462]

Hi. You won't get results if you have missing data on any of your variables and/or if you have Estimate Means and Intercepts clicked under Analyze menu.

[@mikecrowson2462]

Check on whether either of these issues are present

[@ghadalaajili9755]

@@mikecrowson2462 actually no, I checked both of those issues and I don't have them!

[@nuwanchathuranga7226]

Is this measurment model (CFA) part in SEM? I can't see a SEM, please explain

[@mikecrowson2462]

Hi there. I'm not sure I follow your question. CFA is one type of model that is performed using SEM (the other models are path analysis with measured variables & path analysis with latent variables). Typically, a measurement model (using CFA) is tested first prior to modeling a path analysis with latent variables (at a second step). By the way, there is information underneath the video description, including the raw data, the AMOS file used to generate the results, and a powerpoint. Hope this helps!

[@Pleinpotentiel]

I have a question. I get the same model fit when i'm bootstrapping my model as when i do the maximum likelihood method. Is it normal ? Is there something that i am doing wrong ? Thank you

[@mikecrowson2462]

The standard fit indices are all generated using ML estimation, even if you are doing Bollen-Stine bootstrap to evaluate model fit in the presence of non-normality. So, they will be the same irrespective of whether or not you choose to use Bollen-Stine bootstrap. However, you can think of Bollen-Stine as an additional piece of information (or perhaps the primary model fit information) for making decisions about fit in the presence of non-normal data.

[@Pleinpotentiel]

@@mikecrowson2462 Thank you ! Great video by the way.