Model fit during a Confirmatory Factor Analysis (CFA) in AMOS

This is a model fit exercise during a CFA in AMOS. I demonstrate how to build a good looking model, and then I address model fit issues, including modification indices and standardized residual covariances. I also discuss briefly the thresholds for goodness of fit measures. For a reference, you can use:
Hu & Bentler (1999) Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives, Structural Equation Modeling: A Multidisciplinary Journal, 6:1, 1-55
Generally speaking, it is not good practice to covary error terms. See here for an explanation: statwiki.gaskin...

[@Gaskination]

Here's a fun pet project I've been working on: udreamed.com/. It is a dream analytics app. Here is the KZbin channel where we post a new video almost three times per week: kzbin.info/door/iujxblFduQz8V4xHjMzyzQ Also available on iOS: apps.apple.com/us/app/udreamed/id1054428074 And Android: play.google.com/store/apps/details?id=com.unconsciouscognitioninc.unconsciouscognition&hl=en Check it out! Thanks!

[@Gaskination]

I usually do at least the following three: 1. CMIN/DF: should be between 1-3 (this is a measure of absolute fit) 2. CFI: should be greater than 0.95 (this is a measure of relative fit) 3. RMSEA: should be less than 0.6 or so (this is a parsimony adjusted measure of fit)

[@ThanhBinhVu-mj8eg]

Dear James, can you give some references for these fit indices. Thank you very much

[@Gaskination]

@@ThanhBinhVu-mj8eg Here you go: statwiki.gaskination.com/index.php?title=References#Model_Fit

[@lalaliza315]

Sir how can i improve my RMSEA value if it's showing .000 after one modifications. Plz help

[@Gaskination]

@@lalaliza315 RMSEA should be low. So, 0.000 is as "good" as you can get. No need to improve it.

[@lalaliza315]

@@Gaskination thank you so much sir for the reply...

[@Gaskination]

Hi Anthoula, I am unable to reply to you directly for some reason. So, I will reply here. Negative error variance can be caused by several things. You might take a look at my "iteration limit reached in amos" video for some ideas on how to fix it. Also my CFA CMB video from the SEM series shows some tips for this.

[@mikefung5463]

Hi Dr. Gaskin! You are helping many people. Do you know that?. After watching your tutorial, I can solve my problem. Thank you so much!!. Now I am preparing for final defense in this month. Thanks again!!. Wish you all the best!!. Mike (from Taiwan)!

[@heckler2.022]

I am feeling and doing exactly what you did 8 years ago, wow. preparing for my final defense this month and here to thank Dr. Gaskin

[@Gaskination]

hi Sabin Khadka , KZbin wouldn't let me respond directly, so I'll respond here. You can simply constrain the error variance to a small positive number (like 0.05). This might fix it. If not, it is indicative or other underlying issues. You might remove an error covariance if you have one. Or you might identify if two items are too similar.

[@Gaskination]

1. Perhaps you are accidentally looking at unstandardized loadings. Make sure you look at standardized. 2. Dave Kenny has something to say about covarying error terms: davidakenny. net/ cm/ respec. htm

[@MsSerenaSasi]

Thank you for the video!

[@victoriaw7558]

May God (or whoever or whatever) bless you, Dr. Gaskin! You cou can spend weeks and months paying for courses that don't do anything except raise more questions & insecurities, and then comes along such a selfless individual who easily explains everything in a 10minute KZbin video. I got teary-eyed when I realized I was finally understanding something. Instant subscribe.

[@Gaskination]

Thanks for the kind feedback! Makes it all worth it :)

[@Gaskination]

I would recommend following my SEM Series Playlist that takes you through data screening, EFA and then CFA (and then a bunch of stuff after that as well). Just click on my name, then find the playlists on my channel. Find the one called "SEM Series".

[@piermarcoconsiglio8825]

Hi James. The procedure that you used: dealing with covariances' errors and covary errors by looking at the M.I.... can be explained saying as followed??: "you used the expected parameter change (EPC) in combination with the modification index (MI) and the power of the MI test to detect model misspecifications" or it's not correct?? Thanks in advanced, best regards

[@Gaskination]

Yes, that is a correct statement. However, be aware that this practice of correlating errors is widely considered bad practice. Here is a bit of discussion on it: statwiki.kolobkreations.com/index.php?title=Citing_Claims#Covarying_Error_Terms_in_a_Measurement_Model

[@Gaskination]

This is an estimation problem due to items having really high correlation/communalities. To fix this, you might want to try using maximum likelihood (as opposed to principal axis factoring, or principal components analysis). You might also attempt to constrain the number of factors to a few alternative models (like try six instead of five). You might also see if there are items that are nearly identical in their wording, and eliminate one of them. Hope these suggestions help.

[@cunghoctienganh]

Hi James, I am still a bit confused about Modification index. If the Model fit is good and there are some MIs having large values, should I just leave the MI or should I covary the errors? Thank you

[@Gaskination]

I would recommend avoiding covarying errors if at all possible. So, if model fit is already good, then don't covary the errors.

[@cunghoctienganh]

@@Gaskination Thank you :)

[@Gaskination]

+Sabin Khadka, sorry for the delay in responding. KZbin has decided to stop notifying content creators when users post comments... In AMOS you can do it: kzbin.info/www/bejne/mqSyhGyqhs-rjZo

[@toanpham2040]

omg. This is exactly what i'm looking for. Thanks for your videos, it's so helpful to solve my problem with model fit. Love you from Vietnam

[@dn2042]

Hi Mr.Gaskin! Is there a maximum number of covarying the error terms by examining the modification indices? I mean can one say that X number of correlations is too much to be acceptable? I had to link 11 errors to each other in total (within the same factors), I know it is not a good way of doing it but I had to do it to reach the desirable cut-off values. Is there a refrence that I can support my self? Thank you.

[@vivianroth7829]

Dear @james gaskin, the video is really helpful! I have a short question: When I select for "modification indices" in my AMOS model and try to calculate it, I get the following error notification "modification indices cannot be calculated with incomplete data" - do you have a tip for me on how to overcome this and still be able to calculate the modification indices? I did tick the box at "estimate means and intercepts". Would be great to hear from you :) Thanks already!!

[@Gaskination]

If you have missing data, then you cannot calculate modification indices. So, either you must impute that data in SPSS/Excel (and then uncheck 'estimate means and intercepts'), or you will need to work without modification indices.

[@vivianroth7829]

@@Gaskination Thanks, I now found the missing data in SPSS and it worked out just fine :)

[@Gaskination]

I do, but I am fairly expensive. Instead, I am holding an SEM boot camp on July 15th-19th to help out those who want to learn SEM. I have also made dozens of videos and a wiki for people to learn on their own. If you happen to be independently wealthy or you have some sort of grant or funds to pay for the consulting, then we might consider other options. My email is james. gaskin @byu. edu

[@Gaskination]

Oops! I somehow missed this comment. Sorry about that. And thanks to Jonathan Stermac for answering for me. Jonathan is right. Using the latent factor icon to build the latent factors automatically assigns the constraint to the first indicator. So, I did not bring attention to it because it is done behind the scenes. You are correct that the model will not run if left freely estimated.

[@Gaskination]

My apologies, for some reason I thought you were in the EFA stage. During the CFA, if you have this problem, it is usually because you only have two items on a factor (if that is the case, then try to constrain those two items regression weights to the same thing, like "fixed"). If that is not the case, then you might look at the loadings to see if one loading is in the opposite direction of the others. If so, then either constrain it, or remove it. I hope this helps.

[@Gaskination]

Likely this is because you have a factor with only two indicators. Is this the case? If so, does one of them have a standardized regression weight greater than 1.00? If so, you may need to constrain that regression weight to be equal to the regression weight of the other indicator by typing "a" (without quotes) in the regression weight box for that line, and then constraining the variance of the latent factor to equal 1. Hope this helps!

[@Gaskination]

1. loading > 1 is okay if unstandardized, but not if standardized. If standardized and >1, then you might have a negative error variance that needs to be constrained to a small positive number. 2. That is the right order, although I almost never look at standardized residual covariances unless I simply cannot achieve good fit any other way.

[@Gaskination]

The idea is to remove as few as possible, but not to have fewer than three items per factor if possible. Sometimes two items works, but often leads to instability. I cannot think of a good reference for this off the top of my head, and I do not have one handy. Just go to google scholar and search for "confirmatory factor analysis" guidelines.

[@Gaskination]

If you are aiming to confirm your factor structure, then I would run a bootstrap to determine the significance of the path weights/loadings for each item. However, if you ran a successful EFA, then you should have no problem conducting a CFA in AMOS using reflective factors.Then you could also assess model fit.

[@Gaskination]

Yep. I'm a faculty member at Brigham Young University. I made all of this stuff precisely because all the other material on SEM and using AMOS is soooooo esoteric... If you check out my channel (click on my name) you'll be able to see all the videos I've made for AMOS and SPSS, and you'll see a link to my wiki. Hopefully this is helpful.

[@Gaskination]

honestly, those values do not sound so bad. Maridia's cr is a bit strict. You can try the transformation to see if it helps. I cannot remember which transformation for which issue, and I don't have my books handy to investigate. If you look at Hair et al 2010 "Multivariate Data Analysis", that book has a chapter or section on which transformation to use and when.

[@Gaskination]

@ATarhini I don't know if there is a right or wrong answer to this. I would include in the CFA all latent variables that I intended on using in my model. This would establish that they are distinct constructs. Moderators, in particular, should not be strongly correlated with the other variables in the model, so I would include them just to make sure they meet this criteria.

[@Gaskination]

@AtyDeh It definitely works. I'm sorry you are not able to watch it. There may be filter issues at your location. If you are trying to access it from work, then they probably block youtube. If you cannot access it from home, then you probably just need to try again another time. In the meantime, feel free to refer to my wiki for info on model fit: statwiki. kolobkreations. com

[@pooranimani3925]

Sir, from the day i began my tool standardization i had sincerely learned using AMOS through your videos. I post this here as a gratitude, since this was the first video of your i watched. And today, when i have doubts on CFA or SEM, I jus type your name on youtube. Thankyou so much.

[@Gaskination]

You can try this. The argument against it is that you need to definitively establish evidence that your IVs are not the same as your DVs (i.e., that there is sufficient discriminant validity) or else you are running up against an issue of tautological correlations (e.g., age predicts experience).

[@Gaskination]

I have some videos to help you proceed. Check out my SEM series EFA video. The whole SEM series should be helpful. The EFA one shows how to work with mostly clean EFAs. For some instruction on how to deal with messier EFAs, watch my SEM Bootcamp about EFAs. I work through a very messy one in that.

[@Gaskination]

There must either be some missing data, or you have blank rows at the bottom of your dataset. Otherwise you could uncheck estimate means and intercepts. I would not remove items with loadings greater than 0.600. The loadings just need to average out above 0.700 for each factor.

[@Gaskination]

If EDU and EXPER are observed or single indicator variables (rather than reflective latent variables), then you would actually exclude them during your CFA. If they are latent, then include them. I'm not sure why you would want to drop attitude and attention...

[@Gaskination]

what version of AMOS are you using? RMR and GFI should come out in the model fit section. The estimate means and intercepts cannot run at the same time as certain other options (like modification indices). So you need to uncheck it, but you can only do that if you aren't missing any data :)

[@sabinkhdk]

Hi James- Thanks for all your helpful comments. If I want to compute factor scores for each individuals participants/factors from the CFA model, how would I do it? While doing EFA, SPSS would allow you to save the factors scores (using regression, Bartlett and Anderson-Rubin) but AMOS won't. I found a blog where it suggest to standardize the original scores and muliply with factor loading scores and sum them up. Is this a correct approach? If yes, do you know of any literature that I can cite for this approach. TIA

[@Gaskination]

google it. tautological means you are using X to predict X. You are saying that age predicts experience, when in fact, experience is simply a byproduct of age. It's like, the amount of hair on your head predicts the extent of baldness.

[@Gaskination]

Many people choose to examine them separately on the basis that the IV and DV are supposed to be highly correlated. I would never do it this way, but I have heard many who preach this philosophy. I don't know of any references for it though...

[@Gaskination]

I'm not sure I understand the question. If you want to see how few items you can use to still result in a reliable latent construct, then you could use the new video I created to show how to improve reliability. But I'm not sure that was your question.

[@Gaskination]

0.700 or higher is the generally agreed upon "good" factor loading, but really it depends on your sample size and measurement error. Hair et al "multivariate data analysis" has a table that discusses the minimum threshold based on sample size.

[@Gaskination]

Literature says the ideal is four items. Logic says the optimal 'minimum' is three (for stability's sake). Practice says that you can sometimes get away with only two (but this often leads to instability - e.g., standardized loadings greater than 1.00).

[@Gaskination]

I'm sorry I do not. Do you have anyone in your department or college that is clever with AMOS? If not, you could email me your model and data and then I could try to troubleshoot it in my freetime. My email is on my Channel homepage.

[@Gaskination]

I don't know if you need a reference for it. It is simply mathematical. If you increase the sample size, the chi-square increases. If the chi-square increases, the p-value decreases. So citing this would be like citing a more complex version of "1+1=2" :)

[@Gaskination]

It is somewhat subjective. You want to keep all you can and still have good validities. The numeric cuttoff would be an average loading of 0.70. But that means you could have one of 0.90 and another of 0.50. You just want them to average out above 0.70.

[@Gaskination]

You want to use the same dataset to run the EFA and the CFA? Yes! That is the ONLY way to do it. No literature support needed. You explore the factor structure in the EFA and then confirm it in the CFA. You can't do that if you switch datasets.

[@Gaskination]

@ATarhini It depends on if it is adding any value. If it is truly contributing to the factor, then keep it, if it is not, then drop it. covarying the error terms (which is what I assume you are talking about) is just one way to keep it without causing issues.

[@Gaskination]

@vyeniaras Additionally, you may not want to let go of a certain item because it is crucial to your construct (however, this should not be an issue when using interchangeable items, as should be done for reflective constructs).

[@tienganhcham]

Hi James, is it acceptable when the TLI and NFI are close to 0.9, for example, 0.87? All values in my analysis meet the goodness of fit but the TLI and NFI are not greater than 0.9. Should I remove some more items so that it will be greater than 0.9? Or it is still acceptable if the values are close to 0.9? Thanks again James

[@Gaskination]

I never report TLI and NFI (I usually just use CFI, RMSEA/PClose, and SRMR). Model fit has many measures. If there is enough evidence that model fit is good, then a couple metrics suggesting it is borderline is probably not a problem.

[@tienganhcham]

James Gaskin thanks, you saved my life

[@Gaskination]

I don't understand. Do you want to match two factors with a third factor? And what do you mean by matching? Do yo mean a cluster analysis? Factor Analysis? something else? Sorry. I've never used matching in my studies.

[@Gaskination]

EFA should be performed whenever you are using new data, even if the variables are from other studies. And you can see why... You can try to jump to CFA, but you will find that you have discriminant validity issues.

[@Gaskination]

1. Hair et al 2010 "Multivariate Data Analysis" Table 12-4, p. 654 2. Wow! that is a lot! That's great! Just realize you might struggle achieving good fit, but this is not unexpected when you have such a large sample size.

[@Gaskination]

I assume you mean the covariance of errors. This is to account for systematic correlation of errors (usually due to similar wording of survey items). See David Kenny's website about this: davidakenny. net/ cm/ respec. htm

[@Gaskination]

The most likely reason is because the model didn't fully minimize or converge. The iteration limit was reached or something like that. Check out my video on reaching the iteration limit. Hopefully that will help.

[@Gaskination]

I have a few videos that show how to go from spss data to measurement model and then structural model. I just created a new series on my channel for this. Check it out. It's called "SEM Series". Hope these help.

[@Gaskination]

smellofstrings: The reply function on KZbin video pages is not working currently, and KZbin is trying to fix it. So, until then, I will reply to your questions directly on your Channel instead of here.

[@Gaskination]

No. I mean it literally. You might have accidentally drawn a pixel sized ellipse on the screen. This sometimes happens if you just click on the modeling area instead of dragging out the ellipse.

[@Gaskination]

No. I mean it literally. You might have accidentally drawn a pixel sized ellipse on the screen. This sometimes happens if you just click on the modeling area instead of dragging out the ellipse.

[@Gaskination]

1. see dave kenny's website about this: davidakenny. net/ cm/ respec. htm 2. I have several videos about this. Go to my channel by clicking on my name. There you will see all my videos (about 80).

[@Gaskination]

yes, you can. Just draw the whole thing at once. The only issue here is that you won't be able to assess discriminant validity between endogenous and exogenous variables; only the exogenous ones.

[@Gaskination]

I have a few videos on moderation in AMOS. My most recent one is part of an SEM Series playlist. Click on my name to view it in my channel. Or just search google for "SEM Series Moderation"

[@Gaskination]

Sometimes amos doesn't like spaces in the factor names... It can handle underscores_ or hard returns, but not spaces. It also won't allow math symbols like - + / * ( ) =, or possibly other like $%^&#@!

[@Gaskination]

again, if they are greater than 1.0, that is probably because they are on a factor with only two items. If this is the case, then do as instructed in my advice previously given (#2).

[@Gaskination]

1. probably means you have a 2nd order factor, not a bunch of first order ones. 2. I would just do them one at a time and check model fit each time. Then stop once you achieve good fit.

[@Gaskination]

No. More sample is always better. It better represents the population of interest. You can always reduce the sample size after collecting the data by randomly sampling your dataset.

[@Gaskination]

The reason is because you named one of your latent variables (in the circles) the same name as one of the variables in your SPSS dataset. You need to name it something different.

[@Gaskination]

a p-value for the model fit should be greater than 0.05 (although this is often difficult to achieve). The p-value is an indication of poor fit, so we want it to be non-significant.

[@Gaskination]

Sounds like you already have sources to support your model fit. You don't need my additional confirmation. For thresholds I've put together, refer to my wiki: statwiki. kolobkreations. com

[@Gaskination]

Yes, if everything else is good except the p value is less than 0.05 (which is actually bad in this case), then you can report good fit (technically it's "not bad fit").

[@Gaskination]

I usually ignore all standardized residual covariances, but if you are going to look at them, pay attention to the absolute value of them, negative or positive.

[@Gaskination]

No, because 2nd order factors are not represented in the EFA. However, you can modify the CFA to accommodate a 2nd order factor after using the plugin.

[@Gaskination]

David Kenny is a guru on many statistical matters (primarily mediation), and his thoughts on the matter can be found here: davidakenny. net/ cm/ respec

[@Gaskination]

No problem. It just means they are inversely correlated. This means that when one goes up, the other goes down. This is not a problem at all.

[@Gaskination]

Make sure you include your DVs so that you can demonstrate discriminant validity between IVs and DVs. It is a big mistake to not include them.

[@Sonnycpa]

Thank you James! You saved my life for my Ph.D. homework.

[@Gaskination]

I'm not sure. I'd have to see it. You can email it to me if you want (the .amw file and the spss dataset). james. gaskin@ byu. edu

[@Gaskination]

PLS was not meant for model fit because model fit is based on the covariance matrix, but PLS does not rely on the covariance matrix.

[@Gaskination]

I used smartpls because AMOS is not good for formative models. You can just take one dimension, but then you need to justify it.

[@Gaskination]

CFA is done using AMOS, not SPSS. Although you can obtain similar results by just doing an EFA (see my video on EFA in SPSS).

[@Gaskination]

So then you need to only address the problems with IMAGE, not the rest of the factor. As for skewness, no, 1.6 is reasonable.

[@Gaskination]

I'm not sure I understand the problem. Perhaps you have not requested standardized estimates in the output tab.

[@Gaskination]

I would not include the single indicator variable in the measurement model. It will likely cause instability.

[@Gaskination]

Watch my playlist called "SEM Series". This will show you everything to do from start to finish. And yes, you need data to do a CFA.

[@Gaskination]

Report Factor Correlation Matrix (see my validity video). Bootstrap during CFA does not affect model fit.

[@SuzetteScheuermann]

Dr. Gaskin, Thanks so much for the excellent step by step! It was priceless in my assistance with a graduate student soon to be PHD.

[@Gaskination]

No. The criteria is the same. A non-significant p-value indicates "not poor fit" (i.e., good model fit).

[@Gaskination]

It could be any number of things. What is the error it is giving you? What does the error say?

[@Gaskination]

@urownsherry What are the errors? you can email me directly at james. eric. gaskin@ gmail. com

[@011-salsabilaoktavianiputr7]

Hello Mr. James! Thank you for this video. After learning amos dor 2 months, I can solve my problem related to Badness of fit of my mediation model. God bless!!!

[@Gaskination]

3. The conservative estimate is 20x the number of indicators. The liberal estimate is 5x.

[@Gaskination]

It did that because they were all selected (blue highlight). Deselect them first.

[@ThanomsilpJankanakittikul]

Thank you for the video

[@Gaskination]

Emanuele Fino If they still demonstrate sufficient discriminant validity, then just move forward. Otherwise, you might want to consider making them a 2nd order factor (reflective). This will probably turn out better results than a single factor with all items.

[@detful83]

Thanks you!

[@namiraratu7270]

James Gaskin if the data not good in all criteria lika cmin=10, Rmsea>0.08, the IFI, TLI,CFI >0.9 and AGFI, GFI >0.9, my result not good in all criteria. How could i do?

[@Gaskination]

No, but there are some forum discussions about it on the smartpls website.

[@cunghoctienganh]

Hi James, one of the examiners asked me what kind of SEM I am using for analysis, is it PLS SEM or Covariance based SEM? I have been learning a lot from your videos, but I still cannot find the answer for that question. Thank you.

[@Gaskination]

Software like AMOS is covariance based. Software like SmartPLS is PLS SEM.

[@rurazar1686]

@@Gaskination This is another question entirely. But I was wondering if newer iterations of AMOS still require you to redefine the constrained regression weight of an item, upon removing it from the model? As was shown in 6:35

[@Gaskination]

@@rurazar1686 Yes, this is still not done automatically. IBM has not really updated the software, despite coming out with "new" versions each year.

[@rurazar1686]

@@Gaskination Thanks for your reply James! Quite interesting to see how a function like this has still not been implemented yet. I would imagine that this is not entirely a very complex feature to add. Moreso, just for ease of access and for convenience's sake. As I can potentially see this as being quite a repetitive task if let's say you might have a lot of constructs and items attributed to each construct in any given model.

[@Gaskination]

@@rurazar1686 agreed. I wish they would update their software. That would save me a lot of time building plugins and estimands :)

[@Gaskination]

Low residuals are good. I don't think I understand your second question.

[@excelgarden301]

Dear james, After the master validity plugin installed and even get displayed under plugin menu...Am unable to run it because od the error message "Object reference is not set to an instance of an object ".please guide me how to fix it.

[@Gaskination]

I don't understand the first question. You can have negative skewness.

[@Gaskination]

you can send the screenshot. My email is james. gaskin@ byu. edu

[@thechenmin]

Hello, Prof Gaskin; I remember that you mentioned the citation sources of covariate pairs, and their modification indices are high. But I can not find the exact video. Could pls tell me which paper I would probably cite??? Thank you so much.

[@Gaskination]

Generally speaking, it is not good practice to covary error terms. See here for an explanation: statwiki.gaskination.com/index.php?title=Citing_Claims#Covarying_Error_Terms_in_a_Measurement_Model

[@Gaskination]

not very good numbers. Is there any more fitting you can do?

[@Gaskination]

yes, but it is better to use logistic regression in SPSS.

[@Gaskination]

Use the pointer hand, the hand with one finger pointing.