Model fit during a Confirmatory Factor Analysis (CFA) in AMOS
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- เผยแพร่เมื่อ 14 ต.ค. 2024
- 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...
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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)!
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
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 TH-cam video. I got teary-eyed when I realized I was finally understanding something. Instant subscribe.
Thanks for the kind feedback! Makes it all worth it :)
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)
Dear James, can you give some references for these fit indices. Thank you very much
@@ThanhBinhVu-mj8eg Here you go: statwiki.gaskination.com/index.php?title=References#Model_Fit
Sir how can i improve my RMSEA value if it's showing .000 after one modifications. Plz help
@@lalaliza315 RMSEA should be low. So, 0.000 is as "good" as you can get. No need to improve it.
@@Gaskination thank you so much sir for the reply...
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.
Thank you for the video!
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.
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!!!
Dear James Gaskin,
Thanks for the wonderful online tutorial. I have a proposed model that includes 10 independent, 1 moderator and 2 dependent variables. While testing its “model fit” for the first time, I got GFI = 0.888 and the rest of the measures were just perfect. Then I performed following steps to improve GFI:
1) Co-varied the error terms of the same variables as per the modification indices. Then I got:
GFI=0.890, P-value = 0.123, CMIN/DF = 1.051, AGFI=0.871, CFI=0.991, RMSEA=0.012, PClose=1.0
2) Used your stats tool package “Fit check”. It suggested dropping an item. I dropped that item and got:
GFI=0.892, P-value = 0.158, CMIN/DF = 1.045, AGFI=0.873, CFI=0.992, RMSEA=0.011, PClose=1.0
3) Again used your stats tool package “Fit check”. It suggested dropping one more item. I dropped that item and got:
GFI=0.896, P-value = 0.236, CMIN/DF = 1.033, AGFI=0.877, CFI=0.994, RMSEA=0.010, PClose=1.0
As you can see, all the values were perfect except GFI. There was no significant improvement in the value of GFI even on performing these three steps. Kindly suggest how the value of GFI can be improved in such cases.
I usually have trouble with GFI when I have a lot of variables and/or when I have a lot fo sample size. These two things inflate the chi-square, and GFI is not robust to them. I would attribute it to model complexity in your case (not knowing the sample size).
James Gaskin Thanks a lot for the reply Dr. Gaskin.
Sharma et al. (2005), among many others, articulate that in, context of SEM using AMOS, given the issues with GFI, it has lost its popularity in recent years and therefore its use should be discouraged.
Despite this, recent research papers which use AMOS do consider GFI as a measure of model fit. What's your views regarding use of GFI?
Sharma, S., Mukherjee, S., Kumar, A., and Dillon, W.R. (2005), "A simulation study to investigate the use of cutoff values for assessing model fit in covariance structure models," Journal of Business Research, 58 (1), 935-43.
Sumedha Chauhan I never use it unless the reviewers specifically request it. I usually report CFI instead (as well as cmin/df, RMSEA).
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
Dr. Gaskin, just wanted to thank you for putting together such a great walk-through. I've had CFA / SEM covered in a few classes, but only conceptually. I've used your walk-through with some of the data from my dissertation, and it all makes so much more sense (and, I can actually do the analysis now). Thanks for sharing your knowledge!
Thank you James! You saved my life for my Ph.D. homework.
This is an acceptable approach. My recommendation is to use either a random sample of your data for each, or to use the same data that you will be using for the structural model. Most people do not have the luxury of an abundance of data, so they simply use everything they have for both EFA and CFA (which is what I have done here).
The only thing I can think of is to try to find outliers. This doesn't just mean extreme values, it also means unengaged and erroneous responses. For example, if someone responds with all 3s or with 1, 2, 3, 4, 5, 1, 2, 3, etc... or if they respond to a reverse coded question the same way they respond to regular questions.
Great Video. Should I worry & investigate high values of residuals if the model had a good-fit too? My model has very good values but I haven't deleted stuff with high residuals yet. I am aiming to do an SEM next.
Thanks James :)
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).
Very informative, thanks a lot James.
I am at the point of my PhD where I am considering using SEM on my data. I've got two questions if I may:
1) When you were looking at a whole different CFI, RMSEA and all of these different results, Is there a book or page that explains what these are and what the optimum or acceptable values would be?
2) You said that with bigger samples there are issues in getting a good model fit. My representative sample would be at least of 3000 responses. Is SEM bad?
Absolute champion, James Gaskin ❤
Excellent presentation. Clarity at its best. Thank you very much.
Hello .. Thanks a lot for your prompt replies. I agree with you regarding three factors of Burnout (Third one is LACK OF PERSONAL ACCOMPLISHMENT) but my pilot surveys revealed that Lack of Personal Accomplishment does not effect employee burnout, so I have ignored it for the time being. I shall browse your formative construct and shall reconsider it .. Really greatful.
Thank you so much for taking the time to post this! You may have literally saved my manuscript! I don't know why they don't teach us this in grad school or at least sell a good book on it.
+surfergirl0519 without any offense to the great work James has done by uploading this video, there is a book by Hair et al. named Multivariate Data Analysis. It is fantastic!
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.
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.
I have published a paper in springer a renowned journal using your SEM techniques and cite your statwiki. Thank you for your education vedieos..
This is a very helpful video. I do not know much about using AMOS. I am doing my thesis and I need to use AMOS to do the analysis. Here you have shown example about CFA in AMOS. Can you please tell me if its the same way to analyze SEM?
Thanks for all the time and efforts that you put on these videos.
Do you have a video that shows how to conduct a CFA using AMOS when you have a variable (continuous carriable) with a single item?
Do you have a video that shows how to conduct a CFA using AMOS when you have a variable (categorical carriable) with a single item?
Single item factors (i.e., observed variables) do not belong in a CFA. The CFA is meant for multi-item latent factors. You can bring single variables into the path model after the CFA.
Thanks for your answer. I am sorry I just found out your reply.
I was following what you suggested until I found the following answers. What do you think?
........"single indicator variables can and should be included as they a) increase the testability of the CFA model by adding further challenges, and b) provide validation criteria with which you can judge (by means of the latent correlations) whether the latents you intend to measure are actually what you measure.
Instead of using single items as measured variables, it is better, however, to create measurement models with fixed loadings and error variance to separate the single (measured) indicator from its supposed latent variable. Otherwise they are simply the same and you assume that your indicator is error-free.
Here are some references."
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Hayduk, L. A., & Littvay, L. (2012). Should researchers use single indicators, best indicators, or multiple indicators. BMC Medical Research Methodology, 12(159), 1-17. doi:10.1186/1471-2288-12-159
Oberski, D. L., & Satorra, A. (2013). Measurement error models with uncertainty about the error variance. Structural Equation Modeling: A Multidisciplinary Journal, 20(3), 409-428.
Alwin, D. F., Jackson, D. J., & Jackson, E. F. (1980). Measurement models for response errors in surveys: Issues and applications. Sociological Methodology, 11(1980), 68-119. doi:10.2307/270860
Burt, R. S. (1973). Confirmatory factor-analytic structures and the theory construction process. Sociological Methods & Research, 2(2), 131-190. doi:10.1177/004912417300200201
Duncan, O. D., Haller, A. O., & Portes, A. P. (1968). Peer influences on aspirations: A reinterpretation. American Journal of Sociology, 74(2), 119-137. doi:10.1086/224615
Hayduk, L. A., Pazderka-Robinson, H., Cummins, G. G., Boadu, K., Verbeek, E. L., & Perks, T. A. (2007). The weird world, and equally weird measurement models: Reactive indicators and the validity revolution. Structural Equation Modeling, 14(2), 280-310.
Thanks so much for your great help. After reviewing all steps, I think the problem might lie on entering data step. I usually use four to five Liked scale questions for an item, and three to four items to calculate a variable. However, my only way is to use "mean" to calculate all items, which then go into squares in AMOS model. Could you please help me with an instruction on the issue if possible. You and the Internet are my only teachers. Thank in advance.
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.
This means that you have a variable in your dataset called e1, but you are also trying to name a residual (error) e1. I recommend renaming all e1, e2, etc. to something else since e# is default for error terms.
Dear James,
at first I would like to thank you tremendously for setting up your channel. It has been a great help for the work on my dissertation.
I have a question regarding model fit of the structural model. I followed all your advices on model fit for the CFA, i.e. leveraging the modification indices to adjust model fit. I yield good model fit (Chi²/df = 1.540, IFI & CFI = 0.928, SRMR = 0.064, RMSEA = 0.048) for my measurement model. However, if I introduce my structural model and run it, model fit slumps to Chi²/df = 1.639, IFI = 0.907, SRMR = 0.163, RMSEA = 0.052. Is there any chance to increase model fit in the structural model or do I have to get back to the measurement model? The modification indices do not provide much help anymore, since I have covariate all problematic error terms of indicators at the same factors already. All other high error covariations are between error terms I am not allowed to covariate.
Thanks in advance for any follow-up advices. Best regards from Germany, Christoph
In a structural model, the biggest causes of poor model fit are missing regression lines between variables. So, you might have an IV that has a strong effect on a DV, but it is currently not directly connected to it (but instead indirectly through a mediator). The missing lines are what cause the poor fit. Check the regression weights table in the modification indices output to see if there is some huge relationship you're missing. When writing up your findings, you'll either need to incorporate this new line into the theory (some call this fishing...), or say that this relationship had to be included in order to achieve adequate fit, but that you won't explicitly theorize about it.
James Gaskin Thank you very much for that quick and very helpful advice! Adding another regression line was concerning me, because I haven't hypothesized additional relationships. But I will try it out and then make a decision how to cope with that in the story line of the paper. Best regards, Christoph
1. If they overlap, do one at a time.
2. the p-value in this case needs to be greater than 0.05. I know that sounds weird, but the null hypothesis is that it is not good fit, so if you have a significant p-value, then that means you have not good fit. However, when you have large sample sizes, or complex models, it is very difficult to achieve a non-significant p-value for the cmin.
A great help for my Ph.D study. I didn't tie the covariances in the errors and have low values when discriminant validity is done.
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.
@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.
Dear James
I love your videos. Very easy to understand and not boring at all :)
I have a few questions it would be great if you could please answer.
1- Is it okay to apply CFA and SEM for a larger data set ( approx 1080 cases)?
2- What to do if a few observations of the independent or dependent variable have high skewness and kurtosis?
Also, I could not find a pattern matrix plugin for Amos V26.
1. Yes. AMOS should be able to handle this, as long as the model is not too complex (like 50+ variables)
2. If the variables are measured using a Likert scale, then there is little that can be done. If including the indicators corrupts the measurement of the factor (check reliability with and without those variables), then you might be justified to trim them (assuming you still have at least 3 indicators). If the variables are continuous, you can use two-step normalization to fix them: th-cam.com/video/twwT6FgwlAo/w-d-xo.html
3. Thanks for pointing this out. I've now created a version in the expected folder: drive.google.com/file/d/1pYMCJdh3mmonUnyIu6cslyKyCpc2CQ3P/view?usp=sharing
@@Gaskination thanks a lot . You are an angle.
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" :)
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.
go to the object properties of the error term (right click or double click the error term). Then go to the parameters tab. then type 0.05 or something similarly small in the Variance box.
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.
This video helped me a great deal with writing my master's thesis! Thank you!
Great video! I am trying to do CFA using 11 scales from a survey, and your video has been most helpful! Thank you. However, being statistically challenged, I still have some gaps. AMOS required constraints to the factors/scales, so I put variance at 1 in one scale for each of the 3 broad categories the survey authors identified. How should factor constraints be determined? Also,co-varying with modification indices (common factors) improves model fit, but how/why? Disclaimer needed in write up?
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.
Hello Dr Gaskin, I have watched this excellent video many times and it has been extremely helpful. At about 5min 25 seconds you say you can only create additional paths between items on the same factor. I have not read this anywhere and I was wondering if you might have a reference I could use in my thesis that justifies why as this is an issue for my CFA. Many thanks, louise
Here is a place to start: Hermida, R. 2015. "The Problem of Allowing Correlated Errors in Structural Equation Modeling: Concerns and Considerations," Computational Methods in Social Sciences (3:1), pp. 5-17.
1. Either use the default AMOS sets (first item for each factor) or place the constraint of 1 on the item that loaded the strongest in the EFA.
2. Covarying the error terms accounts for additional covariance represented in the covariance matrix. Model fit is the extent to which the proposed model (your CFA) accounts for the covariances in the data. So, naturally this will improve fit.
We can covary the error terms on the same factor; this just means the items are systematically correlated (probably due to wording or position in a survey). Covarying across factors implies the same thing, so we must be justified in covarying those (look at the wording of the items and see if they are too similar).
Hi James, thanks for all the TH-cam vids; really helpful.
I'm running a multi group CFA (3 groups) and am trying to compare constrained and unconstrained model. What do I need to do to test a constrained model?
2nd question, in journals often in model fit comparison a 95% CI is reported. Where can I find this in the AMOS output? It seems that RMSEA is reported with a 90% CI (or am I looking in the wrong place?)
Hope you can help me!
Thanks!
1. No need to transform. The likert values are fine.
2. These are called Heywood cases. You might try covarying the negative error term with another error term in that factor. If that doesn't work, then you might need to constrain the indicator weights to be equal (set their regression weight parameter to all equal "a" (without quotes)). If you do this for more than one factor, make sure the next one is "b", then "c", etc.
Hope this helps.
Hi, I'm really enjoying your videos so far - thanks for taking the time to post these. One of my initial questions (sorry, may have more in the future!) is about missing data - how come AMOS can't handle missing data? If I'm not mistaken, MPlus and Lisrel can create models as long as missing values are set. Is this a limitation of AMOS or is there some theoretical reason no missing data are allowed that I'm overlooking? Thanks!
@farispt
The theoretical basis is that they are reflective and interchangeable items, which means that they were probably worded very similarly, which means that they probably have a systematically related error (rather than a causal one). So, yes, you can covary the error terms as long as they are within the same factor.
Dear Prof. Gaskin,
Thanks for your great instructive vdos!.
Can you suggest how to test most parsimonious model of a measure on the same group?
Thanks again.
I would do it together. The main point of the CFA is to determine if you have distinct factors for measuring your constructs. In order to avoid tautological constructs, I would recommend putting them all together.
@Gaskination Thank you so much. I am going to share your tutorials with students at Information Systems department at Georgia State University. Really appreciate the work Sir.
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.
Handling univariate outliers in CFA is same as EFA. Yes, you can perform CFA using same data as EFA, although if you have a lot of data, you can also randomly sample a portion for EFA and then use the other part to do CFA. This is considered more rigorous.
Hi, Dr.Gaskin. First of all thank you for your informative videos, they are very helpful.
I am trying to do model fit on AMOS. I have 6 factors(It's Holland's RIASEC theory). Using SPSS, I calculated the cronbach alpha for each factor and they were all above .80. So i thought that in the CFA, the fit indices should also be high. But they were not: The TLI=.592, CFI=.612 and RMSEA=.068. I saw the suggestion on modification indices, however i am not sure how and why they works.I watched your videos, but i did not see one when you go back and modify the model. If you help, i will be extremely grateful. Thank you.
The modification indices identify correlations in the data that you have not accounted for. If you account for the large ones, they will improve your model fit (by reducing the chi-square).
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!!
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.
@@Gaskination Thanks, I now found the missing data in SPSS and it worked out just fine :)
1. Sample size inflates the chi-square, but also inflates the CFI and RMSEA.
2. You could do that. Usually when we have more than 500 sample size, we split it for the EFA and CFA randomly.
It only translates the pattern matrix into a measurement model. If you want to tweak things afterwards to include a 2nd order factor, that is fine. But it can't detect that.
Thanks for your wonderful videos. You are really a God sent messenger for statistically trapped souls!!
One query - my loadings are mostly more than 1 for most of the items in my latent variables.Is that a problem ?? what could it indicate in case its a problem. coz for most of the models I have seen the factor loadings range from .6 to .9.
No, but there are some forum discussions about it on the smartpls website.
Thank you so much. This video has been a great help.
Is there any reference I can refer to for removing items with low loading?
This is an old video, in which I am too casual as I remove items. Generally speaking, it is bad practice to remove any items unless abundant evidence suggests that keeping them undermines the validity of the construct measurement. If you must remove them, then you can cite any paper or text on convergent and discriminant validity, such as the Fornell-Larcker paper: Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of marketing research, 39-50.
Here are some other references you may find useful: statwiki.gaskination.com/index.php?title=References#Constructs_and_Validity
Thank you for the quick response. I checked the output. I don't have a similar problem that you explained in the other video. What I have is unidentified parameters. What can I do for that?
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
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
Ive some hiccups running a CFA on a validated scale.
1) I get a not positive definite covariance matrix on a CFA with 4 factors (each having 3-6 indicators, for a total of 21). I believe its because of unusually high correlations between all indicators, across factors).
2) I had 200+ df, so I correlated all the error terms for those items with significant correlations. Now I get an unidentified model. AMOS points to one factor (and its three items) as the "probably unidentified parameters"
James, your videos are great! Thanks! I'm trying to use CFA to validate my hypothesis that aligning two factors affects a third factor. Do you have a video that discusses that?
Hi James, thanks to your guidance, I hv successfully complete EFA and now moved on to CFA. In CFA, I am invariable seeing factor loadings greater than 1 between latent variable and observed variables. What could be cause of it? How to address it. Covariances between latent variables have come out quite nicely like 0.04 etc. Thanks for your time and advice.
Thanks for your videos which will be my tutorials for my study. I am fresh new to CFA and ask basic questions. I just finished EFA and reduced original 8 factor model to 6 based on my targeted samples. I want to run CFA to confirm and report to journal. So, for CFA, it is ok using my modified scales rather than using the original scale?
Hi there Dr. gaskin.
I was hoping to get some help from you. I've recently done a CFA based on an established model that the original authors proposed for a measure of positive automatic thoughts. In one of the factors, the authors only utilised 2 items. One of my supervisors commented that you need at least 3 items. I've been trying to look for literature that would give me some idea of how to discuss this in this discussion section, and I was hoping that you could point me in the right direction. Thus far, what I've found have suggested that 2 items are fine, just that they should be the exception rather than the rule.
Thanks again for all the videos! Fantastic help!
You are correct. Two items are fine, but should be the exception as they often cause instability. As for literature, I know there is some article that says four items is the ideal, but I really cannot remember what the reference is or even how I might go about finding it (other than iterative searches on google scholar).
Ok, thanks for the information sir. So if I were to include the two-item factor, would I be bale to say in not so many words, "use with caution?"
***** correct. When they work it is fine, but it is not ideal.
Thank you very much sir! Have a good one! Thanks again for all the fantastic videos!
Yes, they will be different. We would test measurement hypotheses (which are uncommon) by examining convergent and discriminant validity and reliability, as well as model fit. We test structural hypotheses (much more common) by developing a causal model and examining the regression weights. Hope this helps. I have videos about this stuff too.
James, thanks so much for your tutorials. They've helped tremendously while analyzing my dissertation data. Do you happen to have a reference for removing items which load under .7, as you show in your tutorial? I've only seen citations for removing items under .35, but using a higher cut-off certainly improves fit and subsequent reliability analyses.
The items should average out to around 0.700, but that means you can still have some under that threshold. I usually cut anything under 0.500 for that reason. As for a reference, you could probably reference anything that says you need an AVE of 0.500 (which usually won't happen if you have items with loadings less than 0.500).
@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).
Yes. You don't have a variable in your dataset called "nature of work". So, it can't be included as an observed variable (a rectangle). hope this helps.
Great video James, very useful. I've a question. I know Amos does not provide the Satorra-Bentler Chi square for non-normal data, but instead offers bootstraping. Can you make a similar video highlighting bootstrapping in CFA with Amos?
I have a video on bootstrapping for mediation, but not with CFA. I'll see what I can do. I'll add that to my list of requested videos.
Thank you James, looking forward ....
Hello .. Thanks James .. You are right, as I have these names repeated in dataset. I shall try again with names changed ..
Hats-off ....
Those decisions are driven by logic and theory. You should end up with as many factors as you intended during your theory development. Formative vs. reflective is determined by the relationship of the items within a factor (see Jarvis et al 2003 on specification). Second order is something we sometimes do when we have broader scope constructs (often formative - see Straub et al in MISQ I believe, not sure what year). Hope this helps.
Thanks again James. I saw it 3 times. Very interesting. I have a question with my data: If the loading of some of the items are more than 1 then what can we do? what was wrong with them?
It might be because you are looking at Unstandardized values instead of standardized ones. Or, it might be because you have only two items on a factor (which can get unstable). If it is because of two items, you might have to constrain them to be equal. You can just go to their properties and give them both regression weights of "aaa". This will force them to be equal.
Thank you very much. Your comments were very helpful. We achieved the final models, and they look prety good. Some of them even have CFI and TLI values of 1 and an RMSEA value of 0. I understand that this happens because the chi-square value is inferior to the model's degrees of freedom (which are 5 or less). But I'm strugling to find out wheter this finding is problematic or not. What is your opinion? Thank you in advance. Best wishes!
This happens when there are too few degrees of freedom. In a path model using composite scores or averages, this is expected. In a latent model, this is suspicious. This would imply that too many errors were covaried (the ideal number of covaried errors is zero).
Thank you very much. We don't have covariated errors in those models. So I'm guessing that this is not a problem. Best wishes.
either:
1. you are looking at UN-standardized values (instead, look at standardized) or
2. you have factors with only two indicators. This is unstable. You may need to fix the two indicators to have the same regression weight. You can do this by naming each of their regression weight parameters "a". (see the object properties for the line to assign these values)
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.
Dear Prof. Gaskin,
At the beginning of the video you said, that a PCLOSE of .000 is not acceptable. After optimizing the model, the PCLOSE
it is still at .000. Why do you think, the model is acceptable despite the bad PCLOSE value? Is a bad PCLOSE value not acting as a KO criteria?
Thanks a lot for the great video an your help,
Michael
Ideal model fit will have a PClose of greater than 0.05. However, model fit is usually a combination of indications. Many use CFI, others use SRMR, yet others use TLI, NFI, GFI, RMSEA, etc. So, when I comment that the model is fine, it is probably not ideal, but fine enough.
hi James, Thanks for all those replies. has helped me a great deal in taking my analysis forward. there are two more queries. 1. How do you merge two tent variables with high covarience (say 1 to 1.05). second as I remove some of the variables in the model with low factor loadings the model fit is improving. how many variables can i go on rmoving. i moved around 15 out of my 38 variables & the model fit went on improving. Is it alright to remove so many variables?
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).
Yes, I saw your statwiki as well. I am sharing it with all my fellow doctoral students. I already sent your videos to all. Can you also please share your data sets that you use for demos?
You could use the Delta CFI test. I can't remember the reference for it, but if you go to google scholar, I bet you can find it. I think the test says that if the difference in CFI is more than 0.01, then the model fit is significantly different. So, if Model 1 had CFI=0.987 and Model 2 had CFI=0.975, then Model 1 has significantly better fit.
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.
@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.
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.
Rely on the pattern matrix. You might also try the Maximum Likelihood approach (instead of Principle Components Analysis or Principle Axis Factoring) because this is the algorithm that AMOS uses during the CFA.
I would look at the modification indices. If that still doesn't work, you might need to look at multivariate outliers (Mahalanobis D-squared). I have a video for this somewhere. Search for multivariate outliers.
Hi James, your tutorial are really great! Would it be possible for you to make a new one dealing with bifactor model CFA in AMOS (how to build a bifactor model in AMOS and how to address model fit issues) ? Many thanks.
Eloïse Sengès Do you mean a CFA with just two factors? I'm not familiar with the term "bifactor model".
James Gaskin By bifactor model, I mean a model where "(a) there is a general factor that is hypothesized to account for the commonality of the items and (b) there are multiple domain specific factors, each of which is hypothesized to account for the unique influence of specific domain over and above the general factor" (Chen, West and Sousa, 2006, page 190).
Example of bifactor model (with a figure illustrating this kind of model page 191):
Fang Fang Chen , Stephen G. West & Karen H. Sousa (2006) A Comparison of Bifactor and Second-Order Models of Quality of Life, Multivariate Behavioral Research, 41:2, 189-225.
This kind of model is an alternative to second order model. They are also known as general-specific or nested models. They are increasingly used in research but there is no methodological information on internet describing how to build bifactor model and how to address model fit issues! We need your input!
Many thanks
Eloïse Sengès Interesting article. Looks like they recommend bifactor over 2nd order. Assessing model fit appears to be the same as for the 2nd order model. The figures they show are simple enough to draw in AMOS. You would draw it just like you would draw a Common Latent Factor: th-cam.com/video/etPciNEgWGk/w-d-xo.html
If you have more factors that don't belong to the higher order factor, then you would simply not connect the bifactor to the items of those other latent factors. I'm not sure about the covariances.
If I could tell you how much I appreciate your work. Thank you so so much
Thank you for your reply! I actually meant matching. Do you have any videos on that?
Hi James, Just want to say a massive thank you for all the youtube videos. Am very thankful. I have a question on the rationale, purpose of adding covariances between error terms. I know it does improve the model fit but not sure if I fully understand it. Also would it need to justify all the covariances in a journal article? many thanks for your help!
Here is a site that can help with this issue: davidakenny.net/cm/respec.htm
Hi James,
Thanks for your videos! They're very helpful and wonderfully explained; great work!
I have developed a questionnaire in which I carried out an EFA on 199 participants and now conducting a CFA with a second sample of 155. I am curious about the justification to covary error terms that may lead to improvements in model fit. I have been reading extensively and it seems that the basis for allowing error terms to correlate should largely be theoretically driven (e.g., similar item wording/content) rather than data driven (i.e., the modification indices). One such reference is: Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: Guilford Press.
I am wondering what your opinion is on this? In my model I have allowed two sets of error terms to covary after looking at their modification indices, however there is another set with a high covariance which I'm hesitant to adjust as I can't think of strong theoretical reason to do so! From the readings I have a feeling I would experience some journal backlash if I were to adjust these 'willy nilly' just to attempt to improve my model fit.
Cheers and thanks again!
I definitely agree. In this video from six years ago I was much more willy nilly than I currently am. I now rarely covary error terms unless there is strong theoretical support to do it. I prefer to delete redundant items instead of covarying their errors.
Thank you @James Gaskin for the great tutorial. I managed to to get a CMIN value of 4.101. would you consider that as a good fit?
if you mean cmin/df, then yes, this is probably fine. but i recommend also looking at the CFI and RMSEA
Yes I meant factor analysis. I want to measure how the alignment between two factors affects a third one. I did EFA and correlation analysis using SPSS between the factors themselves but I'm stuck in doing alignment. I was told to try AMOS and CFA. Your videos are extremely helpful but I can't seem to figure out how AMOS helps in finding alignment. Thanks
These depend on many things. You want to decrease Chi-square while increasing degrees of freedom. The fastest way to do this is to address the modification indices. Also, you may have to identify items that are part of separate constructs but that are highly correlated. If possible, remove one of the two items in order to reduce cross loading.
@ecmlau
I am not familiar with your data, but the reason you may be observing poor fit might be due to misspecification of the constructs. Your constructs might be formative, rather than reflective. And if this is the case, then you may need to use partial least squares, rather than covariance based methods (like AMOS).
Many thanks for your useful videos , In 17:17 you did covariance both e6 and e7. is this academically correct? My supervisor told me this I should not do that. If right do you have any reference for it. Many thanks again.
This may also be due to sample size. Large sample sizes artificially inflate the Chi-square. So, lower thresholds are acceptable for higher sample sizes. A "large" sample size is greater than 250. This is according to Hair et al 2010 "multivariate data analysis" book.