Dear Farimah,

In CFA models there are some displays concerning the fitness level of your model. If these displays are in the suitable ranges which are widely known in the literature, do not worry about the factor loadings. But I strongly recommend you to conduct a EFA first to assess your variables then go on with CFA. In EFA it is widely accepted that items with factor loadings less than 0.5, and items having high factor loadings more than one factor are discarded from the model. You can filter your model via EFA.

Feel free to ask any question.

Good luck

Hi,

Your question: What is the acceptable range for factor loading in SEM?

Kindly see the following link:

http://core.ecu.edu/ofe/StatisticsResearch/SEM%20with%20AMOS%20II.pdf

http://www.jblearning.com/samples/0763755486/55485_CH14_Walker.pdf

Dear,

Your question is very much interesting.  KIndly see the attached paper, if you have any doubt kindly reply to me.  I will clarify your further doubts.

Thanks.

with best regards.

Thank you dear Mr. Büchi for your advice and the link..

No! I do not have any assumption in this regard. I have already modified some items culturally.

Regards,

Dear Dr. Turen

Thank you for your recommendations. Yes! it met the criteria of fitness model. 

Regards,

Thank you dear Dr. Vasudevan for the attached files. It helps a lot..

Regards,

Dear Farimah,

as often (always?) in other cases, rules of thumb are simply a myth. There is no optimal strength of factor loadings. A loading connects the factor of theoretical interest with an empirical variable that attempts to measure the factor. Hence, loadings should be conceived as "validity coefficients" giving you some idea if the factor reflects indeed the phenomenon of interest. It may be (and should!) that the model fits but the factor nevertheless has nothing to do with YOUR expected phenomenon. 

Having said that, we (you) should incorporate indicators conceptually as close as possible to the intended factor which will result in strong factor loadings (.80-.90). 

Best,

Holger

Thank you for your complete answer dear Dr. Steinmetz.

Unfortunately factor loading of .80 to .90 are not seen for all items most of the time. What if they are around .40 to .70?!

Regards,

Farimah, 

as I said, the size of the loading must theoretically make sense. What is the fit of the model? Strictly speaking, you should try to get a non-significant chi-square test. A significant test signifies that something (model structure or data assumptions) may fail. Often, such failures consist of wrong factor models in which a bunch of items are forced under one factor where - in reality - these items measure different things.

Low factor loadings also may reflect such a problem. Be sure that you really understand what a factor model is: It is the assumption, that the respective indicators are a result from ONE underlying latent variable - causing each of the indicators. Take a look at the question wordings: Is this reasonable? Often, this "visual CFA" - as I call it :) - reveals subsets of items that are distinct from other subsets.

A second way could be to inspect the correlation matrix of the indicators. Indicators of the same factor should show a homogeneous correlation pattern - ideally with exactly the same correlations among each other. Deviations from this ideal pattern may be caused by different amounts of measurement error (which is no problem) but also by different factors influencing these items.

Best,

Holger

My Dear

It is interesting question. Accept factor loading should be 40 and above. But you need to take in consideration convergent and differentiated validity.  

Once again, thank you for your valuable time dear Dr. Steinmetz.

Best of bests,

it should be more than 0.4

 Thank you dear Dr. Al-Atwi

Best,

Thank you dear Dr. Jeevanand

Best,

Actually in CFA, what you need to focus is the Fitness Indexes since it reflects the Construct Validity. If the Fitness Indexes failed to achieved the required level, the look for low factor loading items. Delete one item at a time from each construct with the lowest among the low factor loading deleted first. Run the model and repeat the same procedure. Once the Fitness Indexes are achieved, then stop. If you examine the factor loading, there are one of two items have low factor loading but no need to be deleted since the Fitness Indexes are already met.

Dear Prof. Zainudin

Thank you much for your complete answer. My CFA models met the fitness criteria and Alhamdulilah the lowest loading factor was found to be 0.29. Now, I faced a new problem!

Fitness index was not achieved in one of my mediating models! (PClose value is significant & RMSEA is greater than 0.08)

I run bootstrapping and calculated Sobel test. Both results are significant. I mean my mediators mediated the the relationship between the IV and DV in the mentioned model. Now, I do not know how I should justify it? 

Would you please guide me in this regard?

Thank you 

Best regards,

Farimah

I would use any factor loading above 0.5.

Hi Dear teacher and students.

I have a question. If there are some factors loading above 1, is there any problems? or it is ok?

I found it, it had a funny answer :) I saw the unstandardized estimates!!

Thank you for your comments.

Best,

Hi folks, I became (again)  aware of this threat and I can only repeat: Refrain from rules of thumb- they are almost always wrong. The same is true for factor loadings. A factor loading isa supposed causal effect of a latent variable and an observed indicator, or - more modest- the correlation between both. The "necessary" strength of the factor loadings depends on the theoretically assumed relationship between both - which in turn depends on the supposed meaning of the latent variabe (i.e. what SHOULD the latent variable reflect IF the model is valid) and the meaning of the observed variable (question wording, results of cognitive interviewing). An indicator that almost perfectly reflects the latent variable (e.g., "I am satisfied with my job") thus should very highly correlate with the latent variable "job satisfaction" (I would expect at least .80-.90). Other indicators that are conceptuelly more distant from the supposed latent variable could result in a lower loading without leading to questioning the validity of the measurement model and latent variable. 

The rule of thumb here is "Apply theoretical thinking and think about what that latent should mean" :)

HTH

Holger

Hi again,

I have a big problem with ave in Amos. I cant calculate it correctly. is there any knows the formula?

Nafis, you can find the formula here:

Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18, 39–50.

Make sure, however, to really test the model instead circumventing tests by using such numbers.

Best,

Holger

Thank you very much for your complete explanation dear Dr. Holger.

Best of bests,

Thank you for your response dear Dr. Mumtaz.

All the best,

Thanks for the explanations, I got the same problems too. Best!!!

 hi all,

Plz answer to this

In a CFA measurement model is standardized beta coefficient actually the corellation between the observed variable and latent construct.

i can read it above in the discussion, can any one give a reference for this

Factor loading should be a minimum of 0.6. Poor factor loading simply means your items are not contributing in measuring the construct it self. That id why, poor loading items should be removed.

Not removing poor loading items will cause your AVE to be lower than 0.5, which means the convergent validity of your construct failed. 

The 'acceptable' size of a factor loading depends on the context. In scale construction the factor loading should be high, and I'm going to swerve stating what 'high' is - there are lots of quotes that you can dig out. However, if you have a few fallible indicators of a latent variable in a SEM model and the factor loadings are low, that's fine. What you are doing is correcting for measurement error that would otherwise introduce a bias to you estimates. It's probably better to control for measurement error using a factor model with low loadings than to pretend that your measures are error free.

mark

Dear Prof. Shevlin

Thank you for your reply.

Best,

factor loading value shows only: amount and direction of relationship but t-value shows that if factor loading is either significant or not. if the amount of t-value is greater than 1.96, the factor loading is meaningful.

too important:

AVE and CR are completely depend on factor loading. in general if factor loading be lower than 0.6 then these statistics show poor than 0.5 & 0.7.

Please, how can one identify factor loading in AMOS outputs?

Dear Mr. Simon

When you click on "view the output path diagram", all values are appeared. Factor loading values are the values shown on the arrows from the latent variable to the observed variables (items). Hope I get what you mean..

Best,

Factor loading should be minimum 0.6. So, remove the poor loading otherwise it will cause your AVE to be lower than 0.5, which means the convergent validity of your construct failed.

Is there any way to improve the values of factor loading

Can an unstandardized factor loading be > 1?

Hi Ifeyinwa,

yes, they can. Loadings are statistically the same as usual regression slopes and depend in their size of the metric of both variables.

Best,

Holger

Factor loading should be minimum 0.50. The AVE, which indicates that the latent construct accounts for at least 50% of the variance in the items .

Dear Simon

Removing the outliers is one way to improve factor loading values.

Hope it helps

Best,

Farimah

Thanks

First of all, you need to understand that in SEM there are Convergent Validity and Composite Reliability that your latent construct need to achieve prior to modelling SEM itself.

And remember - the assessment for Convergent Validity is AVE>0.5 and Composite Reliability is CR>0.6. Both computations for AVE and CR are are based on the factor loading. You may retain the low factor loading items but using that low factor loading , your AVE will be less than 0.5 and your CR will also be less than 0.6 which means your constructs failed Convergent Validity and failed Composite Reliability. Everything become rubbish already! You cannot move further in modelling SEM. So throw away the items having low factor loading (less than 0.6) since it will make your life miserable.

Very informative discussion

Thanks RG!

Very informative discussion this. If I may, how is the t-value calculated?

Farimah,

I would not worry too much about a 'rule of thumb' number for the item loadings. Rather strive to arrive at that peculiar set of items such that several specific reliability and validity metrics are all simultaneously optimized. These include statistical metrics for construct internal reliability, convergent validity and discriminant validity. These standards include Cronbach's alpha, Composite Reliability (CR) and Rho_A for internal reliability; average variance explained (AVE) for convergent validity and; the comparison of the shared variance of each pair of constructs with the respective square root of the AVE's for the test of discriminant validity (Fornell & Larcker). Aim for an AVE of 50% or higher.

Generally, the higher the loadings is the higher the likelihood that Cronbach's alpha, Composite Reliability (CR), Rho_A, AVE will be and hence that construct reliability, convergent validity and discriminant validity will be attained.

Once this simultaneity is achieved, then your models are good.

Hair Black Babin Anderson & Tatham (2006, 127) under the heading "Practical Significance" advises "Because a factor loading is the correlation of the variable (item / indicator) and the factor (potential construct), the squared loading is the amount of the variable’s total variance attributable to the factor. Thus a 0.30 factor loading translates to approximately 10% explanation and a 0.50 loading translates to denotes that a 25% of the variance is accounted for by the factor. The loading must exceed 0.7 for the factor to account for 50% of the variance of the variable. The larger the absolute size, is the more important is the loading to the interpretation of the actor matrix. Using practical significance as a criteria:

· Factor loadings in the range of +/-0.30 to 0.40 are considered to meet the minimal level for interpretation o structure

· Loadings in the +/-0.50 or greater are considered practically significant

· Loadings exceeding +/-0.70 are considered indicative of a well-defined structure and are the goal of any factor analysis.

With a stated aim of achieving a power level of 80%, the use of a 0.05 significance level and the proposed inflation of the standard errors of the factor loadings (Research has indicated that factor loadings have significantly higher standard errors than typical correlations, Cliff & hamburger 1967, Hair et al 2006, 128), in their Table 3.2 sets out the sample sizes necessary for each factor loading value to be considered significant. (see attached)

Also on page 130 on the issue of cross-loading which occurs when a variable is found to have more than one significant loading. "A researcher may find that different rotation methods eliminate cross-loadings and thus define a simple factor structure. If a variable persists in having cross-loadings, it becomes a candidate for deletion."

Some researchers use a rule of thumb of 0.2 for the acceptable difference for the separation of cross-loading

Hi Farimah,

I do agree with Silburn. When conducting EFA, the acceptable minimum of loadings is 0.3

Best regards

Dear Silburn Clarke

if the researchers follow your reference that you mentioned then is it possible to achieve convergent validity through AVE and CR ( AVE>.5 and CR >.6 minimum value is required for convergent validity)? I think the answer is NO.

So, we should follow what Prof. Zainudin Awang mentioned here.

Thank you.

i have a question regarding values of SRMR/WRMR. are these values present in Amos (CFA) output? from where we get these values?

I also faced similar problem, but the discussion above almost solved my problems.

Thanks to everyone.

Dear Farimah,

I will recommend you to please visit the website of Games Jaskin. He provides a very useful lectures on the topic further he has provided stats tool package on his website. His web address is

http://statwiki.kolobkreations.com/

Mrs Dokoushkani

It should be more than 0.4

I agree with Mahboub. A 0.4 threshold is acceptable. For a closed factor loading aggregation, I often set it slightly higher, say 0.55, especially if I am to perform further statistical analyses on the identified factors. Say for instance I wanted to know key managerial factors influencing integrated reporting, I would look for the factors, but then perform an additional set of analyses, including specific corelational or even regression analysed on the identified factors. I hope this helps

I agree with Mahboub. A 0.4 threshold is acceptable. For a closed factor loading aggregation, I often set it slightly higher, say 0.55, especially if I am to perform further statistical analyses on the identified factors. Say for instance I wanted to know key managerial factors influencing integrated reporting, I would look for the factors, but then perform an additional set of analyses, including specific corelational or even regression analysed on the identified factors. I hope this helps

Deah Hoque,

The main thrust of table at Hair et al 2006, p128 is that the sample size influences the magnitude of the practically significant factor loading.

Silburn

Dear Silburn Clarke,

Please give the straight answer of the following.

if the researchers follow your reference that you mentioned then is it possible to achieve convergent validity through AVE and CR (AVE>.5 and CR >.6 minimum value is required for convergent validity)?

Thank you in advance.

I agree with most you, factor loading is set at a minimum of 0.3. However, that is is just a minimum while some researchers take 0.4 as acceptable;but seriously speaking a 0.55 is taken as acceptable/important or significant and only above 0. 7 are taken as a very significant.

A salient Loading , in standardized context, is a loading in excess of 0.32, an item-factor loading exceeding 0.32, in light of sufficient model identification , specification and fit is theoretically Non-objectionable, unless the researchers had sufficiently loading other items to keep I would Not dismiss an Item with item-latent factor loading within (0.32-0.499)-well depending on the background theory/industry .

https://www.parsmodir.com/db/research/sem.php

hi you can find your solution in this link.

And the factor loading myth continues and continues.

A .3-loading implies you supposed underlying latent factor explains 9% of the item's variance and 81% are other causes and random error. I don't know with which background and intention you created that item in the first place: a) if the item is conceptually so ambiguous and error-prone I would have problems to regard it as a useful measurement instrument (if your doctor measures your blood pressure: would you accept such values? OR b) the item is crystal clear, which would create strong doubts that the extracted factor is the thing I think it is.

But the truth behind this is: Researchers who invented these dubious rules of thumbs (and those, you keep them alive) have the routine to create masses of heterogeneous items without any clear concept of the factors. Then, the factor-analytical machinery is employed to find the truth (like an oracle). The result is a messy factor structure with many items loading weakly and on many factors. Next, the next statistical ritual is employed (Cronbach's alpha) and if alpha is .7 than hurray. The fact that alpha will hit that mark whenever you put an increasing number of correlated items in it, does not matter.

If you really are convinced that this will lead to meaningful measures and factors, keep on doing that. I doubt that :)

All the best

Holger

Mahsa,

what exactly are the variables in your model? When you say that the distributions are "extremely non-normal" --perhaps assuming a normal distribution is wrong in the first place. This is always the case when you have count data (which are Poisson-distributed).

Best,

Holger

Hi,

It depends on the size of the sample.

Hi Mahsa,

one option that I forgot: Sometimes, two or more different populations are mixed in the data. Their overlap creates strong deviations from the normal distribution. Since your N is huge, this is very likely. Hence, going to a mixture model / latent profile model is the only choice (apart from manuell comparing the distributions across all your measured cateogorical variabels, such as sex, age groups, occupations etc.).

I know that you have little time but sometimes things need time. This is stressing fact for all of us.

But again: What are you dependent variables?

Best,

Holger

Hi Mahsa,

please create a new thread and post all what you have said, again. I will answer there. Your question is misplaced here and distroys the thread (which is about factor loadings).

Best,

Holger

Hair et al (2010) suggested that factor loading with 0.55 and above is appropriate to calculate the AVE and CR. Otherwise, lower factor loading indicates weak relationship with the construct.

What is the acceptability of factor loading less than 0.70 in AMOS analysis ?

In SEM Analysis, factor loading 0.55 or above are acceptable. You can refer to Hair et al (2020).

Hi Assefa T. Tensay , I would like to know (as I don't know the Hair et al. reference) what arguments or evidence they bring for this -- in my point of view-- strange recommendation. A factor loading of .55 means that around 70% of the indicator's variance is pure error and only around 30% reflects the underlying latent variable. Both from the perspective of a theory-oriented creation or selection of indicators, I would be either skeptical that this indicator really measures the latent variable of interest or if it measures anything at all.

My estimation is that such low loadings predominantly emerge in exploratory situations in which you throw in a mass of indicators with any clear theoretical rationale. Even if these indicators load on some factor, it is absolutely unclear what this factor represents. These kind of approach most often happens in situations in which the goal of the analysis is not to identify valid measures but to reduce a large set of data into smaller chunks. These two goals are often mixed and I guess, Hair et al. refert to the data reduction goal.

But that's only my personal view.

With best regards

Holger

Hey Assefa,

I fully agree with Holger. Besides the critiques about these heutistic rule/rules of thumb, the recommended threshold dependent largely on your type of research, causal research (confirmation and explanation), predictive, and exploratorive research. As Hair does not refer to overall model fit assessment in a serious way in the context of SEM, his rules of thumb should be taken cautiously for causal research.

Best regards,

Florian

Ideally it shd be abv 0.7 .. But abv 0.5 is also acceptable..

we should have loadings more than 0.70 for better results

above 0.5 will give acceptation values of AVE and CR

If factor loading is above 0.6, the AVE and CR would reach the acceptable level of 0.5 and 0.6 respectively. Therefore, retaining the items with loading less than 0.6 would result in validity problems. However, the loading above 0.5 for one or two items of a construct may be ok if other items have high factor loading.

It depend on your data and the objective of your research. Think about it analyse how the loading affect your conclusions. Some times these rule of thumbs are misleading. You need to do more readings and if however, you cannot bring strong arguments or evidences on why your data is ok with loading of say like.40, just follow the rule of thumb it will be more safer.

I think, It should be more than 0.4

acknowledged..

Are there any references?

Confirmatory Factor Analysis for Applied Research, Second Edition

Timothy A. Brown (2015)

First of all look at your fitness indexes. Your fitness indexes indicate construct validity. The index will be low if poor loading item or rubbish is sitting in the model. What should u do in order to achieve construct validity? Remove the rubbish.

I think 0.7 and above

Kindly refer the book multivariate analysis-by hire et. Al. You can take the factors loading g items of 0.3 if you are having more than the sample size of 300

Dear Dhana Lakshmi Thiyaga Rajan

Your suggestion is acceptable cut-off value for factor loading when we run the EFA.

Thaneswary Raveendran

If factor loading is above 0.6, the AVE and CR would reach the acceptable level of 0.5 and 0.6 respectively. is there any reference that supports@ your suggestion?

Factor loading must be above 0.7

I wonder why are so longing to keep the rubbish items in the model? You see, by keeping the poor items you would two problem. First is poor fitness indexes and second is low value for AVE and CR.

Tell u what - poor fitness indexes mean failed construct validity. And poor AVE means failed convergent validity. Plus, low CR means the construct failed composite reliability.

In PLS-SEM, factor loading less than 0.708 must be eliminated, as it gives poor statistics later in the analysis stage.

thanks @Roshan Nimantha Panditharathna

for exploratory studies the limit can be .3 but usually it is .5

thanks everyone

Daer İrfan Yurdabakan ,

can you elaborate on this? Both the CFA and EFA reflect the same data generating process (i.e., the common factor model). Hence, the meaning of the loadings is the same and the EFA is only a less restrictive model (allowing double loadings).

Hence, I would not think that we need to distinguish between both when interpreting or evaluating the indicator-factor relationship bur maybe I miss something.

Best,

Holger

Dear Irfan, yes the purposes and mathematical procedures differ but the essence lies in your first sentence: The have the same meaning and reflect the supposed effect of the latent factor on the indicators. Not indicators explain variance in factors; it is the other way around (the factors explain variance in the indicators) as they represent the effects on these indicators.

I agree that inspecting the fit is in a CFA is an important precondition but it is only half of the story as the interpretation of the factor (again identical to the EFA context) hinges on the loading. A lambda=.40 loading has to be interpreted against the theoretical background a) what the indicator is (i.e. its question wording) and b) the supposed meaning of the latent variable--hence it is a validity coefficient. When, for instance, I create a golden standard indicator that theoretically almost perfectly matches the intended meaning of "my supposed factor" but the loading turns out to be so low, I would have deep concerns whether the latent represents really the part of reality I strive for--no matter how good the fit of the model is. Fit is always ONLY a minimum condition for causal models but not a sufficient.

I can easily simulate data for a factor model that cleanly fits (despite N>100,000) and yet the loadings are zero. The interpretation of the reasonableness of coefficients--besides the fit--is an essential task within every SEM /CFA endeavour.

Best,

Holger