Guidance Request for Data Analysis

[VINCENT DE PAUL SAVARIMUTHU]

Sir

Good Afternoon

Sir when we I did factor analysis  I have got 5 factors. But one of the factors having 5 items have AVE, less than .5.

What can i do ?

May i ignore that factor and retail remaining factors which are having AVE more than 5.

Kindly suggest ways to solve this issue.

regards

[Fatih ÇELİK]

Average Variance Extracted (AVE) is higher than 0.5 but we can accept 0.4. Because Fornell and Larcker said that if AVE is less than 0.5, but composite reliability is higher than 0.6, the convergent validity of the construct is still adequate (Huang et al., 2013: p. 219). (Source: 10.7763/IJIET.2013.V3.267).

AVE varies from 0 to 1, and it represents the ratio of the total variance that is due to the latent variable. Using the logic presented earlier, an AVE of 0.5 or more indicates satisfactory convergent validity, as it means that the latent construct accounts for 50 percent or more of the variance in the observed variables, on the average. If AVE is less than 0.5, the variance due to measurement error is larger than the variance captured by the construct, and the validity of the individual indicators, as well as the construct, is questionable. Note that AVE is a more conservative measure than CR. On the basis of CR alone, the researcher may conclude that the convergent validity of the construct is adequate, even though more than 50 percent of the variance is due to error. One should also interpret the standardized parameter estimates to ensure that they are meaningful and in accordance with theory (Malhotra & Dash, 2016, p. 714).  (Source: Malhotra, N. K., ve Dash, S. (2016). Marketing research: An applied orientation (7th Edition). Pearson.)

4 Ağustos 2020 Salı 11:30:53 UTC+3 tarihinde VINCENT DE PAUL SAVARIMUTHU yazdı:

[VINCENT DE PAUL SAVARIMUTHU]

Dear faith Sir

Thank u very much for ur inpust. I have got the result for EFA. Kindly confirm ur valid points are applicable for EFA also.

Regards

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[Neeraj Kaushik]

Dear Vincent

Although I've replied you earlier about the AVE, Discriminant Validity in EFA but it seems that you're under tremendous pressure to somehow use it. 

I think this confusion may arise because of considering factor and construct the same, while they are not same.

Let me once again, try to clarify the basics:

-------------------------------------------  

First, let's talk of CFA. 

In CFA, we have got a construct and given items (statements) e.g.

Now here we consider the construct as IDV and every item as DV, hence it is a case of Simple Regression (1 DV & 1 IDV). In Simple Regression r=Beta=R (Plz https://youtu.be/_MXQBPJL8Ws) hence just squaring beta, we get r2 (Plz check 0.74*0.74=0.55 and so on)

So, we made a rule that since a construct is explaining the variations of several IDVs (i.e. statements here), there must be on an avg Average Variance Explained >0.5

Since this construct is different from other constructs and may be related to others, we check whether this AVE>r between the various constructs, this is called as Discriminant Validity (AVE>Max r2).

-------------------------------------------

Now coming to EFA

First let's differentiate between the two terms: Factor and Construct

A construct has the same meaning as in CFA but Factor is different here. If you know the calculations steps (Plz refer https://youtu.be/uhWKd1vA8X8) you'll note that in EFA, every statement contributes to every factor. It means a factor is not made of simply 4-5 statements rather all statements of scale.

We subtract the first factor from total to get the second factor, hence there will not be any correlation between the first & the second factor. This process is repeated to get all factors and then we retain the ones having Eigen value>1

Plz note & check all factors extracted from EFA will have their r=0

Hence there is no question of Discriminant Validity or reporting its Discriminant Validity measures or statistics.

Now, since statements of a construct are highly correlated, generally there have high factor loading to a factor. Plz note we get this clean and no cross-loading solution, after rotation as well as by suppressing other statement having low factor loading by clicking on option Suppress small coefficients

 

Now, you wish to compute the AVE by considering the factor loading values of some of the statements

  

So, many scholars try to find out the AVE by squaring the factor loading of every factor and then averaging it but the fact is that the real pic is like this:

Can you see the difference?

So, in EFA output we can say that in a factor generally, any one construct has high factor loading as compared to other constructs. So, scholars consider factor and construct as the same, but they are not as every factor is made up of all statements

Now think yourself, how can you call it AVE of a factor by just taking some of the statements?

And you shd not attempt of computing AVE of a construct as every construct is related to every factor!

Moreover, the question is WHY do you wish to report AVE in EFA?

Why are you mixing the statistics of EFA and CFA?

I hope this clarifies some of your doubts related to EFA/CFA.

Best wishes

Neeraj

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[VINCENT DE PAUL SAVARIMUTHU]

Dear Sir

I extend my sincere gratitude to you for having explained in detail with clarity. Thank u sir.

Regards

To view this discussion on the web visit https://groups.google.com/d/msgid/dataanalysistraining/CAAd%3Dc8PAhoxae63p81X3t5cNUavxfoMd2Z6X5-%3D9w7pTox9R3Q%40mail.gmail.com.

[Pradeepkumar]

Neeraj sir , it was a very clear clarification .

To view this discussion on the web visit https://groups.google.com/d/msgid/dataanalysistraining/CAAd%3Dc8PAhoxae63p81X3t5cNUavxfoMd2Z6X5-%3D9w7pTox9R3Q%40mail.gmail.com.

[Tagiya Mudang]

Very helpful information for me too Sir. Thank you. Regards 

To view this discussion on the web visit https://groups.google.com/d/msgid/dataanalysistraining/CAEFjVHnxYvWNkA67noepzAZvSfuKUxi2AbQoX5e%2B-X9SDriCew%40mail.gmail.com.

[Karan Jit Sharma]

Good Evening

          Neeraj sir has meticulously explained CFA & EFA. Thanks sir.

HBAT CFA

       Factor  Loading, Communalities, TVE, Standard error etc. are explained.

Ref- J F Hair et al.Multivariate Data Analysis page No 632 

Ref-J F Hair et al.Multivariate Data Analysis, CR formula, page No 619
RegardsKaranjit Sharma

Associate Prof

G C Gurdaspur

Very helpful information for me too Sir. Thank you. Regards 

On Wed, 5 Aug 2020, 11:36 Pradeepkumar, <pradeepku...@gmail.com> wrote:

Neeraj sir , it was a very clear clarification .

On Wed, 5 Aug 2020, 10:58 Neeraj Kaushik, <kaushi...@gmail.com> wrote:

Dear Vincent

Although I've replied you earlier about the AVE, Discriminant Validity in EFA but it seems that you're under tremendous pressure to somehow use it. 

I think this confusion may arise because of considering factor and construct the same, while they are not same.

Let me once again, try to clarify the basics:

-------------------------------------------  

First, let's talk of CFA. 

In CFA, we have got a construct and given items (statements) e.g.

<image.png>

Now here we consider the construct as IDV and every item as DV, hence it is a case of Simple Regression (1 DV & 1 IDV). In Simple Regression r=Beta=R (Plz https://youtu.be/_MXQBPJL8Ws) hence just squaring beta, we get r2 (Plz check 0.74*0.74=0.55 and so on)

So, we made a rule that since a construct is explaining the variations of several IDVs (i.e. statements here), there must be on an avg Average Variance Explained >0.5

Since this construct is different from other constructs and may be related to others, we check whether this AVE>r between the various constructs, this is called as Discriminant Validity (AVE>Max r2).

-------------------------------------------

Now coming to EFA

First let's differentiate between the two terms: Factor and Construct

A construct has the same meaning as in CFA but Factor is different here. If you know the calculations steps (Plz refer https://youtu.be/uhWKd1vA8X8) you'll note that in EFA, every statement contributes to every factor. It means a factor is not made of simply 4-5 statements rather all statements of scale.

We subtract the first factor from total to get the second factor, hence there will not be any correlation between the first & the second factor. This process is repeated to get all factors and then we retain the ones having Eigen value>1

Plz note & check all factors extracted from EFA will have their r=0

Hence there is no question of Discriminant Validity or reporting its Discriminant Validity measures or statistics.

Now, since statements of a construct are highly correlated, generally there have high factor loading to a factor. Plz note we get this clean and no cross-loading solution, after rotation as well as by suppressing other statement having low factor loading by clicking on option Suppress small coefficients

 

Now, you wish to compute the AVE by considering the factor loading values of some of the statements

<image.png>  

So, many scholars try to find out the AVE by squaring the factor loading of every factor and then averaging it but the fact is that the real pic is like this:

To view this discussion on the web visit https://groups.google.com/d/msgid/dataanalysistraining/CAC2nAKK7_3jQX8T9Zk9wn4eMxv8Sr_%2Bpi0AW6G5Yk0zFDL0oWQ%40mail.gmail.com.

[Neeraj Kaushik]

Dear All

I forget to mention one thing.

The purpose of AVE in CF is to check how much variations of all statements are explained (on an average basis) by the construct.

A similar thing in EFA is already present and is always reported: 

Variance explained by an individual factor (one shd prefer to report Var explained after Rotation)

Best wishes

To view this discussion on the web visit https://groups.google.com/d/msgid/dataanalysistraining/32E25F5F-F05D-420A-9817-64BF974C45FC%40gmail.com.