factor loadings and item-total correlations

[Maguin, Eugene]

What can be made of a comparison of factor loadings and item-total correlations? I understand the computation of each but I’ve never thought of the two sets of value in relation to each other. To focus comments here are the data for items A, B, C, D. I-T are the item-total correlations and FL are the factor loadings.

 

              A           B           C            D           I-T         FL

A           1.00      .70        .38        .34        .57        .83

B           .70        1.00      .50        .32        .62        .90

C           .38        .50        1.00      .60        .63        .49

D           .34        .32        .60        1.00      .52        .33

 

The surprising result—to me, is similarity of the item-total correlations compared to the factor loadings. I think that can be accounted for by the fact that items A are good proxies for each other and that the same is true for items C and D but to a slightly lesser extent. And also that items B and C are pretty good proxy for each other as well. Is this too much to be made of the data? Can more be said?

 

Thanks, Gene Maguin

 

 

[Rich Ulrich]

I'm surprised that the item-total correlations are not higher,
since putting an item into a total automatically gives the relation
a large amount of shared variance.

Are you reporting the "corrected item-total correlations" that
show the r between each item and the rest of the items (omitting
that item)?

Factor loadings are correlations, too -- the r's between the items
and the theoretical factors.   The loading of 0.83 and 0.90 are high
enough, compared to 0.49 and 0.33, to show that the factor mainly
reflects these two.

--
Rich Ulrich

---

Date: Mon, 12 Aug 2013 11:57:29 -0400
From: [hidden email]
Subject: factor loadings and item-total correlations
To: [hidden email]

What can be made of a comparison of factor loadings and item-total correlations? I understand the computation of each but I’ve never thought of the two sets of value in relation to each other. To focus comments here are the data for items A, B, C, D. I-T are the item-total correlations and FL are the factor loadings.

 

              A           B           C            D           I-T         FL

A           1.00      .70        .38        .34        .57        .83

B           .70        1.00      .50        .32        .62        .90

C           .38        .50        1.00      .60        .63        .49

D           .34        .32        .60        1.00      .52        .33

 

The surprising result—to me, is similarity of the item-total correlations compared to the factor loadings. I think that can be accounted for by the fact that items A are good proxies for each other and that the same is true for items C and D but to a slightly lesser extent. And also that items B and C are pretty good proxy for each other as well. Is this too much to be made of the data? Can more be said?

 

Thanks, Gene Maguin

 

 

[Maguin, Eugene]

It is the corrected item-total from the reliability command.  Sorry, should have made that clear. Gene Maguin

 

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Rich Ulrich
Sent: Monday, August 12, 2013 12:33 PM
To: [hidden email]
Subject: Re: factor loadings and item-total correlations

 

I'm surprised that the item-total correlations are not higher,
since putting an item into a total automatically gives the relation
a large amount of shared variance.

Are you reporting the "corrected item-total correlations" that
show the r between each item and the rest of the items (omitting
that item)?

Factor loadings are correlations, too -- the r's between the items
and the theoretical factors.   The loading of 0.83 and 0.90 are high
enough, compared to 0.49 and 0.33, to show that the factor mainly
reflects these two.

--
Rich Ulrich

---

Date: Mon, 12 Aug 2013 11:57:29 -0400
From: [hidden email]
Subject: factor loadings and item-total correlations
To: [hidden email]

What can be made of a comparison of factor loadings and item-total correlations? I understand the computation of each but I’ve never thought of the two sets of value in relation to each other. To focus comments here are the data for items A, B, C, D. I-T are the item-total correlations and FL are the factor loadings.

 

              A           B           C            D           I-T         FL

A           1.00      .70        .38        .34        .57        .83

B           .70        1.00      .50        .32        .62        .90

C           .38        .50        1.00      .60        .63        .49

D           .34        .32        .60        1.00      .52        .33

 

The surprising result—to me, is similarity of the item-total correlations compared to the factor loadings. I think that can be accounted for by the fact that items A are good proxies for each other and that the same is true for items C and D but to a slightly lesser extent. And also that items B and C are pretty good proxy for each other as well. Is this too much to be made of the data? Can more be said?

 

Thanks, Gene Maguin

 

 

[Kirill Orlov]

Factor loading (correlation item b/w item and factor) and correlation b/w item and the sum of the other items need not be comparable or agreeable to each other. The Loading is one of possible construct validity coefficients. The corrected correlation is one of construct reliability, homogeineity, coefficients. Note that the notion of validity always implies correlating with an external independent criterion; here, factor is such criterion - despite it had been extracted even from those variables as a "construct". The notion of reliability implies correlating within a group of variables that are assumed to measure the same thing as if reasonable "dublicates".

12.08.2013 19:57, Maguin, Eugene пишет:

What can be made of a comparison of factor loadings and item-total correlations? I understand the computation of each but I’ve never thought of the two sets of value in relation to each other. To focus comments here are the data for items A, B, C, D. I-T are the item-total correlations and FL are the factor loadings.

 

              A           B           C            D           I-T         FL

A           1.00      .70        .38        .34        .57        .83

B           .70        1.00      .50        .32        .62        .90

C           .38        .50        1.00      .60        .63        .49

D           .34        .32        .60        1.00      .52        .33

 

The surprising result—to me, is similarity of the item-total correlations compared to the factor loadings. I think that can be accounted for by the fact that items A are good proxies for each other and that the same is true for items C and D but to a slightly lesser extent. And also that items B and C are pretty good proxy for each other as well. Is this too much to be made of the data? Can more be said?

 

Thanks, Gene Maguin