HTMT for second-order construct

[k stol]

Hello,

How would one calculate the HTMT for a second-order construct with lavaan? The semTools htmt() function doesn't seem to help on this occasion.

any pointers appreciated.

thanks

[car...@web.de]

Not at all. This contradicts HTMT logic.

Am 26.05.20, 01:23 schrieb k stol <kjs...@gmail.com>:

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[k stol]

There are at least 2 papers that seem to do it, though:

https://doi.org/10.17705/1thci.00104

and 

https://www.jstor.org/stable/25148669

What would be the logic that HTMT doesn't apply to 2nd order constructs?

thanks

On Tuesday, 26 May 2020 00:45:03 UTC+1, car...@web.de wrote:

Not at all. This contradicts HTMT logic.

Am 26.05.20, 01:23 schrieb k stol <kjs...@gmail.com>:

Hello,

How would one calculate the HTMT for a second-order construct with lavaan? The semTools htmt() function doesn't seem to help on this occasion.

any pointers appreciated.

thanks

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[Nickname]

k stol,
  If I may interject, here is what I think that Carl meant.  MTMM matrices are a methodology for evaluating the validity of tests.  Tests require scores that can be interpreted and used.  You could apply the same formula to the first order latent variable correlations and obtain a value.  However, there would be no scores involved in these correlations, they are correlations between latent variables and the whole idea behind latent variables is that they cannot be observed and thus are not scores.  One cannot validate the use or interpretation of scores that are not available for interpretation or use.  What might make more sense is if you were to compute scores for the tests that correspond to each of the first order factors, perhaps by summing the items that load on that factor. Now you have scores that can be validated and you can apply the same analysis to these scores as you would to item scores.  Alternatively, perhaps you mean to use the HTMT value for some other purpose than test validation, in which case you can compute it as described above but need to explain to your readership why you are doing that.

Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/

[k stol]

hi Keith

Thanks for your explanation. Just following up here to document what I found, might be useful for others.

Searching more info on this issue, I found this article

 https://doi.org/10.1016/j.ausmj.2019.05.003 

which indeed seems not to consider HTMT rations between the higher order constructs and its constituent first-order constructs

thanks again

[car...@web.de]

Thanks, Keith. I'll add more explanation next time.

Am 26.05.20, 16:59 schrieb 'Nickname' via lavaan <lav...@googlegroups.com>:

k stol,
  If I may interject, here is what I think that Carl meant.  MTMM matrices are a methodology for evaluating the validity of tests.  Tests require scores that can be interpreted and used.  You could apply the same formula to the first order latent variable correlations and obtain a value.  However, there would be no scores involved in these correlations, they are correlations between latent variables and the whole idea behind latent variables is that they cannot be observed and thus are not scores.  One cannot validate the use or interpretation of scores that are not available for interpretation or use.  What might make more sense is if you were to compute scores for the tests that correspond to each of the first order factors, perhaps by summing the items that load on that factor. Now you have scores that can be validated and you can apply the same analysis to these scores as you would to item scores.  Alternatively, perhaps you mean to use the HTMT value for some other purpose than test validation, in which case you can compute it as described above but need to explain to your readership why you are doing that.

Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/

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[Kay Smith]

Hi @all,

concerning this topic I would like to know if I can extract the correlation matrix with lavInspect() and use it as input for htmt()?

Thank you in advance for your answer.

Kay

[Kay Smith]

Hi @all,

I have a question concerning this topic. Can I use the correlation matrix from lavInspect(fit, "cor.all") to estimate HTMT with semTools::htmt(model_from_fit, sample.cov = cor.all_from_fit)?

Thanks in advance for your help.

Kay

car...@web.de schrieb am Dienstag, 26. Mai 2020 um 13:29:47 UTC-5:

[Christian Arnold]

Technically, this should work. But why would you want to do that? 

[Kay Smith]

I would like to check discriminant validity (if possible) for a second order construct.

Let's assume the following model:
model <- '
Var1 =~ x1 + x2 + x3
Var2 =~ x4 + x5 + x6
Var3 =~ x7 + x8 + x9
Var2 =~ x10 + x11 + x12

        SecOrd1 =~ Var1 + Var2
SecOrd2 =~ Var3 + Var4
'
Because Var1 to Var4 are no observed values, I can't use the function htmt like htmt(model, data = modelData).
The only solution that I found is the one Keith described above (sum the items) and change my model to use htmt.

I know that it will work from a technical perspective (1. using the correlation matrix from lavInspect or 2. sum the items), but does it make sense to do that?

Thanks,
Kay

[Christian Arnold]

Taken from Henseler et al. (2015, p. 121):"In essence, as suggested by Nunnally (1978) and Netemeyer et al. (2003), the HTMT approach is an estimate of the correlation between the constructs ξi and ξj [...]". Why would one use estimated correlations between factors to estimate the correlations between these factors? You already have the correlations at hand. If you need confidence intervals, you could use the bootstrap, for example.

---

Von: lav...@googlegroups.com <lav...@googlegroups.com> im Auftrag von Kay Smith <wzpa...@gmail.com>
Gesendet: Dienstag, 10. September 2024 03:38
An: lavaan <lav...@googlegroups.com>
Betreff: Re: HTMT for second-order construct

 

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[Kay Smith]

Can I use the estimated correlations from lavInspect() to check discriminant validity according the Henseler et al. (2015) ?

If not, is there any chance to check discriminant validity for second order contructs?

Thank you.

[Christian Arnold]

Well, what exactly do you mean by discriminant validity?

---

From: lav...@googlegroups.com <lav...@googlegroups.com> on behalf of Kay Smith <wzpa...@gmail.com>
Sent: Thursday, September 12, 2024 12:15:03 AM
To: lavaan <lav...@googlegroups.com>
Subject: Re: HTMT for second-order construct

 

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[Kay Smith]

I would like to check if my second order constructs are not related to each other with the HTMT approach by Henseler et al. (2015) among others. (r < H_0,85). 

[Christian Arnold]

As mentioned, HTMT estimates the correlations between factors. The conclusions are then drawn from the bootstrap confidence intervals. The correlations are already available to you. I see no reason to use HTMT.

---

From: lav...@googlegroups.com <lav...@googlegroups.com> on behalf of Kay Smith <wzpa...@gmail.com>

Sent: Friday, September 13, 2024 6:13:33 AM

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[zhao...@gmail.com]

I wonder if summing up the total of all first-order constructs that contribute to second-order constructs, treating the sum scores as first-order (only for the purpose of discriminant validity check) and using HTMT with the rest of the first-order constructs would work?