Specifying a SEM model for Tetrad analysis

[Dikaioplois]

Hello everyone,

I am new in tetrad and I have problems in specifying my model with the GUI interface despite watching tutorial videos and the manual.

I have a covariance matrix as input.

From this covariance input I would like to specify and estimate second-order model (SEM) in order to :

• get loadings and fit.
• get the specific tetrads of the model like in article of Mansolf and Reise enclosed.

j.intell.2017.01.012.pdf

Could you please help in how to link the boxes and how to get the specific tetrads of the model ?

Many thanks in advance for your help

[jdramsey]

I'm not sure I have a good answer to that, as I've not thought much about second-order models of this sort, but I'll ask around for you. -Joe

[Dikaioplois]

Thank you very much for your help.

I would to point out that I know how to specify the second-order model in the graph box.

My problem is that I would like to get the tetrads of the model and do not know how to do.

[jdramsey]

Oh I see. You know, I never made a gadget in the tetrad interface to list tetrads. Let me think about it; it wouldn't be all that hard, I don't think.

[cg09]

Joe, I have often thought that would be useful. Clark

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On Fri, Jun 20, 2025 at 3:40 PM Joseph Ramsey ***@***.***> wrote: *jdramsey* left a comment (cmu-phil/tetrad#1905) <#1905 (comment)> Oh I see. You know, I never made a gadget in the tetrad interface to list tetrads. Let me think about it; it wouldn't be all that hard, I don't think. — Reply to this email directly, view it on GitHub <#1905 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AD4Y3OPWBBIDA6HRYJ6UHDD3ERPSBAVCNFSM6AAAAAB7X36ANKVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDSOJSGYZDCNZUGU> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[jdramsey]

I'll try to get this done this week. I need to think about it a little. For small models of the sort that are in that attached paper, you could conceivably list all significant tetrads, though for large models, perhaps some limit should be placed. Additionally, we have multiple methods for assessing Tetrad; a dropdown menu to select one would likely be helpful.

[Dikaioplois]

Thank you very much. It would be even more useful that the only way to this is to use a macro for stata developed by bollen and bauldry. Also, what could be interesting in addition to get the specific tetrads of each model would be the possibility to compare fit based on tetrads. It is possible with the stata macro.

[jdramsey]

I can't promise that, partly because I'm not sure what you mean by a fit based on tetrads.

[Dikaioplois]

Sorry I was unclear. I mean to compare the fit of two models that are nested in terms of the tetrads that each imply are vanishing.

I enclosed the article of Bollen and Bauldry with a macro dealing with that.

nihms-1038149.pdf

[jdramsey]

I'm not sure I'm going to have time to do that. At least not this week.

[cg09]

Do you have in mind a fit statistic based on tetrads alone? I don't know of one.

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On Sun, Jun 22, 2025 at 1:23 PM Dikaioplois ***@***.***> wrote: *Dikaioplois* left a comment (cmu-phil/tetrad#1905) <#1905 (comment)> Sorry I was unclear. I mean to compare the fit of two models that are nested in terms of the tetrads that each imply are vanishing. I enclosed the article of Bollen and Bauldry with a macro dealing with that. nihms-1038149.pdf <https://github.com/user-attachments/files/20853843/nihms-1038149.pdf> — Reply to this email directly, view it on GitHub <#1905 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AD4Y3OI2ZM75C5SFKDZ4SYT3E3RAXAVCNFSM6AAAAAB7X36ANKVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDSOJUGMZTIMJSGE> . You are receiving this because you commented.Message ID: ***@***.***>

[Dikaioplois]

I have an example based on chi square. Below a citation of Bauldry and Bollen about it :

"With two tetrad-nested models, the difference in chi-square test statistics itself follows a chi-square distribution with degrees of freedom equal to the difference in degrees of freedom between the two models. In other words, Tdiff=T0(1)−T0(2) with dfdiff=df(1)−df(2). Rejection of the null hypothesis provides evidence that model 2, the less restrictive model in terms of vanishing tetrads, has a better fit with the data than model 1, the more restrictive model in terms of vanishing tetrads."

[jdramsey]

I understand how you can use chi-square to distinguish two models; you can already do this in Tetrad. What I don't understand is how you can obtain a model score based on tetrad, which are individual tests, each with its own p-value. Do you have in mind getting an overall p-value for the model based on tetrads, of do you have in mind simply determining whether the set of tetrad implied by one model is a subset of the set of tetrads implied by another model (by statistical tests) and then doing a chi square test of the two model?

[ps7z]

Joe, The Markov checker approach would be to find a set of tetrad constraints entailed by the model that are as independent as possible (e.g. by using the calculation of the number of independent tetrads entailed by a model worked out by Harman.) THose tests should have a uniform distribution. But there are a number of different ways of combining p-values that could be used. Peter Peter Spirtes Marianna Brown Dietrich Professor and Head of Philosophy Carnegie Mellon University ***@***.***

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On Mon, Jun 23, 2025 at 9:43 AM Joseph Ramsey ***@***.***> wrote: *jdramsey* left a comment (cmu-phil/tetrad#1905) <#1905 (comment)> I understand how you can use chi-square to distinguish two models; you can already do this in Tetrad. What I don't understand is how you can obtain a model score based on tetrad, which are individual tests, each with its own p-value. Do you have in mind getting an overall p-value for the model based on tetrads, of do you have in mind simply determining whether the set of tetrad implied by one model is a subset of the set of tetrads implied by another model (by statistical tests) and then doing a chi square test of the two model? — Reply to this email directly, view it on GitHub <#1905 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACSK3QSRPXMC22NB65XSNE33FAAADAVCNFSM6AAAAAB7X36ANKVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDSOJWGU2TMOJYGA> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[Dikaioplois]

I understand how you can use chi-square to distinguish two models; you can already do this in Tetrad. What I don't understand is how you can obtain a model score based on tetrad, which are individual tests, each with its own p-value. Do you have in mind getting an overall p-value for the model based on tetrads, of do you have in mind simply determining whether the set of tetrad implied by one model is a subset of the set of tetrads implied by another model (by statistical tests) and then doing a chi square test of the two model?

I tought "simply determining whether the set of tetrad implied by one model is a subset of the set of tetrads implied by another model (by statistical tests) and then doing a chi square test of the two model"

[jdramsey]

Sorry, I have not been able to get to this project; other work is intervening. But I will. I need to find a couple of days to set aside to focus on it.