Hi Ceren,

I don't know if there's an upper limit. You may take a look into Ross Jacobucci's work on regularized SEM for which he created an R-package. I saw a keynote by him, in which one of his examples was a mimic model with 100 IVs. One problem I personally see in this approach is that in order to function properly the latente variable has to be correctly specified. Hence I would invest some effort to nail that first.

Jacobucci, R., Grimm, K. J., & McArdle, J. J. (2016). Regularized structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 23(4), 555-566.

Best,

Holger

Holger Steinmetz thanks for your help

Hi Ceren,

This appears to be a simple question, but much lies beneath. If I look at a MIMIC model I can see a factor model with predictors. In this case the items are congeneric effect indicators so the item set does not need to be exhaustive. However, I can also look at the MIMIC model as the latent variable being measured by a set of 'causal indicators', and the variables on the right could be thought of as distal outcomes associated with the 'formative' latent variable. In this case all the relevant 'causal indicators' need to be included or else there is a risk of model misspecification. I think this is the interpretation that Holger is referring to when he states that the latent variable needs to be correctly specified.

So for me, the MIMIC model is a bit like the Young Woman, Old Woman Ambiguous Figure or the Necker Cube illusion; what the model means flips between 2 plausible representations.

As for many replies on ReserchGate, I'd suggest that you read the seminal work by Bollen and Lennox from 1991( Article Conventional Wisdom on Measurement: A Structural Equation Perspective

Apologies for not being able to simply reply with a number to answer your question, but sometimes seemingly simple questions have complex answers, and that's what makes this work such fun.

Mark

Hi Mark,

I do not quite see, why all causes of the latent have to be included in either of both perspectives to represent a correct model. Missing "causal indicators" would be present in the error term of the latent and provide no reason for a misspecification.

My comment of the correctness is that the reflective part has to correctly specified, namely that the set of indicators have to share one latent (fulfilling the critical local independence assumption). Besides that, the model could be misspecified by causal indicators having direct effects on the reflective indicators. I do not know whether Ross' approach is able to detect this.

Besides this, Ceren Börüban , I would take a look into the following paper which presents some basic criticism of the MIMIC model.

Cadogan, J. W., Lee, N., & Chamberlain, L. (2013). Formative variables are unreal variables: Why the formative MIMIC model is invalid. AMS Review, 3(1), 38-49. doi:10.1007/s13162-013-0038-9

Best,

Holger

Mark Shevlin Holger Steinmetz Thanks for your help. Maybe i should keep the model simple and put the blame on parsiminous principle:)

best regards,

Hi Holger

To pick up on the point of causal indicators I'll copy and paste a section from Bollen's paper rather than doing it the disservice of restating the issue less eloquently.

Whoops, I couldn't drop in the image so it's attached. I can understand his position that omitting a causal indicator "gives an incomplete picture" of the latent variable. Yes, the omitted variables will be captured by the disturbance term of the latent variable, but the disturbance term could be thought of as a summary of misspecification.

Interesting discussion

Best wishes

Mark

thanks

Hi Mark Shevlin ,

this perspective reflects Ken's differentiation between a "formative variable" as a single composite (aka aggregate/index) vs. the "formative variable" as a true latent variable and its causal "indicators" as simple causes. The latter perspective was strongly recommended by the Howard and colleagues in two special issues (one in Psychological Methods (2000,5(3)) and the other in Journal of Business Research, 2008, 61). I found this differentiation and especially the latter perspective very appealing. Hence, when I mention misspecification, I always mean the misspecification of causal assumptions (about effects and constraints) implied by a causal system referring to effects between *existing variables*.

I would interpret the quote by Ken rather as a kind of "conceptual misspecification"--that is, does a measure of the "construct" represent all facets (in the composite view). However, I don't see (but I guess, this is only as I do not understand the statistical implications), how the incorporation of a singular latent variable (which has just one dimension and no "breadth") can miss facets (it is just a row of numbers) but it could be that leaving out one relevant facet changes the distributional structure of the composite and really biases the effect of the composite.

But that leads to the (rather philosophical question) what the causal effect of an aggregate means. If the aggregate is simply that--an aggregate of (causally influential) facets--then the composite has no real effect by itself. Its effect is rather the sum/average of the individual effects. This is comparable (in my view) to compound interventions that consist of multiple treatments meshed together.

In this scenario, I would not see a misspecifcation, as the (average) effect of the composite does not exist.

However, it may be that the composing mechanisms lead to the emergence of a truely exsting new variable which its own causal effect (aka "the sum is more than its parts"). Perhaps in this case, leaving out one ingredient would reflect a misspecification. I find this really brain-melting :)

If you don't know them already, I found the perspectives of John Cadogan and Nik Lee extremely enlightening. These authors additionally have a very critical view on the inflation of second-order variables which especially troubles me since I returned back to Psych this year.

Best,

Holger

Cadogan, J. W., Lee, N., & Chamberlain, L. (2013). Formative variables are unreal variables: Why the formative MIMIC model is invalid. AMS Review, 3(1), 38-49. doi:10.1007/s13162-013-0038-9

Lee, N., & Cadogan, J. (2016). Welcome to the desert of the real: reality, realism, measurement, and C-OAR-SE. European Journal of Marketing, 50(11), 1959-1968.

Lee, N., & Cadogan, J. W. (2013). Problems with formative and higher-order reflective variables. Journal of Business Research, 66(2), 242-247. doi:10.1016/j.jbusres.2012.08.004

Dear all,

The paper by Aguirre-Urreta et al. (2016) showing that only the reflective indicators in a causal-formative measurement model determine the meaning of the LV might also be useful. See also the follow up research by Guyon & Tensaout (2016).

Best regards,

Florian

References:

Aguirre-Urreta, M. I., Rönkkö, M., & Marakas, G. M. (2016). Omission of causal indicators: Consequences and implications for measurement. Measurement: Interdisciplinary Research and Perspectives, 14(3), 75-97.

Guyon, H., & Tensaout, M. (2016). Are formative indicators superfluous? An extension of Aguirre-Urreta, Rönkkö, and Marakas analysis. Measurement: Interdisciplinary Research and Perspectives, 14(3), 101-104.