I'm very new to SEM (and relatively new to stats generally). I would like to ask whether my plans generally sound reasonable before I get lost for days in the literature.

The model that I try to work with is something very close to the following:

  1. Say my dependent variable is "healthiness of food consumption". My base for this is: (A) 20 survey items that captured how often people bought certain food products within the last month. The scale is ordinal, 5-point. The data is highly skewed towards non-usage for most products. For that reason I have dichotomized the variables into regular consumption and irregular consumption of product x1, x2, x3, ... . (B) In addition to consumption frequency, I have expert ratings on how healthy every food product is (on a 5-point scale).

  2. My final aim is to predict the "Healthiness of food consumption" by three independent variables, personality factors which are measured by three to four items (good reliability) and .

What I plan to do:

  1. In regression analysis, I would have computed "healthiness of food consumption" as a weighted summative index. "Healthiness of food consumption" = "Frequency of consumption of beer" * "expert rating of healthiness of beer" + "Frequency of consumption of avocado" * "expert rating of healthiness of avocado" + ... Now I would like to use SEM, but I thought modelling a traditional (reflective) continuos latent variable would not be the way to go. Consumption decisions are based on many factors, so that indiciators don't correlate highly.

My questions (please forgive me if they sound very naive):

  1. Am I right that in the SEM literature "composite variables" come closest to summative indices, or should I look elsewhere?

  2. Is it generally possible to compute something that resembles a weighted summative index in SEM?

  3. If formative variables are the conceptually right way to go, Is it possible to use them as endogeneous variables in a simple model like the one that I explained above?

I would be very happy to just get a general impression whether I'm heading completely in the wrong direction and whether such a procedure sounds generally feasible? If it were feasible, I would then dig deeper into the challenges that come with the usage of formative indices?

(PS.: Of course, the quickest way would be to compute an index outside the SEM model first. However, I would like to make use of the FIML-functionality. Many respondents did not answer one or two items, and with 20 items this would lead to many lost cases (if I don't substitute them with means or the like.) Hope this makes sense as well. :))

(PPS.: I do have access to Lavaan and Mplus.)

  1. Yes.
  2. Yes. But not always. You need at least two variables to be regressed on that formative latent.
  3. No. You cannot use the formative indicated latent as an endogenous variable. Think about in terms of path tracing. The arrows go from your measured variables to the latent. The arrows from the predictor go from another variable to the latent. The implied correlation/covariance between the two sets of variables is zero.
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  • $\begingroup$ Many thanks Prof Miles! Your answer will save me a few days of work. (I started to read into the debate between Diamantopoulos (2013) and Nick et al. (2013), but it would have taken long hours to reach a point where I could make my own judgement.) For my project, I will use multiple imputation to handle missingness, produce a weighted summative index and use this index as a manifest endogenous variable in the model. $\endgroup$ – Daniel Apr 18 '16 at 11:06
  • $\begingroup$ You're welcome. Do you have the full refs for those two papers? I'm not familiar with them. (Also, no need to call me Prof - I'm not. :) $\endgroup$ – Jeremy Miles Apr 18 '16 at 16:22
  • $\begingroup$ It's a set of articles that all in AMS Review 3(1). This is the rejoinder on comments on their original article that also appeared in the special issue: Cadogan, J. W., Lee, N., & Chamberlain, L. (2013). Formative variables and unreal variables: why the formative MIMIC model is invalid. AMS Review, 3(1), 38-49. 10.1007/s13162-013-0038-9 $\endgroup$ – Daniel Apr 19 '16 at 16:47
  • $\begingroup$ This is their original article: Lee, N., Cadogan, J. W., & Chamberlain, L. (2013). The MIMIC model and formative variables: problems and solutions. AMS Review, 3(1), 3-17. 10.1007/s13162-013-0033-1 $\endgroup$ – Daniel Apr 19 '16 at 16:49
  • $\begingroup$ (Sorry about the Prof, I thought I read it on your website after reading another helpful answer from you some time ago :)!) $\endgroup$ – Daniel Apr 19 '16 at 16:53

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