Hi, 

nice to know you.

1.  The described data set allows to perform a good analysis. I'm just wondering about measurement scale used for the "safety outcomes" variable; even if the procedure will require a statistical standardization of the variable's score, the outcomes couldn't fit the goodness of the statistical model.

2.  I suggest you to follow the methodological procedure required when performing the SEM analysis, i.e. normal distribution of each variable, explorative and confirmatory factor analysis (verifying the multidimensional nature of the variables), SEM. These steps will allow to "design" the model and the formulated hypothesis according to the variable characteristics. Moreover, I suggest you to consider in the model variables with the same number of items (are the proposed scales already validated in literature or are you developing a new ones?). You can have a look to some papers (and the related references) on my profile, which describe, in general, the methodological procedure with SEM. 

3. According to the expected 400-500 respondents, you will not have problem with the SEM analysis.

Best,

Cosimo

I agree with Cosimo.

I think that your study is suitable for SEM.

Also you can ckeck other results from generalized SEM (Stata does it).

Best regards,

Pilar

Hi, I'm afraid I have to disagree slightly with the previous comments. While you certainly have enough observations with respect to 3 of your 4 measures to conduct SEM analysis (which can include latent variable modeling, etc.), the fourth measure consisting of only five observations changes this problem somewhat. Specifically, it sounds like you have nested data, where you will have worker responses nested within construction sites. As a result, you'll have three first-level variables and one second-level variable (first-level being worker responses, second-level being construction site. This may be problematic as only five second-level responses will likely result in very limited power for any analyses involving that variable; it won't have much variability.

Since the variable with only five site observations will be your outcome, my recommendation would be to look for the frequency that those events occurred for the workers you surveyed, rather than an overall score for the site. That is, for those events that occurred for the site, how many can you use to tie to a specific worker or set of workers? Injuries? Were certain workers involved with injuries to non workers? Were certain workers present at the time of these events?I'd seriously consider ways to better link worker responses to the events you're interested in. Then you can treat individual worker outcomes as an outcome of individual worker responses, which is more informative anyway (in my opinion). I'd still be interested in controlling for the nested structure of the data, but now it would be a matter of controlling for site-related variance rather than a site-related outcome. Also, instead of your numerical scale, you may want to consider doing the entire analysis with the final outcome as a dichotomous variable; either for individual target items, or for some combination of all of them. That is, whether or not any item occurred and was linked to a worker or workers (yes/no). This results in a logistic regression for the final outcome, but that's fine since you're interested in occurrence likelihood/risk anyway.

Finally, I agree with previous comments regarding mediation analysis. You may want to incorporate mediated and indirect effects of the measures you indicate earlier in your model leading to your final outcome. I would consider having the final outcome regressed on all three predictors at once initially, along with your lagged path. From there you can try removing and adding regression paths as they seem fit. I would then compare your optimized model against your proposed model to see which is more tenable based on your data.

I'm not sure what your access to articles is, so I'm including some open-source links on multilevel modeling topic that may be useful if you stick with your final outcome variable as presently described, plus one book that I'd liked.

The book link is here, but you can probably borrow/buy a used copy: https://us.sagepub.com/en-us/nam/hierarchical-linear-models/book9230

Online articles and presentations:

http://www.gllamm.org/msem_chap_06.pdf

http://www.ats.ucla.edu/stat/mplus/seminars/mlmMplus_JH/Hopkins_Day2_fixed_May2005_two_per_page.pdf

https://www.statmodel.com/download/pzz_012610_for_web.pdf

Some general open access articles on multilevel SEM: http://journal.frontiersin.org/researchtopic/1530/multilevel-structural-equation-modeling

I agree with Joseph Edward. Additionally, five construction sites is a too small sample if you want to include "site" as observed variable. Do you have theory behind this " model" ?

No problem if your unit of analysis is not "sites". You are not interested to compare between sites but the factors as a whole. However, you need to prove that the data behavior from different sites are identical. You may use Lavenne's Test.

I can only say that  you have not any problem to do SEM analysis by 50-item questionnaire but about the 5 sites it is small to do a SEM analysis if the "sites" are only the observed variables but if the "sites" are latent it would be OK.

Joseph Edward's answers provide the best explanation of the suitability of your data for SEM. Having only the 5 observations for your fourth factor will cause issue for SEM. The comments pertaining to mediation are also good suggestions based on the description of your study and the potential research model you have attached.

If your data are nested into those 5 construction sites, and you still want to use the multiple questions to create latent variables, you might want to try a latent multilevel model. Two resources for those are: Hox, J.J. (2010). Multilevel analysis: techniques and applications, and Peugh, J.L. (2010). Practical guide to multilevel modeling. You should be able to create your latent variables using exploratory and then confirmatory factor analysis, obtain their factor scores for all participants/subjects, and use those factor scores to group mean center around in the multilevel regression. Essentially, you can create your factors 1 through 3 and use the factor scores for each participant/subject as a "variable" in your regression model similar to how you would use any other variable such as age or a scaled item score such as safety level (that could be coded as low, medium, and high). But even then, you might still run into the problem of statistical power and variability (like Joseph mentioned). I would second Joseph's idea of looking at the frequency those events occurred if safety outcomes are your dependent variable. You can use the factor scores as variables in the logistic regression to see the impact of each those factors on safety outcomes. The use of the multilevel model or simple regression model will depend on if your data are nested. You can run a multilevel model to see if you have a nesting effect or not and then proceed with the best option that fits your data as well as that answers your research question. There might be a small possibility that the research question might need to be reworked depending on how you wish to carry out data analysis. Just to make sure you utilizing an appropriate analytic plan.

I apologize for not being familiar with your area of research. Most of my applications of SEM and other latent variable modeling is in criminal justice and criminology when using various scale scores similarly constructed by multiple questions (e.g. risk assessment tools that utilize many questions to address offenders' risks and needs that fall under some predetermined domains (factors) such as substance abuse, physical and mental health, aggression, attitudes and behaviors, etc.). I have utilized factor scores in non-latent regression modeling to predict recidivism

If my understanding is correct, you have a 50 item scale. Make sure that you get at least 250 usable responses. Run each site separately and then compare.