Most commonly in SEM, the (unmeasured) latent variable is believed to be a "cause" of the (measured) indicators. In that case, the measured variables are called "effect indicators," each of which consists of a single observed measure. Sometimes, however, it makes more sense to consider the observed indicators as causing, rather than caused by, the latent variable. Then they are called "formative" indicators.

It seems to me that you are in the latter situation. It is hard for me to see indicators like cost overage, work quality, etc. as being caused by an unmeasured theoretical construct, success. Rather, it sounds like success is a consequence of such indicators. (You also say you think success is a consequence of competitive bidding, but that's apparently a different latent variable.)

With formative indicators, if you use a single question for each one you must assume that each question is a perfect measure of the indicator. It's usually better, and more realistic, to use multiple questions for each formative indicator. You can do so before (i.e., outside of and separate from) the SEM model by taking the sum or average of all the questions for a particular formative indicator (after first putting them on a common scale of, say 0 to 100, or else using z-scores). Maybe use the alpha coefficient to assess the reliability of the resulting composite score. Repeat that process for each formative indicator. Then use the several composite scores in place of your several formative indicators in SEM. And then there's the additional latent variable you mention, competitive bidding. I'm unclear what observed indicators you have for that.

Alternatively, you can do all that within SEM, by specifying a model that has Success as a latent variable, caused by several other latent variables, each one of which is a second-order formative "indicator" with multiple first-order effect indicators -- namely, the questions that would be combined into a composite score if you were doing this outside of the SEM framework. And also caused by another latent variable, bidding.

If my comments above misunderstand what you are trying to do, it could be helpful if you would provide a diagram of the SEM model you hope to estimate, showing all the causal arrows that you think link latent variables to each other and to their respective indicators.

EACH VARIABLE should contain more than one questions, i.e. 3 - 5 questions. This is to assure that there is less uncertainty in the responses. The expected value of the variable score is the mean of the score from 3-5 questions for the variable. on the other hand, if you have only one question for each variable, you may run the risk of design defect, i.e. if one question is unclear there is no context for that variable, this may lead to design defect. Each variable should have more than one indicator. Each indicator may be one question.

Burke D. Grandjean Thanks for your response. In my proposed research model competitive bidding would be the latent variable affecting project success indicators.

Competitive bidding affects these success indicators due to its characteristics in different ways. For example:-

Competitive bidding can affect cost as follows:-

1) would be affected because during design stage the contractor is not involved and this increases the risk of defect design or design with less buildability this would require changes and increase cost

2) it focuses more on lowest price rather than competence and experience and increases the risk of change orders

3) it is associated with fixed price type of payment estimated before project starts without incentives, however due to design changes the risk of cost overage is high

Competitive bidding can affect Time as follows:-

1)would be affected because during design stage the contractor is not involved and this increases the risk of defect design or design with less buildability this would require changes and increase time of completion

2) it focuses more on lowest price rather than competence and experience- this would affect time of completion due to reworks

3) it is associated with fixed price type of payment estimated before project starts without incentives, however due to design changes the risk of time overruns is high

Competitive bidding can affect quality as follows:-

1) it focuses more on lowest price rather than competence and experience

2) Reliance on complete specification before award and more weight of lowest price introduces opportunistic behaviours in case of gaps in specification & plans leading to inferior quality

3) It promotes reliance on third party (consultant) for inspections and that reduces contractor self-control which would enhance quality. Self control would increase contractors concern and commitment to quality.

Competitive can affect variation orders/change orders as follows:-

1) would be affected because during design stage the contractor is not involved and this increases the risk of defect design or design with less buildability this would require changes

2) Incomplete or errors in plans & specifications by the designer due to complexity of projects would lead to change orders

3) change of mind by owner would lead to change orders

Now, my dilemma is :- do you put these sub headings on each of the four indicators as questions in the question to solicit opinion and hope you have measured that aspect of the indicator or one has to measure these by other means? Your input will be greatly appreciated.

Paul Louangrath thanks a lot for your input on the number of questions for each variable

Regards Felix.

Thanks for clarifying. It now sounds to me like each aspect of success you mention (each subheading) should be a latent variable, and each of those latent variables would have several "effect" indicators (the several questions you intend to ask under each subheading). For example, "cost" is a theoretical (latent) construct that would be measured imperfectly by any one question (because of issues such as those noted by Paul Louangrath ), but it can be modeled more accurately using several questions about cost as multiple indicators. (As a rough conceptual guide, you might think of it as follows: if the error in any one question is random, then the errors in several questions will tend to cancel out, and thus reduce, when those questions are summed or averaged.)

Modeling each aspect of success as its own latent variable will allow you to estimate the effects of competitive bidding on each one separately. Your theoretical reasons for expecting those effects are plausible and worth testing. Though plausible, they are not (in my view) so self-evident as to support the face-validity of those aspects as actually measuring competitive bidding. Therefore, it's hard for me to see the aspects as simply indicators of bidding; instead, I see them as theoretical constructs whose relationships to bidding you want to examine.

I'm still unclear whether you have other multiple measures of competitive bidding (several questions asking how competitive the bidding process was), or just a single, yes/no variable (the process was formally competitive, or it wasn't). I think you need to have one or the other. If don't have any direct measures of bidding, then your first-order SEM model would not include bidding at all; it would just be a confirmatory factor analysis for the dimensions of project success. If the model shows that the dimensions are correlated, then an interpretation could be their correlation is due, at least in part, to a second-order latent variable, competitive bidding. A more complex SEM model might then be proposed to examine that interpretation.

If you do have several questions about competitive bidding, you can include a latent variable for competitiveness in your first model, with as many effect indicators as you have questions about that topic, and estimate the effect of that latent variable on each of the latent variables for different aspects of success (the subheadings, or "dimensions" of success).

But if you have only one indicator of competitive bidding, you probably have no choice but to assume it is a perfect measure and simply estimate the effect of that variable on each of the latent variables for the various different aspects of success in your model. You could do that within a SEM model, or form indexes of each dimension and run conventional regression analyses separately for each one. Perhaps you have hard data about whether a particular project was or was not put out for bids; if so, then the assumption that this is measured without error might be quite defensible.

As to your "dilemma": It's often a close call whether or not to include subheadings in the text of a questionnaire. Including the subheadings may help respondents to focus on each specific aspect in turn. But that might also encourage an unconscious response-set, wherein the respondents try to make their answers consistent within each subhead (thereby introducing non-random error, which magnifies rather than canceling out, and would have to be reflected in your SEM model with correlated error terms).

On balance, I generally prefer to omit the subheadings, and also to mix up the order in which the questions are asked so that the cost questions (for example) are not asked consecutively but are instead scattered out among all the other questions about time, etc. Randomizing the order of the questions improves the chances that the measurement errors in the indicators are themselves random, greatly simplifying the problems of getting a statistically "identified" SEM model with acceptable "fit" statistics.

Hi Burke D. Grandjean Thanks for your response, very informative. Please find attached herewith a model that i intend to use. The model has been developed from literature where competitively awarded projects suffer ; cost overrun, schedule overruns, quality issues and frequent change orders. The idea of the research to solicit opinion or perception of practitioners on the issue. Your comment will be appreciated.

Regards Felix.

Your arrow diagram looks fine to me. Do you have any direct measure(s) of competitive bidding? (either a dichotomy, bid vs. no-bid, or one or more questions about the degree of competitiveness). If so, that should be shown in the model as effect indicator(s) of the latent variable of bidding, at the far left in your diagram.

If you don't have any direct measures of bidding, then you'll be doing a second-order CFA on the estimated correlations among the four latent variables of success, in the middle of your diagram. Those can run into problems in identification and/or fit but, in principle, should be do-able.

In all this, I'm assuming that you're designing the research in such a way that competitive bidding is, in fact, variable. If your design has data at the project level, then presumably you will know, and can code, whether each project was or was not let out for bids. If your data consist only of the opinions of practitioners, in general rather than specific to a particular project, then you have to construct the questions so that they can give different opinions about cost, etc. depending on whether they are being asked about bid projects in general or no-bid projects in general. Constructing a questionnaire to do that reliably could be challenging.

If bidding is not explicitly a variable in your design, then your SEM can only examine the practitioners' overall opinions about cost, time, etc. Those opinions could be correlated for any number reasons, not just because of their possible relationships to bidding. So if your CFA does find a second-order latent variable that accounts for the correlations among the first-order latents, interpreting that second-order factor as "bidding" would take a leap of faith that might be hard to defend.

I hope you find these musings helpful; best of luck with your research!