I want tips to design "Structural Equation Modeling" a good questionnaire (size of sample, number of items….), any suggestions can help to reach a good work for my dissertation titled "The Role of Management Competencies in reinforcing Job Engagement case study (Higher Education sector in Laghouat town –Algeria-).
i hope some suggestions about how to reach to this goal
Thank you
kind regard
Hi Widad,
here are my tips:
Learn and understand the meaning of and differences between the terms "construct", "latent variable", "common factor", "formative", "reflective", "aggregate" and "composite". These are fundamental terms and some are identical, others similar, and again others fundamentally different.
When you want to incorporate latent variables into your model (and not multi-facetal composites), learn to know what a latent variable is and avoid typical pitfalls associated with latents (e.g., that latents have some "breadth", are "constructions" and so on).
The goal of this learning process should be that you have a clear understanding of the latent(s) YOU want to incorporate into your model. It is the belief of a specific part of the world that exists and has causal relevance on other parts of the world. This part is as specific as possible - that is a latent variable is a singular, uni-dimensional entity (ONE variable). Once your imagination of the latent(s) is clear, identifying measures is straightforward. Start with selecting one single best indicator that is as closely related to your latent as possible. Then identify a second indicator which (as the first) is a pure and direct reflection of the same underlying latent. Avoid a too strong semantic deviation of both indicators as you will run the risk of measuring something different. Then select a third indicator is this is possible. Than you're done.
The reasonableness of selecting multiple indicators requires a solid understanding of the "common factor model". Note that latent variables are not necessarily common factors: The common factor model presumes that a set of indicators shares an underlying latent variable and that this latent causes the item responses and, hence, the correlations among the indicators. At the same time, the common factor implies the conditional independence of the indicators given the latent. This is the relevant "testable implication" (another important phrase) of the common factor model which is tested in the chi-square test. A violation of this implication may be trivial (that is, the common factor is a solid model albeit some deviations, like correlated errors) or fundamental (the common factor overall is nonsense). And again: A latent variable does not have to be a common factor (see the paper by Hayduk and Littvay). Check YOUR understanding of the structure among the indicators.
Beyond that specific purpose (i.e., testing measurement models), testing causal structures (the measurement models as well as the overall causal structure) is important to make any sense of SEM. That is, learn what a model implies for the data. Again some new terms are "path tracing rules", and "d-separation". Explaining away misfit of a model does not serve anyone. Exploring it and providing future implications for improvement or enrichment of the model in my point of view is its essence.
Sometimes, your imagination of a construct is rather that of an index, composite or aggregate (not a latent variable). This is not the best solution (as a single composite masks the role of its ingredients) but sometimes the only practical solution. In this case, again have a clear conceptualization of the facets that are essential for the composite (the keyword here is "content validity"). And most importantly: do not force the components into a reflective, common factor model. Misspecified common factor models are the most prevalent reason for misfitting models. Often the researchers have a clear "composite-imagination" but nonetheless specify it as a common factor structure.
One last comment about validity: Validity means that your indicators reflect the very latent that you think they measure. Validity is supported (not proven) by
a) the model must cleanly fit. A significant chi-square is an alarm signal that something is wrong. Again, it may be trivial but you have to respect and investigate this. Often the question wording together with inspecting the local misfit can lead to a Eureka-idea :) But sometimes not :(
b) the factor loadings have to make sense. As aforementioned, you intent to incorporate a latent with a specific intended meaning. Based on this intention, you select the indicators. This implies that you have some kind of expectations about the empirical relationship between both. Sometimes, moderate loadings are exactly what you would expect if the latent is the latent you try to "hit" but most often, you will expect very strong loadings. As I voted above for a selection of very conceptually close indicators, I always would expect loadings in the .80-.90s. A sign of problems are substantially different loadigns (one with 1.1, the other with 2.1). Than check if this can be explained (most often it can't as the indicators were supposed to be parallel measures).
Please refrain from rules of thumb about expectable loadings. They stem from a time in which researchers primarily used factor analysis (or even principal component analysis) to reduce the number of items - not to model a latent based on a realist perspective on the world.
The most important step towards a valid measurement is "cognitive pretesting"! No postoc test can give you more information than simply talking with people about your measures. The will explain their item response, give examples and exemplary situations which tell you if you are on the right way (of measuring your intended latents).
Below, I posted a bunch of papers that strongly influenced by view on the aforementioned topics.
Start your journey and don't get distracted by the many many problematic and misleading journal articles and recommendations that you will observe.
Best,
Holger
Bollen, K. A. (2002). Latent variables in psychology and the social sciences. Annual Review of Psychology, 53, 605-634.
Bollen, K. A., & Bauldry, S. (2011). Three Cs in measurement models: Causal indicators, composite indicators, and covariates. Psychological Methods, 16(3), 265-284.
Borsboom, D., Mellenbergh, G. J., & van Heerden, J. (2004). The concept of validity. Psychological Review, 111(4), 1061-1071.
Borsboom, D., Mellenbergh, G. J., & van Heerden, J. (2003). The theoretical status of latent variables. Psychological Review, 110(2), 203-219.
Chen, B., Pearl, J., & Kline, R. B. (forthcoming). Graphical tools for linear path models. Psychometrika.
Chen, B., & Pearl, J. (2014). Graphical tools for linear structural equation modeling. 1-23.
Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5(2), 155-174.
Hayduk, L. A., & Littvay, L. (2012). Should researchers use single indicators, best indicators, or multiple indicators. BMC Medical Research Methodology, 12(159), 1-17. doi:10.1186/1471-2288-12-159
Hayduk, L. A. (2014). Shame for disrespecting evidence: The personal consequences of insufficient respect for structural equation model testing. BMC Medical Research Methodology, 14(1), 124-124. doi:10.1186/1471-2288-14-124
Hayduk, L. A. (2014). Seeing perfectly fitting factor models that are causally misspecified: Understanding that close-fitting models can be worse. Educational and Psychological Measurement, 1-22. doi:10.1177/0013164414527449
Hayduk, L. A., Cummings, G. G., Boadu, K., Pazderka-Robinson, H., & Boulianne, S. (2007). Testing! testing! one, two, three - Testing the theory in structural equation models! Personality and Individual Differences, 42(5), 841-850.
McIntosh, C. (2007). Rethinking fit assessment in structural equation modeling: A commentary and elaboration on Barrett (2007). Personality and Individual Differences, 42(5), 859-867.
Thoemmes, F. (2015). Reversing arrows in mediation models does not distinguish plausible models. Basic and Applied Social Psychology, 37(4), 226-234. doi:10.1080/01973533.2015.1049351
Thoemmes, F., Rosseel, Y., & Textor, J. (2018). Local fit evaluation of structural equation models using graphical criteria. Psychological Methods, 23(1), 27-41. doi:10.1037/met0000147
Willis, G. B. (2005). Cognitive interviewing: A tool for Improving questionnaire design. Thousand Oaks, CA: Sage.
Thank you so much Dr Ajit kumar Roy
, i would like to know more about the good tips to design "Structural Equation Modeling" a questionnaire (a survey )
First The division of the questionnaire into the groups of each group represents a variable of the study variables. Second, the number of paragraphs in each group should be at least 4 and not more than six. Thord@ using of EFA
Dear scholars " how to design a Structural Equation Modeling surveys"?
Your survey design is dependent on which SEM you want to adopt e.g. Covariance-based SEM (software e.g. AMOS) or Variance-based SEM (software e.g. SmartPLS). Following are some of their attributes related to survey design (for other attributes of different SEM types, you can refer to the following RG link):
3) Sample Size
Variance-based SEM - Support small sample e.g. < 100
Covariance-based SEM - Need sizeable sample e.g. > = 300 (so you need to collect more random samples if you'd decided to go with Covariance-based SEM)
4) Data Type
Variance-based SEM - Support both metric & non-metric data types
Covariance-based SEM - Only support metric data types (so you need to structure your survey questionnaire in metric data types if you'd decided to go with Covariance-based SEM)
5) Construct Type
Variance-based SEM - Support both reflective & formative constructs
Covariance-based SEM - Support only reflective constructs (so you need to develop / rephrase your questions in survey questionnaire based on reflective type i.e. arrows coming out from construct to its measurement items)
6) Construct-Item Relationship
Variance-based SEM - Support Construct with single-item
Covariance-based SEM - Support Construct with three-items & above (so you can't have one construct only to have one measurement item)
https://www.researchgate.net/post/What_is_Structural_Equation_Modeling2
Hi Widad,
here are my tips:
Learn and understand the meaning of and differences between the terms "construct", "latent variable", "common factor", "formative", "reflective", "aggregate" and "composite". These are fundamental terms and some are identical, others similar, and again others fundamentally different.
When you want to incorporate latent variables into your model (and not multi-facetal composites), learn to know what a latent variable is and avoid typical pitfalls associated with latents (e.g., that latents have some "breadth", are "constructions" and so on).
The goal of this learning process should be that you have a clear understanding of the latent(s) YOU want to incorporate into your model. It is the belief of a specific part of the world that exists and has causal relevance on other parts of the world. This part is as specific as possible - that is a latent variable is a singular, uni-dimensional entity (ONE variable). Once your imagination of the latent(s) is clear, identifying measures is straightforward. Start with selecting one single best indicator that is as closely related to your latent as possible. Then identify a second indicator which (as the first) is a pure and direct reflection of the same underlying latent. Avoid a too strong semantic deviation of both indicators as you will run the risk of measuring something different. Then select a third indicator is this is possible. Than you're done.
The reasonableness of selecting multiple indicators requires a solid understanding of the "common factor model". Note that latent variables are not necessarily common factors: The common factor model presumes that a set of indicators shares an underlying latent variable and that this latent causes the item responses and, hence, the correlations among the indicators. At the same time, the common factor implies the conditional independence of the indicators given the latent. This is the relevant "testable implication" (another important phrase) of the common factor model which is tested in the chi-square test. A violation of this implication may be trivial (that is, the common factor is a solid model albeit some deviations, like correlated errors) or fundamental (the common factor overall is nonsense). And again: A latent variable does not have to be a common factor (see the paper by Hayduk and Littvay). Check YOUR understanding of the structure among the indicators.
Beyond that specific purpose (i.e., testing measurement models), testing causal structures (the measurement models as well as the overall causal structure) is important to make any sense of SEM. That is, learn what a model implies for the data. Again some new terms are "path tracing rules", and "d-separation". Explaining away misfit of a model does not serve anyone. Exploring it and providing future implications for improvement or enrichment of the model in my point of view is its essence.
Sometimes, your imagination of a construct is rather that of an index, composite or aggregate (not a latent variable). This is not the best solution (as a single composite masks the role of its ingredients) but sometimes the only practical solution. In this case, again have a clear conceptualization of the facets that are essential for the composite (the keyword here is "content validity"). And most importantly: do not force the components into a reflective, common factor model. Misspecified common factor models are the most prevalent reason for misfitting models. Often the researchers have a clear "composite-imagination" but nonetheless specify it as a common factor structure.
One last comment about validity: Validity means that your indicators reflect the very latent that you think they measure. Validity is supported (not proven) by
a) the model must cleanly fit. A significant chi-square is an alarm signal that something is wrong. Again, it may be trivial but you have to respect and investigate this. Often the question wording together with inspecting the local misfit can lead to a Eureka-idea :) But sometimes not :(
b) the factor loadings have to make sense. As aforementioned, you intent to incorporate a latent with a specific intended meaning. Based on this intention, you select the indicators. This implies that you have some kind of expectations about the empirical relationship between both. Sometimes, moderate loadings are exactly what you would expect if the latent is the latent you try to "hit" but most often, you will expect very strong loadings. As I voted above for a selection of very conceptually close indicators, I always would expect loadings in the .80-.90s. A sign of problems are substantially different loadigns (one with 1.1, the other with 2.1). Than check if this can be explained (most often it can't as the indicators were supposed to be parallel measures).
Please refrain from rules of thumb about expectable loadings. They stem from a time in which researchers primarily used factor analysis (or even principal component analysis) to reduce the number of items - not to model a latent based on a realist perspective on the world.
The most important step towards a valid measurement is "cognitive pretesting"! No postoc test can give you more information than simply talking with people about your measures. The will explain their item response, give examples and exemplary situations which tell you if you are on the right way (of measuring your intended latents).
Below, I posted a bunch of papers that strongly influenced by view on the aforementioned topics.
Start your journey and don't get distracted by the many many problematic and misleading journal articles and recommendations that you will observe.
Best,
Holger
Bollen, K. A. (2002). Latent variables in psychology and the social sciences. Annual Review of Psychology, 53, 605-634.
Bollen, K. A., & Bauldry, S. (2011). Three Cs in measurement models: Causal indicators, composite indicators, and covariates. Psychological Methods, 16(3), 265-284.
Borsboom, D., Mellenbergh, G. J., & van Heerden, J. (2004). The concept of validity. Psychological Review, 111(4), 1061-1071.
Borsboom, D., Mellenbergh, G. J., & van Heerden, J. (2003). The theoretical status of latent variables. Psychological Review, 110(2), 203-219.
Chen, B., Pearl, J., & Kline, R. B. (forthcoming). Graphical tools for linear path models. Psychometrika.
Chen, B., & Pearl, J. (2014). Graphical tools for linear structural equation modeling. 1-23.
Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5(2), 155-174.
Hayduk, L. A., & Littvay, L. (2012). Should researchers use single indicators, best indicators, or multiple indicators. BMC Medical Research Methodology, 12(159), 1-17. doi:10.1186/1471-2288-12-159
Hayduk, L. A. (2014). Shame for disrespecting evidence: The personal consequences of insufficient respect for structural equation model testing. BMC Medical Research Methodology, 14(1), 124-124. doi:10.1186/1471-2288-14-124
Hayduk, L. A. (2014). Seeing perfectly fitting factor models that are causally misspecified: Understanding that close-fitting models can be worse. Educational and Psychological Measurement, 1-22. doi:10.1177/0013164414527449
Hayduk, L. A., Cummings, G. G., Boadu, K., Pazderka-Robinson, H., & Boulianne, S. (2007). Testing! testing! one, two, three - Testing the theory in structural equation models! Personality and Individual Differences, 42(5), 841-850.
McIntosh, C. (2007). Rethinking fit assessment in structural equation modeling: A commentary and elaboration on Barrett (2007). Personality and Individual Differences, 42(5), 859-867.
Thoemmes, F. (2015). Reversing arrows in mediation models does not distinguish plausible models. Basic and Applied Social Psychology, 37(4), 226-234. doi:10.1080/01973533.2015.1049351
Thoemmes, F., Rosseel, Y., & Textor, J. (2018). Local fit evaluation of structural equation models using graphical criteria. Psychological Methods, 23(1), 27-41. doi:10.1037/met0000147
Willis, G. B. (2005). Cognitive interviewing: A tool for Improving questionnaire design. Thousand Oaks, CA: Sage.
- Badges
- Science topic
- Similar topics
- Mathematics