Vincenzo,

Rimantas explained it quite convincingly, I would also opt for latent variable models.

Another point: I would not use products of indicators, such as BB1*OE1. The reasons are;

- The distribution of products is always highly kurtotic, therefore you will have problems with parameter estimation, ML is definitely not appropriate.

- If you include the product you need to include both linear predictors, too. This is comparable to moderated regression: You have to include two predictor variables and its product in order to test the moderator effect.

HTH

Karin

Hi Vincenzo,

although I agree with my colleagues that latent variables have many advantages, the question (in case of modeling the beliefs) is would such latent variables reflect something meaningful? As someone who works with the TPB for almost 10 years now, I exactly struggled with the question if the single beliefs are specific influences on the respective TPB core variable (e.g., atttitude) or if they are merely reflections of a more global belief factor. Actually, I tend towards the former - as e.g., the attitude should be influenced by many differtent thoughts and convictions about the behavior in question. 

In this case, modeling a latent overall belief factor would represent nothing meaningful and hence, its effects on the core variables would be nonsence. On the other hand, if specific beliefs are simply an expression of a global belief, than modeling specific beliefs would be nonsense.

We cannot help to model the very kind of structure which we think is plausible from a theoretical point of view and stick to it. Hence, my decision is always to stick with the specific beliefs, and use these as single-indicator latent variables. There are occasions where two beliefs are so simililar in their content that modeling a latent variable makes more sense. Again, express your theoretial imagination of the structure.

That being said, I agree with Karin on the use of BB*OE products, see

Evans, M. G. (1991). The problem of analyzing multiplicative composites - Interactions revisited. American Psychologist, 46(1), 6–15.

The practical problem is that it is simply impossible to set up a complete belief structure with all the linear predictors as well as their product terms in one model. My TPB models usually contain around 15 beliefs - this would result in 15 belief variables, 15 evaluations as well as 15 product terms.....

Consequently, I came to the only solution to avoid the evaluations and simply model only the beliefs. The results are the main effects of the singular beliefs without considerations of their subjective performance. Not ideal, though.....

Best,

Holger

Dear Holger,

thank you for your reply. I am new to TPB. Your arguments sound extremely reasonable. I will check your publications on RG. Thank you,

V

Dear Vincenzo,

There are one or two summer schools I know of that offer training on TPB with or without SEM. This might be of great interest for you:

http://wwwen.uni.lu/international/a_la_une/summer_school_the_theory_of_planned_behaviour

http://www.uib.no/en/rs/ghig/70905/workshop-21-%E2%80%93-23-may-2014

My opinion converges with that of Mr Steinmetz.  Using SEM is the best option if you can afford to collect a big sample size.

However I understand that you have not measured attitude toward the behaviour directly but rather want to use the composite score of Behavioural Beliefs*Outcome Evaluation as a proxy? If I am not mistaken, each behavioural beliefs has its own outcome evaluation, right?

Since I am unsure that Attitudes are the pure statistical interaction of Beliefs*Outcome Evaluation (or be predicted by their interaction... this probably has been tested before), you could use each the product of each belief and its evaluation as parcels (observed indicators) to form a latent attitude variable. Here is an important article that explains the pros and cons of using parcels:

https://www.researchgate.net/publication/228079497_To_parcel_or_not_to_parcel_Exploring_the_question_weighing_the_merits

However if you do have measured attitude items, you could always test whether latent Beliefs & Outcome Evaluation variables interact to predict a latent attitudes variable. There may be a difference between the method used to estimate the interaction term, though. The Klein & Moosbrugger (2000) Latent moderated equations method may be more straight forward, but the original Kenny-Judd method (1984/1994) may more closely match the composite nature of each belief*outcome pair.  Here are some references about interactions:

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

Jöreskog, K. and Yang, F. (1996): Nonlinear structural equation models: the Kenny-Judd model with interaction effects. In G.A. Marcoulides and R.E. Schumacker (Eds.): Advanced Structural Equation Modeling. Mahwah, NJ: Lawrence Erlbaum, 57-89.

Kenny, D.A. and Judd, C. M. (1994): Estimating the non-linear and interactive effects of latent variables. Psychological Bulletin, 96, 201-210.

Klein, A. G., & Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. Psychometrika, 65, 457–474.

Marsh, H. W., Wen, Z. L., & Hau, K. T. (2006). Structural equation models of latent interaction and quadratic effects. In G. R. Hancock & R. O. Mueller (Eds.), A second course in structural equation modeling. Greenwich, CT: Information Age Publishing

Publications by those who organized the TPB*SEM workshop might be the most helpful in telling you what is the most "advanced" way of testing your data. 

Have fun!

Pier

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

http://www.uib.no/en/rs/ghig/70905/workshop-21-%E2%80%93-23-may-2014

http://wwwen.uni.lu/international/a_la_une/summer_school_the_theory_of_planned_behaviour

Article To Parcel or Not to Parcel: Exploring the Question, Weighing...

Hi Vincenzo,

I am facing the same dilemma of whether to use sum of product of behavioral beliefs and outcome evaluations as single indicator or to use product of behavioral belief and outcome evaluation as separate indicators. Please share the option used by you and the reason (support) for using the same. In context of multiple regression, first option is recommended by certain publications and TPB also recommends it.

Thanks

Dear Professor Gupta,

Until Vincenzo responds, maybe I can provide additional insights that will be hopefully useful to you.

Firstly, I would really appreciate that you name some of those publications you mentionned that use/support the first option. My knowledge of the litterature is not fresh enough to think of a specific example, except maybe an unpublished institutional document in French language.

In my opinion, it all depends on whether attitude has been measured with its own items (and not through BB or OE items), and the general purpose of the study: predicting attitude and intentions in a formal test of the theory, or predicting behaviour using the "parcimonious" version of the model.  What is the purpose of your research?

There is a rationale to use separate BB & OE variables (sum/average of BB items & sum/average of OE items) : to test their relative contribution to an attitude variable (sum/average of dedicated attitude items) or intention.The importance of the interation between BB&OE can be assessed in multiple regression, in order to give information such as "The two constructs best predict attitude/intention in presence of the other, but only one construct significantly predict attitude in absence of the other". SEM allows to test this at a deeper level with the methods of Klein & Moosbrugger or Kenny & Judd by defining the latent interaction at item level (i.e. having each BB item interact with its own OE item and not with the others).

The rationale to use the sum of all BB*OE pair products to make a cool, super-saiyan composite variable of attitude is if you wanted to measure attitude with the purest, theorically sound indicators (OE-weighted behavioral beliefs) to maximize its variance in a parsimonious model of intention or behavior (thus optimizing tests of mediation). This is at the condition of measuring most important modal beliefs and having enough room in your questionnaire.  This attitude variable can be observed (sum/average) or latent from BB*OE pair product used as indicators (whether those are really parcels is debatable).

My point is, it seems to make more sense to have BB items interact with their own OE, individually instead of as a group. In the latter case, the high score on a BB item would multiply a high score on an unrelated OE item and contribute to a higher composite score, while this would not happen in the former case. Finer engineering!

I hope that helps! Feel welcome write in private if you want to discuss further.

Regards,

Pier

Dear Pier,

Your insights are very helpful.

Many thanks for the same.

Regards,

Anoop

Dear Pier-Eric,

I have a similar TPB model with twenty beliefs, and I tried to include goal related beliefs. I have a rather dumb question here. When we define the behaviour (which in my case is a 0,1 no or a yes), which is of course is the dependent variable; as a single ordinal indicator latent behaviour? I ask this because I tried using both STATA and LISREl. While STATA did allow me to define behaviour as an observed dependent variable, in Lisrel if I define it as an observed variable, the software uses it as another indicator variable to an independent latent variable. Thus the approach of using a single ordinal indicator dependent variable.

Thanking you in advance

Sandeep

Dear all,

Thank you very much for your thoughts and recommendations. I’m currently facing the same problems in applying SEM for the Theory of Planned Behaviour. Does anyone has got an update or has solved Vincenzo’s problem?

Further, I wondered if anyone has made use of item parcelling for TPB belief items (both, parcels summarising different beliefs and parcels which sum/average the belief*evaluation component). I found only a few TPB studies that applied item parcelling to model the relation between belief components and direct measures (e.g., BB and ATT; two parcels for each belief component; de Leeuw, Valois, Ajzen, Schmidt, 2015; Kaiser, Hübner, Bogner, 2005 ). Two parcels as indicators per latent belief variable reflect a locally underidentified LV which is widely perceived as suboptimal in SEM. In my opinion, parcels might be useful to estimate model fit indices when using complex TPB models as they reduce the number of free parameters and thus, lowers sample size requirements. But as Pier (it’s debatable whether multiplicative terms are parcels) and Holger (beliefs as LV hide the influence of a particular belief) mentioned, parcels and LV might be contradictory for identifying the influence of particular beliefs.

Understanding beliefs as latent variables raise the question if the belief LVs represent formative or reflective measurement models. Does anyone have any suggestion?

Best regards

Benedikt

Article Using the theory of planned behavior to identify key beliefs...

Article Contrasting the Theory of Planned Behavior With the Value‐Be...

Hi .. I have the same problem in understanding beliefs as latent variables raise the question if the belief represent formative or reflective measurement models.

I read an article yesterday and only to be found that it is formative measure.. Anyone would like to share any other relevant articles represent beliefs as formative measure?

Hi Geetha, I actually stumbled across this old thread and saw that I provided a response almost 3 years ago (geez, time is running!). At that time, I argued about using singular belief items as specific causal entities and not to specify latent belief factors. I certainly kept the opinion about the latent factor but I changed my view about the specific belief items.

Together with a doctoral student, I applied network analysis to model the belief structure which changed my mind: Beliefs are organized in cognitive networks (google spreading activation theory) in which beliefs about some similar issue are clustered together - hence treating singular beliefs as specific causes neglects this issue. Since you get partial regression effects in which the associations with other/similar beliefs are controlled, I am sure this will result in strongly downward biased estimates. Rather, I am convinced that a whole part of the network associated with certain beliefs is causally influential.

The technical consequence would be to simply apply principal component analysis to reduce the number of correlating beliefs to overall composites (which reflect the partition of the network). Usually, this results in 3-4 belief composites. In this regard, one could even set up a full regression model with 3-4 product terms (with accompanying evaluations), to overcome the problem of using simple products ob belief_i * evaluation_i (see the post by Karin above).

I have a bad gut feeling though, as even in this case you mesh different evaluations together whose structure could be different from those of the beliefs....

HTH

Holger