Suppose I am studying the construct of "Academic Motivation" (latent variable) in students, which is measured through three observed variables: "Intrinsic Motivation," "Extrinsic Motivation," and "Amotivation." Each of these observed variables is assessed using a set of four survey items.
- **Latent Variable:** Academic Motivation (η)
- **Observed Variables:**
- Intrinsic Motivation (ξ1)
- Items: "I enjoy learning new things" (X₁₁), "I find learning interesting" (X₁₂), "I like challenging tasks" (X₁₃), "I study because I love it" (X₁₄)
- Extrinsic Motivation (ξ2)
- Items: "I study to get good grades" (X₂₁), "I want to make my parents proud" (X₂₂), "I work hard to receive rewards" (X₂₃), "I study to avoid punishment" (X₂₄)
- Amotivation (ξ3)
- Items: "I don't see the point in studying" (X₃₁), "I feel indifferent about my studies" (X₃₂), "I lack interest in my courses" (X₃₃), "I don't care about school" (X₃₄)
In SEM, I would model "Academic Motivation" as a latent variable influenced by the three observed variables (Intrinsic Motivation, Extrinsic Motivation, Amotivation), with each observed variable measured by its respective four items.
What should I do?
Hello Chanhoon,
the subtypes of motivation (intrinsic, extinsic, and amotivation) are not manifest but latent variables themselves. You seem to have some kind of formative structure in mind where these three latent variables form/determine a "overall motivation" variable. Such a variable, however is not identified without modelled outcomes of this overall motivation variable. Hence your model should contain these (at least three). There is a huge literature on formative constructs (although critical). That's the statistical side.
From a philosophical / ontological (not statistical identification) point of view, however, the implications of such a structure is that this overall motivation is some existing entity that is distinct from its constitutents (i.e. the three motivation types). This is where you will find huge differences in the perspectives in the literature (some will say that the constitutents are both parts and causes of this variables, which is nonsense, see Wilcox et al., 2008). The question hence, is whether your idea of "overall motivation" is
a) that it is something that causally is affected/created by the constitutens, but something distinct from them or
b) if it is not only an comprehensive label for the constitutents (like "performance" is a label for severall behaviors, each qualifying as "performance")--that is a kind of umbrella term.
One final comment: I have some problems to believe that amotivation is a distinct latent variable and not the simply the absence of the other two. Hence I would recomment to really rigidly test the primary factor models with a chisquare test.
Best,
Holger
Wilcox, J. B., Howell, R. D., & Breivik, E. (2008). Questions about formative measurement. Journal of Business Research, 61, 1219-1228.
I would suggest reading about second order constructs in SEM you find an answer to your model specification
What is different between second order factorial model and doing item parcelling in first order factorial model Esam Osman
Hi all,
a second order model would sure be an alternative structure but keep in mind what the essence of such a structure is, namely that all three sub-motivations (intrinsic, extrinsic and amotivation) are caused by one underling core motivation. I don't know whether this reasonable. The nice thing however is, that you can test it when the model is overidentified (that is, you would need at least one further observed or latent variable that should be related to the second order factor but not the three submotivations.
Best,
Holger
The difference as long as i am concerned is that items percling is about reducing the number of items in one construct whether it is first or second constructs where secound order is about specifying construct in a SEM according to the theory
Hi Chanhoon! I agree with Holger, the three variables that represent dimensions of academic motivation are also latent variables. First, you have to evaluate if the measurement model of your variables is reflective or formative. It is reflective when the indicators are the reflection of the variables, and formative when they cause the variable. This decision must be done based on the measurement theory, that is the theory that you use to define the concepts and measure the variables that you use as an approximation of these concepts. Then, how this variables are introduced in the model is established by the structural theory, this is the theory that supports your hypotheses. There are other variables in the structural model? How many? Based on this information you can decide if you propose a model with these three variables as first-order or you use them to measure the second-order construct Academic Motivations. See Hair, J.F., Hult, G.T.M., Ringle, C.M., & Sarstedt, M. (2022). A Primer on Partial Least Square Equation Modelling (PLS-SEM) (3rd ed). Thousand Oaks, CA: Sage.
Sarstedt, M., Ringle, C. M., and Hair, J. F. (2024). Partial Least Squares Structural Equation Modeling. In: Homburg, C., Klarmann, M., and Vomberg, A. (Eds.). Handbook ofMarket Research, New York et al.: Springer.
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