Hi, thank you for this! Quick tip: you could substantially improve the quality of the videos by investing in a microphone, and doing some post processing on the audio eg. by using a gate or noise reduction plugin. Best regards,/Ludwig
Yet, I often see people estimate two factors, establish a correlation between them, and then average all items together to create a single composite across the 2 factors. Is it true that the bi-factor model is actually the correct model to test if the goal is to establish that the composite of total items captures a general construct? In what case is just establishing correlated factors appropriate (this model seems to be the norm, in my experience)?
Dear Dr. Geiser, Thank you for explaining the bifactor model and also comparing it to the second order model. In running a bifactor model, I came across one specific outcome that surprised me and I do not fully understand why it happens. I use categorical and right-skewed indicators in the model. When I output the factor scores for each individual after running the model, I get normally distributed factor scores across all individuals. Is there some scaling in the model that causes my right-skewed indicators to become reflected in normally distributed factor scores? Thank you in advance!
I don't know which modeling approach and estimation method you used, but one standard approach for ordinal indicators is to assume that they are crude/discretized indicators of an underlying continuous, normally distributed latent response variable. See, for example, Muthén, B. & Asparouhov, T. (2002). Latent Variable Analysis With Categorical Outcomes: Multiple-Group And Growth Modeling In Mplus. Mplus Webnote, Version 5, December 9, 2002. statmodel.com/download/webnotes/CatMGLong.pdf Finney, S. J., & DiStefano, C. (2006). Non-normal and categorical data in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course. Greenwich, CT: Information Age Publishing. Hence, although the indicators may be categorical/skewed, the underlying latent variables are assumed to be continuous/normal. Best, Christian Geiser
Thank you for your quick response and pointers to the literature, this is very helpful. For completeness, I have used the WLSMV estimator. Out of curiosity, would there be ways to set up my model estimation where I do not assume the underlying latent variable is normally distributed?@@QuantFish
Some CFA-MTMM models (models for multimethod data) have the same structure as a bifactor model, in particular, models for interchangeable (randomly selected) raters/methods. I will make a video on this topic in the near future. In the meantime, you can study the following papers and chapters: Eid, M., Geiser, C., & Koch, T. (2016). Measuring method effects: From traditional to design-oriented approaches. Current Directions in Psychological Science, 25, 275-280. Eid, M., Nussbeck, F., Geiser, C., Cole, D., Gollwitzer, M. & Lischetzke, T. (2008). Structural equation modeling of multitrait-multimethod data: Different models for different types of methods. Psychological Methods, 13, 230-253. Koch, T., Eid, M., & Lochner, K. (2018). Multitrait-multimethod analysis: The psychometric foundation of CFA-MTMM models. In P. Irwing, T. Booth, & D. Hughes (Eds.), The Wiley-Blackwell Handbook of Psychometric Testing (pp. 781-846). West Sussex, UK: John Wiley & Sons. Olsen, J. A., & Kenny, D. A. (2006). Structural equation modeling with interchangeable dyads. Psychological Methods, 11(2), 127-141. I also offer an online workshop on CFA-MTMM models which you can find here: www.goquantfish.com/courses/mtmm-in-mplus I hope this helps! Best, Christian Geiser
Hi, thank you for this! Quick tip: you could substantially improve the quality of the videos by investing in a microphone, and doing some post processing on the audio eg. by using a gate or noise reduction plugin. Best regards,/Ludwig
Yet, I often see people estimate two factors, establish a correlation between them, and then average all items together to create a single composite across the 2 factors. Is it true that the bi-factor model is actually the correct model to test if the goal is to establish that the composite of total items captures a general construct? In what case is just establishing correlated factors appropriate (this model seems to be the norm, in my experience)?
Very useful thank you so much
Dear Dr. Geiser,
Thank you for explaining the bifactor model and also comparing it to the second order model. In running a bifactor model, I came across one specific outcome that surprised me and I do not fully understand why it happens. I use categorical and right-skewed indicators in the model. When I output the factor scores for each individual after running the model, I get normally distributed factor scores across all individuals. Is there some scaling in the model that causes my right-skewed indicators to become reflected in normally distributed factor scores?
Thank you in advance!
I don't know which modeling approach and estimation method you used, but one standard approach for ordinal indicators is to assume that they are crude/discretized indicators of an underlying continuous, normally distributed latent response variable. See, for example,
Muthén, B. & Asparouhov, T. (2002). Latent Variable Analysis With Categorical Outcomes: Multiple-Group And Growth Modeling In Mplus. Mplus Webnote, Version 5, December 9, 2002. statmodel.com/download/webnotes/CatMGLong.pdf
Finney, S. J., & DiStefano, C. (2006). Non-normal and categorical data in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course. Greenwich, CT: Information Age Publishing.
Hence, although the indicators may be categorical/skewed, the underlying latent variables are assumed to be continuous/normal.
Best, Christian Geiser
Thank you for your quick response and pointers to the literature, this is very helpful. For completeness, I have used the WLSMV estimator. Out of curiosity, would there be ways to set up my model estimation where I do not assume the underlying latent variable is normally distributed?@@QuantFish
Thank you for this excellent video. Could you please explain the difference between the bifactor model and the methods effect model?
Some CFA-MTMM models (models for multimethod data) have the same structure as a bifactor model, in particular, models for interchangeable (randomly selected) raters/methods. I will make a video on this topic in the near future. In the meantime, you can study the following papers and chapters:
Eid, M., Geiser, C., & Koch, T. (2016). Measuring method effects: From traditional to design-oriented approaches. Current Directions in Psychological Science, 25, 275-280.
Eid, M., Nussbeck, F., Geiser, C., Cole, D., Gollwitzer, M. & Lischetzke, T. (2008). Structural equation modeling of multitrait-multimethod data: Different models for different types of methods. Psychological Methods, 13, 230-253.
Koch, T., Eid, M., & Lochner, K. (2018). Multitrait-multimethod analysis: The psychometric foundation of CFA-MTMM models. In P. Irwing, T. Booth, & D. Hughes (Eds.), The Wiley-Blackwell Handbook of Psychometric Testing (pp. 781-846). West Sussex, UK: John Wiley & Sons.
Olsen, J. A., & Kenny, D. A. (2006). Structural equation modeling with interchangeable dyads. Psychological Methods, 11(2), 127-141.
I also offer an online workshop on CFA-MTMM models which you can find here:
www.goquantfish.com/courses/mtmm-in-mplus
I hope this helps!
Best, Christian Geiser