Week 7 The unobserved

Latent variables and structural models

Description
The unobserved sounds like the title of a promising horror film; if we have achieved our aims in the module so far, our horror should be ‘merely’ metaphysical by now (Kołakowski anyone? No? Okay, never mind). We have already had to deal with various aspects of latency in our analyses. At the most fundamental level, we speak about population parameters, but we never actually observe them; even a sample statistic can be a purely imaginary case that doesn’t occur in real life. We have discussed the effects of omitted variables, which are thus unobserved by our model, but which we may have access to in our data. And, of course, our most interesting measurements are likely to be proxies of some unobservable theoretical construct (Mulvin (2021) has recently published a wonderfully rich book about proxies in general). This week we pick up an earlier thread from week 4, where we thought about binary and ordered multinomial variables as discretised manifestations of some continuous ‘latent variable’. We expand on this idea by exploring simple and then more complex latent variable models (factor analysis, structural equation modelling), as a further generalisation of the hierarchical perspective introduced earlier. This gives us a few more tools to deal with our radical uncertainty. (n.b. missing data points are another challenge that could fall under this heading, and learning how to deal with them is extremely important; but “The missing” is too good a title not to deserve a high-budget, weak-storyline, full-on special effects sequel somewhere else)

Readings

Textbook

  • Chapters 13 and 14 in Mehmetoglu, M. & Mittner, M. (2022) Applied statistics using R: a guide for the social sciences. London: Sage (NCL library access here)

Video

  • Kubinec, R. (2019) An introduction to latent variable models for data science. Sage Research Methods (video file, 00:17:44) (NCL library access here)

Application

References

David, F. N. 1955. “Studies in the History of Probability and Statistics i. Dicing and Gaming (a Note on the History of Probability).” Biometrika 42 (1/2): 1–15. https://doi.org/10.2307/2333419.
El-Shagi, Makram, and Alexander Jung. 2015. “Have Minutes Helped Markets to Predict the MPC’s Monetary Policy Decisions?” European Journal of Political Economy 39 (September): 222–34. https://doi.org/10.1016/j.ejpoleco.2015.05.004.
Gelman, Andrew, Jennifer Hill, and Aki Vehtari. 2020. Regression and other stories. Cambridge: Cambridge University Press. https://doi.org/10.1017/9781139161879.
Lord, R. D. 1958. “Studies in the History of Probability and Statistics.: VIII. De Morgan and the Statistical Study of Literary Style.” Biometrika 45 (1/2): 282–82. https://doi.org/10.2307/2333072.
McElreath, Richard. 2020. Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Second. CRC Texts in Statistical Science. Boca Raton: Taylor and Francis, CRC Press.
Mulvin, Dylan. 2021. Proxies: The Cultural Work of Standing in. Infrastructures Series. Cambridge, Massachusetts: The MIT Press.
Senn, Stephen. 2003. “A Conversation with John Nelder.” Statistical Science 18 (1): 118–31. https://doi.org/10.1214/ss/1056397489.