I have a terminological question about the use of the terms random intercept models, random slope models and random intercept and slope models.
Through my readings, I find that most authors use the terms random slopes, and random intercepts and slopes interchangeably. At least, this is my understanding so far.
For example, Zuur et. al (2009) use random intercept and slope models in contrast to random intercepts only models whereas Barr et. al (2013) and Winter (2014) use random slopes models vs. random intercepts only models.
So, my question is are the terms random 'intercepts and slopes models' the same as 'random slopes models' or do we have three separate types of models: 'intercepts only', 'slopes only', and 'intercepts and slopes models' (maximal models)?
PS. work cited is below.
Zuur, A. F., Ieno, E. N., Walker, N., Saveliev, A. A., & Smith, G. M. (2009). Mixed effects models and extensions in ecology with R. New York, NY: Springer Science+Business Media, LLC.
Winter, B. (2014). Linear models and linear mixed effects models in R with linguistic applications. arXiv:1308.5499. [arxiv.org/pdf/1308.5499.pdf]
Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of memory and language, 68(3), 255-278. ncbi.nlm.nih.gov/pmc/articles/PMC3881361/pdf/nihms533954.pdf