# What is the proper name of a model that takes as input the output of another model?

Thanks in advance for the help.

I am writing a paper and for the life of me can't remember the proper term for a model that works as follows.

rawData -> model1 -> outputModel1 -> model2 -> outputModel2

More specifically, I have created a linear regression model whose output I pass to a second linear regression model. One could imagine N models strung together like this.

I keep wanting to call this a hierarchical or multi-level model, but I know that isn't right: these types of models are synonymous with mixed models. I know that there is a proper name for this since I remember discussing it in a class that took awhile back. Does anyone know what this is called?

• The word cascaded'' comes to mind... – mcvz Jan 29 '15 at 7:17
• Hierarchical and multilevel are certainly "reserved" for mixed models so using them for this kind of model would certainly be confusing. – Tim Jan 29 '15 at 7:18
• "Hierarchical models" is rather generic, so I do not see why it would not apply. In Econometrics, you also have "simultaneous equation models" where outputs of some equations are input of others. – Xi'an Jan 29 '15 at 11:29
• What about just "two-stage" or "two-step" estimation? – shadowtalker Jan 30 '15 at 5:53

## 2 Answers

The process is known as Cascaded classification/regression or Multi-stage classification/regression. It is a type of ensemble learning with some differences. You can find more in Wikipedia.

I am not sure, if there exists at all a "proper name" for models that you describe, but I would call such models chain models, similarly to the chain procedures, introduced in the following paper: http://www.multxpert.com/doc/md2011.pdf. This term IMHO better reflects the nature of this type of models and, at the same time, prevents potential confusion with hierarchical and multi-level ones.