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Is there a standard way to refer to a statistical model that is not saturated?

It is for paper writing. For the moment, I am using the term "non-saturated model" but I think there must be better words options for it.

EDIT: Here I am considering A saturated model as a model which there are as many estimated parameters as data points.

Suggestions are welcome.

Ps.: I am not sure which tag is appropriate for this question.

Renato Fernandes
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  • what do you mean by saturated? – Aksakal Feb 10 '23 at 17:50
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    @Aksakal: saturated in sense that the number of parameters are equal the number of data points. I will edit my question to include that information. – Renato Fernandes Feb 10 '23 at 18:55
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    Your definition is a particular, common case (or there is inconsistency across fields). A saturated model is one in which all parameters have been estimated, and no further improvement can be made by adding more variables or parameters. So a regression model with two binary categorical covariates and four parameters ($x_1,x_2,x_1 \times x_2, \mathtt{intercept}$) would be saturated but generally has fewer parameters than the number of observations if $N>4=k$. – dimitriy Feb 10 '23 at 19:22
  • What is a "saturated" model? – kjetil b halvorsen Feb 10 '23 at 19:51
  • Thanks for the contribution @dimitriy. The definition that I put in the EDIT maybe is the most precise. I took the definition in the link https://stats.stackexchange.com/questions/283/what-is-a-saturated-model.

    Nevertheless, he question is not about the definition of Saturated model, but of what the name for models that are not saturated.

     – Renato Fernandes Feb 10 '23 at 19:57
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    I doubt there is anything other that non-saturated – kjetil b halvorsen Feb 12 '23 at 16:55

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