Unit-weighted regression

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, unit-weighted regression is a simplified and <a href="/facts/Robust_statistics/RwIMvtD2">robust</a> version (<a href="/facts/Howard_Wainer/T064JhHV">Wainer</a> & Thissen, 1976) of <a href="/facts/Multiple_regression/n6z5Tf7K">multiple regression</a> analysis where only the intercept term is estimated. That is, it fits a model

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    {\displaystyle {\hat {y}}={\hat {f}}(\mathbf {x} )={\hat {b}}+\sum _{i}x_{i}}

where each of the 
 
 
 
 
 x
 
 i
 
 
 
 
 {\displaystyle x_{i}}
 
 are <a href="/facts/Binary_data/PSFa5S2Q">binary variables</a>, perhaps multiplied with an arbitrary weight.
Contrast this with the more common multiple regression model, where each predictor has its own estimated coefficient:

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    {\displaystyle {\hat {y}}={\hat {f}}(\mathbf {x} )={\hat {b}}+\sum _{i}{\hat {w}}_{i}x_{i}}

In the <a href="/facts/Social_science/hAbm1xtD">social sciences</a>, unit-weighted regression is sometimes used for binary <a href="/facts/Statistical_classification/jXXHRkXR">classification</a>, i.e. to <a href="/facts/Binary_classification/MeYYAMwp">predict a yes-no answer</a> where 
 
 
 
 
 
 
 y
 ^
 
 
 
 <
 0
 
 
 {\displaystyle {\hat {y}}<0}
 
 indicates "no", 
 
 
 
 
 
 
 y
 ^
 
 
 
 ≥
 0
 
 
 {\displaystyle {\hat {y}}\geq 0}
 
 "yes". It is easier to interpret than multiple linear regression (known as <a href="/facts/Linear_discriminant_analysis/Mj6KQhRN">linear discriminant analysis</a> in the classification case).

Unit-weighted regression open-in-new

Unit-weighted regression