Statistical model specification

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, model specification is part of the process of building a <a href="/facts/Statistical_model/jKkT5ftm">statistical model</a>: specification consists of selecting an appropriate <a href="/facts/Function_(mathematics)/CdReEKCh">functional form</a> for the model and choosing which variables to include. For example, given <a href="/facts/Personal_income/VW9McI8l">personal income</a> 
 
 
 
 y
 
 
 {\displaystyle y}
 
 together with years of schooling 
 
 
 
 s
 
 
 {\displaystyle s}
 
 and on-the-job experience 
 
 
 
 x
 
 
 {\displaystyle x}
 
, we might specify a functional relationship 
 
 
 
 y
 =
 f
 (
 s
 ,
 x
 )
 
 
 {\displaystyle y=f(s,x)}
 
 as follows:

ln
        ⁡
        y
        =
        ln
        ⁡
        
          y
          
            0
          
        
        +
        ρ
        s
        +
        
          β
          
            1
          
        
        x
        +
        
          β
          
            2
          
        
        
          x
          
            2
          
        
        +
        ε
      
    
    {\displaystyle \ln y=\ln y_{0}+\rho s+\beta _{1}x+\beta _{2}x^{2}+\varepsilon }

where 
 
 
 
 ε
 
 
 {\displaystyle \varepsilon }
 
 is the unexplained <a href="/facts/Errors_and_residuals/Ef0LgAS4">error term</a> that is supposed to comprise <a href="/facts/Independent_and_identically_distributed_random_variables/othIRaWt">independent and identically distributed</a> <a href="/facts/Normal_distribution/UapjjPyQ">Gaussian variables</a>. 
The statistician <a href="/facts/David_Cox_(statistician)/RM7agpV5">Sir David Cox</a> has said, "How [the] translation from subject-matter problem to statistical model is done is often the most critical part of an analysis".

Statistical model specification open-in-new

Statistical model specification