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Table 2 Analysis Models

From: An empirical link between motivation gain and NBA statistics: applying hierarchical linear modelling

Model

Level

Equations

Random-coefficient model

1

\(\begin{aligned} \left( {{\text{Salary}}_{{\text{current season}}} } \right)_{{{\text{ij}}}} = & \, \beta_{{0{\text{j}}}} + \, \beta_{{{\text{1j}}}} \left( {{\text{PL}}} \right)_{{{\text{ij}}}} + \, \beta_{{{\text{2j}}}} \left( {{\text{Statistics}}_{{\text{previous season}}} } \right)_{{{\text{ij}}}} \\ & + \, \beta_{{{\text{3j}}}} \left( {{\text{Statistics}}_{{\text{previous season}}} \times {\text{ PL}}} \right)_{{{\text{ij}}}} + {\text{ r}}_{{{\text{ij}}}} \\ \end{aligned}\)

2

\(\beta_{{0{\text{j}}}} = \, \gamma_{00} + {\text{ U}}_{{0{\text{j}}}} , \, \beta_{{{\text{1j}}}} = \, \gamma_{{{1}0}} + {\text{ U}}_{{{\text{1j}}}} , \, \beta_{{{\text{2j}}}} = \, \gamma_{{{2}0}} + {\text{ U}}_{{{\text{2j}}}} , \, \beta_{{{\text{3j}}}} = \, \gamma_{{{3}0}} + {\text{ U}}_{{{\text{3j}}}}\)

Conditional model

1

\(\begin{aligned} \left( {{\text{Salary}}_{{\text{current season}}} } \right)_{{{\text{ij}}}} = & \, \beta_{{0{\text{j}}}} + \, \beta_{{{\text{1j}}}} \left( {{\text{PL}}} \right)_{{{\text{ij}}}} + \, \beta_{{{\text{2j}}}} \left( {{\text{Statistics}}_{{\text{previous season}}} } \right)_{{{\text{ij}}}} \\ & + \, \beta_{{{\text{3j}}}} \left( {{\text{Statistics}}_{{\text{previous season}}} \times {\text{ PL}}} \right)_{{{\text{ij}}}} + {\text{ r}}_{{{\text{ij}}}} \\ \end{aligned}\)

2

\(\begin{gathered} \beta_{{0{\text{j}}}} = \, \gamma_{00} + \, \gamma_{{0{1}}} \left( {{\text{M}}_{{{\text{slope}}}} {\text{or SD}}_{{{\text{slope}}}} } \right)_{{\text{j}}} + \, \gamma_{{0{2}}} \left( {\text{TM or TSD}} \right)_{{\text{j}}} + {\text{ U}}_{{0{\text{j}}}} \hfill \\ \beta_{{{\text{1j}}}} = \, \gamma_{{{1}0}} + \, \gamma_{{{11}}} \left( {{\text{M}}_{{{\text{slope}}}} {\text{or SD}}_{{{\text{slope}}}} } \right)_{{\text{j}}} + \, \gamma_{{{12}}} \left( {\text{TM or TSD}} \right)_{{\text{j}}} + {\text{ U}}_{{{\text{1j}}}} \hfill \\ \beta_{{{\text{2j}}}} = \, \gamma_{{{2}0}} + \, \gamma_{{{21}}} \left( {{\text{M}}_{{{\text{slope}}}} {\text{or SD}}_{{{\text{slope}}}} } \right)_{{\text{j}}} + \, \gamma_{{{22}}} \left( {\text{TM or TSD}} \right)_{{\text{j}}} + {\text{ U}}_{{{\text{2j}}}} \hfill \\ \beta_{{{\text{3j}}}} = \, \gamma_{{{3}0}} + \, \gamma_{{{31}}} \left( {{\text{M}}_{{{\text{slope}}}} {\text{or SD}}_{{{\text{slope}}}} } \right)_{{\text{j}}} + \, \gamma_{{{32}}} \left( {\text{TM or TSD}} \right)_{{\text{j}}} + {\text{ U}}_{{{\text{3j}}}} \hfill \\ \end{gathered}\)