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Modelo de ajuste a factores ordinales y respuesta.

 

Hola, tengo un diagrama de este tipo y quiero descubrir la ecuación que lo produce:

 

 

 

 

 

 

Uno puede imaginarlo como un espacio tridimensional con respuestas de color para cada combinación S/U/D.

Llené S/U/D en una tabla JMP para que se ajustara a (algún tipo de) modelo, pero me di cuenta inmediatamente de que la respuesta en el código de color (por ejemplo, 1 para verde, 2 para amarillo y 3=rojo) no tiene mucho sentido.

Según tengo entendido, la ecuación detrás de este diagrama genera valores de 4x4x3=48 y los colores corresponden a ciertas partes de los valores. Por ejemplo, el 30% de los valores superiores se vuelven rojos, el 25% inferiores, verdes. El resto es amarillo.

¿Cómo entonces debería representar la respuesta?

¿No son demasiadas incógnitas para esta tarea?

Re: Ajuste del modelo a factores ordinales y respuesta.

La sugerencia de Jim de utilizar un método de partición recursivo es excelente. El hecho es que hay más de una manera de modelar esta respuesta ordinal bajo diferentes condiciones de S, U y D. Aquí hay un resultado usando regresión logística ordinal:

 

dt = New Table( "4x4x3 Factorial",
 Add Rows( 48 ),
 New Table Variable( "Design", "4x4x3 Factorial" ),
 New Script(
  "Model",
  Fit Model(
   Effects( :S, :U, :D, :S * :U, :S * :D, :U * :D</img> ),
   Y( :Y ),
   PERSONALITY( Standard Least Squares )
  )
 ),
 New Script( "Evaluate Design", DOE( Evaluate Design, X( :S, :U, :D</img> ) ) ),
 New Script(
  "DOE Dialog",
  DOE(
   Full Factorial Design,
   {Add Response( Maximize, "Y", ., ., . ),
   Add Factor( Categorical, {"1", "2", "3", "4"}, "S", 0 ),
   Add Factor( Categorical, {"1", "2", "3", "4"}, "U", 0 ),
   Add Factor( Categorical, {"1", "2", "3"}, "D", 0 ),
   Set Random Seed( 873 ), Make Design, Simulate Responses( 0 ),
   Set Run Order( Sort Left to Right ), Make Table}
  )
 ),
 New Script(
  "Graph Builder",
  Graph Builder(
   Size( 566, 1456 ),
   Show Control Panel( 0 ),
   Show Legend( 0 ),
   Variables( Y( :Y ), Page( :D</img> ), Group X( :U ), Group Y( :S ) ),
   Elements( Points( Y, Legend( 7 ) ) ),
   SendToReport(
    Dispatch(
     {},
     "400",
     ScaleBox,
     {Legend Model(
      7,
      Properties( -1, {Line Color( 4 )}, Item ID( "1", 1 ) ),
      Properties( -1, {Line Color( 41 )}, Item ID( "2", 1 ) ),
      Properties( -1, {Line Color( 3 )}, Item ID( "3", 1 ) )
     )}
    )
   )
  )
 ),
 New Column( "Pattern",
  Character,
  "Nominal",
  Set Values(
   {"111", "112", "113", "121", "122", "123", "131", "132", "133", "141",
   "142", "143", "211", "212", "213", "221", "222", "223", "231", "232",
   "233", "241", "242", "243", "311", "312", "313", "321", "322", "323",
   "331", "332", "333", "341", "342", "343", "411", "412", "413", "421",
   "422", "423", "431", "432", "433", "441", "442", "443"}
  )
 ),
 New Column( "S",
  Character,
  "Nominal",
  Set Property( "Value Ordering", {"1", "2", "3", "4"} ),
  Set Property( "Design Role", DesignRole( Categorical ) ),
  Set Property( "Factor Changes", Easy ),
  Set Values(
   {"1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2",
   "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "3", "3", "3", "3",
   "3", "3", "3", "3", "3", "3", "3", "3", "4", "4", "4", "4", "4", "4",
   "4", "4", "4", "4", "4", "4"}
  )
 ),
 New Column( "U",
  Character,
  "Nominal",
  Set Property( "Value Ordering", {"1", "2", "3", "4"} ),
  Set Property( "Design Role", DesignRole( Categorical ) ),
  Set Property( "Factor Changes", Easy ),
  Set Values(
   {"1", "1", "1", "2", "2", "2", "3", "3", "3", "4", "4", "4", "1", "1",
   "1", "2", "2", "2", "3", "3", "3", "4", "4", "4", "1", "1", "1", "2",
   "2", "2", "3", "3", "3", "4", "4", "4", "1", "1", "1", "2", "2", "2",
   "3", "3", "3", "4", "4", "4"}
  )
 ),
 New Column( "D",
  Character,
  "Nominal",
  Set Property( "Value Ordering", {"1", "2", "3"} ),
  Set Property( "Design Role", DesignRole( Categorical ) ),
  Set Property( "Factor Changes", Easy ),
  Set Values(
   {"1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2",
   "3", "1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2", "3", "1",
   "2", "3", "1", "2", "3", "1", "2", "3", "1", "2", "3", "1", "2", "3",
   "1", "2", "3", "1", "2", "3"}
  )
 ),
 New Column( "Y",
  Numeric,
  "Ordinal",
  Format( "Best", 12 ),
  Value Labels( {1 = "Low", 2 = "Med", 3 = "High"} ),
  Use Value Labels( 1 ),
  Set Values(
   [1, 1, 2, 1, 1, 2, 1, 2, 3, 2, 3, 3, 1, 1, 2, 1, 1, 2, 1, 2, 3, 2, 3, 3,
   1, 1, 2, 1, 2, 3, 2, 3, 3, 2, 3, 3, 1, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3]
  )
 ),
 Set Label Columns( :Pattern )
);

dt << Fit Model(
 Y( :Y ),
 Effects( :S, :U, :D</img> ),
 Personality( "Ordinal Logistic" ),
 Run(
  Likelihood Ratio Tests( 1 ),
  Profiler(
   1,
   Term Value(
    S( "1", Lock( 0 ), Show( 1 ) ),
    U( "1", Lock( 0 ), Show( 1 ) ),
    D( "1", Lock( 0 ), Show( 1 ) )
   )
  )
 )
);

Re: Ajuste del modelo a factores ordinales y respuesta.

Quizás quieras intentar construir tu modelo usando Partioning.A continuación se muestra un script que crea su tabla y luego ejecuta un análisis de partición (árbol de decisión).

names default to here(1);
dt = New Table( "Example",
 Add Rows( 48 ),
 New Column( "d",
  Numeric,
  "Nominal",
  Format( "Best", 12 ),
  Set Values(
   [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2,
   2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
  )
 ),
 New Column( "u",
  Numeric,
  "Nominal",
  Format( "Best", 12 ),
  Set Values(
   [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4,
   1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4]
  )
 ),
 New Column( "s",
  Numeric,
  "Nominal",
  Format( "Best", 12 ),
  Set Values(
   [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 1, 1, 1, 1, 2, 2, 2, 2,
   3, 3, 3, 3, 4, 4, 4, 4, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4]
  )
 ),
 New Column( "value",
  Character,
  "Nominal",
  Set Values(
   {"Low", "Low", "Low", "Med", "Low", "Low", "Low", "Med", "Low", "Low",
   "Med", "Med", "Low", "Med", "Med", "Med", "Low", "Low", "Med", "High",
   "Low", "Low", "Med", "High", "Low", "Med", "High", "High", "Med", "High",
   "High", "High", "Med", "Med", "High", "High", "Med", "Med", "High",
   "High", "Med", "High", "High", "High", "High", "High", "High", "High"}
  )
 )
);


dt << Partition(
 Y( :value ),
 X( :d, :u, :s ),
 Informative Missing( 1 ),
 Initial Splits(
  :d == {1},
  {:u == {4, 3}},
  {:u == {1, 2}, {:d == {2}}, {:d == {2}}}
 ),
 SendToReport(
  Dispatch( {}, "Partition Report", FrameBox, {Frame Size( 480, 74 )} )
 )
);