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RegressionGAM


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 -- statistics: OBJ = RegressionGAM (X, Y)
 -- statistics: OBJ = RegressionGAM (..., NAME, VALUE)

     Create a RegressionGAM class object containing a Generalized
     Additive Model (GAM) for regression.

     A RegressionGAM class object can store the predictors and response
     data along with various parameters for the GAM model.  It is
     recommended to use the ‘fitrgam’ function to create a RegressionGAM
     object.

     ‘OBJ = RegressionGAM (X, Y)’ returns an object of class
     RegressionGAM, with matrix X containing the predictor data and
     vector Y containing the continuous response data.

        • X must be a NxP numeric matrix of input data where rows
          correspond to observations and columns correspond to features
          or variables.  X will be used to train the GAM model.
        • Y must be Nx1 numeric vector containing the response data
          corresponding to the predictor data in X.  Y must have same
          number of rows as X.

     ‘OBJ = RegressionGAM (..., NAME, VALUE)’ returns an object of class
     RegressionGAM with additional properties specified by Name-Value
     pair arguments listed below.

          NAME           VALUE
                         
     ---------------------------------------------------------------------------
          "predictors"   Predictor Variable names, specified as a row vector
                         cell of strings with the same length as the columns
                         in X.  If omitted, the program will generate default
                         variable names (x1, x2, ..., xn) for each column in
                         X.
                         
          "responsename" Response Variable Name, specified as a string.  If
                         omitted, the default value is "Y".
                         
          "formula"      a model specification given as a string in the form
                         "Y ~ terms" where Y represents the reponse variable
                         and terms the predictor variables.  The formula can
                         be used to specify a subset of variables for
                         training model.  For example: "Y ~ x1 + x2 + x3 + x4
                         + x1:x2 + x2:x3" specifies four linear terms for the
                         first four columns of for predictor data, and x1:x2
                         and x2:x3 specify the two interaction terms for
                         1st-2nd and 3rd-4th columns respectively.  Only
                         these terms will be used for training the model, but
                         X must have at least as many columns as referenced
                         in the formula.  If Predictor Variable names have
                         been defined, then the terms in the formula must
                         reference to those.  When "formula" is specified,
                         all terms used for training the model are referenced
                         in the IntMatrix field of the OBJ class object as a
                         matrix containing the column indexes for each term
                         including both the predictors and the interactions
                         used.
                         
          "interactions" a logical matrix, a positive integer scalar, or the
                         string "all" for defining the interactions between
                         predictor variables.  When given a logical matrix,
                         it must have the same number of columns as X and
                         each row corresponds to a different interaction term
                         combining the predictors indexed as true.  Each
                         interaction term is appended as a column vector
                         after the available predictor column in X.  When
                         "all" is defined, then all possible combinations of
                         interactions are appended in X before training.  At
                         the moment, parsing a positive integer has the same
                         effect as the "all" option.  When "interactions" is
                         specified, only the interaction terms appended to X
                         are referenced in the IntMatrix field of the OBJ
                         class object.
                         
          "knots"        a scalar or a row vector with the same columns as X.
                         It defines the knots for fitting a polynomial when
                         training the GAM. As a scalar, it is expanded to a
                         row vector.  The default value is 5, hence expanded
                         to ones (1, columns (X)) * 5.  You can parse a row
                         vector with different number of knots for each
                         predictor variable to be fitted with, although not
                         recommended.
                         
          "order"        a scalar or a row vector with the same columns as X.
                         It defines the order of the polynomial when training
                         the GAM. As a scalar, it is expanded to a row
                         vector.  The default values is 3, hence expanded to
                         ones (1, columns (X)) * 3.  You can parse a row
                         vector with different number of polynomial order for
                         each predictor variable to be fitted with, although
                         not recommended.
                         
          "dof"          a scalar or a row vector with the same columns as X.
                         It defines the degrees of freedom for fitting a
                         polynomial when training the GAM. As a scalar, it is
                         expanded to a row vector.  The default value is 8,
                         hence expanded to ones (1, columns (X)) * 8.  You
                         can parse a row vector with different degrees of
                         freedom for each predictor variable to be fitted
                         with, although not recommended.
                         
          "tol"          a positive scalar to set the tolerance for
                         convergence during training.  By default, it is set
                         to 1e-3.

     You can parse either a "formula" or an "interactions" optional
     parameter.  Parsing both parameters will result an error.
     Accordingly, you can only pass up to two parameters among "knots",
     "order", and "dof" to define the required polynomial for training
     the GAM model.

     See also: fitrgam, regress, regress_gp.


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Create a RegressionGAM class object containing a Generalized Additive
Model (...





