\name{RegressionModelling}

\alias{RegressionModelling}

\alias{fREG}
\alias{fREG-class}

\alias{regFit}

\alias{predict.fREG}

\alias{print.fREG}
\alias{plot.fREG}
\alias{summary.fREG}

\alias{fitted.values.fREG}
\alias{residuals.fREG}


\title{Univariate Regression Modelling}


\description{

	A collection and description of easy to use functions to perform 
	a univariate regression analysis from several methods, to analyse 
	and summarize the fit, and to predict for new data records. This 
	wrapper was mainly build for multivariate financial time series 
	analysis.
	\cr
	
	The models include:
	
	\tabular{ll}{
	\code{"LM"} \tab Linear Modelling, \cr
	\code{"GLM"} \tab Generalized Linear Modelling, \cr
	\code{"GAM"} \tab Generalized Additive Modelling, \cr
	\code{"PPR"} \tab Projection Pursuit Regression, \cr
	\code{"MARS"} \tab Multivariate Adaptive Regression Splines, \cr
	\code{"POLYMARS"} \tab Polytochomous MARS, and \cr
	\code{"NNET"} \tab Feedforward Neural Network Modelling. }
			
	Available methods are:
	
	\tabular{ll}{
	\code{predict} \tab Predict method for objects of class 'fARMA', \cr
	\code{print} \tab Print method for objects of class 'fARMA', \cr
	\code{plot} \tab Plot method for objects of class 'fARMA', \cr
	\code{summary} \tab Summary method for objects of class 'fARMA', \cr
	\code{fitted.values} \tab Fitted values method for objects of class 'fARMA', \cr
	\code{residuals} \tab Residuals method for objects of class 'fARMA'. }
			
	The print method prints the returned object from a regression 
	fit, and the summary method performs a diagnostic analysis and 
	summarizes the results of the fit in a detailed form. The plot
	method produces diagostic plots. The predict method forecasts 
	from new data records. Two other methods to print the fitted 
	values, and the residuals are available.
	
}
	

\note{	
	
	This \code{regFit} function offers for several regression models
	an easy to use wrapper. There is nothing really new in this package. 
	However, the benefit you will get is, that all regression 
	models got a common argument list with a formula to desribe 
	the input data to be used, if rquired with an argument to specify
	the family function, and with a string to name the type of the 
	desired regression model. On the other hand, the user can pass 
	additional arguments to the underlying functions. This allows to 
	tailor the modelling process.
	\cr
	
	The output of the \code{print}, \code{plot}, \code{summary}, and 
	\code{predict} methods have all the same style of format. This 
	makes it very easy to compare and to interpret the results 
	obtained from different algorithms implemented in different 
	functions.
	\cr
	
	All beside two of the underlying functions are available in a default
	R Installation. They are already available or loaded when Rmetrics 
	is invoked. For \code{MARS} and \code{POLYMARS} we have implemented
	BUILTIN functions for parameter estimation and prediction, so that it
	is becomes not necessary to install the contribute \code{mars} and
	\code{polyspline} packages. Nevertheless, if loaded you can use them 
	in your environment, they don't intervene with Rmetrics.
	
}


\usage{
regFit(formula, family = gaussian(), data = list(), 
	method = c("LM", "GLM", "GAM", "PPR", "MARS", "POLYMARS", "NNET"), 
	nterms = NA, size = NA, title = "", description = "", \dots) 

\method{predict}{fREG}(object, newdata, type = "response", \dots)

\method{print}{fREG}(x, \dots)
\method{plot}{fREG}(x, y, \dots)
\method{summary}{fREG}(object, \dots)

\method{fitted.values}{fREG}(object, \dots)
\method{residuals}{fREG}(object, \dots)
}


\arguments{
  	
  	\item{data, newdata}{
	    \code{data} is the data frame containing the variables in the 
	    model. By default the variables are taken from 
	    \code{environment(formula)}, typically the environment from 
	    which \code{LM} is called. \code{newdata} is the data frame 
	    from which to predict.
	    }
  	\item{description}{
  		a brief description of the porject of type character.
  		}
  	\item{family}{
	    a description of the error distribution and link function to be 
	    used in \code{glm} and \code{gam} models. See \code{\link{glm}} 
	    and \code{\link{family}} for more details.
	    }
	\item{formula}{
	    a symbolic description of the model to be fit.
	    \cr
	    A typical \code{glm} predictor has the form \code{response ~ terms} 
	    where \code{response} is the (numeric) response vector and \code{terms}
	    is a series of terms which specifies a (linear) predictor for 
	    \code{response}. For \code{binomial} models the response can also 
	    be specified as a \code{factor}.
	    \cr
	    A \code{gam} formula, see also \code{gam.models}, allows
	    that smooth terms can be added to the right hand side of the 
	    formula. See \code{gam.side.conditions} for details and 
	    examples.
	    }  
	\item{method}{
	  	denotes the regression method by a character string used to fit 
	  	the model.
	    \code{method} must be one of the strings in the default argument.\cr
	    \code{"LM"}, for linear regression models, \cr
	    \code{"GLM"} for generalized linear modelling,\cr
		\code{"GAM"} for generalized additive modelling,\cr
		\code{"PPR"} for projection pursuit regression,\cr
		\code{"MARS"} for multivariate adaptive regression splines,\cr
		\code{"POLYMARS"} for molytochomous MARS, and\cr
		\code{"NNET"} for feedforward neural network modelling.
		}
    \item{nterms}{
    	[pprFit] - \cr
  		the number of terms to include in the final projection pursuit 
  		regression model. For further settings consult the 
	    \code{ppr} help page.
  		}
   	\item{object, x, y}{
    	is an object returned by the
    	regression function \code{regFit} and serves as input for the 
    	\code{predict}, \code{print}, \code{summary}, \code{print.summary},
    	and \code{plot} methods. Some methods allow for additional 
    	arguments to be passed.
    	}     
   \item{size}{
   		[nnetFit] - \cr
	    the number of units in the hidden layer of the feedforward
	    neural network model. For further settings consult the
	    \code{nnet} help page.
	    }
    \item{title}{
    	a title string.
    	}
    \item{type}{
    	[predict] - \cr
	    a string denoting the type of input data. By default set to
	    \code{"response"}.
		}
    \item{\dots}{
    	additional optional arguments to be passed to the underlying 
    	functions. For details we refer to inspect the following help 
    	pages: \code{\link{lm}}, \code{\link{glm}}, \code{gam},
		\code{\link{ppr}}, \code{mars}, \code{polymars}, 
		or \code{nnet}. 
    	}
    	
}


\value{

  	\bold{Function regFit:} 
  	\cr
  	returns an S4 object of class \code{"fREG"}, with the folliwing 
  	slots:

  	\item{call}{
    	the matched function call.
    	}
  	\item{data}{
  		the input data in form of a data.frame.
  		}
  	\item{description}{
  		allows for a brief project description.
  		}
  	\item{fit}{
  		the results as a list returned from the underlying
  		regression model function, e.g.\cr
  		\code{fit$parameters} - the fitted model parameters,\cr
  		\code{fit$residuals} - the model residuals, \cr
  		\code{fit$fitted.values} - the fitted values of the model,\cr
  		and many more. For details we refer to the help pages of
  		the selected regression model. 
  		}
  	\item{method}{
    	the selected regression model naming the applied method.
		}
  	\item{formula}{
    	the formula expression describing the model.
    	}
    \item{family}{
    	the selected family and link name if available, otherwise
    	a string vector with to empty strings.
    	}
    \item{parameters}{
    	named parameters or coefficients of the fitted model.
    	}
    \item{title}{
    	a title string.
    	}
    	  	
    \bold{Methods:}
    \cr\cr
    
    The output from the \code{print} method gives information at 
    least about the function call, the fitted model parameters,
    and the residuals variance.
    \cr\cr
    
    The \code{plot} method produces three figures, the first plots
    the series of residuals, the second does a quantile-quantile plot
    of the residual plot, and the third plots the fitted values vs.
    the residuals. Additional plots can be generated from the plot
    method (if available) of the underlying model, see the example below. 
    \cr\cr
    
    The \code{summary} method provides additional information,
    like errors on the model parameters as far as available, and adds 
    additional information about the fit.  
    \cr\cr
    
    The \code{predict} method forecasts from a fitted model. The
    returned values are the same as produced by the prediction
    function of the selected regression model. Especially, \code{$fit} 
    returns the forecast vector.
    \cr\cr
     
    The \code{residuals} and \code{fitted.values} methods return
    the residuals and the fitted values as numeric vectors.

}


\details{

  	\bold{LM -- Linear Modelling:}
  	\cr\cr 	
  	Univariate linear regression analysis is a statistical methodology 
  	that assumes a linear relationship between some predictor variables 
  	and a response variable. The goal is to estimate the coefficients 
  	and to predict new data from the estimated linear relationship.
	The function \code{plot.lm} provides four plots: a plot of residuals 
  	against fitted values, a Scale-Location plot of sqrt{| residuals |} 
  	against fitted values, a normal QQ plot, and a plot of Cook's 
  	distances versus row labels.
  	\cr 
  	\code{[stats:lm]}
  	\cr

	\bold{GLM -- Generalized Linear Models:}
	\cr\cr
	Generalized linear modelling extends the linear model in two directions.
  	(i) with a monotonic differentiable link function describing how the 
  	expected values are related to the linear predictor, and (ii) with 
  	response variables having a probability distribution from an exponential 
  	family. 
  	\cr
  	\code{[stats:glm]}
	\cr
  	
  	\bold{GAM -- Generalized Additive Models:}
  	\cr\cr	
  	An additive model generalizes a linear model by smoothing individually
  	each predictor term. A generalized additive model extends the additive
  	model in the same spirit as the generalized liner amodel extends the 
  	linear model, namely for allowing a link function and for allowing 
  	non-normal distributions from the exponential family. 
  	\cr
  	\code{[mgcv:gam]}
  	\cr
 	
  	\bold{PPR -- Projection Pursuit Regression:}
  	\cr\cr 	
  	The basic method is given by Friedman (1984), and is essentially 
  	the same code used by S-PLUS's \code{ppreg}. It is observed that 
  	this code is extremely sensitive to the compiler used. The algorithm 
  	first adds up to \code{max.terms}, by default \code{ppr.nterms},
  	ridge terms one at a time; it will use less if it is unable to find 
  	a term to add that makes sufficient difference. The levels of 
  	optimization (argument \code{optlevel}), by default 2, differ in 
  	how thoroughly the models are refitted during this process.
  	At level 0 the existing ridge terms are not refitted.  At level 1
  	the projection directions are not refitted, but the ridge
  	functions and the regression coefficients are. Levels 2 and 3 refit 
  	all the terms; level 3 is more careful to re-balance the contributions
  	from each regressor at each step and so is a little less likely to
  	converge to a saddle point of the sum of squares criterion. The 
  	\code{plot} method plots Ridge functions for the projection pursuit 
  	regression fit. 
  	\cr
  	\code{[stats:ppr]}
  	\cr
  	
  	\bold{MARS -- Multivariate Adaptive Regression Splines:}
  	\cr\cr
  	This function was coded from scratch, and did not use any of
  	Friedman's mars code.  It gives quite similar results to  Friedman's
  	program in our tests, but not exactly the same results.  We have not 
  	implemented Friedman's anova decomposition nor are categorical
  	predictors handled properly yet.  Our version does handle multiple
  	response variables, however.  As it is not well-tested, we would like
  	to hear of any bugs. 
  	\cr
  	Additional arguments which can be passed to the \code{"mars"}
  	estimator are:
  	\cr
	\code{w} - an optional vector of observation weights.
	\cr 
	\code{wp} - an optional vector of response weights. 
	\cr
	\code{degree} - an optional integer specifying maximum interaction 
	degree, default is 1. 
	\cr
	\code{nk} - an optional integer specifying the maximum number of model 
	terms. 
	\cr
	\code{penalty} - an optional value specifying the cost per degree of 
	freedom charge, default is 2.
	\cr 
	\code{thresh} - an optional value specifying forward stepwise stopping 
	threshold, default is 0.001. 
	\cr
	\code{prune} - an optional logical value specifying whether the model 
	should be pruned in a backward stepwise fashion, default is \code{TRUE}. 
	\cr
	\code{trace.mars} - an optional logical value specifying whether info 
	should be printed along the way, default is \code{FALSE}. 
	\cr
	\code{forward.step} - an optional logical value specifying whether 
	forward stepwise process should be carried out, default is \code{TRUE}. 
	\cr
	\code{prevfit} - optional data structure from previous fit. To see the 
	effect of changing the penalty paramater, one can use prevfit with 
	\code{forward.step = FALSE}. 
	\cr
  	\code{[mda:mars]}
 	\cr
  	
  	\bold{POLYMARS -- Polytochomous MARS:}
  	\cr\cr
  	The algorithm employed by \code{polymars} is different from the 
  	MARS(tm) algorithm of Friedman (1991), though it has many similarities. 
  	Also the name \code{polymars} has been used for this algorithm well 
  	before MARS was trademarked. 
  	%Two of the main differences are:
  	%\code{polymars} requires linear terms of a predictor to be in the model
  	%before nonlinear terms using the same predictor can be added; and
  	%\code{polymars} requires a univariate basis function to be in the model
  	%before a tensor-product basis function involving the univariate ...
  	\cr
  	Additional arguments which can be passed to the \code{"polymars"}
  	estimator are:
  	\cr
  	\code{maxsize} - the maximum number of basis functions that the model is 
  		allowed to grow to in the stepwise addition procedure. Default is 
		\eqn{\min(6*(n^{1/3}),n/4,100)}, where \code{n} is the number of 
		observations. 
		\cr
	\code{gcv} - parameter used to find the overall best model from a 
		sequence of fitted models. The residual sum of squares of a model 
		is penalized by dividing by the square of 
		\code{1-(gcv x model size)/cases}.   
		A larger gcv value would tend to produce a smaller model.
		\cr	
	\code{additive} - Should the fitted model be additive in the predictors? 
		\cr	
	\code{startmodel} - the first model that is to be fit by \code{polymars}. 
		It is either an object of the class \code{polymars} or a model 
		dreamed up by the user. In that case, it takes the form of a 
		\code{4 x n} matrix, where \code{n} is the  number of basis 
		functions in the starting model excluding the intercept. Each 
		row corresponds to one basis function (with two possible components). 
		Column 1 is the index of the first predictor involved. Column 2 is 
		a possible knot in this predictor. If column 2 is \code{NA}, the 
		first component is linear. Column 3 is the possible second predictor 
		involved (if column 3 is \code{NA} the basis function only depends 
		on one predictor). Column 4 contains the possible knot for the 
		predictor in column 3, and it is \code{NA} when this component is 
		linear.  Example: if a row reads \code{3 NA 2 4.7}, the corresponding 
		basis function is \eqn{[X_3 * (X_2-4.7)_+]}; if a row reads 
		\code{2 4.3 NA NA} the corresponding basis function is 
		\eqn{[(X_2-4.3)_+]}. 
		A fifth column can be added with 1s and 0s, The 1s specify which 
		basis functions of the startmodel must be in each model. Thus, these 
		functions stay in the model during the whole stepwise fitting 
		procedure. If \code{startmodel} is not specified \code{polymars} 
		starts with a model that only contains  the intercept. 
		\cr
	\code{weights} - optional vector of observation weights; if supplied, 
		the algorithm fits to minimize the sum of the weights multiplied 
		by the squared residuals. The length of weights must be the same 
		as the number of observations. The weights must be nonnegative. 
		\cr
	\code{no.interact} - an optional matrix used if certain predictor 
		interactions are not allowed in the model. It is given as a 
		matrix of size \code{2 x m}, with predictor indices as entries.  
		The two predictors of any row cannot have interaction terms with 
		each other. 
		\cr
	\code{knots} - defines how the function is to find potential knots 
		for the spline basis functions.  This can be set to the maximum 
		number of knots you would like to be considered for each predictor. 
		Usually, to avoid the design matrix becoming singular the actual 
		number of knots produced is constrained to at most every third 
		order statistic in any predictor. This constraint can be adjusted 
		using the \code{knot.space} argument. It can also be a vector with 
		the number of potential knots for each predictor. Again the actual 
		number of knots produced is constrained to be at most every 
		third order statistic any predictor.  
		A third possibility is to provide a matrix where each columns 
		corresponds to the ordered knots you would like to have considered 
		for that predictor. 
		This matrix should be filled out to a rectangular data structure 
		with NAs. 
		The default is \code{min(20, round(n/4))} knots per predictor. 
		When specifying knots as a vector an entry of \code{-1} indicates 
		that the predictor is a categorical variable and each unique entry 
		in it's column is treated as a  level. 
		When specifying knots as a single number or a matrix and there are 
		categorical variables these are specified separately as such using 
		the factor argument. 
		\cr
	\code{knot.space} - is an integer describing the minimum number of 
		order statistics apart that two knots can be. Knots should not 
		be too close to insure numerical stability. 
		\cr
	\code{ts.resp} - testset responses for model selection. Should have 
		the same number of columns as the training set response. A testset 
		can be used for the model selection. Depending on the value of 
		classify, either the model with the smallest testset residual 
		sum of squares or the smallest testset classification error is 
		provided. Overrides \code{gcv}. 
	 	\cr
	\code{ts.pred} - testset predictors. Should have the same number of 
		columns as the training set predictors. 
		\cr
	\code{ts.weights} -
		testset observation weights. A vector of length equal to the number 
		of cases of the testset. All weights must be non-negative. 
		\cr
	\code{classify} - when the response is discrete (categorical), polymars 
		can be used for classification. In particular, when 
		\code{classify = TRUE}, a discrete response with \code{K} levels 
		is replaced by \code{K} indicator variables as response. Model 
		selection is still being carried out using gcv, except when a 
		testset is provided, in which case testset misclassification is 
		used to select the best model. 
		\cr
	\code{factors} - used to indicate that certain variables in the predictor 
		set are categorical variables. Specified as a vector containing the 
		appropriate predictor indices (column numbers of categorical 
		variables in predictors matrix). Factors can also be set when the 
		\code{knots} argument is given as a vector, with \code{-1} as  
		the appropriate entries for factors. 
		\cr
	\code{tolerance} - for each possible candidate to be added/deleted 
		the resulting residual sums of squares of the model, with/without 
		this candidate, must be calculated. The inversion of of 
		the "X-transpose by X" matrix, X being the design matrix,  
		is done by an updating procedure c.f. C.R. Rao - Linear 
		Statistical Inference and Its Applications, 2nd. edition, page 33.   
		In the inversion the size of the bottom right-hand entry of this 
		matrix is critical. If it\code{s value is near zero or the value 
		of it}s inverse is almost zero then the  inversion procedure 
		becomes somewhat inaccurate. The lower the tolerance value the  
		more careful the procedure is in selecting candidates for addition 
		to the model but it may exclude too conservatively. And the other 
		hand if the tolerance is set too high a spurious result with a 
		singular or otherwise sub-optimal model may occur. By default 
		tolerance is set to 1.0e-5. 
		\cr
	\code{verbose} - when set  to \code{TRUE}, the function will print 
		out a line for each addition or deletion stage. For 
		example, " + 8 : 5 3.25 2 NA" means adding interaction basis 
		function of predictor 5 with knot at 3.25 and predictor 2 (linear), 
		to make a model of size 8, including intercept. 
  	\cr
  	\code{[polyclass:polymars]}
  	\cr\cr
  	
  	\bold{NNET -- Feedforward Neural Network Regression:}
  	\cr\cr	
  	If the response in \code{formula} is a factor, an appropriate 
	classification network is constructed; this has one output and 
	entropy fit if the number of levels is two, and a number of 
	outputs equal to the number of classes and a softmax output 
	stage for more levels. If the response is not a factor, it is 
	passed on unchanged to \code{nnet.default}. A quasi-Newton 
	optimizer is used, written in \code{C}. 
	\cr
	\code{[nnet:nnet]}
  	
}


\author{

	The R core team for the \code{lm} functions from R's \code{base} package, \cr
	B.R. Ripley for the \code{glm} functions from R's \code{base} package, \cr
	S.N. Wood for the \code{gam} functions from R's \code{mgcv} package, \cr
	N.N. for the \code{ppr} functions from R's \code{modreg} package, \cr
	T. Hastie, R. Tibshirani for the \code{mars} functions from R's \code{?} package, \cr
	M. O' Connors for the \code{polymars} functions from R's \code{?} package, \cr
	The R core team for the \code{nnet} functions from R's \code{nnet} package, \cr
	Diethelm Wuertz for the Rmetrics \R-port.

}



\references{

Belsley D.A., Kuh E., Welsch R.E. (1980);
	\emph{Regression Diagnostics};
	Wiley, New York.
	
Dobson, A.J. (1990);
	\emph{An Introduction to Generalized Linear Models};
	Chapman and Hall, London.

Draper N.R., Smith H. (1981);
	\emph{Applied Regression Analysis}; 
	Wiley, New York.

Friedman, J.H. (1991); 
	\emph{Multivariate Adaptive Regression Splines (with discussion)},
	The Annals of Statistics 19, 1--141.
	
Friedman J.H., and Stuetzle W. (1981); 
	\emph{Projection Pursuit Regression}; 
	Journal of the American Statistical Association 76, 817-823.

Friedman J.H. (1984);
	\emph{SMART User's Guide}; 
	Laboratory for Computational Statistics, 
	Stanford University Technical Report No. 1.
	
Green, Silverman (1994);
	\emph{Nonparametric Regression and Generalized Linear Models};
	Chapman and Hall.

Gu, Wahba (1991); 
	\emph{Minimizing GCV/GML Scores with Multiple
		Smoothing Parameters via the Newton Method};
	SIAM J. Sci. Statist. Comput. 12, 383-398.

Hastie T., Tibshirani R. (1990);
	\emph{Generalized Additive Models};
	Chapman and Hall, London.

Kooperberg Ch., Bose S., and  Stone C.J. (1997);
	\emph{Polychotomous Regression},
	Journal of the American Statistical Association 92, 117--127.

McCullagh P., Nelder, J.A. (1989);
	\emph{Generalized Linear Models};
	Chapman and Hall, London.

Myers R.H. (1986);
	\emph{Classical and Modern Regression with Applications}; 
	Duxbury, Boston.

Rousseeuw P.J., Leroy, A. (1987);
	\emph{Robust Regression and Outlier Detection};
	Wiley, New York.

Seber G.A.F. (1977);
	\emph{Linear Regression Analysis}; 
	Wiley, New York.

Stone C.J., Hansen M., Kooperberg Ch., and Truong Y.K. (1997);
 	\emph{The use of polynomial splines and their tensor products 
 		in extended linear modeling (with discussion)}.

Venables, W.N., Ripley, B.D. (1999);
	\emph{Modern Applied Statistics with S-PLUS}; 
	Springer, New York.
	
Wahba (1990); 
	\emph{Spline Models of Observational Data};
	SIAM.

Weisberg S. (1985);
	\emph{Applied Linear Regression};  
	Wiley, New York.
	
Wood (2000); 
	\emph{Modelling and Smoothing Parameter Estimation  with
	Multiple  Quadratic Penalties};
	JRSSB 62, 413-428.

Wood (2001); 
	\emph{mgcv: GAMs and Generalized Ridge Regression for \R}.
	R News 1, 20-25.

Wood (2001);
	\emph{Thin Plate Regression Splines}.


	There exists a vast literature on regression. The references listed 
	above are just a small sample of what is available. The book by 
	Myers' is an introductory text book that covers discussions of much 
	of the recent advances in regression technology. Seber's book is 
	at a higher mathematical level and covers much of the classical theory 
	of least squares.
	
}


\seealso{

  	\code{\link{lm}}, 
  	\code{\link{glm}},
  	\code{gam},
  	\code{\link{ppr}},
  	\code{mars},
  	\code{polymars},
  	\code{nnet}.

}


\examples{
## regFit -
   xmpSeries("\nStart: Load US Recession Modelling Data Set > ")
   data(recession) 
   
## myPlot -
   xmpSeries("\nNext: Write Internal Plot Function > ")
   myPlot = function(recession, in.sample) {
     Date = recession[, "date"]
     Date = trunc(Date/100) + (Date-100*trunc(Date/100))/12
     Recession = recession[, "recession"]
     inSample = as.vector(in.sample)
     plot(Date, Recession, type = "n", main = "US Recession")
     grid()
     lines(Date, Recession, type = "h", col = "steelblue3")
     lines(Date, inSample) }
   
## Generalized Additive Modelling:
   xmpSeries("\nNext: Generalized Additive Modelling > ")
   require(mgcv)
   par(mfrow = c(2, 2))
   fit = regFit(formula = recession ~ s(tbills3m) + s(tbonds10y),
   	 family = gaussian(), data = recession, method = "GAM")
   # In Sample Prediction:
   in.sample = predict(fit, newdata = recession)$fit  
   myPlot(recession, in.sample)
   # Summary:
   summary(fit)
   # Add plots from the original plot method:
   gam.fit = fit@fit
   class(gam.fit) = "gam"
   plot(gam.fit)
    
## POLYMARS Modelling:
   xmpSeries("\nNext: Polymars Modelling - Mode Parameters> ")
   par(mfrow = c(3, 2), ask = FALSE)
   fit = regFit(formula = recession ~ tbills3m + tbonds10y,
   	 family = gaussian(), data = recession, method = "POLYMARS")
   fit
}


\keyword{models}