Next: Smoothing Spline ANOVA Models Up: Smoothing Spline Regression Models Previous: Inferences

## Partial Spline Models

The linear partial spline model assumes that (Wahba, 1990)

 (14)

where the first part is a linear model of covariates , and as in (). Note that an SS ANOVA model discussed in the next section can also be used for when is multivariate. Partial spline models provide a tool to model multiple covariates when the relationship is unknown for only a few variables. Note that some 's may be functions of . For example, allows a jump in the th derivative at .

Let be the design matrix of : , and . If is of full column rank, the estimate of has the same representation as in (). Furthermore, coefficients and are solutions to equations () with replaced by .

The linear model for in () can be easily specified by adding these covariates to the right hand side of formula. For example, supposing and a cubic spline for , we can fit model () by

    ssr(y~x1+x2+x3+t, rk=cubic(t))


Next: Smoothing Spline ANOVA Models Up: Smoothing Spline Regression Models Previous: Inferences
Yuedong Wang 2004-05-19