R Splines – How to Translate Output from lm() Fit with Cubic Spline into Regression Equation

rsplines

I have some code and output, and I would like to construct a model. I don't know how to construct a model using this output:

 require("splines")
 x   <- c(0.2,   0.23,   0.26,   0.29,   0.33,   0.46,    0.53 )
 y   <- c(0.211, 0.2026, 0.2034, 0.2167, 0.2177, 0.19225, 0.182)
 fit <- lm(y ~ ns(x,3))
 summary(fit)

Note that ns() generates the B-spline basis matrix for a natural cubic spline. Thus this model regresses y against a B-spline for x using three degrees of freedom. What would the equation for such a model look like?

Best Answer

require(rms)
f <- ols(y ~ rcs(x, 3))  # 2 d.f. for x
Function(f)  # represent fitted function in simplest R form
latex(f)     # typeset algebraic representation of fit

rcs "restricted cublic spline" is another representation of a natural spline.

Related Solutions

Solved – Calculation of natural cubic splines in R

Wikipedia has a nice explanation of spline interpolation

I posted the code to create cubic Bezier splines on Rosettacode a while ago.

Also, you can have a look at this discussion on SO about spline extrapolation.

Solved – How to calculate the Tweedie prediction based on model coefficients

When you pass glm() the tweedie family the return value is a glm object. So you can use the predict() method or the predict.glm() method if you prefer to specify to any future readers of your code that this is a glm.

example(tweedie)
twdeReg <- glm(y~x, family=tweedie(var.power=1, link.power=1))
predict(twdeReg)
predict.glm(twdeReg)

In the predict family of functions you pass the argument newdata=newDataName to specify prediction on a new dataset, default behavior is to predict on the current data. Also, read ?predict to see the 3 options of if you want prediction of the linear combination of predictors, on the y-space, or the other one which I've never found super useful.

Added from comment on the reply:

To get this manually you'll need to use the equation from ?tweedie documentation that describes the link. The doc states: $\mu_i^q = \mathbb{E}(y_i|\vec{x}_i)^q = \vec{x}_i^T\vec{\beta}$ so if you want the expected value you'll need to calculate:

$$\mathbb{E}(y_i|\vec{x}_i) = (\vec{x}_i^T\vec{\beta})^{1/q},$$

where $q$ is the link.power=1 value. so if q=1 as the question is written simply take the product of the estimates times the coefficients and add up all of these products ( $\vec{x}_i^T\vec{\hat{\beta}}$ ) where the 'hat' denotes the estimate.

Best Answer

Related Solutions

Solved – Calculation of natural cubic splines in R

Solved – How to calculate the Tweedie prediction based on model coefficients

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