# Tag Info

Accepted

### Why is the use of high order polynomials for regression discouraged?

I cover this in some detail in Chapter 2 of RMS. Briefly, besides extrapolation problems, ordinary polynomials have these problems: The shape of the fit in one region of the data is influenced by ...
• 86.9k
Accepted

### Adaptive GAM smooths in mgcv

Most of the extra smooths in the mgcv toolbox are really there for specialist applications — you can largely ignore them for general GAMs, especially univariate smooths (you don't need a random ...
• 45.8k

• 60.6k
Accepted

### Is a spline interpolation considered to be a nonparametric model?

This is a good question. Frequently, one will see smoothing regressions (e.g., splines, but also smoothing GAMs, running lines, LOWESS, etc.) described as nonparametric regression models. These models ...
• 29.3k

### Smoothing methods for gam in mgcv package?

mgcv uses a thin plate spline basis as the default basis for it's smooth terms. To be honest it likely makes little difference in many applications which of these you choose, though in some situations ...
• 45.8k
Accepted

### Use of splines in parameter estimation

I found their code on the Wayback machine and they used the smooth.spline-function in R. The paper points to http://genomine.org/qvalue/results.html for code and ...
• 2,197
Accepted

### B-Splines VS high order polynomials in regression

I would usually only consider splines rather than polynomials. Polynomials cannot model thresholds and are often undesirably global, i.e., observations at one range of the predictor have a strong ...
• 118k
Accepted

### Splines: relationship of knots, degree and degrees of freedom

In essence, splines are piecewise polynomials, joined at points called knots. The degree specifies the degree of the polynomials. A polynomial of degree 1 is just a line, so these would be linear ...
• 29.5k
Accepted

### GAM vs LOESS vs splines

What matters the most is the number of effective degrees of freedom that you give to each approach. For nonparametric smoothers such as loess this is controlled by the bandwidth whereas for ...
• 86.9k

### Do fractional polynomials have any advantages over restricted cubic splines?

Fractional polynomials and cubic splines each have the defects of their virtues. The point of cubic splines is to be local and flexible and smooth and able to approximate any smooth curve. The point ...
• 34.7k
Accepted

### Can splines be used for prediction?

From my interpretation of the question, the underlying question you are asking is whether or not you can model time as a spline. The first question I will attempt to answer is whether or not you ...
• 1,063
Accepted

### Why are the basis functions for natural cubic splines expressed as they are? (ESL)

First it is not the basis but a basis: We want to build a basis for $K$ knots of natural cubic splines. According to the constraints, "a natural cubic splines with $K$ knots is represented by $K$ ...
• 1,200
Accepted

### Do fractional polynomials have any advantages over restricted cubic splines?

I can think of some, not-too-compelling circumstances where fractional polynomials (FPs) would be preferable to restricted cubic splines (RCSs): Direct interpretation of the functional form is more ...
• 42.6k

### Why is the use of high order polynomials for regression discouraged?

Runge's phenomenon can lead to high-degree polynomials being much wigglier than the variation actually suggested by the data. An appeal of splines as a substitute for high-degree polynomials, ...
• 19.8k

### Ideal Use Cases for Splines

You have to define what you mean by "ideal" or "best" in this question, but I will give you my two cents none the less. Are there any ideal use cases for splines? My (very ...
• 33.5k

### How should I check the assumption of linearity to the logit for the continuous independent variables in logistic regression analysis?

Logistic regression does NOT assume a linear relationship between the dependent and independent variables. It does assume a linear relationship between the log odds of the dependent variable and the ...
• 149

### Splines in GLM and GAM

@AdamO's answer is correct, in that spline-based fits can certainly be done in the standard GLM framework. That's not to say that GAM's are just a special case of GLM's though! While there are a ...
• 20.2k

### Why is the use of high order polynomials for regression discouraged?

If your goal is interpolation, you typically want the simplest function that describes your observations and avoid overfitting. Given that it is unusual to see physical laws and relationships which ...
• 1,066
Accepted

### Motivating use of Bayesian splines in excess mortality estimation

The death rate can't be negative (the pandemic was bad but it wasn't zombie apocalypse bad), so a natural way to enforce that is to fit an additive/linear model on the log scale (hence why the model ...
• 45.8k
Accepted

### Difference between smoothing splines and splines in R

Smoothing splines have all the knots (knots at each point), but then regularizes (shrinks the coefficients/smooths the fit) by adding a roughness penalty term (integrated squared second derivative ...
• 278k

### what is the advantage of b-splines over other splines?

Splines are a large class of methods. The method of B-splines is a simple method for taking a single covariate and expanding it such that it spans the set of all functions that are a polynomial of ...
• 20.2k

### Monotonic splines in Python

Hi I do not know the specifics of your problem but you might find the following reference really interesting: Eilers, 2006 (especially paragraph 3). The idea presented in the reference is rather ...
• 1,151