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Manual specification of knots vs bs() for Piecewise regression

I am learning how to specify and plot piecewise regressions and have encountered a confusing situation. Namely, I have specified the knot for a piecewise regression using 2 methods: (1) manual and (2) ...
Yat-Hon's user avatar
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6 votes
3 answers
483 views

Understanding spline transformation and regression coefficients

I do not understand properly what a spline does even in a simple situation of a piecewise regression, and I need some help. Consider the following basic example: ...
denis's user avatar
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1 vote
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How does Multivariate Adaptive Regression Splines (MARS) consider the minimum number of observations between knots in the forward pass?

I try to explain my question with a simple example. Let's say we have two variables $x_1$ and $x_2$. At the first two stages of the forward pass, effects of $x_1$ with a knot at $a_1$ and $x_2$ with a ...
Shahin Roshani's user avatar
2 votes
0 answers
30 views

Custom contrasts in piecewise mixed effects models

I have longitudinal data from a two-group RCT in which the primary outcome was assessed at baseline, each week during the intervention, post-test and 5-month follow-up (6 times total). I am modeling ...
yeshe's user avatar
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3 votes
2 answers
227 views

How to combine two linear models?

I am trying to predict housing prices using as few variables as possible. One way that yielded the best results so far is splitting the data into two data-sets ($houses < 100m^2$ and $houses >= ...
Anton's user avatar
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0 answers
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How to model suspected piecewise-linear data with a lasso GLM

My data consist ~130 observations. Each observation has several thousand features (including many collinear or otherwise useless features) and a position along a single spatial dimension. Some sets of ...
Neuromancer's user avatar
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0 answers
39 views

Can Piecewise Regression Method of Jean Jacquelin be extended to 4 segments?

I want to identify the matris form of general y=f(x) function for: y(x)=p1x+q1 x<a1 =p2x+q2 x<a2 =p3x+q3 x<a3 =p4x+q4 x>a3 where a1,a2,a3,p1,q1,p2,q2,p3,q3,p4,q4 are unknown parameters to ...
Çağlar Özcan's user avatar
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0 answers
16 views

About Estimating Parameters from Unpaired Datasets

I possess three datasets: $x$, $y$ and $z$. It's hypothesized that a relationship exists between these variables, represented by the equation $z=a*x+b*y$. My goal is to estimate the values of $a$ and $...
JING's user avatar
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0 votes
0 answers
391 views

Fitting multiple piecewise linear regression model (with hinges)

I am trying to fit a multiple piecewise linear regression model, where I coerce the model to have the exact terms I want. For example, let's say I want to fit the exact model below, with predictors $...
Florent H's user avatar
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1 answer
101 views

Fitting a segmented regression with two zero boundary constraints

I am having trouble with this segmented regression as it requires two constraints and so far I have only treated single constraints. Here is an example of some data I am trying to fit: ...
leonardo's user avatar
10 votes
1 answer
2k views

Difference between Spline and Piecewise Regression

I was looking for the difference between spline regression and piecewise regression. Can someone please explain it to me? Also, if someone can provide me good reference on these 2 topics, with ...
ragas's user avatar
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1 vote
0 answers
71 views

Including intercept terms in piecewise linear programming

I am hoping to get some help in understanding whether the intercept terms are required in the objective function for piecewise linear programming (using the below code). ...
Marley's user avatar
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0 votes
1 answer
249 views

How to code time for a piecewise growth model for experimental data

I have data from an experiment that records the effects of stress on blood pressure. The study went as follows: Participants had their blood pressure measured 4 times over ten minutes to assess their ...
aaaa's user avatar
  • 11
2 votes
0 answers
78 views

Piecewise orthogonal regression

I want to fit data points by linear segments. The summed squared orthogonal distance of the points to the fitting lines shall be minimized, preferably using weights for the data points and for a ...
granular_bastard's user avatar
2 votes
1 answer
872 views

Fit points with a continuous, piecewise linear function with minimum number of points for each segment

I have a set of two-dimensional data points that I want to fit with a continuous piecewise linear function with one break point. However, I want each of the two segments to be supported by a minimum ...
frog's user avatar
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1 vote
1 answer
144 views

Latent growth curve with three latent variable and piecewise linear regression

I already heard about piecewise linear regression but I have no experience with latent growth curves. I came across it in that paper. As far as I understood based on Figure 1 (observed sample means) ...
Mas A's user avatar
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3 votes
4 answers
5k views

How to detect trend changes in noise time series?

wget -q -O- https://i.sstatic.net/xczQ1.gif | tail -c +43 R> with(f, plot(x, log10(y), type='l')) I have a series whose ...
user1424739's user avatar
5 votes
1 answer
808 views

Is there a formal test for model comparison between polynomial regression and piecewise/segmented regression? (i.e., are these models nested?)

I am interested in comparing three models a linear regression model: mod_linear <- lm (dv ~ iv) a polynomial regression model: mod_polynomial <- lm (dv ~ iv + I(iv^2)) a one-breakpoint ...
Annalise's user avatar
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0 votes
3 answers
327 views

Is there a "canonical" probabilistic version of the step function?

Step and switch-like functions can be thought of as deterministic switches at some threshold, so smooth sigmoidal-like functions describe that switch with uncertainty around that value. The machine ...
caesoma's user avatar
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4 votes
1 answer
1k views

Generalized Linear Model in a Piecewise SEM?

I have applied a piecewise structural equation model to my data using generalised linear models. I have used the glm() R function along with psem in the "piecewiseSEM" R package. It has ...
Will 's user avatar
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3 votes
1 answer
943 views

How to fit a piecewise assembly of nonlinear functions?

I am trying to model vegetation spectral signatures (grey lines) using a two-part piecewise function (black dotted lines). In it, I am trying to use only a few points (red dots) to fit a linear (first ...
Gustavo's user avatar
  • 51
2 votes
2 answers
472 views

How do you fix one slope coefficient in an interaction term?

hoping someone can help me with what (on the face of it) appears to be a relatively simple problem but which I can't current code out. Basically, I would like to fit a GLM in R with a simple two-way ...
kernowsam's user avatar
1 vote
1 answer
1k views

In hierarchical regression, the first step is not significant but later steps are

I ran a hierarchical regression comparing different models, in order of complexity. The first step was not significant (the simplest model vs a more complex model). However the next two steps were ...
Annalise's user avatar
  • 107
1 vote
1 answer
248 views

Select model in piecewise regression

How could we compare models fitted with piecewise regression that have different breakpoints? I used the code written here. In the example below, the "best" model, i.e. minimizing the residuals is ...
user3631369's user avatar
0 votes
2 answers
213 views

Simple algorithm to detect change point in time series

Apologies if this question has already been asked, but a lot of similar questions are regarding R or complex algorithms that I don't want. I have numerous 2-dimensional time series, eacch plotting ...
brianmchoi11's user avatar
0 votes
1 answer
1k views

How to do a discontinuos segmented logistic regression in R?

I'm trying to do a discontinuous segmented logistic regression, something like this: https://i.sstatic.net/AO1Mh.jpg . The 6 breaking points are predetermined from domain knowledge. Unfortunately my ...
user272593's user avatar
1 vote
1 answer
186 views

Don't understand why the first variable in a piecewise regression spans all the domain

Let us consider one predictor $X \in [a,b] \subset \mathbb{R}$ and one response $Y \in \mathbb{R}$. I need to perform a piecewise linear regression: $$ Y \sim \beta_0 + \beta_{1,1} X + \beta_{1,2} (X ...
Andry's user avatar
  • 219
1 vote
0 answers
49 views

Optimal penalty for finding changepoints with the fused lasso, assuming some probabilistic model?

I am interested in detecting changepoints in a signal using the fused lasso (as implemented here for example). I am in particular interested in getting estimates of changepoints which are close to the ...
user54038's user avatar
  • 543
0 votes
0 answers
32 views

Can I set the breakpoint of piecewise regression by medical reference?

I want to prove different regression coefficient for SBP on BMI according to BMI categories. So I want to use piecewise regression. BMI is categorized by WHO guideline which means medicaly proven ...
Koh Heebyung's user avatar
1 vote
2 answers
86 views

Regression: checking effect of negative vs positive regressor

I'm fitting a linear model of the following form: $Y_{i} = \alpha + \beta_1X_{i} + \beta_2Z_{i} + \beta_3X_{i}\times Z_{i}+e_i$ All the variables are continuous. I'm interested in the sign of the ...
Ali Gröch's user avatar
4 votes
3 answers
4k views

Piecewise linear with constraints with the segmented function on R

I want to make a piecewise linear regression in R. I have a large dataset with 3 segments where I want the first and third segment to be without slope, i.e. ...
Cyrielle's user avatar
1 vote
0 answers
104 views

Finding the distribution of a piecewise function of a Gamma random variable

Let random variable $X \sim \text{Gamma}(\alpha,\beta)$. I want to derive the distribution of $Y$, where: $$ Y = \left\{ \begin{array}{ll} a X - k & \quad X \geq \frac{k}{a} \...
DavidL's user avatar
  • 11
1 vote
1 answer
55 views

Censoring linearly splined predictor in regression

I'm developing a logistic regression where one of the independent variables has a non-linear relationship to the probability of the event occurring. I have created linear splines based on this ...
MrT's user avatar
  • 151
6 votes
1 answer
1k views

Position of knots in piecewise linear regression as 'random effects'

TL;DR: Is there some way I can do 'random knots' (where the position of the knot varies according to some group, not the number)? Full question: After obtaining experimental data, I find that one of ...
WavesWashSands's user avatar
3 votes
2 answers
1k views

Piecewise regression vs multiple models

Say you have a piecewise regression model with one breakpoint. Is there any difference between that and just creating a separate simple regression model for each segment of the IV?
Ashish's user avatar
  • 305
2 votes
0 answers
543 views

Understanding the Math of Segmented and Splines2 packages.

I was trying to teach myself the math behind what produces the slope and intercept of a segmented variable in the segmented package using the plant data set. My ...
Jordan 's user avatar
  • 235
3 votes
0 answers
271 views

Looking for references - ReLU neural networks vs Fitting continuous piecewise linear function

ReLU activated neural networks with a linear output are continuous piecewise linear functions (CPLF). There are technuques to fit CPLF functions, so comparison of those methods seems very natural, ...
them's user avatar
  • 702
2 votes
1 answer
232 views

How to adjust the parameters of a Piecewise regression model in Matlab?

I have an existent piecewise regression model correlating the parameters X and Y as follows: If X<0.1, then Y=0.744. If X>=0.1 & X<=0.8, then Y=0.842-0.977*X. If X>0.8, then Y=0.06. The ...
Muhammed A. Zidan's user avatar
1 vote
0 answers
214 views

Finding an inflection point between two conditions

The figure below illustrates a sample data from a numerosity estimation experiment with an uncalibrated (i.e., spontaneous) estimation condition (blue) and a calibrated estimation condition (orange). ...
DJY's user avatar
  • 73
1 vote
1 answer
119 views

How to estimate parameters of a (almost) linear model from unpaired observations?

I have this model: $a_i=mod(\lfloor i\cdot T+Normal(0,\sigma_a)\rfloor,Q)$ $b_i=mod(\lfloor a_i+D+Normal(0,\sigma_b)\rfloor,Q)$ with $i=1..N$ $N\in\mathbb{N}$ $Q\in\mathbb{N}$ $T\in\mathbb{R}, ...
Alessandro Jacopson's user avatar
1 vote
0 answers
99 views

segmented piece wise linear regression problem?

I want to get a piecewise linear regression model with the function "segmented". ...
user163494's user avatar
1 vote
1 answer
699 views

What is the difference between linear interpolation and piece-wise linear interpolation?

I'm familiar with linear interpolation. I tried to search some details about piece-wise linear interpolation but failed to understand this method. Can someone explain the difference between these two ...
YQ.Wang's user avatar
  • 429
4 votes
2 answers
3k views

Sampling from a piecewise linear probability density function

I have a pdf modelled as a piecewise linear function that I can represent as the sequence of pairs of real numbers standing for the points in the of the piecewise line: $\{(x_{1}, y_{1}), \dots, (x_{n}...
rano's user avatar
  • 421
0 votes
1 answer
87 views

piecewise regression into a for loop [closed]

I´m trying get a piecewise regression. ...
Alex's user avatar
  • 3
0 votes
0 answers
533 views

Model with piecewise-linear functions

I have a model which is of the following deterministic form: Y = A + B + C A, B and C are piecewise-linear functions of a, b and c, which are macroeconomic variables. I have the values (nodes, ...
Des's user avatar
  • 31
1 vote
1 answer
626 views

How to find the best piecewise-smooth fit

I have data points $(\theta,y)$ that when plotted in a x-y (with $\theta$ being the x) graph can be fit by the curve $$y=-\alpha-\frac{\beta}{\cos(\theta_{0}-\theta)}$$ i.e. I can find $\alpha, \...
user2175783's user avatar
7 votes
1 answer
4k views

Test for the significance of the effect of an intervention in a time series

I am looking for the best approach to test for the significance of the effect of an intervention that occurred at a known time on a time series data. Using a toy dataset as an example, I have come up ...
Mihail's user avatar
  • 542
6 votes
3 answers
373 views

"Branching Stick" Regression

With piecewise, or so-called broken-stick regression it is possible to fit two lines to data, But what if I wanted to fit data to two lines, one main and one branch which connects to a primary line ...
BBSysDyn's user avatar
  • 1,032
1 vote
0 answers
450 views

Can a Piecewise Linear Regression Approximate a Neural Network?

I have a piecewise linear regression model that performs quite well (CVd) on subsets of a small data set (Ns between 30 and 90 for the subsets, with a total of 222 records). So there are separate ...
WDCR's user avatar
  • 11
2 votes
2 answers
127 views

Estimating failure-point when failed datapoints are unobservable

I have several datasets of two variables, y and time. Datapoints are objects subject to physical wear, and wear-rates are (roughly) constant over the life of the objects. y is defined as the ...
bshane's user avatar
  • 203