Questions tagged [piecewise-linear]
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60
questions
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8 views
Formula for cyclic continuous piecewise Regression
I am interested in running a piecewise linear regression in R. I would like to specify the model matrix for the piecewise regression myself so I am not interested in using a pre-coded solution from a ...
4
votes
1answer
53 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 ...
0
votes
3answers
193 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 ...
1
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0answers
100 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 ...
3
votes
1answer
97 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 ...
2
votes
2answers
113 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 ...
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0answers
29 views
How do I calculate the standard error and p value for a piecewise linear mixed model with lmer?
I have fit a piecewise spline linear mixed model with multiple knots:
...
1
vote
1answer
255 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 ...
1
vote
1answer
45 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 ...
0
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2answers
59 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 ...
0
votes
1answer
331 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://imgur.com/ON4k1hy .
The 6 breaking points are predetermined from domain knowledge.
Unfortunately my ...
0
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1answer
48 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:
$$
Y \sim \beta_0 + \beta_{1,1} X + \beta_{1,2} (X ...
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0answers
35 views
Optimal penalty for finding changepoints with the fused lasso, assuming some probabilistic model?
I am interested in detecting changepoints in a signal using the fused lasso (as implemented here for example). I am in particular interested in getting estimates of changepoints which are close to the ...
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0answers
24 views
Can I set the breakpoint of piecewise regression by medical reference?
I want to prove different regression coefficient for SBP on BMI according to BMI categories.
So I want to use piecewise regression.
BMI is categorized by WHO guideline which means medicaly proven ...
1
vote
2answers
57 views
Regression: checking effect of negative vs positive regressor
I'm fitting a linear model of the following form:
$Y_{i} = \alpha + \beta_1X_{i} + \beta_2Z_{i} + \beta_3X_{i}\times Z_{i}+e_i$
All the variables are continuous. I'm interested in the sign of the ...
4
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3answers
2k views
Piecewise linear with constraints with the segmented function on R
I want to make a piecewise linear regression in R. I have a large dataset with 3 segments where I want the first and third segment to be without slope, i.e. parallel to x-axis and I also want the ...
1
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0answers
66 views
Finding the distribution of a piecewise function of a Gamma random variable
Let random variable $X \sim \text{Gamma}(\alpha,\beta)$. I want to derive the distribution of $Y$, where:
$$
Y = \left\{
\begin{array}{ll}
a X - k & \quad X \geq \frac{k}{a} \...
1
vote
1answer
44 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 ...
6
votes
1answer
501 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 ...
3
votes
2answers
481 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?
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0answers
389 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 ...
3
votes
0answers
242 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, ...
1
vote
1answer
193 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 ...
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0answers
153 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).
...
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1answer
105 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}, ...
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0answers
87 views
segmented piece wise linear regression problem?
I want to get a piecewise linear regression model with the function "segmented".
...
1
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1answer
332 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 ...
3
votes
2answers
2k 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}...
0
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1answer
72 views
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427 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, ...
1
vote
1answer
341 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, \...
6
votes
1answer
3k 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 ...
6
votes
3answers
243 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 ...
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0answers
420 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 ...
1
vote
2answers
99 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 ...
0
votes
2answers
4k views
Determine breakpoints in time series data where values change significantly
Given the following chart of data:
which represents duration metrics gathered at absolute times, I am trying to determine when/if any of the values exhibit a jump in durations. In the example chart, ...
4
votes
1answer
1k views
Gaussian Process Regression for piecewise linear response functions
I am performing Gaussian Process Regression (without noise) for response functions which are piecewise linear.
My question: Does there exist a covariance function, such that sample paths from a ...
5
votes
3answers
3k views
Piecewise regression with constraints
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. parallel to x-axis and I also want the ...
2
votes
1answer
110 views
Transforming TS for better fit
I'm trying to find transformation for my explanatory variable (outside temperature) to better explain heating power usage. I have data from one year here.
...
6
votes
2answers
1k views
R - how to get standard error for a breakpoint/parameter in a piecewise regression
I'm new to asking questions here, so I hope this is a reasonable place for this.
I am trying to fit a piece-wise regression. I expect my response (y) to increase from x0 to somewhere along x, then to ...
2
votes
0answers
250 views
Change of variables with a continuous but not differentiable mapping
Suppose that Y is a continuous random variable with a density function $f_{Y}(y)$. We transform $Y$ by the following mapping
\begin{equation} Y^{*} = \left \{ \begin{array}{ll}
\alpha Y + \beta &...
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0answers
245 views
Piecewise linear / spline regression: explaining changes in standard error
I have a model to estimate the effect of gas prices on a dependent variable Y. In the piecewise linear regression model (Gujarati 1995, p.519), I included a dummy ...
2
votes
2answers
2k views
Testing slopes in multivariate adaptive regression splines (MARS/earth)
I am using the earth package in R to estimate the number of breakpoints in a curve. There is only a single predictor.
I was ...
5
votes
2answers
3k views
Generate random number from a piecewise exponential distribution
I would like to generate a random number from a piecewise exponential distribution.
I consider that the time-scale is divided in $J$ intervals with bounds $(s_{j-1},s_j]$, for $j=1,...,J$, and ...
2
votes
0answers
161 views
Weighted piecewise regression to model proportion?
I was trying to model the relationship between utilization of service (from 0 to 1) and travel distance. First I binned travel distance by each 20 km and then calculate utilization for each bin (count ...
2
votes
0answers
1k views
Is segmented (piecewise) regression possible with a dichotomous dependent variable?
I have created a model of American cities with a dichotomous Y variable using logistic regression. I have theoretical reasons to believe that the model will differ significantly between larger and ...
4
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1answer
2k views
Piecewise regression
I have a time series where I want to fit a piecewise regression equation. Now the problem occurs when I try to fit equations of different degree in different segments of the series. Please provide me ...
2
votes
1answer
207 views
Are the slopes of two segmented lines important in recognition of a breakpoint?
I have found one breakpoint in my linear regression but the slope of two lines have the same decreasing slope, I was wondering if the change of the slope is necessary in recognition of breakpoints.
3
votes
1answer
906 views
Adding additional terms to a piecewise regression
I am exploring the probability of flight in a seabird (1=flight, 0=no flight) using binomial logistic regression. My predictors are distance to a disturbance (continuous), hour of the day (continuous),...
2
votes
0answers
716 views
Estimating break point in a broken stick / piecewise linear model for one variable while including other as model terms
I am interested in estimating a break point in response to one explanatory variable, while also including other variables as terms in the linear model. One reason to include additional terms is to ...
