Questions tagged [piecewise-linear]

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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 ...
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1answer
62 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 ...
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2answers
69 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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25 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: ...
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1answer
124 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 ...
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1answer
42 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 ...
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2answers
53 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 ...
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1answer
236 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 ...
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1answer
35 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
31 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
23 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 ...
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2answers
53 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 ...
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3answers
1k 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 ...
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0answers
62 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} \...
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1answer
43 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 ...
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1answer
441 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
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2answers
418 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
375 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 ...
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0answers
233 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, ...
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1answer
188 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
150 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
103 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
84 views

segmented piece wise linear regression problem?

I want to get a piecewise linear regression model with the function "segmented". ...
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1answer
323 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 ...
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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}...
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1answer
70 views

piecewise regression into a for loop [closed]

I´m trying get a piecewise regression. ...
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0answers
411 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, ...
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1answer
308 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
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1answer
2k 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
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3answers
225 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
416 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 ...
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2answers
98 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 ...
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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, ...
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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
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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
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1answer
108 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
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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
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0answers
237 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
232 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 ...
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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
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2answers
2k 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
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0answers
148 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 ...
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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
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1answer
195 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.
2
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1answer
865 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
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0answers
713 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 ...
5
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2answers
8k views

Correct way to compare two (very) different regression models?

I'm working with some piecewise linear regression models, and I'd like to compare their predictions with those produced by multiple (weighted) linear regression models. Both models describe the same ...
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4answers
5k views

Piecewise linear regression with knots as parameters

I would like to fit a piecewise linear regression with knots as parameters. I would like to know what's the best solution. Should I run a set of regressions with all the possible knots and choosing ...
4
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0answers
125 views

Parametric segmented or piecewise regression with heteroscedastic errors

I am fitting longitudinal data with an increase in variance over time. The standard physiological model is a bi- or tri-linear model with variable breakpoints. The estimated parameters are used to ...