Questions tagged [nonlinear-regression]

Use this tag only for regression models in which the response is a nonlinear function of the parameters. Do not use this tag for nonlinear data transformation.

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10 views

Estimating function - f(x,y) for the given minimums (Python)

I was given 3 minimums of Y = f(X1, X2) such that: Local Minimum1: X1 = 0.20; X2 = 0.30; Ymin1 = 0.70 Local Minimum2: X1 = 0.60; X2 = 0.80; Ymin2 = 0.80 Global Minimum: X1 = 0.85; X2 = 0....
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17 views

Bias of estimated maximum value of a function [closed]

If you fit a nonlinear function f(x) to some noisy (x,y) data, and if f(x) is maximized at x=x', how much positive bias will there tend to be in your estimate of the function maximum f(x')? You expect ...
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12 views

How to deal with Non-Linear prediction intervals with horizontal asymptotes?

I'm using a weibull regression on a data set which reports % total expenditures over time. Time is measured by % of project total completed, therefore neither the dependent or independent variable can ...
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40 views

Using R^2 in nonlinear regression

This page discusses why Minitab does not compute $R^2$ for nonlinear regression. I understand that calculating $R^2$ between the response and the predictor ($y$ vs $x$) is not justified. However, is ...
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18 views

Regression on matrices

Given an equation in the form of $R(\lambda) = \left ( \sum_{i=1}^{4} R_i(\lambda)^\frac{1}{n} \right )^n$ where $R$ is a $m$ by one matrix and a number of data matrices for $R$, can nonlinear least ...
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1answer
80 views

Regularization (L1 or L2) for non-linear parameters

I was wondering whether it is possible to regularize (L1 or L2) non-linear parameters in a general regression model. Say, I have the following cost function, where 𝑝 is a 3𝑑 vector of fitting ...
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1answer
51 views

Non-Linear regression and variance misspecification

Given a non-linear regression model for cross-section data $$y_i = f(x_i,\theta_0) + \epsilon_i,$$ where it is assumed that $\mathbb E[y_i\lvert x_i] = f(x_i,\theta_0)$, I understand that it is a ...
5
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1answer
61 views

Confidence intervals of percentiles in non-linear regression

I'm fitting a log-logistic model, $Y=1/\left(1+10^{((\log a-\log X)/b)}\right),$ to toxicity data ($X$ are concentrations and $Y$ are mortalities) using SPSS and Graphpad Prism. I get the fitting ...
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1answer
50 views

Multivariate Nonlinear Mixed Effects Model

I want to estimate a multivariate nonlinear mixed effect models where the random effects are not assumed to be normal. What approach should I take ?
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1answer
17 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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1answer
72 views

Partial effect in non-linear regression [closed]

If I have estimated a non-linear regression model $$y_t = f(x_t,\theta) + e_t$$ then how can I calculate the average partial effects?
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23 views

Shape preserving spline regression

There are shape-preserving, preserving especially positivity, monotonicity or convexity, spline interpolations such as described here and here. Are there similar shape-preserving spline regression ...
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14 views

Inputs which return optimal output of a blackbox model

I am currently working on a problem and now got stuck to implement one of it's steps. This is a simple attempt to explain what I am currently facing, which is something that I am aiming to implement ...
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5 views

Effect of heteroskedasticity in hierarchical (non-)linear models

Unlike linear models estimated via OLS where heteroskedasticity lead to inconsistency of the variance estimator but not the coefficient estimates, heteroskedasticity causes inconsistency of both ...
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6 views

Using Self-Starting Functions For Exponential Decay Rates

I am trying to decide how to get my starting parameters optimized for a simple exponential decay model. My regression formula is: y ~ Be^(at) Where y is the remaining value at time,t, remaining ...
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11 views

Error propagation with non-linear least squares

How do you take the variance of the datapoints into account to compute variance estimates of the parameters of a non-linear least squares fit? Suppose, I fit a non-linear model to a dataset $\mathbf{...
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23 views

Non-linear autoregressions (with financial application)

I stumbled upon a regression that I haven't seen before, if anyone can provide some info that'd be great. Define the dependent variable as: $y_{i,t} = x_{i,t} - x_{i,t-1}$ $y_{i,t} = ax_{i,t} + b$ $...
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36 views

Standardized beta coefficients in nonlinear regression

In linear models $Y=X\beta+\epsilon$, where the errors $\epsilon_i\sim\text{Normal}(0,\sigma^2)$ are independent, the standardized beta coefficients are given by $$ \beta_i^*=\beta_i\frac{\sigma_{x_i}}...
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29 views

Fitting curves in Jupyter Notebook without using the fit function [closed]

For a task for school, I have to write my own fit function by using the least squares method. The problem is I don't know how to do that, specifically I don't know how to minimize my function to ...
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3answers
155 views

Forecasting/predicting total sum of donations (following GLM with poisson family and log link)

I am trying to predict the total sum of donations that Monica will receive on https://www.gofundme.com/f/stop-stack-overflow-from-defaming-its-users/ I copied the data and summed for all days the ...
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30 views

Importance of absolute values of the covariance matrix in the nonlinear mixed models

I am fitting a nonlinear mixed model (three-parameter logistic function) without any hierarchical structure. I have adopted an unstructured variance-covariance structure for the random effects. Is it ...
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17 views

Polynomial regression : how to find the best polynomial degree ? Chi2 or equivalent already built-in in Python numpy?

I am studying the stability of numerical derivatives as a function of the step I take to compute these derivatives. With a derivative with 15 points (obtained by the finite difference method), I get ...
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9 views

What is the name of this simple model? [duplicate]

Given data $d_i$ captured at corresponding times $t_i$, my model is $$ d_i = \sum_{j=1}^m b_j f_j(t_i,θ) + e_i $$ where as usual $e_i \sim N(0,σ^2)$. In other words, the data is expanded in $m$ ...
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7 views

Survival Analysis/Customer Attrition Model for Balances

I’m looking to model balance, meaning dollars, decay(attrition). In brief, I have time series customer data, which is aggregated to get customer’s balances for a specific product. Over time, the ...
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16 views

Extension of Lee-Carter model with parametric functions of age and time

A standard model of mortality is the Lee-Carter model where Deaths at age $x$ and time $t$ are given by $D_{xt}\sim Poisson(E_{xt}\mu{xt})$. $E_{xt}$ and $\mu_{xt}$ are, respectively, the average ...
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1answer
55 views

How to interpret “quantile residuals”

The DHARMa package in R aims to provide scaled (quantile) residuals that, according to the DHARMa vignette, "can be interpreted as intuitively as residuals from ...
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28 views

How to fit a non-linear expression of type $ Y=A(1-e^{-t/B})$ to the data set without using any package? [duplicate]

I am a newbie in statistics. I have collected data for a parameter Y at different time t. I would like to fit a function $ Y=A(1-...
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54 views

feature importance for SVM with a nonlinear kernel

Using sklearn, I did SVR using rbf kernel. Though I got good results, problem is I don't know how to get the important feature that the algorithm used. Also coef_ ...
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0answers
27 views

Maximum Likelihood with Experimental Data: Standard Errors and Standard Deviations

Suppose we have a set of experimental data $\{(x_i, Y_i, S_i)\}_{i=1}^N$ where the $x_i$'s are our measurement points, the $Y_i$'s are the mean value of the response $y$ over $m$ experiments at $x_i$, ...
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2answers
39 views

XOR with Neural Network [closed]

I'm trying to implement a simple neural network to fit a XOR function as shown in the book 'Deep Learning' by Ian Goodfellow, Yoshua Bengio and Aaron Courville (2016). Here is my python code using ...
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0answers
24 views

How can you derive confidence intervals for a bent cable model?

Using the function bent.cable in the SiZer package in R, one can fit a "bent cable model" in R. Here is an example of how I used it and the plot it made. ...
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27 views

difference between RBF kernel ridge and gaussian kernel regression

This may seem a very naif question: theory frameworks behind kernel ridge regression and classic, non-parametric, kernel regression are very different, but still, from a practical point of view, I can'...
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1answer
64 views

How to incorporate a non-linear relationship in a multiple regression model?

Suppose the beta coefficients of a weighted multiple regression model is given by the matrix formulation: ${\boldsymbol \beta} = ({\bf X}^T{\bf W}{\bf X})^{-1}{\bf X}^T{\bf Wy}$ Suppose that the ...
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0answers
20 views

Combining features linearly before non-linear modelling

I want to construct a model like this: $$y = g(X, Z)$$ $$X = \alpha_1 x_1 + \alpha_2 x_2 + \dots + \alpha_n x_n$$ $$Z = \beta_1 z_1 + \beta_2 z_2 + \dots + \beta_n z_n$$ Where $x_i \text{ and } z_i$ ...
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0answers
18 views

Significance of initialisation of Kernel in sklearn.gaussian_process.kernels

I have been going through Gaussian Processes. In one of the code I stumbled upon there is this statement, I am not quite sure of the parameters that are passed to initialise it. Please help me. ...
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1answer
52 views

How to compute confidence and prediction intervals for (nonlinear) regression using non squared “loss function”

Does somebody know (or can point me to a reference) how can I compute a confidence and prediction intervals for (posibly nonlinear) regression using non squared "loss functions"? Let me add some ...
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0answers
7 views

How to interprete relation in MAE with independent variable while ME is zero?

I have done a regression with mgcv based on 2 independent continious variables (x1, x2) and a dependent continious variable (y) and an interaction term. ...
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0answers
27 views

Exponential regression fit overestimates

I have a non-linear data set that I used to fit an hyperbolic curve of the following format: $$ q = \frac{q_i}{(1+bD_it)^{1/b}}$$ $t$ is the x-axis (independent variable), $q$ is the y-axis (...
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0answers
33 views

Confidence intervals when fitting non-linear curves

I have data for a device that dispenses material and I want to use an exponential decay model in python to relate the flow rate to the mass left inside the device, in particular $flow=a-b\times e^{-c\...
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2answers
379 views

Literature review on non-linear regression

Does anyone know of a good review article for the statistical literature on non-linear regression? I am primarily interested in consistency results and asymptotics. Of particular interest is the ...
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0answers
21 views

Interpretation of a quadratic term on a log transformed target variable

I've done some searching and found several posts related to this, e.g.: In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? Suppose I ...
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1answer
35 views

Fundamental understanding of Gaussian Process and their terminology [closed]

I am new to this site as well as Machine learning, so kindly bear with me. I have been trying to understand Gaussian process and their implementation. Notation: 1) Let's say that the $\vec{x}$ $\in ...
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1answer
72 views

Difference in R-squared values for MATLAB and Python

I've fitted a data with following sigmoidal function with MATLAB using Curve Fitting Tool and with Python with scipy.curve_fit() ...
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0answers
23 views

Estimate variance of parameters in non-linear ridge regression

I am basically estimating the shape of an unknown function f(x) from multi-dimensional chemical reaction data by estimating the most likely function values $f$ on a grid $x$ with kernel regression. To ...
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0answers
74 views

Neural Net Regression SSE Loss

Notation $y_i$ is observation $i$ of some response variable $Y$. $\hat{y}_i$ is the value of $y_i$ predicted by the regression. $\bar{y}$ is the average of all observations of the response variable....
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17 views

Grouped Logit vs. Non-Linear Least Squares vs. Negative Binomial w/ Exposure?

I'm currently working on a project looking at the effect of competition on the type of appeals candidates make in their campaign advertisements. My dataset consists of a list of candidates, the ...
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0answers
70 views

Checking non linear effects in LASSO regression

This might be a weird question and I understand that LASSO is mainly using as a variable selection method. But I want to know that is it possible to check non-linear effects of a LASSO logistic ...
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1answer
113 views

Bell-curve shape regression [duplicate]

I am trying to fit some data that looks like a bell-curve: we reach a maximum at some value close to the mean, then the graph falls towards zero as we get further away from it. I am not the "owner" of ...
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0answers
32 views

Residuals in OLS/linear regression with restricted cubic splines

I have a dataset where dependent variable (y) seems to be nonlinearly associated to independent (x). Fitting a RCS in OLS seems to be a good option to assess their relationship. What assumptions ...
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0answers
31 views

Analyzing individual + aggregate-level data (with individual DV) : what statistical model to use?

Greetings, I have pooled cross-sectional survey data spanning several decades. Separately, using LexisNexis, I also created an index of issue-salience that stores the % of monthly newspaper articles ...