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.

328 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
7
votes
0answers
171 views

Efficient nonparametric estimation of confidence intervals and p-values for nonlinear regression

I'm estimating parameters for a complex, "implicit" nonlinear model $f(\mathbf{x}, \boldsymbol{\theta})$. It's "implicit" in the sense that I don't have an explicit formula for $f$: its value is the ...
6
votes
0answers
866 views

Confidence interval of the mean response from nonlinear model

My problem (question at the end) is to calculate confidence interval (CI) (NOT prediction interval) of the response of a nonlinear model. I am working with R but this question is not R-specific. I ...
5
votes
0answers
598 views

F-test to determine whether more than two sets of data differ

Here is the context for my question: I understand that you can fit the same model to two different datasets separately and then fit the model to the datasets pooled together as a way to discern ...
5
votes
0answers
745 views

Gauss-Newton method for MA parameter estimation

Please check my solution below for estimating Moving Average parameter using the Gauss-Newton (Linearization) method. I consider MA(1). MA(1) model: $$z_t=a_t-\theta_1a_{t-1}.$$ Solution: The ...
5
votes
1answer
214 views

Regression estimator where exponents are freely varying?

Is there a regression estimation methodology that can estimate the following: $$Y_t = \alpha + \beta X_t^x + \gamma Z_t^z + \epsilon_t$$ where $x,z\in \mathbb{R}$, are freely varying and are chosen ...
4
votes
1answer
84 views

regression - does R2 only apply to measure linear regression performance?

Background According to Wiki: https://en.wikipedia.org/wiki/Coefficient_of_determination, $R^2$ is coefficient of determinant. The definition is $$ R^2 = 1 - \dfrac{SSE}{SST} $$ Since $SSE$ is ...
4
votes
0answers
270 views

Non-Linear modelling in R

I have a dataset which contains Retention (DV) and Customer Satisfaction data (IV, 7 variables, scale 1-10) for 55000 observations. Now I want to know which increase in number has the biggest impact ...
4
votes
0answers
195 views

How to build and interpret Q-Q plots when data can be grouped by a factor

I have a dataset $D=\{(\mathbf{x}_i,y_i)\}_{i=1}^N$, with $N\sim150$. The data come from 7 different test campaigns, which are not mere repetitions of the same tests, but actually different tests with ...
4
votes
0answers
227 views

Modern approaches to nonlinear regression which are available in R

I would like to fit a complex nonlinear regression model: basically, I have a complex computer code which has an input vector $\mathbf{x}$, a vector of calibration parameters $\boldsymbol{\theta}$ and ...
4
votes
0answers
1k views

How to find marginal effect of restricted cubic spline

I'm trying to figure out how to find the marginal effect of an interaction term from a restricted cubic spline in a non-linear model. The post Nonlinear effect in an interaction term is a good start ...
4
votes
0answers
312 views

Generalized logistic model, sometimes with a bump

I am trying to fit a generalized sigmoidal function with a bump which is a Gaussian kernel to some data. My model is of the form $y\sim f(t)+\epsilon$ where $f$ is the function: $$ f(t) = A + \frac{K}{...
4
votes
0answers
449 views

How to calculate uncertainty in bacterial growth rates (or in the slope of any local regression)?

I'm using a plate reader to measure optical density of different bacterial strains so I can compare their responses (growth rates and changes in them over time) to stress conditions. The growth curves ...
4
votes
0answers
615 views

How to fit an exponential equation of the form $Y = A + Be^{CX}$ to data

I need some assistance with a nonlinear adjust. I am trying to make a mathematical model that describes the rate of silicic acid escaping from an underwater sediment. For theoretical reasons, the ...
4
votes
0answers
53 views

Fit a line pattern on curve with unknown number of points

I've got a sample curve which ends theoretically with decreasing exponential. The curve end falls into noise. The sample points are given in log scale. What I want to do, is to find and fit the linear ...
4
votes
0answers
1k views

How to calculate standard errors of a non-linear model prediction?

I'm trying to understand how to show the prediction error of a model fit in R using the non-linear least squares function nls. Although there is an argument ...
4
votes
0answers
367 views

On nonlinear regression, fits, and transformations

I am trying to fit a nonlinear regression model in R using nls(). I have a form of the equation I want to fit to: $$y = (a \times x_{1}^c +b \times x_{2}^d) (x_{3}^...
4
votes
0answers
94 views

Can parameter uncertainties be salvaged when the residuals are correlated?

I have a nonlinear physical model for which I'm trying to determine parameter uncertainties using Monte Carlo. Instead of describing the nitty-gritty details, I will use a series of figures: The ...
4
votes
0answers
1k views

Intuitive explanation of Gauss-Newton regression

I read from a textbook that Gauss-Newton regression is also called 'artificial regression'. Please give me an example, how does it work? And what's the relation with Newton's method? Thank you.
3
votes
0answers
115 views

Should I standardize my variable for regression before nonlinear feature transformation?

I would like to fit a non-linear model by doing nonlinear feature transformation first (e.g. exp, log) and then using linear regression (or regularized linear regression). However, I am stuck at ...
3
votes
0answers
259 views

Measure of relationship between two variables that are percentages containing many zeros

I am working with various different data sets (in the context of forest reclamation on industrial disturbed landscapes) that contain percent cover values of desired (planted) and undesired plant ...
3
votes
0answers
64 views

What are some machine learning problems that can be attacked with continuous multiobjective optimization?

I am working on continuous vector optimization, and hence continuous multiobjective optimization is a particular case. I am interested in finding applications in machine learning for this problems. Is ...
3
votes
0answers
303 views

Nonlinear regression for a log-linear model

I have data points $(x_i, y_i), i = 1, \dots, N$, and a model (log-linear) with parameters $w_j, j = 0, \dots, m$ such that $y_i=\alpha_i e^{w_0+w_1x_i+w_2x_i^2+\dots+w_mx_i^m}+ n_i$, where $n_i$ are ...
3
votes
0answers
46 views

Can parameter distributions be estimated well for a nonlinear model using penalized MLE?

I have measured a spectrum with a line shape that obeys a known parametric model $f$, given by a physical theory. Assuming the responses $y_i$ are given by $y_i=f(x_i;\{\theta_n\}) + \varepsilon_i, ...
3
votes
0answers
199 views

Which non-parametric multiple-regression methods are computationally efficient with respect to the number of regressors?

I did some regression in R with random forests and got some decent results, $1-\sum{|e_i|}/\sum{|y_i-\bar{y}|}=0.692$, but I want to do better than this. Through my research, I have concluded that the ...
3
votes
0answers
117 views

Exponential regression and focus on small values

I have a set of data with 3 numeric variables: X, Y and Z. I have access to data with 15 &...
3
votes
0answers
223 views

Fitting a non-linear model where observations at each time are random variables drawn from a different (non-Gaussian) distribution

I have a non-linear (and not clearly linearizable) function of a few parameters that models a response over an independent variable (time): $$ f(t;\lambda_1,\lambda_2,\lambda_3). $$ The function $f$ ...
3
votes
0answers
120 views

Linear regression with prior on $\arctan \beta_1$

Suppose we have $\hat{y} = \beta_1 x + \beta_0$ (I ask only for the univariate case.) A typical Bayesian approach might involve Normal priors on both parameters. I was thinking today about a ...
3
votes
0answers
5k views

Gini Coefficient - Variable Importance Measure

There is a whitepaper for selecting important variables in a linear regression model. The URL of the whitepaper is http://support.sas.com/resources/papers/proceedings15/3242-2015.pdf . It explains ...
3
votes
0answers
57 views

Multiple comparisons of parameters from non-linear regression

Hei, I want to compare parameters a_i and b_i estimated by nonlinear regression (y=a_i*x/(b_i+x)) for different data-sets (let's say 8 different data sets). I have calculated the non-linear ...
3
votes
0answers
105 views

Trouble fitting mathematical model to data in R

I am trying to select the correct mathematical model for my standard curve. This data was collected from spectrophotometry. I am hoping to get a model to help me detect very small absorbance. ...
3
votes
0answers
338 views

'systemfit' package and systems of non-linear equations/regression

I am trying to estimate a system of non-linear equations using 'systemfit' package in R. I have had issues with it. The two equations share the same parameters i.e. "sigma", "al" and "ae". I expect ...
3
votes
0answers
753 views

Catagorical variables with very uneven distributions? Removal/modify/leave?

In my current dataset I have quite a few categorical variables. Most have decent distributions between the categories. 30:40:30 splits etc. where these are percentage of dataset members per category ...
3
votes
0answers
1k views

Bayesian inference and curve fitting

I'm a silly scientist, and I've got a process I'm interested in. It gives me lots of time-series data. I've got an explicit, analytical model that is firmly rooted in reality, and basically boils down ...
3
votes
0answers
2k views

Comparing nonlinear regression coefficients from independent datasets

I performed enzyme kinetics experiments on a three independent preparations of an enzyme and produced the following three datasets which I separately fit to the Michaelis-Menten equation: $$ V= \frac{...
3
votes
0answers
506 views

Relaxing the parallel lines assumption in a proportional odds model

I tried to specify a partial proportional odds regression in STATA using the gologit2 command. However, gologit2 runs ...
3
votes
0answers
323 views

AR1 Modelling using dlmModReg

I'm trying to model AR1 using dlmModReg(). The main purpose is to keep phi a variable so that if phi >1, I know that mean reversion is not occurring. Below is my ...
3
votes
0answers
786 views

How to find the “optimal” cutoff-points in a non-linear relationship?

I have the following challenge: The dataset has one dependent and one independent variable which are connected in a non-linear fashion. I am trying to give a more qualitative picture here because I am ...
3
votes
1answer
2k views

Specifying parameter constraints in nls()

Is it possible to specify that one parameter must be larger than another parameter in an nls call in my R script? Here's my nls call: ...
3
votes
1answer
90 views

Interpreting Regression Results: Combined Data Points

I'm new to statistics, so I'm having some trouble interpreting some results. Let's say I was interested in creating a daily wind speed profile for the arctic during a 30 day period. I have 5 ...
2
votes
0answers
45 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}}...
2
votes
0answers
96 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....
2
votes
0answers
82 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 ...
2
votes
0answers
67 views

Nonlinear quantile regression SSReg analogue

I have recently remembered that $SSTot = SSRes + SSReg$ fails to hold in the case of nonlinear regression. $$ y_i-\bar{y} = (y_i - \hat{y_i} + \hat{y_i} - \bar{y}) = (y_i - \hat{y_i}) + (\hat{y_i} - ...
2
votes
0answers
33 views

Regression model form

I have the following exercise: US.pop dataset from car package contains information about USA population from 1790 to 1990. Find regression model in form of $y = a / (1 + \exp((b-x)/c) )$ for ...
2
votes
0answers
94 views

Is there a measure of “complexity” for linear/nonlinear model terms?

My apologies if this is grossly misunderstood or mis-worded, but I've been mildly bugged by a question to which I've not found a satisfactory answer. I can't say that I have seen a discussion about ...
2
votes
0answers
30 views

Non-linear regression. Obtain B.spline coefficients using Fourier Transform?

I came up with a idea to estimate the coefficients of a B-spline fit by using the Fourier Transform but I don't know if it makes any sense to estimate them in this way. Given that $$s(x)=\sum_kc(k)\...
2
votes
0answers
41 views

Piecewise integration

I am trying to estimate residential demand for electricity in a country where electricity is sold (to all households (HH)) at an increasing two-part tariff. By choosing marginal prices as my key ...
2
votes
0answers
64 views

Relevance of residual normally distributed residuals in nonlinear regression

I have a mathematical equation, based on physics, that requires estimating several parameters via nonlinear regression. I have conducted such nonlinear regression estimation with a dataset of 1100 ...
2
votes
0answers
35 views

How to Estimate a Multi-variable Harmonic Function on a Grid?

What estimation schemes do you suggest for solving the following discrete problem: $$y=f(X)+\epsilon,\\$$ $$\Delta f=0.$$ Here, $X=(x_1,\cdots,x_p)\in\mathbb{R}^{p}$ and $\Delta=\sum_{i=1}^p \frac{\...
2
votes
0answers
432 views

Fitting a sinusoidal curve only with max-min values

I have a series of high-low tide values, approx. every 6h, and each one has the corresponding time. I would like to get (an estimation of) the values between each record. I was thinking I could create ...

1
2 3 4 5
7