# 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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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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### 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 ...
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.
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 ...
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 ...
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 ...
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 ...
46 views