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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1answer
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Exponential curve fitting with a constant

Assuming I have the following model: $$ y(t) = \alpha {e}^{- \beta t} + \gamma + n(t) $$ Where $ n(t) $ is additive white Gaussian noise (AWGN) and $ \alpha, \beta, \gamma $ are the unknown ...
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0answers
2k views

Log-normal distribution versus chi-square distribution for comparing RMSE of nonlinear fits

I have parameter estimates fitting a particular nonlinear model for thousands of experimental cycles. My goal is to find a nice way to tag those cycles which didn't fit the model very well. Currently ...
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1answer
1k views

Uncertainties on parameters from maximum likelihood fitting

I am trying to fit a model to binomially distributed data, which I have done via the maximum likelihood method. Normally I'm working with normally distributed data (or data which I can convince myself ...
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1answer
1k views

Normalizing error variance scale

Imagine we have two sets of data m1 and m2. m1 components have the dimension of [m^2/s] and m2 components are measured in [cm^2/s]. e.g. ...
3
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1answer
1k views

Putting limits on estimated coefficient values

I recently came across an example of using eviews to put non-linear/convex limits on estimated coeficients on OLS. I could track down a link to a forum describing how this is done (here)... But I ...
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3answers
743 views

How to select best model out of linear, quadratic, and a model involving an exponential? Are the models nested?

I'm examining the growth rate of species en function of ion carbonate. For each specie, I have different measured of ion carbonate, it can be in different temperature or pH. For each measure, I'm ...
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774 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 ...
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0answers
118 views

Regression in projective space?

Is there a method for (nonlinear? kernelized?) regression of functions with output in projective space? That is, given a series of examples $x_i\in\mathbb{R}^n$ (or $x_i\in\mathbb{P}^n$) and $y_i\in\...
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328 views

Variance of coefficients in nonlinear regression

I was reading the short intro to nonlinear regression in R by John Fox (Link) and was wondering where the formula for the variance of the coefficients come from (page 1). The formula for the variance-...
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1answer
10k views

How to compute prediction bands for non-linear regression?

The help page for Prism gives the following explanation for how it computes the prediction bands for non-linear regression. Please excuse the long quote, but I am not following the second paragraph (...
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3answers
4k views

How to assess goodness of fit of a particular nonlinear model? [closed]

I have a nonlinear model $y=\Phi(f(x,a)) + \varepsilon$, where $\Phi$ is the cdf of the standard normal distribution and f is nonlinear (see below). I want to test the goodness of fit of this model ...
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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: ...
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1answer
2k views

Definition of “degree of interaction” in the MARS model

What exactly is the meaning of the "degree of interaction" or "interaction degree" in the MARS model? e.g. R: earth(..., degree=2)
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1answer
3k views

R package for smooth transition regression models

Is there a R package that I can use to specify Smooth Transition Models. I'm looking specifically for something that allows me to specify a TAR model for a given time series. In 2008, a package, ...
4
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1answer
339 views

Best functional form to describe a scatterplot with a z-shape appearance with noise

What might be the general form of the equation can be fitted to the below scatter plot? The result should look like an smooth Z
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0answers
1k views

Correct use of partial derivatives? (Example: polynomial regression)

[update] It seems I had my question's original title misfocused a bit; concerning the use of partial derivatives I found some explanation/confirmation in wikipedia's partial derivative There it is ...
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2answers
43k views

Singular gradient error in nls with correct starting values

I'm trying to fit a line+exponential curve to some data. As a start, I tried to do this on some artificial data. The function is: $$y=a+b\cdot r^{(x-m)}+c\cdot x$$ It is effectively an exponential ...
10
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1answer
826 views

Is it allowed to include time as a predictor in mixed models?

I always believed that time should not be used as a predictor in regressions (incl. gam's) because, then, one would simply "describe" the trend itself. If the aim of a study is to find environmental ...
3
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1answer
496 views

How to handle gaps in a time series when doing GAMM?

I want to apply a GAMM with R to this time series but I am not sure how to handle the station P18, as shown in the figure below. If I shrink the dataset to the point where P18 ends (i.e. left side of ...
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1answer
2k views

Segmented nonlinear regression in R? [duplicate]

Possible Duplicate: Change point analysis using R's nls() I want to do a nonlinear regression with nls() but also include a specific type of segmented or piecewise regression. The Formula I ...
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1answer
2k views

Fitting conditional functions in nls

I'm trying to fit two equations with nls() function in R. The two functions are: $f(x) = c_{1} \exp\left(-\left(\frac{x-\mu}{\sigma_{(x)}}\right)^2\right)$ where $\sigma_{(x)} = \sigma_{11}$ if $...
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1answer
279 views

Estimating effect of latent variable in regression

I believe that independent variables $X_1,X_2$ affect the dependent variable $Y$ through a latent variable $Z$ such that $$ \begin{align} Y &= \beta_0 + \beta_1Z \\ Z &= \operatorname{...
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1answer
8k views

How do I choose what SVM kernels to use?

I am having trouble determining what kernel I should use in a non-linear SVM without testing in advance. I want to know if there are any other ways to determine the best kernel without tests? How does ...
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2answers
3k views

How to summarize and compare non-linear relationships?

I have data on the percent of organic matter in lake sediments from 0 cm (i.e., the sediment - water interface) down to 9 cm for approximately 25 lakes. In each lake 2 cores were taken from each ...
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3answers
6k views

Having trouble with nls function in R [closed]

I've tough luck with the use of nls() in R for the following model $$N_e = N_o\{1-exp[\frac{(d+bN_o)(T_h N_e - T)}{(1+c N_o)}]\}$$ where $b>0$, $c\geq 0$, $T_h>0$, and $T=72$. This code <...
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1answer
719 views

Minimum distance estimator

I'm trying to replicate the paper of Blundell et al. (2008) to separate permanent and transitory shocks on income on a panel dataset. He solves the non-linear system of equations using Chamberlain's ...
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2answers
373 views

How can I compute regression for several longitudinal data sets (thus, with auto-correlated error)?

My actual project is a bit complicated, but I'll explain by analogy (which I hope facilitates response): I have 3 substances, say water, motor oil, and ethanol. For each substance, I have 5 samples ...
6
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2answers
271 views

How can I demonstrate non-linearity without categorising a predictor?

I don't know what is the appropriate term for my question. The scenario is described as following. In the analysis there one dependent variable Y and two independent variable X1 and X2. All three ...
4
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1answer
863 views

Reconciling different parameterizations of the same nonlinear model

a journal article has a method for designing experiments to be fit to a 4-parameter logistic model. The model used is $y= D + \frac{A - D}{1 + (\frac{x}{C}) ^ B}$ A = upper asymptote B = maximum ...
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1answer
879 views

Significance of (GAM) regression coefficients when model likelihood is not significantly higher than null

I am running a GAM-based regression using the R package gamlss and assuming a zero-inflated beta distribution of the data. I have only a single explanatory variable in my model, so it's basically: <...
2
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1answer
151 views

The source of ENSO data from NIST

I'm using ENSO dataset from the NIST Statistical Reference Datasets as a test for nonlinear regression code. The data are monthly averaged atmospheric pressure differences between Easter Island and ...
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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.
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0answers
245 views

The usage of Newton's method in nonlinear regression

Would you please give an intuitive illustration of Newton's Method, when we deal with nonlinear regression? Basically I understand that if we can use Taylor's theorem to expand the RSS function of ...
4
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1answer
1k views

Non-linear regression fails to converge, but fit appears good

I'm fitting a 4 parameter nonlinear regression model to multiple datasets, some of which fail to converge, however, the parameters output after a failure provide a fit that looks good, if not ...
10
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3answers
4k views

Estimation of exponential model

An exponential model is a model described by following equation: $$\hat{y_{i}}=\beta_{0}\cdot e^{\beta_{1}x_{1i}+\ldots+\beta_{k}x_{ki}}$$ The most common approach used to estimate such model is ...
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1answer
2k views

Geometric circle fitting with known radius

I have data points from a half circle and I already know the radius. I want to find the circle which best fits the points using a fixed radius. How can I do this? If I solve the problem using a ...
5
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1answer
316 views

Nonlinear models which are hard to estimate

Genetic algorithms are avoided in econometry literature as often as possible, but still sometimes they are inevitable. The question is: Which well known models are the most difficult to estimate using ...
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1answer
1k views

Comparing model fits across a set of nonlinear regression models

CONTEXT: I am modelling the relation between time (1 to 30) and a DV for a set of 60 participants. Each participant has their own time series. For each participant I am examining the fit of 5 ...
4
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1answer
331 views

Quantifying the degree of consistency of two fitted curves

I previously asked how to estimate the latent potential of a runner who ran the 100 metres each day for 200 days. Latent skill was defined as "the latent time it would take the individual to run if ...

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